Add Batch 5eda740c-9351-4d21-b61c-190c62b25ca5 data

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@@ -1108,3 +1108,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2024/Infinite-ID_ Identity-preserved Personalization via ID-semantics Decoupling Paradigm/6b2c0220-7e0d-410c-b7de-7b3ff87a9f85_content_list.json

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+        "text": "Infinite-ID: Identity-preserved Personalization via ID-semantics Decoupling Paradigm",
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+        "text": "Yi Wu $^{1\\star}$ , Ziqiang Li $^{1,2\\star}$ , Heliang Zheng $^{1}$ , Chaoyue Wang $^{3\\star\\star}$ , and Bin Li $^{1\\star\\star}$",
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+        "text": "<sup>1</sup> University of Science and Technology of China, China",
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+        "text": "$^{2}$  Nanjing University of Information Science and Technology, China",
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+        "text": "<sup>3</sup> The University of Sydney, Australia",
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+        "text": "Abstract. Drawing on recent advancements in diffusion models for text-to-image generation, identity-preserved personalization has made significant progress in accurately capturing specific identities with just a single reference image. However, existing methods primarily integrate reference images within the text embedding space, leading to a complex entanglement of image and text information, which poses challenges for preserving both identity fidelity and semantic consistency. To tackle this challenge, we propose Infinite-ID, an ID-semantics decoupling paradigm for identity-preserved personalization. Specifically, we introduce identity-enhanced training, incorporating an additional image cross-attention module to capture sufficient ID information while deactivating the original text cross-attention module of the diffusion model. This ensures that the image stream faithfully represents the identity provided by the reference image while mitigating interference from textual input. Additionally, we introduce a feature interaction mechanism that combines a mixed attention module with an AdaIN-mean operation to seamlessly merge the two streams. This mechanism not only enhances the fidelity of identity and semantic consistency but also enables convenient control over the styles of the generated images. Extensive experimental results on both raw photo generation and style image generation demonstrate the superior performance of our proposed method.",
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+    {
+        "type": "text",
+        "text": "Keywords: Personalized Text-to-image Generation, Stable Diffusion, Identity-preserved Personalization",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        "text": "Human photo synthesis [19,38] has experienced notable advancements, particularly with the introduction of large text-to-image diffusion models such as Stable",
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+    {
+        "type": "page_footnote",
+        "text": "* First two authors contributed equally to this work.",
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+        "type": "page_footnote",
+        "text": "\\*\\* Corresponding Authors.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/4e341a16035d1d8bddf81feb9456875b5cb78d771d719f6b70dffc7434288e56.jpg",
+        "image_caption": [
+            "Fig. 1: With just a single reference image, our Infinite-ID framework excels in synthesizing high-quality images while maintaining superior identity fidelity and text semantic consistency in various styles."
+        ],
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+    {
+        "type": "text",
+        "text": "Diffusion (SD) [27], Imagen [30], and DALL-E 3 [3]. Benefit from personalized text-to-image generation, recent researches focus on Identity-preserved personalization. This specialized area aims to produce highly customized photos that faithfully reflect a specific identity in novel scenes, actions, and styles, drawing inspiration from one or more reference images. This task has garnered considerable attention, leading to the development of numerous applications, including personalized AI portraits and virtual try-on scenarios. In the context of Identity-preserved personalization, the emphasis is placed on maintaining the invariance of human facial identity (ID), requiring a heightened level of detail and fidelity compared to more general styles or objects.",
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+        "type": "text",
+        "text": "Recent tuning-free methods exhibit promise for large-scale deployment, yet they face a notable challenge in balancing the trade-off between the fidelity of identity representation (ID fidelity) and the consistency of semantic understanding conveyed by the text prompt. This challenge arises due to the inherent entanglement of image and text information. Typically, tuning-free methods extract ID information from reference images and integrate it into the semantic information in two distinct ways. The first type, exemplified by PhotoMaker [17], incorporates text information with ID details in the text embedding space of the text encoder. While this merging approach aids in achieving semantic consistency, it compresses image features into the text embedding space, thereby weakening the ID information of the image and compromising identity fidelity. The second type, demonstrated by IP-Adapter [40], directly injects ID information into the U-Net of the diffusion model through an additional trainable cross-attention module. Although this approach aims to enhance the strength of ID information for improved fidelity, it tends to favor the image branch during training, consequently weakening the text branch and compromising semantic consistency. In summary, existing methods entangle image and text information, resulting in a significant trade-off between ID fidelity and semantic consistency.",
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+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "header",
+        "text": "Yi Wu et al.",
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+    {
+        "type": "text",
+        "text": "To address the entanglement between image and text information, we propose Infinite-ID, an innovative approach to personalized text-to-image generation. Our method tackles the trade-off between maintaining high fidelity of identity and ensuring semantic consistency of the text prompt by implementing the ID-semantics decoupling paradigm. Specifically, we adopt identity-enhanced training that introduces an additional image cross-attention module to capture sufficient ID information and deactivate the original text cross-attention module to avoid text interference during training stage. Accordingly, our method can faithfully capture identity information from reference image, significantly improving the ID fidelity. Additionally, we employ a novel feature interaction mechanism that leverages a mixed attention module and an AdaIN-mean operation to effectively merge text information and identity information. Notably, our feature interaction mechanism not only preserves both identity and semantic details effectively but also enables convenient control over the styles of the generated images (as depicted in Fig. 1). Our contributions are summarized as:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel ID-semantics decoupling paradigm to resolve the entanglement between image and text information, acquiring a remarkable balance between ID fidelity and semantic consistency in Identity-preserved personalization.",
+            "- We propose a novel feature interaction mechanism incorporating a mixed attention module and an AdaIN-mean operation to effectively merge ID information and text information and also conveniently control the styles of the generated image in diffusion models.",
+            "- Experimental results demonstrate the excellent performance of our proposed method as compared with current state-of-the-art methods on both raw photo generation and style image generation."
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2 Related Works",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "2.1 Text-to-image Diffusion Models",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Text-to-image diffusion models, such as those explored in [3, 13, 27, 30, 43, 45], have garnered significant attention due to their impressive image generation capabilities. Current research endeavors aim to further enhance these models along multiple fronts, including the utilization of high-quality and large-scale datasets [18, 20, 32, 33], refinements to foundational architectures [3, 27, 30], and advancements in controllability [12, 29, 45]. Present iterations of text-to-image diffusion models typically follow a two-step process: first, encoding the text prompt using pre-trained text encoders such as CLIP [24] or T5 [26], and then utilizing the resulting text embedding as a condition for generating corresponding images through the diffusion process. Notably, the widely adopted Stable Diffusion model [27] distinguishes itself by executing the diffusion process in latent space instead of the original pixel space, leading to significant reductions in computation and time costs. An important extension to this framework is the Stable Diffusion XL (SDXL) [23], which enhances performance by scaling",
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+    {
+        "type": "header",
+        "text": "Infinite-ID",
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+    {
+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "up the U-Net architecture and introducing an additional text encoder. Thus, our proposed method builds upon the SDXL. However, our method can also be extended to other text-to-image diffusion models.",
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+    {
+        "type": "text",
+        "text": "2.2 Identity-preserved personalization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Identity-preserved personalization aims to generate highly customized photos that accurately reflect a specific identity across various scenes, actions, and styles, drawing inspiration from one or more reference images. Initially, tuning-based methods, exemplified by DreamBooth [29], Textual Inversion [8] and Celeb-Basis [41], employ images of the same identity (ID) to fine-tune the model. While these methods yield results with high fidelity in preserving facial identity (ID), a significant drawback emerges: the customization of each ID necessitates a time investment of 10-30 minutes [15], consuming substantial computing resources and time. This limitation poses a significant obstacle to large-scale deployment in commercial applications. Consequently, recent advancements in tuning-free methods [6,7,9,16,17,21,35,36,39,40] have been introduced to streamline the generation process. These methods specifically leverage the construction of a vast amount of domain-specific data and the training of an encoder or hyper-network to represent input ID images as embeddings or LoRA weights within the model. Post-training, users need only input an image of the ID for customization, enabling personalized generation within seconds during the inference phase. These tuning-free methods typically contain two distinct manners.",
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+        "type": "text",
+        "text": "On one hand, methods [1, 17, 22, 39] incorporate text information alongside identity details within the text embedding space of the text encoder. For example, PhotoMaker [17] extracts identity embeddings from single or multiple reference images and merges them with corresponding class embeddings (e.g., \"man\" and \"woman\") in the text embedding space of the text encoder. While this stacking operation aids in achieving semantic consistency, it compresses image features into the text embedding space, leading to compromised identity fidelity. On the other hand, some studies [6, 36, 40] directly integrate identity information into the U-Net of the diffusion model. IP-Adapter [40] distinguishes itself by incorporating a additional cross-attention layer for each existing cross-attention layer within the original UNet model. This approach merges identity information with semantic details directly within the U-net but leads to distortion of the semantic space of the U-Net model. Consequently, this compromises the semantic consistency of the text prompt.",
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+    {
+        "type": "text",
+        "text": "In summary, existing methods entangle the identity and text information, leading to a significant trade-off between ID fidelity and semantic consistency. To mitigate these limitations, we propose an identity-enhanced training to capture ID and text information separately. Moreover, we design an effective feature interaction mechanism leveraging a mixed attention module and an AdaIN-mean operation to preserve both identity and semantic details while also enabling convenient control over the styles of generated images.",
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+        "page_idx": 3
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+    {
+        "type": "page_number",
+        "text": "4",
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+    {
+        "type": "header",
+        "text": "Yi Wu et al.",
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+    {
+        "type": "text",
+        "text": "2.3 Attention Control in Diffusion model",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Previous studies have investigated various attention control techniques within diffusion models. Hertz et al. [10] employed a shared attention mechanism, concatenating and applying an AdaIN module on the key and value between reference and synthesis images within the self-attention layer to ensure style-consistent image generation using a reference style. Cao et al. [5] utilized a mutual self-attention approach to achieve consistent image generation and non-rigid image editing, wherein the key and value of the synthesis image were replaced with those of the reference image within the self-attention layers of the diffusion model. Similarly, Shi et al. [34] proposed a method termed reference attention, enabling consistent multi-view generation of target objects by concatenating the key and value features between the condition signal and the synthesis image in the self-attention layers. Wang et al. [39] and Avrahami et al. [2] exploited attention maps within the cross-attention layers to guide the optimization process towards disentangling learned concepts in personalized generation tasks.",
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+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "3.1 Preliminaries",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Stable Diffusion XL. Our method builds upon Stable Diffusion XL [23], comprising three core components: a Variational AutoEncoder (VAE) denoted as  $\\xi(\\cdot)$ , a conditional U-Net [28] represented by  $\\epsilon_{\\theta}(\\cdot)$ , and two pre-trained text encoders [25] denoted as  $\\Theta_1(\\cdot)$  and  $\\Theta_2(\\cdot)$ . Specifically, given a training image  $x_0$  and its corresponding text prompt  $T$ , the VAE encoder  $\\xi$  transforms  $x_0$  from its original space  $R^{H\\times W\\times 3}$  to a compressed latent representation  $z_0 = \\xi(x_0)$ , where  $z_0 \\in R^{h\\times w\\times c}$  and  $c$  denotes the latent dimension. Subsequently, the diffusion process operates within this compressed latent space to conserve computational resources and memory. Once the two text encoders process the text prompt  $T$  into a text embedding  $c = \\mathrm{Concat}(\\Theta_1(T), \\Theta_2(T))$ , the conditional U-Net  $\\epsilon_{\\theta}$  predicts the noise  $\\epsilon$  based on the current timestep  $t$ , the  $t$ -th latent representation  $z_t$ , and the text embedding  $c$ . The training objective is formulated as follows:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {d i f f u s i o n}} = E _ {z _ {t}, t, c, \\epsilon \\in N (0, I)} [ | | \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, c) | | _ {2} ^ {2} ]. \\tag {1}\n$$\n",
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+    {
+        "type": "text",
+        "text": "Attention mechanism in diffusion models. The fundamental unit of the stable diffusion model comprises a resblock, a self-attention layer, and a cross-attention layer. The attention mechanism is represented as follows:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t n} (Q, K, V) = \\operatorname {S o f t m a x} (\\frac {Q K ^ {T}}{\\sqrt {d}}) V, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $Q$  denotes the query feature projected from the spatial features generated by the preceding resblock,  $K$  and  $V$  represent the key and value features projected from the same spatial features as the query feature (in self-attention) or the text embedding extracted from the text prompt (in cross-attention).",
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+    {
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+    {
+        "type": "image",
+        "img_path": "images/bc8b81633e4218c09ab22f6c46b8e81ccab461952e9aab4409f34a539fb94514.jpg",
+        "image_caption": [
+            "Fig. 2: Framework of ID-semantics Decoupling Paradigm. In the training phase, we adopt Face embeddings extractor to extract rich identity information and identity-enhanced training for faithfully representing the identity provided by the reference image while mitigating interference from textual input. In the inference stage, a mixed attention module is introduced to replace the original self-attention mechanism within the denoising U-Net model, facilitating the fusion of both identity and text information."
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+        "text": "3.2 Methodology",
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+        "type": "text",
+        "text": "Overview. In this section, we introduce our ID-semantics decoupling paradigm, as illustrated in Fig. 2, which effectively addresses the severe trade-off between high-fidelity identity and semantic consistency within identity-preserved personalization. Subsequently, we present our mixed attention mechanism, depicted in Fig. 3, designed to seamlessly integrate ID information and semantic information within the diffusion model during the inference stage. Additionally, we utilize an adaptive mean normalization (AdaIN-mean) operation to precisely align the style of the synthesized image with the desired style prompts.",
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+    {
+        "type": "text",
+        "text": "ID-semantics Decoupling Paradigm. To faithfully capture high-fidelity identity, we implement a novel identity-enhanced strategy during the training stage, as depicted in Fig. 2. Diverging from conventional methods [6,17,40] that utilize text-image pairs for training, we opt to exclude the text prompt input and deactivate cross-attention modules for text embeddings within the U-Net model. Instead, we establish a training pair consisting of an ID image, where the face is aligned to extract identity information, and denoising image ( $x_{t}$  in Fig. 2). Both the denoising image used for training and the ID image belong to the same individual, but they vary in factors such as viewpoints and facial expressions. This approach fosters a more comprehensive learning process [17]. We adopt Face embeddings extractor to accurately capture and leverage identity information from",
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+        "text": "6",
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+    {
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+        "image_caption": [
+            "(a) Mixed Attention",
+            "Fig. 3: Mixed attention mechanism. On the left side, we employ mixed attention to fuse identity and text information. This involves concatenating their respective key and value features and subsequently applying mixed attention, where identity features are updated based on the concatenated key and value features. On the right side, for style merging, we introduce an additional AdaIN-mean operation (as depicted in Eq. 8) to the concatenated key and value features."
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+        "image_caption": [
+            "(b) Mixed Attention with AdaIN-mean"
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+    {
+        "type": "text",
+        "text": "the input ID image. Additionally, to seamlessly integrate identity information into the denoising U-Net model, we introduce an extra trainable cross-attention mechanism ( $K_{id}'$  and  $V_{id}'$  in Fig. 2) for image embeddings.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Throughout the training phase, we exclusively optimize the parameters associated with the face mapper, CLIP mapper, and the image cross-attention module, while keeping the parameters of the pre-trained diffusion model fixed. The optimization loss closely resembles the original diffusion loss formulation (as delineated in Eq. 1), with the sole distinction being the shift from a text condition to an identity condition as the conditional input.",
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+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {d i f f u s i o n}} = E _ {z _ {t}, t, c _ {i d}, \\epsilon \\in N (0, I)} [ | | \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, c _ {i d}) | | _ {2} ^ {2} ], \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where the  $c_{id}$  is the identity embeddings of the input ID image.",
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+    {
+        "type": "text",
+        "text": "During the inference phase, we align the desired face within the ID image to afford identity information. Following the approach adopted during the training phase, we utilize a face recognition backbone and a CLIP image encoder to extract identity features from the aligned face image. Leveraging the trained face mapper, clip mapper, and image cross-attention mechanisms, these identity features are seamlessly integrated into the denoising U-Net model. Subsequently, we compute the key and value features for self-attention in the original stable",
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+    {
+        "type": "header",
+        "text": "Infinite-ID",
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+    {
+        "type": "page_number",
+        "text": "7",
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+    {
+        "type": "text",
+        "text": "diffusion model, considering only the text prompt input. These text key and value features are instrumental in the mixed attention process (illustrated in Fig. 3), facilitating the fusion of text and identity information. Moreover, to further augment the text information during the denoising process, we incorporate the original text cross-attention mechanism, integrating the resulting text hidden states with the output image hidden states obtained from the image cross-attention module.",
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+    {
+        "type": "text",
+        "text": "Face Embeddings Extractor. We adopt a multifaceted approach by incorporating pre-trained models to extract facial features. Firstly, following the methodologies of prior research, we utilize a pre-trained CLIP image encoder as one of our facial feature extractors. Specifically, we leverage the local embeddings, comprising the last hidden states obtained from the CLIP image encoder, forming a sequence of embeddings with a length of N (N=257 in our implementation). Subsequently, we employ a CLIP mapper to project these image embeddings (with a dimensionality of 1664) to the same dimension as the text features in the pre-trained diffusion model. As elucidated in [40], the features extracted by the CLIP image encoder are instrumental in capturing the structural information pertinent to the identity face within identity-preserved personalization tasks. Additionally, we leverage the backbone of a face recognition model as another facial feature extractor. As highlighted in [40], features extracted by the face recognition backbone are adept at capturing the characteristics associated with human facial features within identity-preserved personalization tasks. More specifically, we utilize the global image embedding derived from the extracted features and subsequently employ a face mapper to align the dimensionality (512 dimensions) of the extracted global image embedding with the dimensionality of the text features in the pre-trained diffusion model.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In summary, the identity embeddings  $c_{id}$  corresponding to the ID image  $x$  can be expressed as:",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nc _ {i d} = \\operatorname {C o n c a t} \\left(\\mathrm {M} _ {\\text {c l i p}} \\left(\\mathrm {E} _ {\\text {c l i p}} (\\mathrm {F A} (x))\\right), \\mathrm {M} _ {\\text {f a c e}} \\left(\\mathrm {E} _ {\\text {f a c e}} (\\mathrm {F A} (x))\\right)\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            587,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{Concat}(\\cdot, \\cdot)$ ,  $\\mathrm{M}_{\\mathrm{clip}}(\\cdot)$ ,  $\\mathrm{E}_{\\mathrm{clip}}(\\cdot)$ ,  $\\mathrm{M}_{\\mathrm{face}}(\\cdot)$ ,  $\\mathrm{E}_{\\mathrm{face}}(\\cdot)$ , and  $\\mathrm{FA}(\\cdot)$  denote the concatenation function, CLIP mapper, CLIP image encoder, face mapper, face recognition backbone, and face alignment module [44], respectively.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Mixed Attention Mechanism. As explored in previous studies [5, 14, 37], the features in the self attention layers play a crucial role in consistency image generation (across-frame in text-to-video works), which indicates these features provide a refined and detailed semantics information. In our study, we extract features from the self-attention layers of the original text-to-image diffusion model to capture rich semantic information, represented as  $K_{t}$  and  $V_{t}$ . We enhance the self-attention mechanism by incorporating it into a mixed attention framework, depicted in Fig. 3 (a). This fusion enables the integration of semantic features  $(K_{t}$  and  $V_{t}$ ) with the identity-based features  $(K_{id}$  and  $V_{id}$ ), thereby encapsulating identity information. Through this integration, the mixed attention mechanism seamlessly merges semantic details into the generated features",
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Yi Wu et al.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "across different resolutions. The formulation of the mixed attention mechanism is as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t n} _ {\\operatorname {m i x}} (Q, K, V) \\triangleq \\operatorname {A t t n} (Q, \\hat {K}, \\hat {V})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l l} \\text {w . r . t} & \\hat {K} = \\underset {i d} {\\operatorname {C o n c a t}} \\left(K _ {i d}, K _ {t}\\right), \\quad \\hat {V} = \\underset {t} {\\operatorname {C o n c a t}} \\left(V _ {i d}, V _ {t}\\right), \\end{array} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nK _ {i d} = W _ {k} ^ {i d} Z _ {i d}, \\quad K _ {t} = W _ {k} ^ {t} Z _ {t},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nV _ {i d} = W _ {v} ^ {i d} Z _ {i d}, \\quad V _ {t} = W _ {v} ^ {t} Z _ {t},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $Z_{id}$  and  $Z_{t}$  are the corresponding spatial features of generated features and semantic features, respectively. The parameters  $W_{k}^{id}$ ,  $W_{k}^{t}$ ,  $W_{v}^{id}$ , and  $W_{v}^{t}$  correspond to the weights of the corresponding fully connected layers.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Cross-attention Merging. To further refine semantic control, we incorporate text features into the identity feature within the cross-attention layers using the following formulation:",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t n} _ {\\text {c r o s s}} (Q, K, V) \\triangleq \\operatorname {A t t n} \\left(Q, K _ {i d} ^ {\\prime}, V _ {i d} ^ {\\prime}\\right) + \\operatorname {A t t n} \\left(Q, K _ {t} ^ {\\prime}, V _ {t} ^ {\\prime}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            369,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $K_{id}^{\\prime} = \\hat{W}_{k}^{id}c_{id}$ ,  $V_{id}^{\\prime} = \\hat{W}_{v}^{id}c_{id}$ ,  $K_{t}^{\\prime} = \\hat{W}_{k}^{t}c_{t}$ , and  $V_{t}^{\\prime} = \\hat{W}_{v}^{t}c_{t}$ .  $c_{id}$  and  $c_{t}$  are the identity embedding and text embedding, respectively.  $\\hat{W}_{k}^{id}$ ,  $\\hat{W}_{v}^{id}$ ,  $\\hat{W}_{k}^{t}$ , and  $\\hat{W}_{v}^{t}$  correspond to the weights of the trainable fully connected layers within cross-attention module.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Style Information Merging. Inspired by [10], we propose an adaptive mean normalization (AdaIN-mean) operation to further align the style of the synthesis image with the style prompts. Concretely, we align the key and value features projected from identity features in both mixed attention and cross-attention with the key and value features projected from text features, formulated as follows:",
+        "bbox": [
+            212,
+            458,
+            784,
+            532
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l l l} K _ {i d} = \\operatorname {A d a I N - m} \\left(K _ {i d}, K _ {t}\\right), & V _ {i d} = \\operatorname {A d a I N - m} \\left(V _ {i d}, V _ {t}\\right), & \\text {F o r M i x e d A t t e n t i o n} \\\\ K _ {i d} ^ {\\prime} = \\operatorname {A d a I N - m} \\left(K _ {i d} ^ {\\prime}, K _ {t} ^ {\\prime}\\right), & V _ {i d} ^ {\\prime} = \\operatorname {A d a I N - m} \\left(V _ {i d} ^ {\\prime}, V _ {t} ^ {\\prime}\\right), & \\text {F o r C r o s s A t t e n t i o n} \\end{array} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            225,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where the AdaIN-mean operation (AdaIN-m(\\cdot)) is defined as:",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A d a I N} - \\mathrm {m} (x, y) = x - \\mu (x) + \\mu (y), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            380,
+            616,
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+            631
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu (x)\\in R^{d_k}$  is the mean of key and value features across different pixels. The mixed attention with AdaIN-mean has been illustrated in Fig. 3 (b).",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "After outlining the experimental setup in Sec. 4.1, we conduct a comparative analysis of raw photo generation and style image generation in Sec. 4.2. Ablation studies, highlighting the significance of various components, are presented in Sec. 4.3. Additionally, experiments involving multiple input ID images including identity mixing and identity linear interpolation are detailed in Sec. A.7 of the supplementary materials. For further insights, Sec. A.8 and Sec. A.9 of the supplementary materials provide additional qualitative results for raw photo generation and style photo generation, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "Infinite-ID",
+        "bbox": [
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+            114,
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+            126
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            774,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/ce66ee3a3d30418f47ba6bf5dc8d7764ec132a6e50227e46137dfc4dbb4ba01d.jpg",
+        "image_caption": [
+            "Fig. 4: Qualitative comparison on raw photo generation. The results demonstrate that our Infinite-ID consistently maintains identity fidelity and achieves high-quality semantic consistency with just a single input image."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            143,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.1 Experimental Setup",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Our experiments leverage a pre-trained Stable Diffusion XL (SDXL) model [23]. For image encoding, we utilize the OpenCLIP ViT-H/14 [42] and the backbone of ArcFace [11]. The SDXL model consists of 70 cross-attention layers, to each of which we append an additional image cross-attention module. Training is conducted on 16 A100 GPUs for 1 million steps, with a batch size of 4 per GPU. We employ the AdamW optimizer with a fixed learning rate of 1e-4 and weight decay set to 0.01. During inference, we employ the DDIM Sampler with 30 steps and guidance scale is set to 5.0. Training data are sourced from multiple datasets, including the LAION-2B dataset [33], the LAION-Face dataset [46], and few high-quality images collected from the Websites<sup>4</sup>. We curate a dataset where each individual is represented by multiple photographs.",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Evaluation. We assess the efficacy of our approach in preserving both identity fidelity and semantic consistency. Specifically, we measure identity fidelity, utilizing metrics such as  $M_{\\mathrm{FaceNet}}$  (measured by FaceNet [31]) and CLIP-I [8]. Identity fidelity is evaluated based on the similarity of detected faces between the",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
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+            126
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "Yi Wu et al.",
+        "bbox": [
+            271,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_footnote",
+        "text": "4 https://www.pexels.com, https://pixabay.com.",
+        "bbox": [
+            217,
+            824,
+            545,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "image",
+        "img_path": "images/01d499f8c7db4e1c3c67dccca8ae2f10d8c2b4af6eeadea587c0d1c24f4ba24e.jpg",
+        "image_caption": [
+            "Fig. 5: Qualitative comparison on style image generation. The results demonstrate that our method maintains strong identity fidelity, high-quality semantic consistency, and precise stylization using only a single reference image."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            223,
+            147,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "reference image and generated images. Semantic consistency is quantified using CLIP text-image consistency (CLIP-T [24]), which compares the text prompt with the corresponding generated images. More details of evaluation are shown in Sec. A.1 and Sec. A.2 of the supplementary materials.",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "4.2 Comparison to Previous Methods",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Raw Photo Generation. We benchmark our Infinite-ID against established identity-preserving personalization approaches. The qualitative outcomes are illustrated in Fig. 4, while quantitative results are provided in Table 1. Notably, all methods are tuning-free, necessitating no test-time adjustments. FastComposer [39] exhibits challenges in maintaining identity fidelity, often presenting undesired artifacts in synthesized images. While IP-Adapter [40] and IP-Adapter-Face [40] demonstrates relatively fewer artifacts, its semantic consistency falls short. This phenomenon arises from the direct fusion of identity information with semantic details within the U-net model, leading to a compromise in semantic consistency. In contrast, PhotoMaker [17] exhibits commendable semantic consistency but falls short in preserving identity fidelity. Leveraging our ID-semantics decoupling paradigm, our method excels in preserving identity fidelity. Furthermore, our mixed attention mechanism effectively integrate the semantic",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "header",
+        "text": "Infinite-ID",
+        "bbox": [
+            658,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/2b75eef9a25fc951129ca904fc62075ac9b77aa18a1485e1c02e9c17b8452f5a.jpg",
+        "table_caption": [
+            "Table 1: Quantitative comparison. The evaluation metrics encompass CLIP-T, CLIP-I, and  $M_{\\text{FaceNet}}$ . Our approach outperforms other methods in terms of identity fidelity while simultaneously achieving satisfactory semantic consistency. The best result is shown in bold, and the second best is underlined. Additionally, the quantitative comparison of ablation studies have been shown in the gray part."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CLIP-T ↑</td><td>CLIP-I ↑</td><td>M_FaceNet ↑</td></tr><tr><td>FastComposer [39]</td><td>0.292</td><td>0.887</td><td>0.556</td></tr><tr><td>IP-Adapter [40]</td><td>0.274</td><td>0.905</td><td>0.474</td></tr><tr><td>IP-Adapter-Face [40]</td><td>0.313</td><td>0.919</td><td>0.513</td></tr><tr><td>PhotoMaker [17]</td><td>0.343</td><td>0.814</td><td>0.502</td></tr><tr><td>Ours</td><td>0.340</td><td>0.913</td><td>0.689</td></tr><tr><td>Ours (w/o identity-enhanced training)</td><td>0.329</td><td>0.891</td><td>0.593</td></tr><tr><td>Ours (w/o Mixed Attention)</td><td>0.331</td><td>0.905</td><td>0.700</td></tr><tr><td>Ours (Mixed Attention ⇒ Mutual Attention)</td><td>0.316</td><td>0.808</td><td>0.398</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "information into the denoising process, positioning our method favorably against existing techniques. More comparison results are shown in Sec. A.4, Sec. A.5 and Sec. A.6 of the supplementary materials.",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Style Image Generation. We demonstrate the results of the stylization results in Fig. 5, which compare our method with state-of-the-art tuning-free identity-preserving personalization methods. The style of the synthesis images include anime style, comic book style, and line art style. According to the stylization results, the IP-Adapter [40] and IP-Adapter-Face fails to depict the desired style in the prompt and the style of generation results always obey the tone in the reference image. The training pipeline of the IP-Adapter and IP-Adapter-Face entangles the text embedding and image embedding which leads to the distortion of the text embeddings space. FastComposer [39] also fails in stylization generation and shows undesired artifacts. PhotoMaker [17] achieves a better semantic consistency and stylization, but the identity fidelity is still unsatisfactory. In contrast, our method achieves high identity fidelity, appealing semantic consistency, and precise stylization meantime.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "4.3 Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section, we begin by conducting ablation studies to assess the influence of our identity-enhanced training and mixed attention mechanism. Furthermore, we conduct style image generation to evaluate the effectiveness of our AdaIN-mean operation in regulating the style of the generated images. More ablation studies are demonstrated in Sec. A.3 of the supplementary materials.",
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+    },
+    {
+        "type": "text",
+        "text": "Ablation of identity-enhanced training. In Fig. 6 and Table 1, we compare our method with \"Ours (w/o identity-enhanced training)\", which is implemented using an identity-semantics entangled training strategy. This strategy utilizes text-image pairs during training and activates cross-attention modules for text embeddings within the original U-Net model. It is noteworthy that both methods",
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+        "page_idx": 11
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+        "type": "page_number",
+        "text": "12",
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+        "text": "Yi Wu et al.",
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+    {
+        "type": "image",
+        "img_path": "images/2337fa1f5f28299abc98a7e44b4eb7e3ab6aca5208d2f2f8925f440af4c5d3ad.jpg",
+        "image_caption": [],
+        "image_footnote": [
+            "a woman wearing purple sweater, facing and smiling to the camera, in a forest"
+        ],
+        "bbox": [
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+        "page_idx": 12
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+        "img_path": "images/8bcc8b60ad7cba6d6f482b5c449c104eb748bcb263cf27be832b956c32954ca2.jpg",
+        "image_caption": [],
+        "image_footnote": [
+            "a photo of a man wearing a colorful shirt, in the living room"
+        ],
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+        "page_idx": 12
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+        "img_path": "images/ab5fdf84a765b7d1e7e633e134b54e7ef4a12f2ec0abe906dd12b8c51b8bc05e.jpg",
+        "image_caption": [
+            "ID image"
+        ],
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+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/df1a192a31f1f6bad742e8cdef1e7990cb0235d6f9f194f3ec1024d796f1fdb3.jpg",
+        "image_caption": [],
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+            "a woman wearing a red hat, smiling and facing to the camera, sunset, on the beach",
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+        "image_caption": [
+            "Fig. 6: Ablation study of our identity-enhanced training and mixed attention (M-A). It is evident that identity-enhanced training significantly improves the identity fidelity, and mixed-attention mechanism enhances semantic consistency compared to mutual attention (MU-A) approach [5]."
+        ],
+        "image_footnote": [
+            "awearing a blue clothing, facing and smiling to the snow. A snowy, snowy, in an anime style"
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+        "image_caption": [
+            "ID Image",
+            "Fig. 7: Ablation study of our AdaIN-mean operation. The results show that AdaIN-mean play a crucial role in style image generation. Compare to AdaIN [10] module, our AdaIN-mean helps to achieve a higher identity fidelity."
+        ],
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+        "image_caption": [
+            "Ours (AdaIN-mean  $\\Rightarrow$  AdaIN)"
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+    {
+        "type": "text",
+        "text": "share the same inference processing. The qualitative comparison demonstrates that our identity-enhanced training notably enhances identity fidelity.",
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+        "type": "text",
+        "text": "Ablation of mixed attention mechanism. To assess the effectiveness of our proposed mixed attention (M-A) mechanism, we compare our method with \"Ours (w/o M-A)\" and \"Ours (M-A  $\\Rightarrow$  MU-A)\" in Fig. 6 and Table 1. Mutual self-attention (MU-A) [5] converts the existing self-attention into 'cross-attention' for consistent image editing, where the crossing operation happens in the self-attention of two related diffusion processes. The results show that our mixed attention mechanism demonstrates superior ability to improve semantic consistency while maintaining identity fidelity.",
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+    {
+        "type": "text",
+        "text": "Ablation of AdaIN-mean operation. To assess the effectiveness of our proposed AdaIN-mean operation, we compare our Infinite-ID model with variations, namely Ours (w/o AdaIN-mean) and Ours (AdaIN-mean  $\\Rightarrow$  AdaIN), as depicted",
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+    {
+        "type": "header",
+        "text": "Infinite-ID",
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+    {
+        "type": "page_number",
+        "text": "13",
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+    {
+        "type": "text",
+        "text": "in Fig. 7. The results reveal that: i) Ours (w/o AdaIN-mean) exhibits superior ID fidelity compared to Infinite-ID but fails to achieve style consistency with the text prompt; ii) Both our AdaIN-mean and AdaIN modules successfully achieve style consistency with the text prompt, yet AdaIN-mean maintains better ID fidelity than AdaIN. In conclusion, our proposed AdaIN-mean operation facilitates precise stylization while concurrently preserving ID fidelity.",
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+    {
+        "type": "text",
+        "text": "5 Conclusion and limitations.",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we introduce Infinite-ID, an innovative identity-preserved personalization method designed to meet the requirement of identity (ID) fidelity and semantic consistency of the text prompt, all achievable with just one reference image and completed within seconds. Infinite-ID comprises three key components: the identity-enhanced training, mixed attention mechanism, and adaptive mean normalization (AdaIN-mean). Through extensive experimentation, our results illustrate that Infinite-ID outperforms baseline methods, delivering strong ID fidelity, superior generation quality, and precise semantic consistency in both raw photo generation and style image generation tasks. However, it's important to note that our method lacks multi-object personalization capability. Moreover, artifacts may occur when the human face occupies only a small portion of the entire image, attributed to limitations inherent in the original diffusion model. Furthermore, the image encoders employed in the identity-preserved personalization remain to be further explored.",
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+    {
+        "type": "text",
+        "text": "6 Copyright of Training Data and Ethical Considerations.",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Copyright of Training Data. We construct our training dataset from the open-source public image dataset, including LAION-2B dataset, the LAION-Face dataset and few high-quality images collected from the Website<sup>5</sup> which supports the CC0 (Creative Commons Zero) 1.0 Universal license<sup>6</sup>.",
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+    {
+        "type": "text",
+        "text": "Ethical Considerations. We recognize the ethical considerations about improper use of such high-quality human photo synthesis techniques. Therefore, we emphasize the significance of establishing and complying to ethical guidelines [4] and using this technology responsibly. We hope that our work will drive further discussions and research on the security and ethical use of the human photo generation in computer vision. Moreover, we will employ the watermark and safety checker (NSFW classifiers) to attempt to avoid inappropriate content generation.",
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+        "page_idx": 13
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+    {
+        "type": "page_number",
+        "text": "14",
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+    {
+        "type": "header",
+        "text": "Yi Wu et al.",
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+    {
+        "type": "page_footnote",
+        "text": "$^{5}$  https://www.pexels.com, https://pixabay.com.",
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+        "page_idx": 13
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+    {
+        "type": "page_footnote",
+        "text": "6 The person who associated a work with this deed has dedicated the work to the public domain by waiving all of his or her rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This research was funded by the National Natural Science Foundation of China (U19B2044), supported by the Fundamental Research Funds for the Central Universities (WK2100000045).",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 14
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+        "list_items": [
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+        ],
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+    {
+        "type": "header",
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2024/Infinite-ID_ Identity-preserved Personalization via ID-semantics Decoupling Paradigm/6b2c0220-7e0d-410c-b7de-7b3ff87a9f85_origin.pdf

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2024/Infinite-ID_ Identity-preserved Personalization via ID-semantics Decoupling Paradigm/full.md

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+# Infinite-ID: Identity-preserved Personalization via ID-semantics Decoupling Paradigm
+
+Yi Wu $^{1\star}$ , Ziqiang Li $^{1,2\star}$ , Heliang Zheng $^{1}$ , Chaoyue Wang $^{3\star\star}$ , and Bin Li $^{1\star\star}$
+
+<sup>1</sup> University of Science and Technology of China, China
+
+$^{2}$  Nanjing University of Information Science and Technology, China
+
+<sup>3</sup> The University of Sydney, Australia
+
+wuyi2021@mail.ustc.edu.cn, iceli@mail.ustc.edu.cn,
+
+zhenghl@mail.ustc.edu.cn,
+
+chaoyue.wang@outlook.com, binli@ustc.edu.cn
+
+Abstract. Drawing on recent advancements in diffusion models for text-to-image generation, identity-preserved personalization has made significant progress in accurately capturing specific identities with just a single reference image. However, existing methods primarily integrate reference images within the text embedding space, leading to a complex entanglement of image and text information, which poses challenges for preserving both identity fidelity and semantic consistency. To tackle this challenge, we propose Infinite-ID, an ID-semantics decoupling paradigm for identity-preserved personalization. Specifically, we introduce identity-enhanced training, incorporating an additional image cross-attention module to capture sufficient ID information while deactivating the original text cross-attention module of the diffusion model. This ensures that the image stream faithfully represents the identity provided by the reference image while mitigating interference from textual input. Additionally, we introduce a feature interaction mechanism that combines a mixed attention module with an AdaIN-mean operation to seamlessly merge the two streams. This mechanism not only enhances the fidelity of identity and semantic consistency but also enables convenient control over the styles of the generated images. Extensive experimental results on both raw photo generation and style image generation demonstrate the superior performance of our proposed method.
+
+Keywords: Personalized Text-to-image Generation, Stable Diffusion, Identity-preserved Personalization
+
+# 1 Introduction
+
+Human photo synthesis [19,38] has experienced notable advancements, particularly with the introduction of large text-to-image diffusion models such as Stable
+
+![](images/4e341a16035d1d8bddf81feb9456875b5cb78d771d719f6b70dffc7434288e56.jpg)  
+Fig. 1: With just a single reference image, our Infinite-ID framework excels in synthesizing high-quality images while maintaining superior identity fidelity and text semantic consistency in various styles.
+
+Diffusion (SD) [27], Imagen [30], and DALL-E 3 [3]. Benefit from personalized text-to-image generation, recent researches focus on Identity-preserved personalization. This specialized area aims to produce highly customized photos that faithfully reflect a specific identity in novel scenes, actions, and styles, drawing inspiration from one or more reference images. This task has garnered considerable attention, leading to the development of numerous applications, including personalized AI portraits and virtual try-on scenarios. In the context of Identity-preserved personalization, the emphasis is placed on maintaining the invariance of human facial identity (ID), requiring a heightened level of detail and fidelity compared to more general styles or objects.
+
+Recent tuning-free methods exhibit promise for large-scale deployment, yet they face a notable challenge in balancing the trade-off between the fidelity of identity representation (ID fidelity) and the consistency of semantic understanding conveyed by the text prompt. This challenge arises due to the inherent entanglement of image and text information. Typically, tuning-free methods extract ID information from reference images and integrate it into the semantic information in two distinct ways. The first type, exemplified by PhotoMaker [17], incorporates text information with ID details in the text embedding space of the text encoder. While this merging approach aids in achieving semantic consistency, it compresses image features into the text embedding space, thereby weakening the ID information of the image and compromising identity fidelity. The second type, demonstrated by IP-Adapter [40], directly injects ID information into the U-Net of the diffusion model through an additional trainable cross-attention module. Although this approach aims to enhance the strength of ID information for improved fidelity, it tends to favor the image branch during training, consequently weakening the text branch and compromising semantic consistency. In summary, existing methods entangle image and text information, resulting in a significant trade-off between ID fidelity and semantic consistency.
+
+To address the entanglement between image and text information, we propose Infinite-ID, an innovative approach to personalized text-to-image generation. Our method tackles the trade-off between maintaining high fidelity of identity and ensuring semantic consistency of the text prompt by implementing the ID-semantics decoupling paradigm. Specifically, we adopt identity-enhanced training that introduces an additional image cross-attention module to capture sufficient ID information and deactivate the original text cross-attention module to avoid text interference during training stage. Accordingly, our method can faithfully capture identity information from reference image, significantly improving the ID fidelity. Additionally, we employ a novel feature interaction mechanism that leverages a mixed attention module and an AdaIN-mean operation to effectively merge text information and identity information. Notably, our feature interaction mechanism not only preserves both identity and semantic details effectively but also enables convenient control over the styles of the generated images (as depicted in Fig. 1). Our contributions are summarized as:
+
+- We propose a novel ID-semantics decoupling paradigm to resolve the entanglement between image and text information, acquiring a remarkable balance between ID fidelity and semantic consistency in Identity-preserved personalization.  
+- We propose a novel feature interaction mechanism incorporating a mixed attention module and an AdaIN-mean operation to effectively merge ID information and text information and also conveniently control the styles of the generated image in diffusion models.  
+- Experimental results demonstrate the excellent performance of our proposed method as compared with current state-of-the-art methods on both raw photo generation and style image generation.
+
+# 2 Related Works
+
+# 2.1 Text-to-image Diffusion Models
+
+Text-to-image diffusion models, such as those explored in [3, 13, 27, 30, 43, 45], have garnered significant attention due to their impressive image generation capabilities. Current research endeavors aim to further enhance these models along multiple fronts, including the utilization of high-quality and large-scale datasets [18, 20, 32, 33], refinements to foundational architectures [3, 27, 30], and advancements in controllability [12, 29, 45]. Present iterations of text-to-image diffusion models typically follow a two-step process: first, encoding the text prompt using pre-trained text encoders such as CLIP [24] or T5 [26], and then utilizing the resulting text embedding as a condition for generating corresponding images through the diffusion process. Notably, the widely adopted Stable Diffusion model [27] distinguishes itself by executing the diffusion process in latent space instead of the original pixel space, leading to significant reductions in computation and time costs. An important extension to this framework is the Stable Diffusion XL (SDXL) [23], which enhances performance by scaling
+
+up the U-Net architecture and introducing an additional text encoder. Thus, our proposed method builds upon the SDXL. However, our method can also be extended to other text-to-image diffusion models.
+
+# 2.2 Identity-preserved personalization
+
+Identity-preserved personalization aims to generate highly customized photos that accurately reflect a specific identity across various scenes, actions, and styles, drawing inspiration from one or more reference images. Initially, tuning-based methods, exemplified by DreamBooth [29], Textual Inversion [8] and Celeb-Basis [41], employ images of the same identity (ID) to fine-tune the model. While these methods yield results with high fidelity in preserving facial identity (ID), a significant drawback emerges: the customization of each ID necessitates a time investment of 10-30 minutes [15], consuming substantial computing resources and time. This limitation poses a significant obstacle to large-scale deployment in commercial applications. Consequently, recent advancements in tuning-free methods [6,7,9,16,17,21,35,36,39,40] have been introduced to streamline the generation process. These methods specifically leverage the construction of a vast amount of domain-specific data and the training of an encoder or hyper-network to represent input ID images as embeddings or LoRA weights within the model. Post-training, users need only input an image of the ID for customization, enabling personalized generation within seconds during the inference phase. These tuning-free methods typically contain two distinct manners.
+
+On one hand, methods [1, 17, 22, 39] incorporate text information alongside identity details within the text embedding space of the text encoder. For example, PhotoMaker [17] extracts identity embeddings from single or multiple reference images and merges them with corresponding class embeddings (e.g., "man" and "woman") in the text embedding space of the text encoder. While this stacking operation aids in achieving semantic consistency, it compresses image features into the text embedding space, leading to compromised identity fidelity. On the other hand, some studies [6, 36, 40] directly integrate identity information into the U-Net of the diffusion model. IP-Adapter [40] distinguishes itself by incorporating a additional cross-attention layer for each existing cross-attention layer within the original UNet model. This approach merges identity information with semantic details directly within the U-net but leads to distortion of the semantic space of the U-Net model. Consequently, this compromises the semantic consistency of the text prompt.
+
+In summary, existing methods entangle the identity and text information, leading to a significant trade-off between ID fidelity and semantic consistency. To mitigate these limitations, we propose an identity-enhanced training to capture ID and text information separately. Moreover, we design an effective feature interaction mechanism leveraging a mixed attention module and an AdaIN-mean operation to preserve both identity and semantic details while also enabling convenient control over the styles of generated images.
+
+# 2.3 Attention Control in Diffusion model
+
+Previous studies have investigated various attention control techniques within diffusion models. Hertz et al. [10] employed a shared attention mechanism, concatenating and applying an AdaIN module on the key and value between reference and synthesis images within the self-attention layer to ensure style-consistent image generation using a reference style. Cao et al. [5] utilized a mutual self-attention approach to achieve consistent image generation and non-rigid image editing, wherein the key and value of the synthesis image were replaced with those of the reference image within the self-attention layers of the diffusion model. Similarly, Shi et al. [34] proposed a method termed reference attention, enabling consistent multi-view generation of target objects by concatenating the key and value features between the condition signal and the synthesis image in the self-attention layers. Wang et al. [39] and Avrahami et al. [2] exploited attention maps within the cross-attention layers to guide the optimization process towards disentangling learned concepts in personalized generation tasks.
+
+# 3 Method
+
+# 3.1 Preliminaries
+
+Stable Diffusion XL. Our method builds upon Stable Diffusion XL [23], comprising three core components: a Variational AutoEncoder (VAE) denoted as  $\xi(\cdot)$ , a conditional U-Net [28] represented by  $\epsilon_{\theta}(\cdot)$ , and two pre-trained text encoders [25] denoted as  $\Theta_1(\cdot)$  and  $\Theta_2(\cdot)$ . Specifically, given a training image  $x_0$  and its corresponding text prompt  $T$ , the VAE encoder  $\xi$  transforms  $x_0$  from its original space  $R^{H\times W\times 3}$  to a compressed latent representation  $z_0 = \xi(x_0)$ , where  $z_0 \in R^{h\times w\times c}$  and  $c$  denotes the latent dimension. Subsequently, the diffusion process operates within this compressed latent space to conserve computational resources and memory. Once the two text encoders process the text prompt  $T$  into a text embedding  $c = \mathrm{Concat}(\Theta_1(T), \Theta_2(T))$ , the conditional U-Net  $\epsilon_{\theta}$  predicts the noise  $\epsilon$  based on the current timestep  $t$ , the  $t$ -th latent representation  $z_t$ , and the text embedding  $c$ . The training objective is formulated as follows:
+
+$$
+L _ {\text {d i f f u s i o n}} = E _ {z _ {t}, t, c, \epsilon \in N (0, I)} [ | | \epsilon - \epsilon_ {\theta} (z _ {t}, t, c) | | _ {2} ^ {2} ]. \tag {1}
+$$
+
+Attention mechanism in diffusion models. The fundamental unit of the stable diffusion model comprises a resblock, a self-attention layer, and a cross-attention layer. The attention mechanism is represented as follows:
+
+$$
+\operatorname {A t t n} (Q, K, V) = \operatorname {S o f t m a x} (\frac {Q K ^ {T}}{\sqrt {d}}) V, \tag {2}
+$$
+
+where  $Q$  denotes the query feature projected from the spatial features generated by the preceding resblock,  $K$  and  $V$  represent the key and value features projected from the same spatial features as the query feature (in self-attention) or the text embedding extracted from the text prompt (in cross-attention).
+
+![](images/bc8b81633e4218c09ab22f6c46b8e81ccab461952e9aab4409f34a539fb94514.jpg)  
+Fig. 2: Framework of ID-semantics Decoupling Paradigm. In the training phase, we adopt Face embeddings extractor to extract rich identity information and identity-enhanced training for faithfully representing the identity provided by the reference image while mitigating interference from textual input. In the inference stage, a mixed attention module is introduced to replace the original self-attention mechanism within the denoising U-Net model, facilitating the fusion of both identity and text information.
+
+# 3.2 Methodology
+
+Overview. In this section, we introduce our ID-semantics decoupling paradigm, as illustrated in Fig. 2, which effectively addresses the severe trade-off between high-fidelity identity and semantic consistency within identity-preserved personalization. Subsequently, we present our mixed attention mechanism, depicted in Fig. 3, designed to seamlessly integrate ID information and semantic information within the diffusion model during the inference stage. Additionally, we utilize an adaptive mean normalization (AdaIN-mean) operation to precisely align the style of the synthesized image with the desired style prompts.
+
+ID-semantics Decoupling Paradigm. To faithfully capture high-fidelity identity, we implement a novel identity-enhanced strategy during the training stage, as depicted in Fig. 2. Diverging from conventional methods [6,17,40] that utilize text-image pairs for training, we opt to exclude the text prompt input and deactivate cross-attention modules for text embeddings within the U-Net model. Instead, we establish a training pair consisting of an ID image, where the face is aligned to extract identity information, and denoising image ( $x_{t}$  in Fig. 2). Both the denoising image used for training and the ID image belong to the same individual, but they vary in factors such as viewpoints and facial expressions. This approach fosters a more comprehensive learning process [17]. We adopt Face embeddings extractor to accurately capture and leverage identity information from
+
+![](images/77312140525ed59cbd83583c6bab7affe65f8d203ba21ec5e32ac9b6e5dbcb74.jpg)  
+(a) Mixed Attention  
+Fig. 3: Mixed attention mechanism. On the left side, we employ mixed attention to fuse identity and text information. This involves concatenating their respective key and value features and subsequently applying mixed attention, where identity features are updated based on the concatenated key and value features. On the right side, for style merging, we introduce an additional AdaIN-mean operation (as depicted in Eq. 8) to the concatenated key and value features.
+
+![](images/0b4fd8e1db8bf40fe9c7f7a5c537cbda2c1af8d258d98ef0d3b1ffded6a26f95.jpg)  
+(b) Mixed Attention with AdaIN-mean
+
+the input ID image. Additionally, to seamlessly integrate identity information into the denoising U-Net model, we introduce an extra trainable cross-attention mechanism ( $K_{id}'$  and  $V_{id}'$  in Fig. 2) for image embeddings.
+
+Throughout the training phase, we exclusively optimize the parameters associated with the face mapper, CLIP mapper, and the image cross-attention module, while keeping the parameters of the pre-trained diffusion model fixed. The optimization loss closely resembles the original diffusion loss formulation (as delineated in Eq. 1), with the sole distinction being the shift from a text condition to an identity condition as the conditional input.
+
+$$
+L _ {\text {d i f f u s i o n}} = E _ {z _ {t}, t, c _ {i d}, \epsilon \in N (0, I)} [ | | \epsilon - \epsilon_ {\theta} (z _ {t}, t, c _ {i d}) | | _ {2} ^ {2} ], \tag {3}
+$$
+
+where the  $c_{id}$  is the identity embeddings of the input ID image.
+
+During the inference phase, we align the desired face within the ID image to afford identity information. Following the approach adopted during the training phase, we utilize a face recognition backbone and a CLIP image encoder to extract identity features from the aligned face image. Leveraging the trained face mapper, clip mapper, and image cross-attention mechanisms, these identity features are seamlessly integrated into the denoising U-Net model. Subsequently, we compute the key and value features for self-attention in the original stable
+
+diffusion model, considering only the text prompt input. These text key and value features are instrumental in the mixed attention process (illustrated in Fig. 3), facilitating the fusion of text and identity information. Moreover, to further augment the text information during the denoising process, we incorporate the original text cross-attention mechanism, integrating the resulting text hidden states with the output image hidden states obtained from the image cross-attention module.
+
+Face Embeddings Extractor. We adopt a multifaceted approach by incorporating pre-trained models to extract facial features. Firstly, following the methodologies of prior research, we utilize a pre-trained CLIP image encoder as one of our facial feature extractors. Specifically, we leverage the local embeddings, comprising the last hidden states obtained from the CLIP image encoder, forming a sequence of embeddings with a length of N (N=257 in our implementation). Subsequently, we employ a CLIP mapper to project these image embeddings (with a dimensionality of 1664) to the same dimension as the text features in the pre-trained diffusion model. As elucidated in [40], the features extracted by the CLIP image encoder are instrumental in capturing the structural information pertinent to the identity face within identity-preserved personalization tasks. Additionally, we leverage the backbone of a face recognition model as another facial feature extractor. As highlighted in [40], features extracted by the face recognition backbone are adept at capturing the characteristics associated with human facial features within identity-preserved personalization tasks. More specifically, we utilize the global image embedding derived from the extracted features and subsequently employ a face mapper to align the dimensionality (512 dimensions) of the extracted global image embedding with the dimensionality of the text features in the pre-trained diffusion model.
+
+In summary, the identity embeddings  $c_{id}$  corresponding to the ID image  $x$  can be expressed as:
+
+$$
+c _ {i d} = \operatorname {C o n c a t} \left(\mathrm {M} _ {\text {c l i p}} \left(\mathrm {E} _ {\text {c l i p}} (\mathrm {F A} (x))\right), \mathrm {M} _ {\text {f a c e}} \left(\mathrm {E} _ {\text {f a c e}} (\mathrm {F A} (x))\right)\right), \tag {4}
+$$
+
+where  $\mathrm{Concat}(\cdot, \cdot)$ ,  $\mathrm{M}_{\mathrm{clip}}(\cdot)$ ,  $\mathrm{E}_{\mathrm{clip}}(\cdot)$ ,  $\mathrm{M}_{\mathrm{face}}(\cdot)$ ,  $\mathrm{E}_{\mathrm{face}}(\cdot)$ , and  $\mathrm{FA}(\cdot)$  denote the concatenation function, CLIP mapper, CLIP image encoder, face mapper, face recognition backbone, and face alignment module [44], respectively.
+
+Mixed Attention Mechanism. As explored in previous studies [5, 14, 37], the features in the self attention layers play a crucial role in consistency image generation (across-frame in text-to-video works), which indicates these features provide a refined and detailed semantics information. In our study, we extract features from the self-attention layers of the original text-to-image diffusion model to capture rich semantic information, represented as  $K_{t}$  and  $V_{t}$ . We enhance the self-attention mechanism by incorporating it into a mixed attention framework, depicted in Fig. 3 (a). This fusion enables the integration of semantic features  $(K_{t}$  and  $V_{t}$ ) with the identity-based features  $(K_{id}$  and  $V_{id}$ ), thereby encapsulating identity information. Through this integration, the mixed attention mechanism seamlessly merges semantic details into the generated features
+
+across different resolutions. The formulation of the mixed attention mechanism is as follows:
+
+$$
+\operatorname {A t t n} _ {\operatorname {m i x}} (Q, K, V) \triangleq \operatorname {A t t n} (Q, \hat {K}, \hat {V})
+$$
+
+$$
+\begin{array}{l l} \text {w . r . t} & \hat {K} = \underset {i d} {\operatorname {C o n c a t}} \left(K _ {i d}, K _ {t}\right), \quad \hat {V} = \underset {t} {\operatorname {C o n c a t}} \left(V _ {i d}, V _ {t}\right), \end{array} \tag {5}
+$$
+
+$$
+K _ {i d} = W _ {k} ^ {i d} Z _ {i d}, \quad K _ {t} = W _ {k} ^ {t} Z _ {t},
+$$
+
+$$
+V _ {i d} = W _ {v} ^ {i d} Z _ {i d}, \quad V _ {t} = W _ {v} ^ {t} Z _ {t},
+$$
+
+where  $Z_{id}$  and  $Z_{t}$  are the corresponding spatial features of generated features and semantic features, respectively. The parameters  $W_{k}^{id}$ ,  $W_{k}^{t}$ ,  $W_{v}^{id}$ , and  $W_{v}^{t}$  correspond to the weights of the corresponding fully connected layers.
+
+Cross-attention Merging. To further refine semantic control, we incorporate text features into the identity feature within the cross-attention layers using the following formulation:
+
+$$
+\operatorname {A t t n} _ {\text {c r o s s}} (Q, K, V) \triangleq \operatorname {A t t n} \left(Q, K _ {i d} ^ {\prime}, V _ {i d} ^ {\prime}\right) + \operatorname {A t t n} \left(Q, K _ {t} ^ {\prime}, V _ {t} ^ {\prime}\right), \tag {6}
+$$
+
+where  $K_{id}^{\prime} = \hat{W}_{k}^{id}c_{id}$ ,  $V_{id}^{\prime} = \hat{W}_{v}^{id}c_{id}$ ,  $K_{t}^{\prime} = \hat{W}_{k}^{t}c_{t}$ , and  $V_{t}^{\prime} = \hat{W}_{v}^{t}c_{t}$ .  $c_{id}$  and  $c_{t}$  are the identity embedding and text embedding, respectively.  $\hat{W}_{k}^{id}$ ,  $\hat{W}_{v}^{id}$ ,  $\hat{W}_{k}^{t}$ , and  $\hat{W}_{v}^{t}$  correspond to the weights of the trainable fully connected layers within cross-attention module.
+
+Style Information Merging. Inspired by [10], we propose an adaptive mean normalization (AdaIN-mean) operation to further align the style of the synthesis image with the style prompts. Concretely, we align the key and value features projected from identity features in both mixed attention and cross-attention with the key and value features projected from text features, formulated as follows:
+
+$$
+\begin{array}{l l l} K _ {i d} = \operatorname {A d a I N - m} \left(K _ {i d}, K _ {t}\right), & V _ {i d} = \operatorname {A d a I N - m} \left(V _ {i d}, V _ {t}\right), & \text {F o r M i x e d A t t e n t i o n} \\ K _ {i d} ^ {\prime} = \operatorname {A d a I N - m} \left(K _ {i d} ^ {\prime}, K _ {t} ^ {\prime}\right), & V _ {i d} ^ {\prime} = \operatorname {A d a I N - m} \left(V _ {i d} ^ {\prime}, V _ {t} ^ {\prime}\right), & \text {F o r C r o s s A t t e n t i o n} \end{array} \tag {7}
+$$
+
+where the AdaIN-mean operation (AdaIN-m(\cdot)) is defined as:
+
+$$
+\operatorname {A d a I N} - \mathrm {m} (x, y) = x - \mu (x) + \mu (y), \tag {8}
+$$
+
+where  $\mu (x)\in R^{d_k}$  is the mean of key and value features across different pixels. The mixed attention with AdaIN-mean has been illustrated in Fig. 3 (b).
+
+# 4 Experiments
+
+After outlining the experimental setup in Sec. 4.1, we conduct a comparative analysis of raw photo generation and style image generation in Sec. 4.2. Ablation studies, highlighting the significance of various components, are presented in Sec. 4.3. Additionally, experiments involving multiple input ID images including identity mixing and identity linear interpolation are detailed in Sec. A.7 of the supplementary materials. For further insights, Sec. A.8 and Sec. A.9 of the supplementary materials provide additional qualitative results for raw photo generation and style photo generation, respectively.
+
+![](images/ce66ee3a3d30418f47ba6bf5dc8d7764ec132a6e50227e46137dfc4dbb4ba01d.jpg)  
+Fig. 4: Qualitative comparison on raw photo generation. The results demonstrate that our Infinite-ID consistently maintains identity fidelity and achieves high-quality semantic consistency with just a single input image.
+
+# 4.1 Experimental Setup
+
+Implementation Details. Our experiments leverage a pre-trained Stable Diffusion XL (SDXL) model [23]. For image encoding, we utilize the OpenCLIP ViT-H/14 [42] and the backbone of ArcFace [11]. The SDXL model consists of 70 cross-attention layers, to each of which we append an additional image cross-attention module. Training is conducted on 16 A100 GPUs for 1 million steps, with a batch size of 4 per GPU. We employ the AdamW optimizer with a fixed learning rate of 1e-4 and weight decay set to 0.01. During inference, we employ the DDIM Sampler with 30 steps and guidance scale is set to 5.0. Training data are sourced from multiple datasets, including the LAION-2B dataset [33], the LAION-Face dataset [46], and few high-quality images collected from the Websites<sup>4</sup>. We curate a dataset where each individual is represented by multiple photographs.
+
+Evaluation. We assess the efficacy of our approach in preserving both identity fidelity and semantic consistency. Specifically, we measure identity fidelity, utilizing metrics such as  $M_{\mathrm{FaceNet}}$  (measured by FaceNet [31]) and CLIP-I [8]. Identity fidelity is evaluated based on the similarity of detected faces between the
+
+![](images/01d499f8c7db4e1c3c67dccca8ae2f10d8c2b4af6eeadea587c0d1c24f4ba24e.jpg)  
+Fig. 5: Qualitative comparison on style image generation. The results demonstrate that our method maintains strong identity fidelity, high-quality semantic consistency, and precise stylization using only a single reference image.
+
+reference image and generated images. Semantic consistency is quantified using CLIP text-image consistency (CLIP-T [24]), which compares the text prompt with the corresponding generated images. More details of evaluation are shown in Sec. A.1 and Sec. A.2 of the supplementary materials.
+
+# 4.2 Comparison to Previous Methods
+
+Raw Photo Generation. We benchmark our Infinite-ID against established identity-preserving personalization approaches. The qualitative outcomes are illustrated in Fig. 4, while quantitative results are provided in Table 1. Notably, all methods are tuning-free, necessitating no test-time adjustments. FastComposer [39] exhibits challenges in maintaining identity fidelity, often presenting undesired artifacts in synthesized images. While IP-Adapter [40] and IP-Adapter-Face [40] demonstrates relatively fewer artifacts, its semantic consistency falls short. This phenomenon arises from the direct fusion of identity information with semantic details within the U-net model, leading to a compromise in semantic consistency. In contrast, PhotoMaker [17] exhibits commendable semantic consistency but falls short in preserving identity fidelity. Leveraging our ID-semantics decoupling paradigm, our method excels in preserving identity fidelity. Furthermore, our mixed attention mechanism effectively integrate the semantic
+
+Table 1: Quantitative comparison. The evaluation metrics encompass CLIP-T, CLIP-I, and  $M_{\text{FaceNet}}$ . Our approach outperforms other methods in terms of identity fidelity while simultaneously achieving satisfactory semantic consistency. The best result is shown in bold, and the second best is underlined. Additionally, the quantitative comparison of ablation studies have been shown in the gray part.  
+
+<table><tr><td></td><td>CLIP-T ↑</td><td>CLIP-I ↑</td><td>M_FaceNet ↑</td></tr><tr><td>FastComposer [39]</td><td>0.292</td><td>0.887</td><td>0.556</td></tr><tr><td>IP-Adapter [40]</td><td>0.274</td><td>0.905</td><td>0.474</td></tr><tr><td>IP-Adapter-Face [40]</td><td>0.313</td><td>0.919</td><td>0.513</td></tr><tr><td>PhotoMaker [17]</td><td>0.343</td><td>0.814</td><td>0.502</td></tr><tr><td>Ours</td><td>0.340</td><td>0.913</td><td>0.689</td></tr><tr><td>Ours (w/o identity-enhanced training)</td><td>0.329</td><td>0.891</td><td>0.593</td></tr><tr><td>Ours (w/o Mixed Attention)</td><td>0.331</td><td>0.905</td><td>0.700</td></tr><tr><td>Ours (Mixed Attention ⇒ Mutual Attention)</td><td>0.316</td><td>0.808</td><td>0.398</td></tr></table>
+
+information into the denoising process, positioning our method favorably against existing techniques. More comparison results are shown in Sec. A.4, Sec. A.5 and Sec. A.6 of the supplementary materials.
+
+Style Image Generation. We demonstrate the results of the stylization results in Fig. 5, which compare our method with state-of-the-art tuning-free identity-preserving personalization methods. The style of the synthesis images include anime style, comic book style, and line art style. According to the stylization results, the IP-Adapter [40] and IP-Adapter-Face fails to depict the desired style in the prompt and the style of generation results always obey the tone in the reference image. The training pipeline of the IP-Adapter and IP-Adapter-Face entangles the text embedding and image embedding which leads to the distortion of the text embeddings space. FastComposer [39] also fails in stylization generation and shows undesired artifacts. PhotoMaker [17] achieves a better semantic consistency and stylization, but the identity fidelity is still unsatisfactory. In contrast, our method achieves high identity fidelity, appealing semantic consistency, and precise stylization meantime.
+
+# 4.3 Ablation Study
+
+In this section, we begin by conducting ablation studies to assess the influence of our identity-enhanced training and mixed attention mechanism. Furthermore, we conduct style image generation to evaluate the effectiveness of our AdaIN-mean operation in regulating the style of the generated images. More ablation studies are demonstrated in Sec. A.3 of the supplementary materials.
+
+Ablation of identity-enhanced training. In Fig. 6 and Table 1, we compare our method with "Ours (w/o identity-enhanced training)", which is implemented using an identity-semantics entangled training strategy. This strategy utilizes text-image pairs during training and activates cross-attention modules for text embeddings within the original U-Net model. It is noteworthy that both methods
+
+![](images/2337fa1f5f28299abc98a7e44b4eb7e3ab6aca5208d2f2f8925f440af4c5d3ad.jpg)  
+a woman wearing purple sweater, facing and smiling to the camera, in a forest
+
+![](images/8bcc8b60ad7cba6d6f482b5c449c104eb748bcb263cf27be832b956c32954ca2.jpg)  
+a photo of a man wearing a colorful shirt, in the living room
+
+![](images/ab5fdf84a765b7d1e7e633e134b54e7ef4a12f2ec0abe906dd12b8c51b8bc05e.jpg)  
+ID image
+
+![](images/10a0c5816810dbe015c626d4041327b6f61c4f147cc8463e6962a9f478caf51c.jpg)
+
+![](images/df1a192a31f1f6bad742e8cdef1e7990cb0235d6f9f194f3ec1024d796f1fdb3.jpg)
+
+![](images/c9720f8d102dd20dd49713e63b974affa08146157b85f3616678df783acddf2b.jpg)
+
+Ours  
+![](images/939905821752ac9b1156d38a0bb51381a3134c39e960af462d2ae55427e69975.jpg)  
+a woman wearing a red hat, smiling and facing to the camera, sunset, on the beach  
+Ours (w/o identity-enhanced training)
+
+![](images/3b164df0b3cddb42c19fe4e4042690a18573786ea330f15b130117cb7d17a85d.jpg)
+
+![](images/f0297b2b1e480601e5270170046b85ebda0b05559abe54dc644e74df6863dc73.jpg)
+
+![](images/49a3475032c54d73935d3f51366f60732f52fbc8699a4b055164cc5ed54c7923.jpg)  
+Ours (M-A  $\Rightarrow$  MU-A)
+
+Fig. 6: Ablation study of our identity-enhanced training and mixed attention (M-A). It is evident that identity-enhanced training significantly improves the identity fidelity, and mixed-attention mechanism enhances semantic consistency compared to mutual attention (MU-A) approach [5].  
+![](images/8fbf6616ec2483404a4b7d2399eee2847d481cebb3030e2bba8de7834fe9a83c.jpg)  
+awearing a blue clothing, facing and smiling to the snow. A snowy, snowy, in an anime style
+
+ID Image  
+Fig. 7: Ablation study of our AdaIN-mean operation. The results show that AdaIN-mean play a crucial role in style image generation. Compare to AdaIN [10] module, our AdaIN-mean helps to achieve a higher identity fidelity.  
+![](images/9a1c3b99492fc94af69f9a0838f250c115911615070ac6db8a20e09586ce23e7.jpg)  
+a woman wearing a purple dress and smiling to the camera, on a beach, sunset, comic book style
+
+![](images/8d1c57c74125779832a2b402dbf91d09755bd61eca819c7b94c846fadd7592a2.jpg)
+
+![](images/e46e5ccadcd2615e9b1fe5dadd204d460988396d27a7e752dc92d9cebc2e94e5.jpg)  
+Ours
+
+![](images/0bcf974314745e99ea2c32b5ec3637174b3d274b3dd1ec56afad195a9dfe6e6f.jpg)
+
+![](images/22a87f3a44b42531fb9abd58dadcbe61d4125c02c416795ca24e670f5f0ef109.jpg)  
+Ours (AdaIN-mean  $\Rightarrow$  AdaIN)
+
+share the same inference processing. The qualitative comparison demonstrates that our identity-enhanced training notably enhances identity fidelity.
+
+Ablation of mixed attention mechanism. To assess the effectiveness of our proposed mixed attention (M-A) mechanism, we compare our method with "Ours (w/o M-A)" and "Ours (M-A  $\Rightarrow$  MU-A)" in Fig. 6 and Table 1. Mutual self-attention (MU-A) [5] converts the existing self-attention into 'cross-attention' for consistent image editing, where the crossing operation happens in the self-attention of two related diffusion processes. The results show that our mixed attention mechanism demonstrates superior ability to improve semantic consistency while maintaining identity fidelity.
+
+Ablation of AdaIN-mean operation. To assess the effectiveness of our proposed AdaIN-mean operation, we compare our Infinite-ID model with variations, namely Ours (w/o AdaIN-mean) and Ours (AdaIN-mean  $\Rightarrow$  AdaIN), as depicted
+
+in Fig. 7. The results reveal that: i) Ours (w/o AdaIN-mean) exhibits superior ID fidelity compared to Infinite-ID but fails to achieve style consistency with the text prompt; ii) Both our AdaIN-mean and AdaIN modules successfully achieve style consistency with the text prompt, yet AdaIN-mean maintains better ID fidelity than AdaIN. In conclusion, our proposed AdaIN-mean operation facilitates precise stylization while concurrently preserving ID fidelity.
+
+# 5 Conclusion and limitations.
+
+In this paper, we introduce Infinite-ID, an innovative identity-preserved personalization method designed to meet the requirement of identity (ID) fidelity and semantic consistency of the text prompt, all achievable with just one reference image and completed within seconds. Infinite-ID comprises three key components: the identity-enhanced training, mixed attention mechanism, and adaptive mean normalization (AdaIN-mean). Through extensive experimentation, our results illustrate that Infinite-ID outperforms baseline methods, delivering strong ID fidelity, superior generation quality, and precise semantic consistency in both raw photo generation and style image generation tasks. However, it's important to note that our method lacks multi-object personalization capability. Moreover, artifacts may occur when the human face occupies only a small portion of the entire image, attributed to limitations inherent in the original diffusion model. Furthermore, the image encoders employed in the identity-preserved personalization remain to be further explored.
+
+# 6 Copyright of Training Data and Ethical Considerations.
+
+Copyright of Training Data. We construct our training dataset from the open-source public image dataset, including LAION-2B dataset, the LAION-Face dataset and few high-quality images collected from the Website<sup>5</sup> which supports the CC0 (Creative Commons Zero) 1.0 Universal license<sup>6</sup>.
+
+Ethical Considerations. We recognize the ethical considerations about improper use of such high-quality human photo synthesis techniques. Therefore, we emphasize the significance of establishing and complying to ethical guidelines [4] and using this technology responsibly. We hope that our work will drive further discussions and research on the security and ethical use of the human photo generation in computer vision. Moreover, we will employ the watermark and safety checker (NSFW classifiers) to attempt to avoid inappropriate content generation.
+
+# Acknowledgements
+
+This research was funded by the National Natural Science Foundation of China (U19B2044), supported by the Fundamental Research Funds for the Central Universities (WK2100000045).
+
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2024/Infinite-ID_ Identity-preserved Personalization via ID-semantics Decoupling Paradigm/images.zip

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+    {
+        "type": "text",
+        "text": "InfoNorm: Mutual Information Shaping of Normals for Sparse-View Reconstruction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Xulong Wang $^{1,2*}$  Siyan Dong $^{3*}$  Youyi Zheng $^{1\\dagger}$  Yanchao Yang $^{3,4\\dagger}$",
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+    {
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+        "text": "<sup>1</sup> State Key Lab of CAD&CG, Zhejiang University <sup>2</sup> Chohotech co. Ltd.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "<sup>3</sup> Institute of Data Science, The University of Hong Kong",
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+    {
+        "type": "text",
+        "text": "$^{4}$  Department of Electrical and Electronic Engineering, The University of Hong Kong",
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+        "text": "Abstract. 3D surface reconstruction from multi-view images is essential for scene understanding and interaction. However, complex indoor scenes pose challenges such as ambiguity due to limited observations. Recent implicit surface representations, such as Neural Radiance Fields (NeRFs) and signed distance functions (SDFs), employ various geometric priors to resolve the lack of observed information. Nevertheless, their performance heavily depends on the quality of the pre-trained geometry estimation models. To ease such dependence, we propose regularizing the geometric modeling by explicitly encouraging the mutual information among surface normals of highly correlated scene points. In this way, the geometry learning process is modulated by the second-order correlations from noisy (first-order) geometric priors, thus eliminating the bias due to poor generalization. Additionally, we introduce a simple yet effective scheme that utilizes semantic and geometric features to identify correlated points, enhancing their mutual information accordingly. The proposed technique can serve as a plugin for SDF-based neural surface representations. Our experiments demonstrate the effectiveness of the proposed in improving the surface reconstruction quality of major states of the arts. Our code is available at: https://github.com/Muliphein/InfoNorm.",
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+    {
+        "type": "text",
+        "text": "Keywords: 3D from multi-view images  $\\cdot$  surface reconstruction",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
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+        "type": "text",
+        "text": "3D surface reconstruction from multi-view images is an essential task in the computer vision and graphics community, with practical applications including content creation for virtual reality and robot-scene interaction. However, indoor scenes present challenges due to the large and complex scenes captured from sparse viewpoints. These challenges encompass issues such as occlusion and ambiguity arising from limited observations. As a result, traditional Multi-View Stereo (MVS) methods [28,36], which require substantial overlap among images, may not produce satisfactory results in these scenarios.",
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+    {
+        "type": "page_footnote",
+        "text": "* Equal contributions (wangxulong@zju.edu.cn, siyan3d@hku.hk).",
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+        "text": "† Corresponding authors.",
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+        "text": "2 This work was done during the author's internship at Chohotech Co. Ltd..",
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+            "VoISDF+ (Ours)"
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+        "image_caption": [
+            "GeoNeuS",
+            "Fig. 1: 3D scene reconstruction from sparse views on Replica [26] (first row) and ScanNet++ [38] (second row). By enforcing the mutual information between the normals of highly correlated scene points, the proposed method can effectively enhance the reconstruction quality of the baselines (VolSDF [37] and GeoNeuS [8])."
+        ],
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+        "image_caption": [
+            "GeoNeuS $^{+}$  (Ours)"
+        ],
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+        "img_path": "images/163c73317edb184b56866c497313fa562e0cfff80ed358069df6bcaa7a5f696a.jpg",
+        "image_caption": [
+            "Ground truth"
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+    {
+        "type": "text",
+        "text": "Recently, implicit scene representations, e.g., Neural Radiance Fields (NeRFs) [21], have been proposed to encode 3D scenes into a set of neural network parameters, with subsequent works enhancing the representational capacity for geometry to enable surface extraction. The key idea involves incorporating signed distance functions (SDFs) [23] into the learned radiance field. Although NeRFs with SDF produce high-quality reconstructions of simple scenes with sufficient images, they still underperform in large and complex scenes captured from sparse viewpoints. More recent approaches, such as NeuRIS [29] and MonoSDF [40], propose using monocular geometric priors to guide the learning of the radiance field. However, they can be affected by inevitable errors and noise in the monocular geometry estimation modules.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We explore geometric regularization in a second-order perspective. We argue that both the geometry itself and the correlation of geometry among scene regions are crucial for surface reconstruction, especially when dealing with varying indoor scenes under sparse views with noisy geometry estimates. The correlation is expressed as mutual information between scene entities under random perturbations of the network weights. More explicitly, we propose to enforce the mutual information between the normals of two points in the scene that are considered geometrically correlated, where the mutual information can be efficiently computed by measuring the cosine similarity between the gradients of the normals with respect to the perturbed weights. Further, we leverage a combination of pretrained semantic and geometric features [4,7,12] to identify the correlated scene regions that endorse high mutual information. This results in an easy-to-use geometric shaping<sup>1</sup> technique that can be applied to any SDF-based neural radiance fields. To thoroughly evaluate its effectiveness, we test the proposed with",
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+    {
+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup> We use the term \"shaping\" to refer to the process of optimizing network parameters to enforce consistencies in the scene geometry via aligning the gradients.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "multiple state-of-the-art neural surface reconstruction models. The experimental results confirm the effectiveness of the proposed shaping technique, showing improved surface reconstruction quality (e.g., Fig. 1) on challenging scenes with limited views. To summarize:",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose to leverage second-order geometric correlation in the form of mutual information between normals to regularize the surface reconstruction of SDF-based NeRF representations.",
+            "- We develop a pipeline that efficiently enforces the mutual information of the normals of points, deemed geometrically correlated with pre-trained multimodal features, to improve the reconstruction quality of the scene.",
+            "- We verify the effectiveness of the proposed second-order regularization technique across a broad spectrum of baselines and demonstrate its usefulness as an easy-to-use plugin in improving 3D surface modeling."
+        ],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3D Reconstruction with neural radiance fields (NeRFs). NeRF [21] is originally designed for novel view synthesis, with its variants serving as scene representations [15, 32, 33, 35, 39] for tasks related to editing [2, 31, 44], semantic segmentation [5, 14, 16, 34], 3D shape generation [20, 27], and so on. We mainly focus on neural surface representations that enable the extraction of high-quality 3D meshes from the trained NeRFs.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Early works such as NeuS [30] and VolSDF [37] combine signed distance functions (SDFs) with volume rendering to extract high-quality surfaces. Recently, SparseNeuS [17] introduces a cascaded geometry reasoning framework that generalizes well to novel scenes. GeoNeuS [8] uses surface points from structure-from-motion and neighbor-view patches to reconstruct surfaces, while NeuDA [3] employs a deformable anchor to adaptively encode geometric details. NeAT [19] broadens the scope of reconstruction to arbitrary topology, no longer confining to watertight surfaces. Moreover, Neuralangelo [13] uses a hash grid for position encoding and implements a coarse-to-fine optimization with numerical gradients. Despite their promising results, most of these methods need sufficient training views, and their performance declines when dealing with large and complex scenes under sparse viewpoints.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Incorporating priors into NeRFs. One can augment scene representations by introducing various priors to NeRFs. VDN-NeRF [43] normalizes the spatial feature to align with monocular features. LERF [11] introduces a new branch whose outputs align with DINO [4] and CLIP [24] features. Semantic-NeRF [42] encodes semantic information for segmentation tasks, while JacobiNeRF [34] shapes the color gradients to encode the mutual information in terms of semantic similarity from DINO [4] features for label propagation.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For surface reconstruction, GeoNeuS [8] incorporates patch similarity from neighboring images and sparse surface points derived from structure-from-motion",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "[25], while I²-SDF [44] combines the rendering equation with VolSDF [37] for better novel views and geometry. To cope with complex indoor scenes, NeuRIS [29] incorporates the normal priors as additional geometric supervision. Further, MonoSDF [40] uses both depth and normal to improve the surface reconstruction quality. However, these methods highly depend on the quality of the supplemented geometric information. In contrast, our method leverages the second-order information in geometric prior, rather than directly using the prior as a first-order supervision signal, which makes it more robust to errors and noise. There are also methods utilizing strong assumptions derived for human-made scenes. For instance, ManhattanSDF [10] works under the assumption that all captured scenes adhere to the Manhattan-world concept, thus, predicting semantic segmentation to identify walls and floors. While these methods primarily focus on planar scenes, the proposed technique can work for general scenes under noisy correlation information.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
+            215,
+            383,
+            330,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We start with a discussion on the preliminaries in Sec. 3.1 to provide the background on how we can learn from posed images an implicit scene representation (NeRF), improve 3D scene reconstruction via the combination of NeRF and SDF representations, and employ mutual information as a constraint in the NeRF training process. Following this, in Sec. 3.2, we delve into how mutual information can be used as constraints on NeRF's implied surfaces, so that we can learn better geometries for higher-quality 3D reconstruction of the scene. Finally, we elaborate on how we can employ off-the-shelf semantic and geometry features to assist the encoding of mutual information through the proposed geometric shaping framework.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1 Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Neural radiance fields. NeRF [21] learns an implicit scene representation from a set of posed images. For a specific pixel in an image, NeRF samples a list of 3D points,  $\\{x|x_{t} = \\mathbf{o} + t\\mathbf{v},t\\in [t_{near},t_{far}]\\}$ , from the camera center  $\\mathbf{o}$  along the viewing direction  $\\mathbf{v}$  within a bounded space. Specifically, it employs a Multilayer Perceptron (MLP) to encode the volume density and color of each sampled point. We denote all the parameters of NeRF as  $\\theta$ , the density function as  $\\sigma$ , and the color function as  $c$ . The pixel's rendered color  $\\hat{\\mathbf{C}}$  from a NeRF is calculated by the discrete volume rendering:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {C}} (\\mathbf {o}, \\mathbf {v}; \\theta) = \\sum_ {i = 1} ^ {N} \\omega (\\mathbf {o}, \\mathbf {v}, t _ {i}; \\theta) c \\left(x _ {t _ {i}}, \\mathbf {v}; \\theta\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\text {w h e r e} \\omega (\\mathbf {o}, \\mathbf {v}, t _ {i}; \\theta) = \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) \\alpha_ {i}.\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "page_number",
+        "text": "4",
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+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\alpha_{i} = 1 - \\exp (-\\sigma_{i}\\delta_{i})$ , where  $\\sigma_{i}$  is the abbreviation of  $\\sigma (x_{t_i};\\theta)$  and  $\\delta_{i} = t_{i + 1} - t_{i}$ . A photometric loss is utilized to minimize the discrepancy between the rendered color and its ground truth:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {C} = \\left\\| \\mathbf {C} - \\hat {\\mathbf {C}} \\right\\| _ {1}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "so that the parameters  $\\theta$  can be optimized to fit the scene. Despite the ability to handle photorealistic novel view synthesis, NeRFs suffer from noisy and unrealistic surface extraction when it comes to 3D reconstruction, as discussed in the literature [30, 37].",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "NeRFs with signed distance functions. To produce high-quality surfaces, it is beneficial to use signed distance functions (SDFs) [6, 23] to represent geometry. Consequently, the surface can be reconstructed by extracting the zero-level set [18] of the SDF values. The combination of NeRF and SDF can be achieved by deriving the NeRF's densities from the SDF, or defining Laplace's cumulative distribution function. Accordingly,  $\\alpha_{i}$  in Eq. 1 can be represented by a function  $\\varPhi$  which converts SDF values to volume densities as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i} = \\Phi (x, f (x; \\theta), i). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Generally, NeRFs with an SDF achieve improved surface reconstruction quality, where the key to maintaining the characteristics of SDF is an eikonal loss [9]:",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {E} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\left| \\left| \\nabla f \\left(x _ {i}\\right) \\right| \\right| _ {2} - 1\\right) ^ {2}. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Mutual information in NeRFs. Mutual information (MI) quantifies the statistical dependence between two random variables, providing an estimate of how much information they share. It has been introduced for semantic segmentation and motion modeling tasks [34, 41]. In this paper, We study the mutual information under perturbations of the NeRF parameters, and focus more on the geometry properties. Let  $I(p_{i})$  and  $I(p_{j})$  denote two pixels derived from the NeRF rendering process  $\\mathbb{F}$ . And we assume that a subset of the NeRF weights, denoted by  $\\theta^{D}$ , is perturbed by a random noise vector  $\\mathbf{n} \\in \\mathbb{R}^{D}$  sampled from a uniform distribution on the sphere  $\\mathbb{S}^{D - 1}$  by a small step  $\\gamma \\ll 1.0$ . The random variables corresponding to the perturbed pixels can be written through a Taylor expansion:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {I} (p _ {i}) = I (p _ {i}) + \\gamma \\mathbf {n} \\frac {\\partial \\mathbb {F} _ {i}}{\\partial \\theta^ {D}},\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {I} (p _ {j}) = I (p _ {j}) + \\gamma \\mathbf {n} \\frac {\\partial \\mathbb {F} _ {j}}{\\partial \\theta^ {D}}.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We can now characterize the mutual information between  $\\hat{I}(p_i)$  and  $\\hat{I}(p_j)$  under the joint probability distribution  $\\mathbb{P}(\\hat{I}(p_i), \\hat{I}(p_j))$ . As derived in JacobiNeRF, the",
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
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+    {
+        "type": "text",
+        "text": "mutual information can be computed as:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbb {I} (\\hat {I} (p _ {i}), \\hat {I} (p _ {j})) = \\mathbb {H} (\\hat {I} (p _ {i})) - \\mathbb {H} (\\hat {I} (p _ {i}) | \\hat {I} (p _ {j})) \\\\ = \\log (\\frac {1}{\\sqrt {1 - \\cos^ {2} \\beta}}) + \\mathrm {c o n s t .}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\beta$  denotes the angle between  $\\partial \\mathbb{F}_i / \\partial \\theta^D$  and  $\\partial \\mathbb{F}_j / \\partial \\theta^D$ . It is observed that:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {I} (\\hat {I} (p _ {i}), \\hat {I} (p _ {j})) \\propto | | \\cos \\beta | |. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Therefore, to enhance the MI between two random pixels induced by NeRF perturbations, one can enforce the absolute value of the cosine similarity. That is, if two pixels  $p_i$ ,  $p_j$  come with high correlation (e.g., from the same object in the scene), their gradients regarding the perturbed parameters should be in the same or opposite direction.",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "3.2 Mutual Information Shaping of Geometry in SDF-based NeRFs",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While the previous approach focuses on enforcing mutual information for image synthesis, we explore a mutual information shaping of the geometries for quality surface reconstruction in SDF-based NeRFs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Specifically, we represent a scene via a NeRF backbone with an SDF head and a color head, as shown in Fig. 2. Note that the method to be proposed is capable of being applied to any network similar to NeRF and SDF representations. Given that the two heads partially share parameters, we denote all the parameters as  $\\theta$ , and use  $f(x;\\theta)$  and  $c(x,\\mathbf{v};\\theta)$  to represent the SDF and color branches, respectively. To achieve mutual information shaping of the geometry, we focus on manipulating the parameters of  $f(x;\\theta)$ , while keeping  $c(x,\\mathbf{v};\\theta)$  unchanged. Below, we first explain why and how we compute mutual information with surface normals derived from SDF, i.e.,  $f(x;\\theta)$ , as a geometry-aware constraint. Next, we present a simple yet effective strategy that extracts regions with high correlation, which need to be encoded into the weights using the mutual information shaping technique. Finally, we elaborate on our loss function and training process to reconstruct the scene from posed images.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Mutual information among surface normals. We explicitly encode mutual information into the function  $f(x; \\theta)$ . However, instead of computing mutual information between the density values, we proceed by manipulating the surface normal vectors that can be derived from  $f$ . Specifically, for a 3D point  $x$  on a surface of the scene, its normal vector  $N(x; \\theta)$  can be calculated as the partial derivative of the 3D coordinate:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nN (x; \\theta) = \\frac {\\partial f (x ; \\theta)}{\\partial x}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "There are several reasons to manipulate surface normal vectors but not SDF values: 1) Shaping the SDF values with respect to a subset  $\\theta^D$  of the parameters may not effectively impose the constraints on all parameters. However, the",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "6",
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+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
+            271,
+            114,
+            444,
+            128
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f17f63afda6c3119d5acae9d04874923ea056d465e48b6553b8bf4685feb5f3.jpg",
+        "image_caption": [
+            "Fig. 2: An overview of the pipeline, where we apply mutual information shaping on the geometric branch to enforce consistencies that help enhance the surface reconstruction. Specifically, the model consists of the NeRF backbone, an SDF head, and a color head. The predicted density and color are supervised by the classic eikonal loss  $L_{E}$  and the photometric reconstruction loss  $L_{C}$ , respectively. We encode geometry-aware mutual information into a subset of the parameters  $\\theta^{D}$  of  $f(x)$  to constrain the density field learning for better surface quality, which is achieved by the proposed mutual information loss  $L_{M}$  computed on top of the estimated surface normal."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            145,
+            781,
+            268
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "calculation of the surface normal includes the entire set of parameters in  $f$ , thus a more global regularity. 2) Moreover, shaping  $f$  with the mutual information between its values may induce side effects as density could be distorted to satisfy the constraints. However, shaping the normal  $\\partial f / \\partial x$  leave more space for the SDF values to cope with the scene reconstruction task, thus minimizing potential negative effects.",
+        "bbox": [
+            212,
+            420,
+            782,
+            508
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "According to Eq. 5, we need to calculate the partial gradients  $\\partial N / \\partial \\theta^D$  to compute the mutual information. When it comes to a vector rather than a scalar, the gradients consist of three components corresponding to the  $\\mathbf{x}$ ,  $\\mathbf{y}$ , and  $\\mathbf{z}$  axes:",
+        "bbox": [
+            214,
+            511,
+            784,
+            556
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\frac {\\partial N (x ; \\theta)}{\\partial \\theta^ {D}} = \\frac {\\partial N _ {\\mathbf {x}} (x ; \\theta)}{\\partial \\theta^ {D}}, \\frac {\\partial N _ {\\mathbf {y}} (x ; \\theta)}{\\partial \\theta^ {D}}, \\frac {\\partial N _ {\\mathbf {z}} (x ; \\theta)}{\\partial \\theta^ {D}}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            336,
+            566,
+            784,
+            597
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For ease of computation, we concatenate the gradients into a vector, denoted as  $\\partial N$  for simplicity:",
+        "bbox": [
+            214,
+            601,
+            782,
+            630
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\partial N = \\operatorname {C o n c a t} \\left(\\frac {\\partial N _ {\\mathbf {x}}}{\\partial \\theta^ {D}}, \\frac {\\partial N _ {\\mathbf {y}}}{\\partial \\theta^ {D}}, \\frac {\\partial N _ {\\mathbf {z}}}{\\partial \\theta^ {D}}\\right). \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            380,
+            628,
+            784,
+            657
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Since a 2D pixel is accumulated from 3D, we aggregate the normal-based information along a viewing ray as in Eq. 1 as:",
+        "bbox": [
+            214,
+            662,
+            782,
+            693
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {N} \\left(p _ {i}\\right) = \\sum_ {x \\in \\text {r a y}} \\omega \\left(t _ {i}; \\theta\\right) \\partial N. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            408,
+            702,
+            784,
+            734
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Finally, we obtain that the mutual information between two normals is:",
+        "bbox": [
+            214,
+            743,
+            732,
+            758
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {I} (\\hat {N} (p _ {i}), \\hat {N} (p _ {j})) \\propto | | \\frac {\\mathbb {N} (p _ {i}) \\cdot \\mathbb {N} (p _ {j})}{| \\mathbb {N} (p _ {i}) | | \\mathbb {N} (p _ {j}) |} | |. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            369,
+            767,
+            784,
+            801
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Please refer to our supplementary material for a detailed derivation. From Eq. 10, we observe that the mutual information in surface normal vectors correlates",
+        "bbox": [
+            214,
+            809,
+            782,
+            839
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+            114,
+            784,
+            125
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a1037c099eeadeb4e12569c2335a9d39eec82a6e6ce806b409303ba67e34c5c1.jpg",
+        "image_caption": [
+            "Anchor pixel"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            220,
+            145,
+            356,
+            224
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/fdc6e8d50ef3f3f196ffc7ad2e20073c5eefb613a549457884295d170dcec5a5.jpg",
+        "image_caption": [
+            "Similar semantic features",
+            "Fig. 3: An example of positive samples from different features. Given an anchor pixel (marked by a blue circle in the first image) on the wall-like cabinet, semantic features like DINO often correlate both the cabinet and the ceiling (as shown by the red area in the second image). Meanwhile, geometric features such as (noisy) monocular normals can not distinguish between parallel planes that are not connected (the third image). By combining semantic and geometric features, we can obtain positive samples of the anchor pixel with better geometric consistency, thus, high mutual correlation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            361,
+            145,
+            498,
+            224
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/0713b265af24b7ebbaeed91bc4e2fbefb2b1432c4c0011904bb28b4c17d96bbc.jpg",
+        "image_caption": [
+            "Similar geometric features"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
+            145,
+            638,
+            224
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c5e4fb51e95f325dfde32be6d991727a9691233107efa75288aab21b7ee2d042.jpg",
+        "image_caption": [
+            "Combined (Ours)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            643,
+            145,
+            782,
+            224
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "positively with the cosine similarity of their gradients to the network parameters. This conclusion is similar to that of Eq. 5. As a result, we can now identify the pixels that are of high correlations, and increase the aggregated mutual information during the NeRF training process.",
+        "bbox": [
+            212,
+            375,
+            787,
+            436
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Extracting correlated scene regions from image pixels. To extract scene regions that need to be shaped to have high mutual information, we present a simple yet effective approach with off-the-shelf visual features. Given the input images, we extract pixel-wise semantic and geometric features to identify correlated scene regions. Following previous research [34], we apply DINO [4] as the semantic feature extractor to obtain a high-level understanding of the scene regions. Meanwhile, as we shape mutual information on top of the surface normal, we employ a monocular normal estimator [7] as the geometric feature extractor for a detailed low-level perception of the 3D points in the scene.",
+        "bbox": [
+            212,
+            446,
+            787,
+            582
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "DINO features can group different parts of an object, like the seat and back of a chair, which share similar semantics. However, the surface normal vectors from these parts have limited correlation, thus should not be constrained. Conversely, using only geometric features can wrongly suggest high correlation between unrelated areas, like the seat and the floor. As these areas aren't closely connected in 3D space, there is no reason to have better surface reconstruction when enhancing their mutual information. Similar phenomena on wall-like structures can be observed in Fig. 3, where we show that by combining semantic and geometric features together we can better identify scene regions that are spatially connected and have similar normal directions.",
+        "bbox": [
+            212,
+            583,
+            787,
+            733
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "More explicitly, we combine semantic and geometric features with an intersection operator. It is simple yet effective. The process of identifying correlated scene regions (in normal) is implemented as positive pixel pair selection from input images. Given a randomly selected pixel from an image, we first extract similar pixels from neighboring images using semantic and geometric features, respectively. This extraction is implemented by applying two thresholds,  $\\beta_{S}$  and  $\\beta_{G}$ , to filter the cosine similarity for semantic and geometric features. We then",
+        "bbox": [
+            212,
+            734,
+            787,
+            840
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
+            217,
+            114,
+            228,
+            126
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
+            271,
+            114,
+            444,
+            128
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "feed the intersection of the top similar pixels from each feature type into NeRF's training process as positive samples, allowing us to shape them with high mutual information. In order to leverage the contrastive learning framework to encourage mutual information, we randomly select pixels not involved in the aforementioned process to serve as negative samples (independent pixels that are not correlated to the anchor pixel).",
+        "bbox": [
+            212,
+            146,
+            782,
+            238
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Loss functions for training. The aforementioned contrastive learning process is performed with a tailored InfoNCE loss [22]:",
+        "bbox": [
+            214,
+            248,
+            782,
+            280
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {M} = - \\log \\frac {\\sum \\exp (| | \\cos (\\partial \\mathbb {N} _ {i} , \\partial \\mathbb {N} _ {i +}) | |)}{\\sum_ {j} \\exp (| | \\cos (\\partial \\mathbb {N} _ {i} , \\partial \\mathbb {N} _ {j}) | |)}, \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            362,
+            286,
+            785,
+            321
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $i$ ,  $i+$ , and  $j$  denote the anchor, positive, and negative pixels, respectively. This loss function effectively enhances mutual information (according to Eq. 10) among correlated pixels, while maintaining low mutual information among independent pixels. Finally, to train the NeRF backbone and retain the characteristics of the SDF, we adopt the basic photometric loss (Eq. 2) and the eikonal loss (Eq. 4). The latter two are derived from single images, while the former can be calculated from either single images or a set of neighboring images. The full loss function is defined as the weighted sum of three loss terms:",
+        "bbox": [
+            214,
+            327,
+            784,
+            446
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL = L _ {C} + \\lambda_ {E} L _ {E} + \\lambda_ {M} L _ {M}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            406,
+            455,
+            784,
+            470
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "With the above, all network parameters  $\\theta$  can be trained end-to-end.",
+        "bbox": [
+            214,
+            479,
+            712,
+            494
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
+            214,
+            513,
+            375,
+            532
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this section, we evaluate the effectiveness of our method through experiments conducted on multiple datasets with various baselines. First, we introduce the two datasets used to conduct the experiments in Sec. 4.1. Next, we detail the implementation of the proposed method in Sec. 4.2, where we adapt a spectrum of state-of-the-art models for validating the effectiveness of the geometric shaping. Then, we report the comparisons between the baselines and our models in Sec. 4.3. Lastly, we conduct a series of ablation studies in Sec. 4.4, to verify the necessity of each component in our method.",
+        "bbox": [
+            212,
+            542,
+            784,
+            662
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.1 Datasets",
+        "text_level": 1,
+        "bbox": [
+            214,
+            681,
+            334,
+            696
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the proposed method using two public datasets from the literature: ScanNet++ [38] and the Replica [26] dataset. For the ScanNet++ dataset, we choose 8 representative scenes, while for the Replica dataset, we select 4 representative scenes. The scenes from both datasets represent a variety of indoor settings, including offices, bedrooms, and so on. As our focus is on scene reconstruction from sparse views, we uniformly sample 50-85 images from the official (and Replica from Semantic-NeRF [42]) scanning sequences for each scene to use as input in our evaluation. For detailed statistics of each scene, please refer to our supplementary material.",
+        "bbox": [
+            212,
+            704,
+            787,
+            840
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
+            114,
+            730,
+            127
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            774,
+            116,
+            785,
+            126
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. Following previous works [13, 30, 40], we evaluate the quality of surface reconstruction using two metrics: Chamfer distance and F-score. Chamfer distance is a measure that evaluates the difference between reconstructed and ground-truth points sets. F-score is a statistical metric that integrates precision and recall, providing a more comprehensive understanding of the reconstruction quality.",
+        "bbox": [
+            212,
+            146,
+            787,
+            238
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.2 Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            215,
+            258,
+            457,
+            273
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "As the proposed geometric shaping can be easily integrated into any network similar to NeRF with SDF representations, we select several state-of-the-art models as our baselines and apply the proposed to them for demonstrating the effectiveness of our approach. We first choose NeuS [30] and VolSDF [37], the two representative pioneers for NeRFs with SDFs. We also apply our method to the following works: GeoNeuS [8], I²-SDF [44], NeuRIS [29], MonoSDF [40], and Neuralangelo [13]. In addition to the basic loss functions for NeRF and SDF, GeoNeuS incorporates patch similarity from neighboring views and surface points derived from structure-from-motion. I²-SDF integrates the rendering equation with VolSDF. We disregard its normal and depth loss terms. NeuRIS utilizes monocular normal estimation as a supervision on the geometry, and discards the low-quality normal information that lacks sufficient confidence through multi-view patching. MonoSDF employs both depth and normal estimation, for which we set the decay of the normal and depth at 30k iterations to prevent the method from degeneration. Neuralangelo utilizes a multi-resolution hash grid and numerical gradient. We set the hash encoding dictionary size to 20, and the encoding dimension to 4. For all the base models mentioned above, we enhance them by incorporating our proposed mutual information loss during training. The resulting methods are respectively labeled as  $\\mathrm{NeuS^{+}}$ , VolSDF+, GeoNeuS+, and so on.",
+        "bbox": [
+            212,
+            281,
+            787,
+            583
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.3 Comparisons",
+        "text_level": 1,
+        "bbox": [
+            215,
+            604,
+            370,
+            619
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Results on the ScanNet++ dataset. The quantitative comparisons are reported in Tab. 1. We also visualize the surface reconstruction results in Fig. 4 for qualitative comparisons. We can observe that by applying the proposed mutual information shaping on the geometry, the surface reconstruction quality can be improved across all baselines, as measured by mean Chamfer distance, F-score, and the visuals.",
+        "bbox": [
+            212,
+            628,
+            787,
+            718
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "NeuS and VolSDF tend to produce rough surfaces and excessively smoothed boundaries. However, with our geometry-aware mutual information, the surfaces become smoother, while the boundaries are more crispy. Compared to GeoNeuS, a method that uses patch-similarity among neighboring views and requires sufficient textures, our method provides significant improvements. Applying the proposed technique to  $\\mathrm{I}^2$ -SDF can also enhance its reconstruction quality.",
+        "bbox": [
+            212,
+            719,
+            787,
+            809
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "As for more recent works, we find that NeuRIS is somewhat sensitive to the quality of normal estimation. It can either be affected by noise in the normal",
+        "bbox": [
+            212,
+            809,
+            787,
+            839
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
+            217,
+            114,
+            235,
+            126
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
+            271,
+            114,
+            442,
+            128
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/6f95acba95b601c8f059e1f4c6c843acaf0fecec1f6f13a14a91ffef6e2753f6.jpg",
+        "table_caption": [
+            "Table 1: Quantitative results on the ScanNet++ dataset. Each cell includes the original baseline number in black, followed by the improvement using our mutual information. Positive and negative improvements are marked in green and orange, respectively. The last column shows the average improvement over all scenes, validating the effectiveness of the proposed shaping for better geometric reconstruction (despite a small potion of noise on a few scenes)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>0a7c</td><td>0a18</td><td>6ee2</td><td>7b64</td><td>56a0</td><td>9460</td><td>a08d</td><td>e0ab</td><td>Mean</td></tr><tr><td>NeuS [30]+</td><td>0.08-0.04</td><td>0.05-0.03</td><td>0.03+0.01</td><td>0.06-0.04</td><td>0.01-0.00</td><td>0.24-0.14</td><td>0.04-0.03</td><td>0.02-0.00</td><td>0.07-0.03</td></tr><tr><td>VolSDF [37]+</td><td>0.90-0.83</td><td>0.31-0.29</td><td>0.04+0.02</td><td>0.10-0.03</td><td>0.03-0.01</td><td>0.14+0.03</td><td>0.39-0.38</td><td>0.04-0.00</td><td>0.24-0.19</td></tr><tr><td>GeoNeuS [8]+</td><td>0.03-0.02</td><td>1.03-1.02</td><td>0.28-0.27</td><td>0.05-0.03</td><td>0.02-0.01</td><td>0.22-0.20</td><td>0.01-0.01</td><td>0.26-0.25</td><td>0.24-0.23</td></tr><tr><td>I2-SDF [44]+</td><td>0.27-0.24</td><td>0.22-0.03</td><td>0.04-0.01</td><td>0.47-0.45</td><td>0.03-0.02</td><td>0.13+0.05</td><td>0.03+0.02</td><td>0.30-0.07</td><td>0.19-0.09</td></tr><tr><td>NeuRIS [29]+</td><td>0.01-0.00</td><td>0.01-0.00</td><td>0.03+0.02</td><td>0.07-0.04</td><td>0.04-0.03</td><td>0.41-0.21</td><td>0.03-0.01</td><td>0.03-0.00</td><td>0.08-0.03</td></tr><tr><td>MonoSDF [40]+</td><td>0.01-0.00</td><td>0.01+0.02</td><td>0.02-0.01</td><td>0.02-0.00</td><td>0.01-0.00</td><td>0.05-0.02</td><td>0.01-0.00</td><td>0.01-0.00</td><td>0.02-0.00</td></tr><tr><td>Neuralangelo [13]+</td><td>0.17-0.01</td><td>0.84-0.66</td><td>0.52-0.33</td><td>0.05-0.01</td><td>0.04+0.02</td><td>4.76-2.85</td><td>0.33+0.05</td><td>0.12+0.03</td><td>0.85-0.48</td></tr><tr><td>NeuS [30]+</td><td>0.49+0.06</td><td>0.48+0.10</td><td>0.67+0.00</td><td>0.58+0.16</td><td>0.81-0.01</td><td>0.58-0.02</td><td>0.67+0.17</td><td>0.75+0.09</td><td>0.63+0.07</td></tr><tr><td>VolSDF [37]+</td><td>0.45+0.35</td><td>0.47+0.27</td><td>0.67+0.00</td><td>0.55+0.05</td><td>0.71+0.06</td><td>0.52+0.18</td><td>0.48+0.35</td><td>0.70+0.02</td><td>0.57+0.16</td></tr><tr><td>GeoNeuS [8]+</td><td>0.69+0.20</td><td>0.47+0.44</td><td>0.52+0.34</td><td>0.70+0.06</td><td>0.87+0.03</td><td>0.68+0.23</td><td>0.75+0.14</td><td>0.37+0.51</td><td>0.63+0.24</td></tr><tr><td>I2-SDF [44]+</td><td>0.33+0.52</td><td>0.28+0.00</td><td>0.58+0.15</td><td>0.41+0.43</td><td>0.75+0.10</td><td>0.65+0.07</td><td>0.65+0.07</td><td>0.40+0.25</td><td>0.51+0.20</td></tr><tr><td>NeuRIS [29]+</td><td>0.72+0.03</td><td>0.68+0.01</td><td>0.65+0.01</td><td>0.69+0.06</td><td>0.85+0.01</td><td>0.24+0.17</td><td>0.64+0.13</td><td>0.69+0.09</td><td>0.65+0.06</td></tr><tr><td>MonoSDF [40]+</td><td>0.92-0.01</td><td>0.88-0.01</td><td>0.81+0.04</td><td>0.79+0.06</td><td>0.89+0.00</td><td>0.88+0.05</td><td>0.91+0.00</td><td>0.89-0.01</td><td>0.87+0.01</td></tr><tr><td>Neuralangelo [13]+</td><td>0.42+0.05</td><td>0.14+0.30</td><td>0.35+0.12</td><td>0.63+0.05</td><td>0.71-0.01</td><td>0.17+0.22</td><td>0.29+0.06</td><td>0.51-0.01</td><td>0.40+0.10</td></tr></table>",
+        "bbox": [
+            220,
+            239,
+            782,
+            406
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/1ab590405cf2035dc2662145551ba9a56b42fa584ba3629c28d927463d808a7c.jpg",
+        "table_caption": [
+            "Table 2: Quantitative results on the Replica dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>office0</td><td>office1</td><td>room0</td><td>room1</td><td>Mean</td></tr><tr><td>NeuS [30]+</td><td>0.005+0.001</td><td>0.023-0.012</td><td>0.068-0.038</td><td>0.130-0.087</td><td>0.057-0.035</td></tr><tr><td>VolSDF [37]+</td><td>0.004+0.006</td><td>0.016-0.004</td><td>0.080-0.071</td><td>0.034-0.025</td><td>0.033-0.023</td></tr><tr><td>GeoNeuS [8]+</td><td>0.023-0.021</td><td>0.014-0.009</td><td>0.040-0.035</td><td>0.002-0.000</td><td>0.020-0.017</td></tr><tr><td>I2-SDF [44]+</td><td>0.032-0.009</td><td>0.056-0.033</td><td>-</td><td>-</td><td>0.044-0.021</td></tr><tr><td>NeuRIS [29]+</td><td>0.014-0.006</td><td>3.975-3.963</td><td>0.025-0.017</td><td>0.015+0.002</td><td>1.007-0.996</td></tr><tr><td>MonoSDF [40]+</td><td>0.003-0.000</td><td>0.005-0.001</td><td>0.004-0.000</td><td>0.004-0.001</td><td>0.004-0.001</td></tr><tr><td>Neuralangelo [13]+</td><td>0.024-0.018</td><td>0.030-0.019</td><td>0.146-0.012</td><td>0.082-0.047</td><td>0.070-0.024</td></tr><tr><td>NeuS [30]+</td><td>0.92+0.00</td><td>0.80+0.01</td><td>0.78-0.03</td><td>0.72+0.08</td><td>0.80+0.02</td></tr><tr><td>VolSDF [37]+</td><td>0.94-0.04</td><td>0.78+0.01</td><td>0.78+0.16</td><td>0.82+0.07</td><td>0.83+0.05</td></tr><tr><td>GeoNeuS [8]+</td><td>0.89+0.08</td><td>0.91+0.04</td><td>0.90+0.09</td><td>0.98+0.01</td><td>0.920+0.05</td></tr><tr><td>I2-SDF [44]+</td><td>0.72+0.09</td><td>0.56+0.20</td><td>-</td><td>-</td><td>0.64+0.14</td></tr><tr><td>NeuRIS [29]+</td><td>0.79+0.06</td><td>0.01+0.68</td><td>0.89+0.05</td><td>0.77+0.03</td><td>0.61+0.20</td></tr><tr><td>MonoSDF [40]+</td><td>0.96+0.00</td><td>0.90+0.02</td><td>0.98+0.00</td><td>0.95+0.02</td><td>0.95+0.01</td></tr><tr><td>Neuralangelo [13]+</td><td>0.89+0.07</td><td>0.49+0.36</td><td>0.65+0.15</td><td>0.71+0.18</td><td>0.69+0.19</td></tr></table>",
+        "bbox": [
+            290,
+            452,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "or completely disregard the normal information due to low confidence. Particularly, when images are sparse, the regions covered by fewer viewpoints tend to lose supervision. Our mutual information scheme does not depend on the absolute values of the surface normal, but on the similarity among these values. This makes it more robust to noise and less likely to discard low-quality but useful normal information. Consequently, our method enhances the reconstruction quality of NeuRIS. MonoSDF achieves the best overall performance among the baselines because it uses both depth and normal estimations as geometry supervision. However, our method still offers improvements. Notably, it produces smoother planes and clearer boundaries. This indicates that not only the supervision of geometric cues is important, but also the correlation between the geometric entities matters.",
+        "bbox": [
+            212,
+            657,
+            787,
+            839
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
+        "bbox": [
+            767,
+            114,
+            782,
+            126
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/85fcbe70ebb8b419ecd0f5736e2a72107774160c5cf350c90b8e8223928071d9.jpg",
+        "image_caption": [
+            "Fig. 4: Visual results on the ScanNet++ dataset. Each row shows a comparison with a different baseline, from top to bottom, NeuS  $[30]^+$ , VolSDF  $[37]^+$ , GeoNeuS  $[8]^+$ , I²-SDF  $[44]^+$ , NeuRIS  $[29]^+$ , MonoSDF  $[40]^+$ , and Neuralangelo  $[13]^+$ . Red boxes are overlaid to help the contrast."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            218,
+            143,
+            781,
+            728
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "12",
+        "bbox": [
+            217,
+            114,
+            235,
+            126
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "header",
+        "text": "X. Wang & S. Dong et al.",
+        "bbox": [
+            271,
+            114,
+            442,
+            128
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/c3b66e13e0a8712a4ccb6d1eeba48ff3a6730ef1a34898ee902321c2a9046255.jpg",
+        "image_caption": [
+            "Reference image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            220,
+            145,
+            352,
+            223
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/12b7055978d076432f27e37e27bcf5105d4b8a6caddf0c26c3ce3c4e5a6b914d.jpg",
+        "image_caption": [
+            "NeuS",
+            "Fig. 5: Reconstruction results after 10K iterations in the training process with  $(\\mathrm{NeuS}^{+})$  and without (NeuS) the proposed geometric shaping technique."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            364,
+            145,
+            496,
+            223
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/1934989b75e764148aeab0fdca00ee343919dd3f6fea03c82d22737ae5d6ba6b.jpg",
+        "image_caption": [
+            "Neu $^{+}$  (Ours)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            145,
+            638,
+            223
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/3d686b691ed9650ea1c7a36938a87db1535ca26e1281f93b6ada1fecee39a744.jpg",
+        "image_caption": [
+            "Ground truth"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            650,
+            145,
+            781,
+            223
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Last but not least, the experiments on Neuralangelo demonstrate the potential of our method in working with hash grid encoding and numerical gradient. This highlights our method's versatility and ease of use, which can be broadly applied in various reconstruction architectures.",
+        "bbox": [
+            212,
+            306,
+            782,
+            367
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Results on the Replica dataset. In Tab. 2 we report the numerical results on the Replica dataset, with respect to NeuS [30], VolSDF [37], GeoNeuS [8], I²-SDF [44], NeuRIS [29], MonoSDF [40], and Neuralangelo [13]. As observed, the proposed geometric shaping technique still provides positive improvements when incorporated into these baselines, aligning with the conclusion drawn from the ScanNet++ data. Qualitative examples can also be found in Fig. 1.",
+        "bbox": [
+            212,
+            382,
+            784,
+            473
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "4.4 Analyses",
+        "text_level": 1,
+        "bbox": [
+            215,
+            496,
+            334,
+            512
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Ablation studies. We select three representative scenes from the ScanNet++ dataset and conduct ablation studies to evaluate the effectiveness of our method designs. We conduct ablation studies using two top-performing baselines: NeuRIS and MonoSDF.",
+        "bbox": [
+            212,
+            522,
+            429,
+            657
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "The results are reported in Tab. 3. Instead of using the surface normal formula to inject mutual information, we first perform a basic mutual information shaping separately in the color and SDF values. These two variations are labeled as base $^{+}$  (color)",
+        "bbox": [
+            212,
+            659,
+            429,
+            794
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "and base $^{+}$  (SDF), respectively. Interestingly, we find that, even though color is not directly related to geometry, by shaping it, we can still obtain improvements on the geometry in some cases. Moreover, shaping directly on the SDF values",
+        "bbox": [
+            212,
+            794,
+            785,
+            839
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/2199c25153cdaabb203df08322dabc11494f48b939ed42552af69e28972dbd91.jpg",
+        "table_caption": [
+            "Table 3: Ablation studies on three scenes from ScanNet++. The best and second-best results are marked in bold and underlined."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"4\">Chamfer (m)↓</td><td colspan=\"4\">F-score ↑</td></tr><tr><td>6ee2</td><td>7b64</td><td>9460</td><td>Mean</td><td>6ee2</td><td>7b64</td><td>9460</td><td>Mean</td></tr><tr><td>NeuRIS [30]</td><td>0.029</td><td>0.070</td><td>0.405</td><td>0.168</td><td>0.65</td><td>0.69</td><td>0.24</td><td>0.53</td></tr><tr><td>NeuRIS+ (color)</td><td>0.023</td><td>0.038</td><td>0.315</td><td>0.125</td><td>0.72</td><td>0.68</td><td>0.34</td><td>0.58</td></tr><tr><td>NeuRIS+ (SDF)</td><td>0.127</td><td>0.053</td><td>0.360</td><td>0.180</td><td>0.47</td><td>0.61</td><td>0.30</td><td>0.46</td></tr><tr><td>NeuRIS+ w/o normal</td><td>0.036</td><td>0.025</td><td>0.338</td><td>0.133</td><td>0.66</td><td>0.75</td><td>0.32</td><td>0.58</td></tr><tr><td>NeuRIS+ w/o DINO</td><td>0.061</td><td>0.033</td><td>0.381</td><td>0.158</td><td>0.63</td><td>0.72</td><td>0.32</td><td>0.56</td></tr><tr><td>NeuRIS+ (Full)</td><td>0.044</td><td>0.033</td><td>0.198</td><td>0.092</td><td>0.66</td><td>0.76</td><td>0.41</td><td>0.61</td></tr><tr><td>MonoSDF [40]</td><td>0.020</td><td>0.016</td><td>0.046</td><td>0.028</td><td>0.81</td><td>0.79</td><td>0.88</td><td>0.83</td></tr><tr><td>MonoSDF+ (color)</td><td>0.024</td><td>0.019</td><td>0.033</td><td>0.025</td><td>0.79</td><td>0.78</td><td>0.87</td><td>0.81</td></tr><tr><td>MonoSDF+ (SDF)</td><td>0.588</td><td>0.029</td><td>3.443</td><td>1.353</td><td>0.38</td><td>0.65</td><td>0.21</td><td>0.42</td></tr><tr><td>MonoSDF+ w/o normal</td><td>0.128</td><td>0.023</td><td>0.066</td><td>0.072</td><td>0.68</td><td>0.73</td><td>0.80</td><td>0.74</td></tr><tr><td>MonoSDF+ w/o DINO</td><td>0.064</td><td>0.016</td><td>0.022</td><td>0.034</td><td>0.78</td><td>0.83</td><td>0.93</td><td>0.85</td></tr><tr><td>MonoSDF+ (Full)</td><td>0.014</td><td>0.020</td><td>0.023</td><td>0.019</td><td>0.85</td><td>0.85</td><td>0.93</td><td>0.87</td></tr></table>",
+        "bbox": [
+            444,
+            609,
+            782,
+            758
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "header",
+        "text": "InfoNorm",
+        "bbox": [
+            663,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "13",
+        "bbox": [
+            767,
+            114,
+            784,
+            126
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "severely degrade the reconstruction quality, which evidences that the shaping on SDF values could incur a competition with the goal to faithfully learn the geometry within the neural radiance field. We further examine the effectiveness of combining semantic and geometric features to identify geometrically highly correlated regions. As demonstrated in Fig. 3, using only one type of the features can lead to incorrect correlations. Tab. 3 also shows that eliminating any one of the features can decrease the performance, confirming the effectiveness of our positive-negative sample selection mechanism leveraging the multimodal features.",
+        "bbox": [
+            212,
+            146,
+            787,
+            268
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Time and memory consumption. Our method provides benefits for 3D reconstruction with limited additional effort. Specifically, it only increases the optimization time and memory usage during the training process, without affecting the model architecture and final storage. The time and memory consumption are reported in Tab. 4. It is observed that the overhead on the training time highly depends on the architecture used in each baseline. For example, the train",
+        "bbox": [
+            212,
+            282,
+            486,
+            477
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "ing time increase on NeuRIS is marginal while more significant on VolSDF. These studies provide comprehensive information on the trade-offs between training time and performance gain. However, we do find that baselines with the proposed shaping technique can achieve a better performance (e.g., early geometries from NeuS and  $\\mathrm{NeuS^{+}}$  shown in Fig. 5) at the same training steps due to the effective regularization by mutual information.",
+        "bbox": [
+            212,
+            479,
+            787,
+            570
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/c427bf7809e6fe8cede9ddd17ce7837b9eceb758239fe1b10de076dcb76eabca.jpg",
+        "table_caption": [
+            "Table 4: Time and memory consumption."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Training Time (h)</td><td>VRAM (GB)</td></tr><tr><td>NeuS [30]+</td><td>3.00+0.37</td><td>7.89+1.68</td></tr><tr><td>VolSDF [37]+</td><td>3.18+1.96</td><td>16.36+4.68</td></tr><tr><td>GeoNeuS [8]+</td><td>3.26+0.16</td><td>5.72+3.56</td></tr><tr><td>I2-SDF [44]+</td><td>3.47+2.84</td><td>10.08+8.09</td></tr><tr><td>NeuRIS [29]+</td><td>3.70+0.20</td><td>11.73+4.12</td></tr><tr><td>MonoSDF [40]+</td><td>2.65+1.32</td><td>12.83+9.42</td></tr><tr><td>Neuralangelo [13]+</td><td>3.12+2.06</td><td>16.44+1.00</td></tr></table>",
+        "bbox": [
+            503,
+            340,
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+            444
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion",
+        "text_level": 1,
+        "bbox": [
+            214,
+            592,
+            359,
+            608
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We explore the usage of the second-order geometric correlations as a regularization and introduce a mutual information shaping technique of the normals for better surface reconstruction quality. With a simple yet effective correlated point selection mechanism that does not depend on accurate geometry information, we can perform a contrastive learning that maximizes the detected correlations. In return, we can observe a boost in the geometric quality of the reconstructed surfaces in state-of-the-art neural scene representations.",
+        "bbox": [
+            212,
+            625,
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+            729
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Extensive evaluations on various baselines and datasets show the effectiveness of our method, which improves 3D reconstruction quality without resorting to a more sophisticated surface modeling. The overhead caused by the shaping of the normals varies with different neural architectures of the scene representation, e.g., some are marginal, and some are significant, which we deem as a limitation of our current pipeline. We believe that an acceleration in computation can be achieved using a coarse-to-fine strategy, which we leave as a future work.",
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+        "text": "14",
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+    {
+        "type": "text",
+        "text": "Acknowledgments. We thank the anonymous reviewers for their valuable feedback. This work is supported by the Early Career Scheme of the Research Grants Council (grant # 27207224), the HKU-100 Award, and in part by NSF China (No. 62172363). Siyan Dong would also like to thank the support from HKU Musketeers Foundation Institute of Data Science for the Postdoctoral Research Fellowship.",
+        "bbox": [
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+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            215,
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+            277
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2024/InfoNorm_ Mutual Information Shaping of Normals for Sparse-View Reconstruction/8f9c186f-c37a-4b28-8f4e-c701ceacc591_origin.pdf

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2024/InfoNorm_ Mutual Information Shaping of Normals for Sparse-View Reconstruction/full.md

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+# InfoNorm: Mutual Information Shaping of Normals for Sparse-View Reconstruction
+
+Xulong Wang $^{1,2*}$  Siyan Dong $^{3*}$  Youyi Zheng $^{1\dagger}$  Yanchao Yang $^{3,4\dagger}$
+
+<sup>1</sup> State Key Lab of CAD&CG, Zhejiang University <sup>2</sup> Chohotech co. Ltd.
+
+<sup>3</sup> Institute of Data Science, The University of Hong Kong
+
+$^{4}$  Department of Electrical and Electronic Engineering, The University of Hong Kong
+
+Abstract. 3D surface reconstruction from multi-view images is essential for scene understanding and interaction. However, complex indoor scenes pose challenges such as ambiguity due to limited observations. Recent implicit surface representations, such as Neural Radiance Fields (NeRFs) and signed distance functions (SDFs), employ various geometric priors to resolve the lack of observed information. Nevertheless, their performance heavily depends on the quality of the pre-trained geometry estimation models. To ease such dependence, we propose regularizing the geometric modeling by explicitly encouraging the mutual information among surface normals of highly correlated scene points. In this way, the geometry learning process is modulated by the second-order correlations from noisy (first-order) geometric priors, thus eliminating the bias due to poor generalization. Additionally, we introduce a simple yet effective scheme that utilizes semantic and geometric features to identify correlated points, enhancing their mutual information accordingly. The proposed technique can serve as a plugin for SDF-based neural surface representations. Our experiments demonstrate the effectiveness of the proposed in improving the surface reconstruction quality of major states of the arts. Our code is available at: https://github.com/Muliphein/InfoNorm.
+
+Keywords: 3D from multi-view images  $\cdot$  surface reconstruction
+
+# 1 Introduction
+
+3D surface reconstruction from multi-view images is an essential task in the computer vision and graphics community, with practical applications including content creation for virtual reality and robot-scene interaction. However, indoor scenes present challenges due to the large and complex scenes captured from sparse viewpoints. These challenges encompass issues such as occlusion and ambiguity arising from limited observations. As a result, traditional Multi-View Stereo (MVS) methods [28,36], which require substantial overlap among images, may not produce satisfactory results in these scenarios.
+
+![](images/9b8401e3fa530d78df7d772cbc467ce6c418352d13234aeaf0b6384a2139842b.jpg)  
+VoISDF
+
+![](images/806ffe2576270f50b515b669174c1942b2de766ad6891de348a0e98e77682aa9.jpg)  
+VoISDF+ (Ours)
+
+![](images/4fa19faf7ef2ee3e5792b72952735bf2af6b7b5b9c5badae8ff9e895d4e9b334.jpg)  
+Ground truth
+
+![](images/5a2d9d718867f7ac2f1ce0a97aca24769f738ae92246bee6311fadca4d578343.jpg)  
+GeoNeuS  
+Fig. 1: 3D scene reconstruction from sparse views on Replica [26] (first row) and ScanNet++ [38] (second row). By enforcing the mutual information between the normals of highly correlated scene points, the proposed method can effectively enhance the reconstruction quality of the baselines (VolSDF [37] and GeoNeuS [8]).
+
+![](images/ca123373e0b175854094b84eb9138c7da3f4b7698a126c30ac38be6287709a8c.jpg)  
+GeoNeuS $^{+}$  (Ours)
+
+![](images/163c73317edb184b56866c497313fa562e0cfff80ed358069df6bcaa7a5f696a.jpg)  
+Ground truth
+
+Recently, implicit scene representations, e.g., Neural Radiance Fields (NeRFs) [21], have been proposed to encode 3D scenes into a set of neural network parameters, with subsequent works enhancing the representational capacity for geometry to enable surface extraction. The key idea involves incorporating signed distance functions (SDFs) [23] into the learned radiance field. Although NeRFs with SDF produce high-quality reconstructions of simple scenes with sufficient images, they still underperform in large and complex scenes captured from sparse viewpoints. More recent approaches, such as NeuRIS [29] and MonoSDF [40], propose using monocular geometric priors to guide the learning of the radiance field. However, they can be affected by inevitable errors and noise in the monocular geometry estimation modules.
+
+We explore geometric regularization in a second-order perspective. We argue that both the geometry itself and the correlation of geometry among scene regions are crucial for surface reconstruction, especially when dealing with varying indoor scenes under sparse views with noisy geometry estimates. The correlation is expressed as mutual information between scene entities under random perturbations of the network weights. More explicitly, we propose to enforce the mutual information between the normals of two points in the scene that are considered geometrically correlated, where the mutual information can be efficiently computed by measuring the cosine similarity between the gradients of the normals with respect to the perturbed weights. Further, we leverage a combination of pretrained semantic and geometric features [4,7,12] to identify the correlated scene regions that endorse high mutual information. This results in an easy-to-use geometric shaping<sup>1</sup> technique that can be applied to any SDF-based neural radiance fields. To thoroughly evaluate its effectiveness, we test the proposed with
+
+multiple state-of-the-art neural surface reconstruction models. The experimental results confirm the effectiveness of the proposed shaping technique, showing improved surface reconstruction quality (e.g., Fig. 1) on challenging scenes with limited views. To summarize:
+
+- We propose to leverage second-order geometric correlation in the form of mutual information between normals to regularize the surface reconstruction of SDF-based NeRF representations.  
+- We develop a pipeline that efficiently enforces the mutual information of the normals of points, deemed geometrically correlated with pre-trained multimodal features, to improve the reconstruction quality of the scene.  
+- We verify the effectiveness of the proposed second-order regularization technique across a broad spectrum of baselines and demonstrate its usefulness as an easy-to-use plugin in improving 3D surface modeling.
+
+# 2 Related Work
+
+3D Reconstruction with neural radiance fields (NeRFs). NeRF [21] is originally designed for novel view synthesis, with its variants serving as scene representations [15, 32, 33, 35, 39] for tasks related to editing [2, 31, 44], semantic segmentation [5, 14, 16, 34], 3D shape generation [20, 27], and so on. We mainly focus on neural surface representations that enable the extraction of high-quality 3D meshes from the trained NeRFs.
+
+Early works such as NeuS [30] and VolSDF [37] combine signed distance functions (SDFs) with volume rendering to extract high-quality surfaces. Recently, SparseNeuS [17] introduces a cascaded geometry reasoning framework that generalizes well to novel scenes. GeoNeuS [8] uses surface points from structure-from-motion and neighbor-view patches to reconstruct surfaces, while NeuDA [3] employs a deformable anchor to adaptively encode geometric details. NeAT [19] broadens the scope of reconstruction to arbitrary topology, no longer confining to watertight surfaces. Moreover, Neuralangelo [13] uses a hash grid for position encoding and implements a coarse-to-fine optimization with numerical gradients. Despite their promising results, most of these methods need sufficient training views, and their performance declines when dealing with large and complex scenes under sparse viewpoints.
+
+Incorporating priors into NeRFs. One can augment scene representations by introducing various priors to NeRFs. VDN-NeRF [43] normalizes the spatial feature to align with monocular features. LERF [11] introduces a new branch whose outputs align with DINO [4] and CLIP [24] features. Semantic-NeRF [42] encodes semantic information for segmentation tasks, while JacobiNeRF [34] shapes the color gradients to encode the mutual information in terms of semantic similarity from DINO [4] features for label propagation.
+
+For surface reconstruction, GeoNeuS [8] incorporates patch similarity from neighboring images and sparse surface points derived from structure-from-motion
+
+[25], while I²-SDF [44] combines the rendering equation with VolSDF [37] for better novel views and geometry. To cope with complex indoor scenes, NeuRIS [29] incorporates the normal priors as additional geometric supervision. Further, MonoSDF [40] uses both depth and normal to improve the surface reconstruction quality. However, these methods highly depend on the quality of the supplemented geometric information. In contrast, our method leverages the second-order information in geometric prior, rather than directly using the prior as a first-order supervision signal, which makes it more robust to errors and noise. There are also methods utilizing strong assumptions derived for human-made scenes. For instance, ManhattanSDF [10] works under the assumption that all captured scenes adhere to the Manhattan-world concept, thus, predicting semantic segmentation to identify walls and floors. While these methods primarily focus on planar scenes, the proposed technique can work for general scenes under noisy correlation information.
+
+# 3 Method
+
+We start with a discussion on the preliminaries in Sec. 3.1 to provide the background on how we can learn from posed images an implicit scene representation (NeRF), improve 3D scene reconstruction via the combination of NeRF and SDF representations, and employ mutual information as a constraint in the NeRF training process. Following this, in Sec. 3.2, we delve into how mutual information can be used as constraints on NeRF's implied surfaces, so that we can learn better geometries for higher-quality 3D reconstruction of the scene. Finally, we elaborate on how we can employ off-the-shelf semantic and geometry features to assist the encoding of mutual information through the proposed geometric shaping framework.
+
+# 3.1 Preliminaries
+
+Neural radiance fields. NeRF [21] learns an implicit scene representation from a set of posed images. For a specific pixel in an image, NeRF samples a list of 3D points,  $\{x|x_{t} = \mathbf{o} + t\mathbf{v},t\in [t_{near},t_{far}]\}$ , from the camera center  $\mathbf{o}$  along the viewing direction  $\mathbf{v}$  within a bounded space. Specifically, it employs a Multilayer Perceptron (MLP) to encode the volume density and color of each sampled point. We denote all the parameters of NeRF as  $\theta$ , the density function as  $\sigma$ , and the color function as  $c$ . The pixel's rendered color  $\hat{\mathbf{C}}$  from a NeRF is calculated by the discrete volume rendering:
+
+$$
+\hat {\mathbf {C}} (\mathbf {o}, \mathbf {v}; \theta) = \sum_ {i = 1} ^ {N} \omega (\mathbf {o}, \mathbf {v}, t _ {i}; \theta) c \left(x _ {t _ {i}}, \mathbf {v}; \theta\right), \tag {1}
+$$
+
+$$
+\text {w h e r e} \omega (\mathbf {o}, \mathbf {v}, t _ {i}; \theta) = \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}) \alpha_ {i}.
+$$
+
+Here,  $\alpha_{i} = 1 - \exp (-\sigma_{i}\delta_{i})$ , where  $\sigma_{i}$  is the abbreviation of  $\sigma (x_{t_i};\theta)$  and  $\delta_{i} = t_{i + 1} - t_{i}$ . A photometric loss is utilized to minimize the discrepancy between the rendered color and its ground truth:
+
+$$
+L _ {C} = \left\| \mathbf {C} - \hat {\mathbf {C}} \right\| _ {1}, \tag {2}
+$$
+
+so that the parameters  $\theta$  can be optimized to fit the scene. Despite the ability to handle photorealistic novel view synthesis, NeRFs suffer from noisy and unrealistic surface extraction when it comes to 3D reconstruction, as discussed in the literature [30, 37].
+
+NeRFs with signed distance functions. To produce high-quality surfaces, it is beneficial to use signed distance functions (SDFs) [6, 23] to represent geometry. Consequently, the surface can be reconstructed by extracting the zero-level set [18] of the SDF values. The combination of NeRF and SDF can be achieved by deriving the NeRF's densities from the SDF, or defining Laplace's cumulative distribution function. Accordingly,  $\alpha_{i}$  in Eq. 1 can be represented by a function  $\varPhi$  which converts SDF values to volume densities as
+
+$$
+\alpha_ {i} = \Phi (x, f (x; \theta), i). \tag {3}
+$$
+
+Generally, NeRFs with an SDF achieve improved surface reconstruction quality, where the key to maintaining the characteristics of SDF is an eikonal loss [9]:
+
+$$
+L _ {E} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\left| \left| \nabla f \left(x _ {i}\right) \right| \right| _ {2} - 1\right) ^ {2}. \tag {4}
+$$
+
+Mutual information in NeRFs. Mutual information (MI) quantifies the statistical dependence between two random variables, providing an estimate of how much information they share. It has been introduced for semantic segmentation and motion modeling tasks [34, 41]. In this paper, We study the mutual information under perturbations of the NeRF parameters, and focus more on the geometry properties. Let  $I(p_{i})$  and  $I(p_{j})$  denote two pixels derived from the NeRF rendering process  $\mathbb{F}$ . And we assume that a subset of the NeRF weights, denoted by  $\theta^{D}$ , is perturbed by a random noise vector  $\mathbf{n} \in \mathbb{R}^{D}$  sampled from a uniform distribution on the sphere  $\mathbb{S}^{D - 1}$  by a small step  $\gamma \ll 1.0$ . The random variables corresponding to the perturbed pixels can be written through a Taylor expansion:
+
+$$
+\hat {I} (p _ {i}) = I (p _ {i}) + \gamma \mathbf {n} \frac {\partial \mathbb {F} _ {i}}{\partial \theta^ {D}},
+$$
+
+$$
+\hat {I} (p _ {j}) = I (p _ {j}) + \gamma \mathbf {n} \frac {\partial \mathbb {F} _ {j}}{\partial \theta^ {D}}.
+$$
+
+We can now characterize the mutual information between  $\hat{I}(p_i)$  and  $\hat{I}(p_j)$  under the joint probability distribution  $\mathbb{P}(\hat{I}(p_i), \hat{I}(p_j))$ . As derived in JacobiNeRF, the
+
+mutual information can be computed as:
+
+$$
+\begin{array}{l} \mathbb {I} (\hat {I} (p _ {i}), \hat {I} (p _ {j})) = \mathbb {H} (\hat {I} (p _ {i})) - \mathbb {H} (\hat {I} (p _ {i}) | \hat {I} (p _ {j})) \\ = \log (\frac {1}{\sqrt {1 - \cos^ {2} \beta}}) + \mathrm {c o n s t .}. \\ \end{array}
+$$
+
+Here,  $\beta$  denotes the angle between  $\partial \mathbb{F}_i / \partial \theta^D$  and  $\partial \mathbb{F}_j / \partial \theta^D$ . It is observed that:
+
+$$
+\mathbb {I} (\hat {I} (p _ {i}), \hat {I} (p _ {j})) \propto | | \cos \beta | |. \tag {5}
+$$
+
+Therefore, to enhance the MI between two random pixels induced by NeRF perturbations, one can enforce the absolute value of the cosine similarity. That is, if two pixels  $p_i$ ,  $p_j$  come with high correlation (e.g., from the same object in the scene), their gradients regarding the perturbed parameters should be in the same or opposite direction.
+
+# 3.2 Mutual Information Shaping of Geometry in SDF-based NeRFs
+
+While the previous approach focuses on enforcing mutual information for image synthesis, we explore a mutual information shaping of the geometries for quality surface reconstruction in SDF-based NeRFs.
+
+Specifically, we represent a scene via a NeRF backbone with an SDF head and a color head, as shown in Fig. 2. Note that the method to be proposed is capable of being applied to any network similar to NeRF and SDF representations. Given that the two heads partially share parameters, we denote all the parameters as  $\theta$ , and use  $f(x;\theta)$  and  $c(x,\mathbf{v};\theta)$  to represent the SDF and color branches, respectively. To achieve mutual information shaping of the geometry, we focus on manipulating the parameters of  $f(x;\theta)$ , while keeping  $c(x,\mathbf{v};\theta)$  unchanged. Below, we first explain why and how we compute mutual information with surface normals derived from SDF, i.e.,  $f(x;\theta)$ , as a geometry-aware constraint. Next, we present a simple yet effective strategy that extracts regions with high correlation, which need to be encoded into the weights using the mutual information shaping technique. Finally, we elaborate on our loss function and training process to reconstruct the scene from posed images.
+
+Mutual information among surface normals. We explicitly encode mutual information into the function  $f(x; \theta)$ . However, instead of computing mutual information between the density values, we proceed by manipulating the surface normal vectors that can be derived from  $f$ . Specifically, for a 3D point  $x$  on a surface of the scene, its normal vector  $N(x; \theta)$  can be calculated as the partial derivative of the 3D coordinate:
+
+$$
+N (x; \theta) = \frac {\partial f (x ; \theta)}{\partial x}. \tag {6}
+$$
+
+There are several reasons to manipulate surface normal vectors but not SDF values: 1) Shaping the SDF values with respect to a subset  $\theta^D$  of the parameters may not effectively impose the constraints on all parameters. However, the
+
+![](images/6f17f63afda6c3119d5acae9d04874923ea056d465e48b6553b8bf4685feb5f3.jpg)  
+Fig. 2: An overview of the pipeline, where we apply mutual information shaping on the geometric branch to enforce consistencies that help enhance the surface reconstruction. Specifically, the model consists of the NeRF backbone, an SDF head, and a color head. The predicted density and color are supervised by the classic eikonal loss  $L_{E}$  and the photometric reconstruction loss  $L_{C}$ , respectively. We encode geometry-aware mutual information into a subset of the parameters  $\theta^{D}$  of  $f(x)$  to constrain the density field learning for better surface quality, which is achieved by the proposed mutual information loss  $L_{M}$  computed on top of the estimated surface normal.
+
+calculation of the surface normal includes the entire set of parameters in  $f$ , thus a more global regularity. 2) Moreover, shaping  $f$  with the mutual information between its values may induce side effects as density could be distorted to satisfy the constraints. However, shaping the normal  $\partial f / \partial x$  leave more space for the SDF values to cope with the scene reconstruction task, thus minimizing potential negative effects.
+
+According to Eq. 5, we need to calculate the partial gradients  $\partial N / \partial \theta^D$  to compute the mutual information. When it comes to a vector rather than a scalar, the gradients consist of three components corresponding to the  $\mathbf{x}$ ,  $\mathbf{y}$ , and  $\mathbf{z}$  axes:
+
+$$
+\frac {\partial N (x ; \theta)}{\partial \theta^ {D}} = \frac {\partial N _ {\mathbf {x}} (x ; \theta)}{\partial \theta^ {D}}, \frac {\partial N _ {\mathbf {y}} (x ; \theta)}{\partial \theta^ {D}}, \frac {\partial N _ {\mathbf {z}} (x ; \theta)}{\partial \theta^ {D}}. \tag {7}
+$$
+
+For ease of computation, we concatenate the gradients into a vector, denoted as  $\partial N$  for simplicity:
+
+$$
+\partial N = \operatorname {C o n c a t} \left(\frac {\partial N _ {\mathbf {x}}}{\partial \theta^ {D}}, \frac {\partial N _ {\mathbf {y}}}{\partial \theta^ {D}}, \frac {\partial N _ {\mathbf {z}}}{\partial \theta^ {D}}\right). \tag {8}
+$$
+
+Since a 2D pixel is accumulated from 3D, we aggregate the normal-based information along a viewing ray as in Eq. 1 as:
+
+$$
+\mathbb {N} \left(p _ {i}\right) = \sum_ {x \in \text {r a y}} \omega \left(t _ {i}; \theta\right) \partial N. \tag {9}
+$$
+
+Finally, we obtain that the mutual information between two normals is:
+
+$$
+\mathbb {I} (\hat {N} (p _ {i}), \hat {N} (p _ {j})) \propto | | \frac {\mathbb {N} (p _ {i}) \cdot \mathbb {N} (p _ {j})}{| \mathbb {N} (p _ {i}) | | \mathbb {N} (p _ {j}) |} | |. \tag {10}
+$$
+
+Please refer to our supplementary material for a detailed derivation. From Eq. 10, we observe that the mutual information in surface normal vectors correlates
+
+![](images/a1037c099eeadeb4e12569c2335a9d39eec82a6e6ce806b409303ba67e34c5c1.jpg)  
+Anchor pixel
+
+![](images/fdc6e8d50ef3f3f196ffc7ad2e20073c5eefb613a549457884295d170dcec5a5.jpg)  
+Similar semantic features  
+Fig. 3: An example of positive samples from different features. Given an anchor pixel (marked by a blue circle in the first image) on the wall-like cabinet, semantic features like DINO often correlate both the cabinet and the ceiling (as shown by the red area in the second image). Meanwhile, geometric features such as (noisy) monocular normals can not distinguish between parallel planes that are not connected (the third image). By combining semantic and geometric features, we can obtain positive samples of the anchor pixel with better geometric consistency, thus, high mutual correlation.
+
+![](images/0713b265af24b7ebbaeed91bc4e2fbefb2b1432c4c0011904bb28b4c17d96bbc.jpg)  
+Similar geometric features
+
+![](images/c5e4fb51e95f325dfde32be6d991727a9691233107efa75288aab21b7ee2d042.jpg)  
+Combined (Ours)
+
+positively with the cosine similarity of their gradients to the network parameters. This conclusion is similar to that of Eq. 5. As a result, we can now identify the pixels that are of high correlations, and increase the aggregated mutual information during the NeRF training process.
+
+Extracting correlated scene regions from image pixels. To extract scene regions that need to be shaped to have high mutual information, we present a simple yet effective approach with off-the-shelf visual features. Given the input images, we extract pixel-wise semantic and geometric features to identify correlated scene regions. Following previous research [34], we apply DINO [4] as the semantic feature extractor to obtain a high-level understanding of the scene regions. Meanwhile, as we shape mutual information on top of the surface normal, we employ a monocular normal estimator [7] as the geometric feature extractor for a detailed low-level perception of the 3D points in the scene.
+
+DINO features can group different parts of an object, like the seat and back of a chair, which share similar semantics. However, the surface normal vectors from these parts have limited correlation, thus should not be constrained. Conversely, using only geometric features can wrongly suggest high correlation between unrelated areas, like the seat and the floor. As these areas aren't closely connected in 3D space, there is no reason to have better surface reconstruction when enhancing their mutual information. Similar phenomena on wall-like structures can be observed in Fig. 3, where we show that by combining semantic and geometric features together we can better identify scene regions that are spatially connected and have similar normal directions.
+
+More explicitly, we combine semantic and geometric features with an intersection operator. It is simple yet effective. The process of identifying correlated scene regions (in normal) is implemented as positive pixel pair selection from input images. Given a randomly selected pixel from an image, we first extract similar pixels from neighboring images using semantic and geometric features, respectively. This extraction is implemented by applying two thresholds,  $\beta_{S}$  and  $\beta_{G}$ , to filter the cosine similarity for semantic and geometric features. We then
+
+feed the intersection of the top similar pixels from each feature type into NeRF's training process as positive samples, allowing us to shape them with high mutual information. In order to leverage the contrastive learning framework to encourage mutual information, we randomly select pixels not involved in the aforementioned process to serve as negative samples (independent pixels that are not correlated to the anchor pixel).
+
+Loss functions for training. The aforementioned contrastive learning process is performed with a tailored InfoNCE loss [22]:
+
+$$
+L _ {M} = - \log \frac {\sum \exp (| | \cos (\partial \mathbb {N} _ {i} , \partial \mathbb {N} _ {i +}) | |)}{\sum_ {j} \exp (| | \cos (\partial \mathbb {N} _ {i} , \partial \mathbb {N} _ {j}) | |)}, \tag {11}
+$$
+
+where  $i$ ,  $i+$ , and  $j$  denote the anchor, positive, and negative pixels, respectively. This loss function effectively enhances mutual information (according to Eq. 10) among correlated pixels, while maintaining low mutual information among independent pixels. Finally, to train the NeRF backbone and retain the characteristics of the SDF, we adopt the basic photometric loss (Eq. 2) and the eikonal loss (Eq. 4). The latter two are derived from single images, while the former can be calculated from either single images or a set of neighboring images. The full loss function is defined as the weighted sum of three loss terms:
+
+$$
+L = L _ {C} + \lambda_ {E} L _ {E} + \lambda_ {M} L _ {M}. \tag {12}
+$$
+
+With the above, all network parameters  $\theta$  can be trained end-to-end.
+
+# 4 Experiments
+
+In this section, we evaluate the effectiveness of our method through experiments conducted on multiple datasets with various baselines. First, we introduce the two datasets used to conduct the experiments in Sec. 4.1. Next, we detail the implementation of the proposed method in Sec. 4.2, where we adapt a spectrum of state-of-the-art models for validating the effectiveness of the geometric shaping. Then, we report the comparisons between the baselines and our models in Sec. 4.3. Lastly, we conduct a series of ablation studies in Sec. 4.4, to verify the necessity of each component in our method.
+
+# 4.1 Datasets
+
+We evaluate the proposed method using two public datasets from the literature: ScanNet++ [38] and the Replica [26] dataset. For the ScanNet++ dataset, we choose 8 representative scenes, while for the Replica dataset, we select 4 representative scenes. The scenes from both datasets represent a variety of indoor settings, including offices, bedrooms, and so on. As our focus is on scene reconstruction from sparse views, we uniformly sample 50-85 images from the official (and Replica from Semantic-NeRF [42]) scanning sequences for each scene to use as input in our evaluation. For detailed statistics of each scene, please refer to our supplementary material.
+
+Evaluation metrics. Following previous works [13, 30, 40], we evaluate the quality of surface reconstruction using two metrics: Chamfer distance and F-score. Chamfer distance is a measure that evaluates the difference between reconstructed and ground-truth points sets. F-score is a statistical metric that integrates precision and recall, providing a more comprehensive understanding of the reconstruction quality.
+
+# 4.2 Implementation Details
+
+As the proposed geometric shaping can be easily integrated into any network similar to NeRF with SDF representations, we select several state-of-the-art models as our baselines and apply the proposed to them for demonstrating the effectiveness of our approach. We first choose NeuS [30] and VolSDF [37], the two representative pioneers for NeRFs with SDFs. We also apply our method to the following works: GeoNeuS [8], I²-SDF [44], NeuRIS [29], MonoSDF [40], and Neuralangelo [13]. In addition to the basic loss functions for NeRF and SDF, GeoNeuS incorporates patch similarity from neighboring views and surface points derived from structure-from-motion. I²-SDF integrates the rendering equation with VolSDF. We disregard its normal and depth loss terms. NeuRIS utilizes monocular normal estimation as a supervision on the geometry, and discards the low-quality normal information that lacks sufficient confidence through multi-view patching. MonoSDF employs both depth and normal estimation, for which we set the decay of the normal and depth at 30k iterations to prevent the method from degeneration. Neuralangelo utilizes a multi-resolution hash grid and numerical gradient. We set the hash encoding dictionary size to 20, and the encoding dimension to 4. For all the base models mentioned above, we enhance them by incorporating our proposed mutual information loss during training. The resulting methods are respectively labeled as  $\mathrm{NeuS^{+}}$ , VolSDF+, GeoNeuS+, and so on.
+
+# 4.3 Comparisons
+
+Results on the ScanNet++ dataset. The quantitative comparisons are reported in Tab. 1. We also visualize the surface reconstruction results in Fig. 4 for qualitative comparisons. We can observe that by applying the proposed mutual information shaping on the geometry, the surface reconstruction quality can be improved across all baselines, as measured by mean Chamfer distance, F-score, and the visuals.
+
+NeuS and VolSDF tend to produce rough surfaces and excessively smoothed boundaries. However, with our geometry-aware mutual information, the surfaces become smoother, while the boundaries are more crispy. Compared to GeoNeuS, a method that uses patch-similarity among neighboring views and requires sufficient textures, our method provides significant improvements. Applying the proposed technique to  $\mathrm{I}^2$ -SDF can also enhance its reconstruction quality.
+
+As for more recent works, we find that NeuRIS is somewhat sensitive to the quality of normal estimation. It can either be affected by noise in the normal
+
+Table 1: Quantitative results on the ScanNet++ dataset. Each cell includes the original baseline number in black, followed by the improvement using our mutual information. Positive and negative improvements are marked in green and orange, respectively. The last column shows the average improvement over all scenes, validating the effectiveness of the proposed shaping for better geometric reconstruction (despite a small potion of noise on a few scenes).  
+
+<table><tr><td></td><td>0a7c</td><td>0a18</td><td>6ee2</td><td>7b64</td><td>56a0</td><td>9460</td><td>a08d</td><td>e0ab</td><td>Mean</td></tr><tr><td>NeuS [30]+</td><td>0.08-0.04</td><td>0.05-0.03</td><td>0.03+0.01</td><td>0.06-0.04</td><td>0.01-0.00</td><td>0.24-0.14</td><td>0.04-0.03</td><td>0.02-0.00</td><td>0.07-0.03</td></tr><tr><td>VolSDF [37]+</td><td>0.90-0.83</td><td>0.31-0.29</td><td>0.04+0.02</td><td>0.10-0.03</td><td>0.03-0.01</td><td>0.14+0.03</td><td>0.39-0.38</td><td>0.04-0.00</td><td>0.24-0.19</td></tr><tr><td>GeoNeuS [8]+</td><td>0.03-0.02</td><td>1.03-1.02</td><td>0.28-0.27</td><td>0.05-0.03</td><td>0.02-0.01</td><td>0.22-0.20</td><td>0.01-0.01</td><td>0.26-0.25</td><td>0.24-0.23</td></tr><tr><td>I2-SDF [44]+</td><td>0.27-0.24</td><td>0.22-0.03</td><td>0.04-0.01</td><td>0.47-0.45</td><td>0.03-0.02</td><td>0.13+0.05</td><td>0.03+0.02</td><td>0.30-0.07</td><td>0.19-0.09</td></tr><tr><td>NeuRIS [29]+</td><td>0.01-0.00</td><td>0.01-0.00</td><td>0.03+0.02</td><td>0.07-0.04</td><td>0.04-0.03</td><td>0.41-0.21</td><td>0.03-0.01</td><td>0.03-0.00</td><td>0.08-0.03</td></tr><tr><td>MonoSDF [40]+</td><td>0.01-0.00</td><td>0.01+0.02</td><td>0.02-0.01</td><td>0.02-0.00</td><td>0.01-0.00</td><td>0.05-0.02</td><td>0.01-0.00</td><td>0.01-0.00</td><td>0.02-0.00</td></tr><tr><td>Neuralangelo [13]+</td><td>0.17-0.01</td><td>0.84-0.66</td><td>0.52-0.33</td><td>0.05-0.01</td><td>0.04+0.02</td><td>4.76-2.85</td><td>0.33+0.05</td><td>0.12+0.03</td><td>0.85-0.48</td></tr><tr><td>NeuS [30]+</td><td>0.49+0.06</td><td>0.48+0.10</td><td>0.67+0.00</td><td>0.58+0.16</td><td>0.81-0.01</td><td>0.58-0.02</td><td>0.67+0.17</td><td>0.75+0.09</td><td>0.63+0.07</td></tr><tr><td>VolSDF [37]+</td><td>0.45+0.35</td><td>0.47+0.27</td><td>0.67+0.00</td><td>0.55+0.05</td><td>0.71+0.06</td><td>0.52+0.18</td><td>0.48+0.35</td><td>0.70+0.02</td><td>0.57+0.16</td></tr><tr><td>GeoNeuS [8]+</td><td>0.69+0.20</td><td>0.47+0.44</td><td>0.52+0.34</td><td>0.70+0.06</td><td>0.87+0.03</td><td>0.68+0.23</td><td>0.75+0.14</td><td>0.37+0.51</td><td>0.63+0.24</td></tr><tr><td>I2-SDF [44]+</td><td>0.33+0.52</td><td>0.28+0.00</td><td>0.58+0.15</td><td>0.41+0.43</td><td>0.75+0.10</td><td>0.65+0.07</td><td>0.65+0.07</td><td>0.40+0.25</td><td>0.51+0.20</td></tr><tr><td>NeuRIS [29]+</td><td>0.72+0.03</td><td>0.68+0.01</td><td>0.65+0.01</td><td>0.69+0.06</td><td>0.85+0.01</td><td>0.24+0.17</td><td>0.64+0.13</td><td>0.69+0.09</td><td>0.65+0.06</td></tr><tr><td>MonoSDF [40]+</td><td>0.92-0.01</td><td>0.88-0.01</td><td>0.81+0.04</td><td>0.79+0.06</td><td>0.89+0.00</td><td>0.88+0.05</td><td>0.91+0.00</td><td>0.89-0.01</td><td>0.87+0.01</td></tr><tr><td>Neuralangelo [13]+</td><td>0.42+0.05</td><td>0.14+0.30</td><td>0.35+0.12</td><td>0.63+0.05</td><td>0.71-0.01</td><td>0.17+0.22</td><td>0.29+0.06</td><td>0.51-0.01</td><td>0.40+0.10</td></tr></table>
+
+Table 2: Quantitative results on the Replica dataset.  
+
+<table><tr><td></td><td>office0</td><td>office1</td><td>room0</td><td>room1</td><td>Mean</td></tr><tr><td>NeuS [30]+</td><td>0.005+0.001</td><td>0.023-0.012</td><td>0.068-0.038</td><td>0.130-0.087</td><td>0.057-0.035</td></tr><tr><td>VolSDF [37]+</td><td>0.004+0.006</td><td>0.016-0.004</td><td>0.080-0.071</td><td>0.034-0.025</td><td>0.033-0.023</td></tr><tr><td>GeoNeuS [8]+</td><td>0.023-0.021</td><td>0.014-0.009</td><td>0.040-0.035</td><td>0.002-0.000</td><td>0.020-0.017</td></tr><tr><td>I2-SDF [44]+</td><td>0.032-0.009</td><td>0.056-0.033</td><td>-</td><td>-</td><td>0.044-0.021</td></tr><tr><td>NeuRIS [29]+</td><td>0.014-0.006</td><td>3.975-3.963</td><td>0.025-0.017</td><td>0.015+0.002</td><td>1.007-0.996</td></tr><tr><td>MonoSDF [40]+</td><td>0.003-0.000</td><td>0.005-0.001</td><td>0.004-0.000</td><td>0.004-0.001</td><td>0.004-0.001</td></tr><tr><td>Neuralangelo [13]+</td><td>0.024-0.018</td><td>0.030-0.019</td><td>0.146-0.012</td><td>0.082-0.047</td><td>0.070-0.024</td></tr><tr><td>NeuS [30]+</td><td>0.92+0.00</td><td>0.80+0.01</td><td>0.78-0.03</td><td>0.72+0.08</td><td>0.80+0.02</td></tr><tr><td>VolSDF [37]+</td><td>0.94-0.04</td><td>0.78+0.01</td><td>0.78+0.16</td><td>0.82+0.07</td><td>0.83+0.05</td></tr><tr><td>GeoNeuS [8]+</td><td>0.89+0.08</td><td>0.91+0.04</td><td>0.90+0.09</td><td>0.98+0.01</td><td>0.920+0.05</td></tr><tr><td>I2-SDF [44]+</td><td>0.72+0.09</td><td>0.56+0.20</td><td>-</td><td>-</td><td>0.64+0.14</td></tr><tr><td>NeuRIS [29]+</td><td>0.79+0.06</td><td>0.01+0.68</td><td>0.89+0.05</td><td>0.77+0.03</td><td>0.61+0.20</td></tr><tr><td>MonoSDF [40]+</td><td>0.96+0.00</td><td>0.90+0.02</td><td>0.98+0.00</td><td>0.95+0.02</td><td>0.95+0.01</td></tr><tr><td>Neuralangelo [13]+</td><td>0.89+0.07</td><td>0.49+0.36</td><td>0.65+0.15</td><td>0.71+0.18</td><td>0.69+0.19</td></tr></table>
+
+or completely disregard the normal information due to low confidence. Particularly, when images are sparse, the regions covered by fewer viewpoints tend to lose supervision. Our mutual information scheme does not depend on the absolute values of the surface normal, but on the similarity among these values. This makes it more robust to noise and less likely to discard low-quality but useful normal information. Consequently, our method enhances the reconstruction quality of NeuRIS. MonoSDF achieves the best overall performance among the baselines because it uses both depth and normal estimations as geometry supervision. However, our method still offers improvements. Notably, it produces smoother planes and clearer boundaries. This indicates that not only the supervision of geometric cues is important, but also the correlation between the geometric entities matters.
+
+![](images/85fcbe70ebb8b419ecd0f5736e2a72107774160c5cf350c90b8e8223928071d9.jpg)  
+Fig. 4: Visual results on the ScanNet++ dataset. Each row shows a comparison with a different baseline, from top to bottom, NeuS  $[30]^+$ , VolSDF  $[37]^+$ , GeoNeuS  $[8]^+$ , I²-SDF  $[44]^+$ , NeuRIS  $[29]^+$ , MonoSDF  $[40]^+$ , and Neuralangelo  $[13]^+$ . Red boxes are overlaid to help the contrast.
+
+![](images/c3b66e13e0a8712a4ccb6d1eeba48ff3a6730ef1a34898ee902321c2a9046255.jpg)  
+Reference image
+
+![](images/12b7055978d076432f27e37e27bcf5105d4b8a6caddf0c26c3ce3c4e5a6b914d.jpg)  
+NeuS  
+Fig. 5: Reconstruction results after 10K iterations in the training process with  $(\mathrm{NeuS}^{+})$  and without (NeuS) the proposed geometric shaping technique.
+
+![](images/1934989b75e764148aeab0fdca00ee343919dd3f6fea03c82d22737ae5d6ba6b.jpg)  
+Neu $^{+}$  (Ours)
+
+![](images/3d686b691ed9650ea1c7a36938a87db1535ca26e1281f93b6ada1fecee39a744.jpg)  
+Ground truth
+
+Last but not least, the experiments on Neuralangelo demonstrate the potential of our method in working with hash grid encoding and numerical gradient. This highlights our method's versatility and ease of use, which can be broadly applied in various reconstruction architectures.
+
+Results on the Replica dataset. In Tab. 2 we report the numerical results on the Replica dataset, with respect to NeuS [30], VolSDF [37], GeoNeuS [8], I²-SDF [44], NeuRIS [29], MonoSDF [40], and Neuralangelo [13]. As observed, the proposed geometric shaping technique still provides positive improvements when incorporated into these baselines, aligning with the conclusion drawn from the ScanNet++ data. Qualitative examples can also be found in Fig. 1.
+
+# 4.4 Analyses
+
+Ablation studies. We select three representative scenes from the ScanNet++ dataset and conduct ablation studies to evaluate the effectiveness of our method designs. We conduct ablation studies using two top-performing baselines: NeuRIS and MonoSDF.
+
+The results are reported in Tab. 3. Instead of using the surface normal formula to inject mutual information, we first perform a basic mutual information shaping separately in the color and SDF values. These two variations are labeled as base $^{+}$  (color)
+
+and base $^{+}$  (SDF), respectively. Interestingly, we find that, even though color is not directly related to geometry, by shaping it, we can still obtain improvements on the geometry in some cases. Moreover, shaping directly on the SDF values
+
+Table 3: Ablation studies on three scenes from ScanNet++. The best and second-best results are marked in bold and underlined.  
+
+<table><tr><td rowspan="2"></td><td colspan="4">Chamfer (m)↓</td><td colspan="4">F-score ↑</td></tr><tr><td>6ee2</td><td>7b64</td><td>9460</td><td>Mean</td><td>6ee2</td><td>7b64</td><td>9460</td><td>Mean</td></tr><tr><td>NeuRIS [30]</td><td>0.029</td><td>0.070</td><td>0.405</td><td>0.168</td><td>0.65</td><td>0.69</td><td>0.24</td><td>0.53</td></tr><tr><td>NeuRIS+ (color)</td><td>0.023</td><td>0.038</td><td>0.315</td><td>0.125</td><td>0.72</td><td>0.68</td><td>0.34</td><td>0.58</td></tr><tr><td>NeuRIS+ (SDF)</td><td>0.127</td><td>0.053</td><td>0.360</td><td>0.180</td><td>0.47</td><td>0.61</td><td>0.30</td><td>0.46</td></tr><tr><td>NeuRIS+ w/o normal</td><td>0.036</td><td>0.025</td><td>0.338</td><td>0.133</td><td>0.66</td><td>0.75</td><td>0.32</td><td>0.58</td></tr><tr><td>NeuRIS+ w/o DINO</td><td>0.061</td><td>0.033</td><td>0.381</td><td>0.158</td><td>0.63</td><td>0.72</td><td>0.32</td><td>0.56</td></tr><tr><td>NeuRIS+ (Full)</td><td>0.044</td><td>0.033</td><td>0.198</td><td>0.092</td><td>0.66</td><td>0.76</td><td>0.41</td><td>0.61</td></tr><tr><td>MonoSDF [40]</td><td>0.020</td><td>0.016</td><td>0.046</td><td>0.028</td><td>0.81</td><td>0.79</td><td>0.88</td><td>0.83</td></tr><tr><td>MonoSDF+ (color)</td><td>0.024</td><td>0.019</td><td>0.033</td><td>0.025</td><td>0.79</td><td>0.78</td><td>0.87</td><td>0.81</td></tr><tr><td>MonoSDF+ (SDF)</td><td>0.588</td><td>0.029</td><td>3.443</td><td>1.353</td><td>0.38</td><td>0.65</td><td>0.21</td><td>0.42</td></tr><tr><td>MonoSDF+ w/o normal</td><td>0.128</td><td>0.023</td><td>0.066</td><td>0.072</td><td>0.68</td><td>0.73</td><td>0.80</td><td>0.74</td></tr><tr><td>MonoSDF+ w/o DINO</td><td>0.064</td><td>0.016</td><td>0.022</td><td>0.034</td><td>0.78</td><td>0.83</td><td>0.93</td><td>0.85</td></tr><tr><td>MonoSDF+ (Full)</td><td>0.014</td><td>0.020</td><td>0.023</td><td>0.019</td><td>0.85</td><td>0.85</td><td>0.93</td><td>0.87</td></tr></table>
+
+severely degrade the reconstruction quality, which evidences that the shaping on SDF values could incur a competition with the goal to faithfully learn the geometry within the neural radiance field. We further examine the effectiveness of combining semantic and geometric features to identify geometrically highly correlated regions. As demonstrated in Fig. 3, using only one type of the features can lead to incorrect correlations. Tab. 3 also shows that eliminating any one of the features can decrease the performance, confirming the effectiveness of our positive-negative sample selection mechanism leveraging the multimodal features.
+
+Time and memory consumption. Our method provides benefits for 3D reconstruction with limited additional effort. Specifically, it only increases the optimization time and memory usage during the training process, without affecting the model architecture and final storage. The time and memory consumption are reported in Tab. 4. It is observed that the overhead on the training time highly depends on the architecture used in each baseline. For example, the train
+
+ing time increase on NeuRIS is marginal while more significant on VolSDF. These studies provide comprehensive information on the trade-offs between training time and performance gain. However, we do find that baselines with the proposed shaping technique can achieve a better performance (e.g., early geometries from NeuS and  $\mathrm{NeuS^{+}}$  shown in Fig. 5) at the same training steps due to the effective regularization by mutual information.
+
+Table 4: Time and memory consumption.  
+
+<table><tr><td></td><td>Training Time (h)</td><td>VRAM (GB)</td></tr><tr><td>NeuS [30]+</td><td>3.00+0.37</td><td>7.89+1.68</td></tr><tr><td>VolSDF [37]+</td><td>3.18+1.96</td><td>16.36+4.68</td></tr><tr><td>GeoNeuS [8]+</td><td>3.26+0.16</td><td>5.72+3.56</td></tr><tr><td>I2-SDF [44]+</td><td>3.47+2.84</td><td>10.08+8.09</td></tr><tr><td>NeuRIS [29]+</td><td>3.70+0.20</td><td>11.73+4.12</td></tr><tr><td>MonoSDF [40]+</td><td>2.65+1.32</td><td>12.83+9.42</td></tr><tr><td>Neuralangelo [13]+</td><td>3.12+2.06</td><td>16.44+1.00</td></tr></table>
+
+# 5 Conclusion
+
+We explore the usage of the second-order geometric correlations as a regularization and introduce a mutual information shaping technique of the normals for better surface reconstruction quality. With a simple yet effective correlated point selection mechanism that does not depend on accurate geometry information, we can perform a contrastive learning that maximizes the detected correlations. In return, we can observe a boost in the geometric quality of the reconstructed surfaces in state-of-the-art neural scene representations.
+
+Extensive evaluations on various baselines and datasets show the effectiveness of our method, which improves 3D reconstruction quality without resorting to a more sophisticated surface modeling. The overhead caused by the shaping of the normals varies with different neural architectures of the scene representation, e.g., some are marginal, and some are significant, which we deem as a limitation of our current pipeline. We believe that an acceleration in computation can be achieved using a coarse-to-fine strategy, which we leave as a future work.
+
+Acknowledgments. We thank the anonymous reviewers for their valuable feedback. This work is supported by the Early Career Scheme of the Research Grants Council (grant # 27207224), the HKU-100 Award, and in part by NSF China (No. 62172363). Siyan Dong would also like to thank the support from HKU Musketeers Foundation Institute of Data Science for the Postdoctoral Research Fellowship.
+
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+        "type": "text",
+        "text": "Information Bottleneck Based Data Correction in Continual Learning",
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+        "type": "text",
+        "text": "Shuai Chen $^{1,2}$ , Mingyi Zhang $^{1}$ , Junge Zhang $^{1*}$ , and Kaiqi Huang $^{1,2,3*}$",
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+        "text": "$^{1}$  CRISE, Institute of Automation, Chinese Academy of Sciences  \n $^{2}$  School of Artificial Intelligence, University of Chinese Academy of Sciences  \n $^{3}$  CAS Center for Excellence in Brain Science and Intelligence Technology",
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+        "text": "Abstract. Continual Learning (CL) requires model to retain previously learned knowledge while learning new tasks. Recently, experience replay-based methods have made significant progress in addressing this challenge. These methods primarily select data from old tasks and store them in a buffer. When learning new task, they train the model using both the current and buffered data. However, the limited number of old data can lead to the model being influenced by new tasks. The repeated replaying of buffer data and the gradual discarding of old task data (un-sampled data) also result in a biased estimation of the model towards the old tasks, causing overfitting issues. All these factors can affect the CL performance. Therefore, we propose a data correction algorithm based on the Information Bottleneck (IBCL) to enhance the performance of the replay-based CL system. This algorithm comprises two components: the Information Bottleneck Task Agnostic Constraints (IBTA), which encourages the buffer data to learn task-relevant features related to the old tasks, thereby reducing the impact of new tasks. The Information Bottleneck Unsampled Data Surrogate (IBDS), which models the information of the unsampled data in the old tasks to alleviate data bias. Our method can be flexibly combined with most existing experience replay methods. We have verified the effectiveness of our method through a series of experiments, demonstrating its potential for improving the performance of CL algorithms.",
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+    {
+        "type": "text",
+        "text": "Keywords: Continual learning  $\\cdot$  Incremental learning  $\\cdot$  Experience replay",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        "page_idx": 0
+    },
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+        "type": "text",
+        "text": "Modern deep learning algorithms have achieved remarkable performance in a diverse range of tasks [48-50]. However, one of their significant limitations is the inability to retain knowledge from previously learned tasks when receiving training on new tasks, known as catastrophic forgetting [18, 25]. Addressing this issue has been a subject of extensive research in the field of continual learning (CL) [12, 36, 52, 53]. Among the proposed methods, the experience replay approaches have received significant attention [11, 13, 31, 54]. These methods aim to",
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+    {
+        "type": "page_footnote",
+        "text": "* Corresponding author.",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/8085fa4ba7d2799a4275bbe20286b80cd1bdbd100f9f00759e6f7bcdafeea710.jpg",
+        "image_caption": [
+            "Fig. 1: During the process of CL, when the old task is sampled, there is a consequent discarding of some unsampled data. This leads to bias in the model's estimation of the distribution of the old task."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "overcome catastrophic forgetting by selectively storing a subset of data from old tasks in the buffer and then combining buffer data with new task data for joint training. Various replay methods have been investigated from different perspectives to address the challenge of sample selection and balancing the contributions of new and old samples during the replay process [6,14,37].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite the progress made in reducing catastrophic forgetting through replay methods, certain limitations still exist. A major issue is that the memory of the buffer is too small, and the model cannot store enough data to restore previously learned knowledge [4, 21, 35]. This will give rise to two significant problems. Firstly, the scarcity of old data will result in an imbalance between the number of new and old tasks, leading to a disruption of knowledge from the old task during the learning process of the new task. Secondly, in the CL process, each time the old task data is sampled, some unsampled data will be discarded, introducing bias in the model's estimation of the old task distribution. Moreover, the repeated replaying of buffer data can contribute to overfitting of this specific data. All of these factors can significantly impact the CL performance. Currently, there are some methods to address the above issues, such as selecting more representative samples [20], increasing the diversity of old samples through data expansion [3], and improving the generalization ability of the model [5].",
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+        "type": "text",
+        "text": "This work aims to tackle the aforementioned challenges from a different perspective. Regarding the first issue, we propose encouraging the data in the buffer to acquire task agnostic features related to the old task, thereby mitigating the impact of the new task. For the second issue, we focus on an important yet under-investigated question: How can unsampled data effectively contribute to learning new tasks? In Figure 1, we illustrate the cause of model overfitting, which arises because replay-based methods often utilize only a subset of data from old task, leading to biased results. When training on new tasks, we design the objective function as follows:",
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+        "text": "\n$$\n\\mathcal {L} _ {\\text {n e w}} = \\frac {1}{N _ {\\text {b u f f e r}} + N _ {\\text {n e w}}} \\sum_ {i = 1} ^ {N _ {n}} \\ell_ {i} (\\hat {Y}, Y). \\tag {1}\n$$\n",
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\ell_i(\\hat{Y}, Y)$  represents the loss function that takes the true outcome  $Y$  and predicts outcome  $\\hat{Y}$  as inputs.  $N_{buffer}$  and  $N_{new}$  denote the numbers of buffer and new task data, respectively.  $N_n$  is the sum of these two quantities. However, this loss function does not provide an unbiased estimate of the loss function for both new and old tasks, as the model gradually loses some data from past tasks during training. The unbiased loss function for new and old tasks should be formulated as follows:",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} [ \\mathcal {L} _ {\\text {n e w}} ] \\neq \\mathcal {L} := \\frac {1}{N _ {\\text {o l d}} + N _ {\\text {n e w}}} \\sum_ {i = 1} ^ {N} \\ell_ {i} (\\hat {Y}, Y). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            266,
+            785,
+            305
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $N_{old}$  and  $N_{new}$  represent the numbers of old task and new task data, respectively, and  $N$  signifies the sum of these two quantities. To address the bias arising from the discarding of unsampled data from old task, our method aims to estimate the information of the unsampled data using specific strategies. However, unsampled data cannot directly participate in the training of new tasks, we indirectly obtain a surrogate for the information about unsampled data through the relationship between sampled and unsampled data. This information related to the unsampled data serves as a regularization term to constrain the training process of the model, thereby achieving bias correction for the dataset.",
+        "bbox": [
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+            320,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Based on the intuition presented above, we propose an Information Bottleneck based data correction algorithm (IBCL). The information bottleneck method is a technique in information theory used to find the best compromise between accuracy and complexity [41]. It is regarded as the theoretical foundation of deep learning and has been applied in many fields, such as robust or invariant representation learning, causal reasoning, and so on [17]. This theory suggests that the model gradually eliminates irrelevant noise information during the learning process, retaining the most relevant feature information to the task. Borrowing the ability of this method, our algorithm mainly consists of two parts: Information Bottleneck Task Agnostic Constraints (IBTA): During the update process of new tasks, we introduce a constraint on the learning process of the buffer data. This constraint encourages the model to learn task agnostic features that are relevant to the old tasks, effectively preventing interference from the new tasks. Information Bottleneck Unsampled Data Surrogate (IBDS): This module is designed to model the information of the unsampled data. As the unsampled data cannot be directly trained, our method decouples the features of the unsampled data from the sampled data after the completion of learning old tasks. This decoupling allows model to leverage the relationship between the two types of data to estimate the surrogate influence of unsampled data. Consequently, this achieves an indirect implementation of the impact of unsampled data on learning new tasks.",
+        "bbox": [
+            212,
+            458,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overall, our work makes the following contributions:",
+        "bbox": [
+            238,
+            777,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "- We propose a data correction framework based on information bottleneck to mitigate model bias when the number of old task samples is small.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
+            511,
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+            127
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
+            774,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "- To mitigate the problem of the influence of new tasks on old sample features during the learning process, we propose IBTA to encourage the model to learn task agnostic features.",
+        "bbox": [
+            223,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "- To counter the issue of overfitting caused by the repeated replay of buffer data and gradual discarding of unsampled data, we propose IBDS to incorporate the information from unsampled data to assist in the training of the new model.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "- Our method can be combined with most replay based methods to improve their performance.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
+            215,
+            306,
+            387,
+            321
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.1 Experience Replay Continual Learning",
+        "text_level": 1,
+        "bbox": [
+            215,
+            340,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In the context of CL, there are three main approaches to retaining knowledge of past tasks: using a fixed-sized buffer for replaying past samples (replay-based approach) [2, 3, 7, 8, 43], regulating model parameter changes through learning (regularization-based approach) [16, 40, 42], or dynamically expanding model architecture as needed (expansion-based approach) [15, 28, 47]. Despite its simplicity, the replay-based approach has shown promising results in CL settings. Experience Replay (ER) [19] is a widely-used technique, which maintains a fixed-sized buffer to store and replay selected data, helping to mitigate the forgetting of previously learned knowledge. Incremental Classifier and Representation Learning (iCaRL) [37] uses the herding strategy to select a few representative samples. Rainbow Memory [3] proposes a diversity sampling strategy based on per-sample classification uncertainty. However, these methods primarily concentrate on how to choose which old data to store in the buffer, while neglecting the unsampled data. We argue that the unsampled data can also be beneficial in mitigating deviation and should be utilized. To this end, we propose a data correction method that employs the information bottleneck theory to model the information of the unsampled data in the old task, thereby enhancing the performance of several state-of-the-art methods.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.2 Information Bottleneck",
+        "text_level": 1,
+        "bbox": [
+            215,
+            662,
+            454,
+            676
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Information bottleneck (IB) is a classical concept in information theory, which is used to explain the behavior of deep learning [41]. Furthermore, IB has been extensively utilized in diverse applications, including but not limited to, representation learning decoupling [23, 33], recommendation systems [29, 45], and enhancing model robustness [17]. Recently, there have been some other works that apply information theory to CL, such as [27, 46], but there are fewer works based on the IB theory. The fundamental construct of IB is based on mutual information. In a previous work [20], the maximization of mutual information is employed to learn adequate feature expression. In contrast, our proposed method concentrates on modeling the unsampled data in the previous task.",
+        "bbox": [
+            212,
+            688,
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+            840
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
+            217,
+            114,
+            228,
+            126
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            127
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ff358228f58fb0907ffd9d15fd833630364b4c1bd2fd93c8aa1a9041b1ec48ae.jpg",
+        "image_caption": [
+            "Fig. 2: During the updating of new tasks, we constrain the learning process of buffer data, encouraging the model to learn task agnostic features related to the old tasks, thus avoiding the interference of new tasks."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            148,
+            782,
+            268
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
+            215,
+            349,
+            330,
+            366
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our method consists of two key processes: the learning process of new tasks and the processing process after learning old tasks. We introduce IBTA and IBDS separately.",
+        "bbox": [
+            212,
+            378,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1 Problem Formulation",
+        "text_level": 1,
+        "bbox": [
+            215,
+            444,
+            437,
+            458
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In CL scenarios, tasks are introduced one after another and handled separately. We consider a total of  $T$  tasks. Each task  $D_{t} = \\{x_{i}^{t},y_{i}^{t}\\}_{i = 1}^{n_{t}}$  comprises  $n_t$  input-target pairs  $(x_i^t,y_i^t)$ , which are assumed to be independent and identically distributed (i.i.d.). The aim for each task is to train a model  $f_{\\theta}:X\\to Y$  with parameters  $\\theta$ , capable of predicting the class label  $y$  for a new image  $x$ . In CL algorithms that utilize experience replay, the methods typically store some data from previous task data  $x_{old}$  in a buffer. This stored data is referred to as sampled data  $x_{m}$ , with its features denoted as  $z_{m}$ . The data not selected for storage is called unsampled data  $x_{u}$ , and its features are represented as  $z_{u}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 Information Bottleneck Task Agnostic Constraints",
+        "text_level": 1,
+        "bbox": [
+            215,
+            623,
+            676,
+            638
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During the learning of new tasks, the model focuses on the new task due to the limited data available in the buffer. In order to mitigate the impact of new tasks, our method encourages the buffer data to focus on learning the task-specific features, thus minimizing their influence. In order to compress the information in the dataset into the features of the sampled data as much as possible, the mutual information between the features  $z_{m}$  of the sampled data and the buffer dataset  $x_{m}$  should be minimized; In order to make the feature be able to distinguish well, the feature  $z_{m}$  of the sample needs to predict the label  $y_{old}$  as accurately as possible. The weighting parameters  $\\alpha$  is used to balance the contributions of different components in the overall objective function.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {I B T A} := \\min  \\underbrace {\\alpha I \\left(z _ {m} ; x _ {\\mathrm {m}}\\right)} _ {(1)} - \\underbrace {I \\left(z _ {m} ; y _ {\\text {o l d}}\\right)} _ {(2)}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            354,
+            805,
+            785,
+            843
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
+            511,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
+            774,
+            116,
+            784,
+            126
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the given framework, the expression (1) represents a compression component that characterizes the mutual information between the buffer dataset  $x_{m}$  and the sampled data features  $z_{m}$ . This component aims to capture the relevance of  $z_{m}$  to the old dataset  $x_{m}$ . The expression (2) corresponds to an accuracy component that measures the effectiveness of  $z_{m}$  in representing the underlying distribution of the dataset. It aims to ensure that the sampled features  $z_{m}$  preserve sufficient information about the original data. Next, we will proceed to optimize the compression term  $I(z_{m};x_{m})$ . This term can be quantified using the Kullback-Leibler (KL) divergence as follows:",
+        "bbox": [
+            212,
+            146,
+            787,
+            282
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} I (z _ {m}; x _ {\\mathrm {m}}) = \\mathbb {E} _ {x} \\left[ \\mathrm {K L} (p (z _ {m} | x _ {\\mathrm {m}}) \\parallel p (z _ {m})) \\right] \\\\ = \\mathbb {E} _ {x} \\left[ \\int p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\log p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) d z - \\int p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\log p \\left(z _ {m}\\right) d z \\right]. \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            228,
+            292,
+            784,
+            343
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Nonetheless, due to the computational complexity involved in calculating  $p(z_{m}) = \\int p(z_{m}|x_{m})p(x_{m})dx$ , we resort to the utilization of a variational approximation approach. Instead of using  $p(z_{m})$ , we adopt a variational distribution denoted as  $q(z_{m})$ . Leveraging Gibbs' inequality, we recognize the non-negativity of the Kullback-Leibler (KL) divergence. Thus, we can establish an upper bound for Equation (4),",
+        "bbox": [
+            214,
+            349,
+            789,
+            441
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} - \\int p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\log p \\left(z _ {m}\\right) d z \\leq - \\int p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\log q \\left(z _ {m}\\right) d z \\tag {5} \\\\ \\Rightarrow \\operatorname {K L} \\left(p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\| p \\left(z _ {m}\\right)\\right) \\leq \\operatorname {K L} \\left(p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\| q \\left(z _ {m}\\right)\\right). \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            307,
+            450,
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+            500
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Similar to prior research [1, 29, 34, 44, 45], we can make the assumption that the posterior distribution  $p(z_{m} \\mid x_{m})$  follows a Gaussian distribution and set it  $\\mathcal{N}(e(x_m),\\mathrm{diag}(\\sigma (x_m)))$ . In this context,  $e(x_{m})$  represents the encoded embedding of the variables  $x_{m}$ , and  $\\mathrm{diag}(\\sigma (x_m))$  indicates the variance in a diagonal matrix form. By employing the reparameterization trick, the embedding  $z_{m}$  can be generated through the formula  $z_{m} = e(x_{m}) + \\epsilon \\odot \\sigma (x_{m})$ , where  $\\epsilon \\sim \\mathcal{N}(0,I)$ . Notably, if we set  $\\sigma (x_{m})$  as an all-zero matrix,  $z_{m}$  will effectively become a deterministic embedding. Conversely, the prior distribution  $q(z_{m})$  is assumed to adhere to a standard Gaussian variational distribution, namely  $q(z_{m}) = \\mathcal{N}(0,I)$ . Ultimately, the previously mentioned upper bound can be rephrased as follows:",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {K L} \\left(p \\left(z _ {m} \\mid x _ {\\mathrm {m}}\\right) \\| q \\left(z _ {m}\\right)\\right) = \\| e \\left(x _ {\\mathrm {m}}\\right) \\| _ {2} ^ {2} + \\sum_ {d} \\left(\\sigma_ {d} - \\frac {1}{2} \\log \\sigma_ {d} - 1\\right). \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            279,
+            666,
+            784,
+            702
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma_d$  corresponds to an element within  $\\operatorname{diag}\\{\\sigma(x_m)\\}$ . This signifies that for a deterministic embedding  $z_m$ , we can enhance the optimization of this upper bound by directly implementing  $\\ell_2$ -norm regularization on the embedding vector  $z_m$ . This process is equivalent to refining the compression term  $I(z_m; x_m)$ . When considering the mutual information  $I(z_m; y_{old})$  within Equation (3), we can express it as  $I(z_m; y_{old}) = H(y_{old}) - H(y_{old} \\mid z_m)$ . As  $H(y_{old})$  is a positive constant that can be disregarded, the following inequality holds:",
+        "bbox": [
+            212,
+            709,
+            787,
+            816
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI \\left(z _ {m}; y _ {\\text {o l d}}\\right) \\geq - H \\left(y _ {\\text {o l d}} \\mid z _ {m}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
+            217,
+            114,
+            228,
+            126
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            127
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/65ac90514e9c443546e403e7d5158f0ce4fbb1558b966208a78394fa8412f3ea.jpg",
+        "image_caption": [
+            "Fig. 3: This module is used to model the information of unsampled data. Because unsampled data cannot be trained directly, our method decouples the features of unsampled data and sampled data after the completion of the old task learning, so that it is convenient to estimate the surrogate loss of unsampled data in the new task by using the relationship between them, and indirectly realize the influence of unsampled data on the new task learning."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            222,
+            148,
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+            266
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "This term can be seen as a cross entropy loss function. Therefore, we have implemented the constraint process for learning buffer data. However, the loss function obtained in this way is still biased, as there is missing unsampled data, which means that the contribution to the old task label  $y_{old}$  should be  $I(z; y) = I(z_m, z_u; y)$ , where  $z_u$  is unsampled data feature. During the learning process of the new task, this item cannot be directly calculated. We will calculate it indirectly in the following section.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3 Information Bottleneck Unsampled Data Surrogate",
+        "text_level": 1,
+        "bbox": [
+            214,
+            534,
+            684,
+            550
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To estimate the mutual information  $I(z; y) = I(z_{m}, z_{u}; y)$  during the learning process of new task, it becomes essential to obtain  $z_{u}$ . Given that  $x_{u}$  denotes unsampled data, we cannot directly calculate  $z_{u}$  from  $x_{u}$  when learning new task. This necessitates an indirect estimation of  $z_{u}$  from old task model. As shown in Fig.3, during the learning stage of old task, both sampled  $x_{m}$  and unsampled  $x_{u}$  data are involved in the training process. After training completion, the features corresponding to these two parts  $z_{m}$  and  $z_{u}$  are tightly coupled. Consequently, a specific operation is needed after training ends to decouple these two features. If we can decouple the features of sampled and unsampled data by optimizing  $I(z_{m}; z_{u})$ , we can get  $I(z; y) = I(z_{m}; y) + I(z_{u}; y)$ . In this case, the estimate of  $I(z_{u}; y)$  can be used as a surrogate for the unsampled data information during learning new task. The feature  $z_{m}$  of the sampled data and the feature  $z_{u}$  of the unsampled data must maintain as much independence from one another as possible to obtain better discrimination. Drawing on principles from information theory, we are inspired to derive a minimization objective function based on the aforementioned analysis:",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {I B D S} := \\min  I \\left(z _ {m}; z _ {u}\\right). \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            410,
+            824,
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+            840
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
+            511,
+            114,
+            730,
+            126
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
+            774,
+            114,
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+            125
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "represents a decoupling component, capturing the level of interdependence between  $z_{u}$  and  $z_{m}$ . It aims to minimize the dependence of  $z_{u}$  on  $z_{m}$ , ensuring that  $z_{u}$  provides additional information beyond what is already captured by  $z_{m}$ .",
+        "bbox": [
+            215,
+            146,
+            784,
+            191
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Inspired by previous research work [1, 29, 34, 44, 45], utilizing the chain rule of mutual information, we derive the subsequent equation pertaining to the decoupling component:",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI \\left(z _ {m}; z _ {u}\\right) = I \\left(z _ {m}; y _ {o l d}\\right) - I \\left(z _ {m}; y _ {o l d} \\mid z _ {u}\\right) + I \\left(z _ {m}; z _ {u} \\mid y _ {o l d}\\right). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We proceed to analyze the expression  $I(z_{m};z_{u}\\mid y_{old})$  in greater detail. Given that the distribution of  $z_{m}$  exclusively hinges on the variables  $x_{m}$ , and the latter is influenced by  $y_{old}$ , we establish  $H(z_{m}\\mid y_{old},z_{u}) = H(z_{m}\\mid y_{old})$ , where  $H(\\cdot \\mid \\cdot)$  signifies conditional entropy. By combining the attributes of mutual information, we arrive at the following relationship:",
+        "bbox": [
+            214,
+            277,
+            785,
+            353
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} I (z _ {m}; z _ {u} \\mid y _ {\\mathrm {o l d}}) = H (z _ {m} \\mid y _ {\\mathrm {o l d}}) - H (z _ {m} \\mid y _ {\\mathrm {o l d}}, z _ {u}) \\\\ = H \\left(z _ {m} \\mid y _ {\\text {o l d}}\\right) - H \\left(z _ {m} \\mid y _ {\\text {o l d}}\\right) = 0. \\tag {10} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            323,
+            366,
+            784,
+            400
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "By substituting Eq.(9), we have,",
+        "bbox": [
+            215,
+            412,
+            452,
+            428
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI \\left(z _ {m}; z _ {u}\\right) = I \\left(z _ {m}; y _ {\\text {o l d}}\\right) - I \\left(z _ {m}; y _ {\\text {o l d}} \\mid z _ {u}\\right) \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            359,
+            440,
+            784,
+            455
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Since the term  $I(z_{m};y_{old} \\mid z_{u})$  in Eq.(11) is still difficult to be calculated, we simplify it further by using the form of conditional entropy:",
+        "bbox": [
+            212,
+            465,
+            785,
+            498
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} I \\left(z _ {m}; y _ {\\text {o l d}} \\mid z _ {u}\\right) = H \\left(z _ {m} \\mid z _ {u}\\right) + H \\left(y _ {\\text {o l d}} \\mid z _ {u}\\right) - I \\left(z _ {m}; y _ {\\text {o l d}} \\mid z _ {u}\\right) \\\\ = H \\left(z _ {m} \\mid z _ {u}\\right) - H \\left(z _ {m} \\mid y _ {\\text {o l d}}, z _ {u}\\right) \\tag {12} \\\\ = H \\left(y _ {\\text {o l d}} \\mid z _ {u}\\right) - H \\left(y _ {\\text {o l d}} \\mid z _ {m}, z _ {u}\\right) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            287,
+            510,
+            784,
+            563
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI \\left(z _ {m}; z _ {u}\\right) = I \\left(z _ {m}; y _ {o l d}\\right) - H \\left(y _ {o l d} \\mid z _ {u}\\right) + H \\left(y _ {o l d} \\mid z _ {m}, z _ {u}\\right). \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            302,
+            580,
+            784,
+            597
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Finally, combining Eq.(7) and Eq.(13), we can rewrite the objective function  $\\mathcal{L}_{IBDS}$  in Eq.(8) as follows,",
+        "bbox": [
+            215,
+            603,
+            784,
+            635
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {I B D S} = - H \\left(y _ {o l d} \\mid z _ {m}\\right) - H \\left(y _ {o l d} \\mid z _ {u}\\right) + H \\left(y _ {o l d} \\mid z _ {m}, z _ {u}\\right). \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            297,
+            647,
+            784,
+            662
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "By optimizing  $\\mathcal{L}_{IBDS}$ , we get the decoupled expression  $z_{u}$ . Now we can compute  $I(z_{u};y)$ , which acts as a surrogate loss to compensate for missing weights due to unsampled data.",
+        "bbox": [
+            215,
+            672,
+            785,
+            718
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "During the training process of neural network, the model will encounter the problem of semantic drift [22,24,51], which means that the feature distribution of sampled data will change with the learning of new tasks. This concept highlights a significant challenge: using the fixed features of unsampled data as constraints in the learning of new task becomes problematic. As the model trains on new tasks, the estimation of unsampled data features gradually deviates from their true values, which not only affects the effectiveness of bias correction but also, to some extent, impacts the overall learning process. Just as the \"no free lunch\"",
+        "bbox": [
+            212,
+            719,
+            785,
+            840
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
+            217,
+            114,
+            228,
+            126
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            127
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "theorem advocated in machine learning. Once samples are lost, it becomes difficult to perfectly estimate the distribution of unsampled data, the best one can do is to minimize the model's bias when addressing old tasks. To mitigate this impact, it's essential to consider the characteristics of neural networks in CL [9]. Early in the learning of new tasks, gradients undergo significant changes, and the model frequently encounters considerable biases. A viable strategy involves imposing stricter constraints on the new task learning process during the initial stages of model training. This approach instructs the model in reducing biases when learning new tasks. As the training advances, these constraints are gradually relaxed, permitting the model to better adjust to the learning requirements of new tasks during the slower update phases. To address the processing of unsampled data features, a dynamic decay strategy is employed to balance the learning conflicts between old and new tasks, thereby optimizing the model's overall performance. This method allows the model to discover a more balanced learning point between preserving old knowledge and acquiring new tasks, enhancing its learning efficiency and effectiveness. Specifically, inspired by [30], we propose a dynamic cosine annealing factor  $\\eta$  for constraint terms when updating unsampled data.",
+        "bbox": [
+            212,
+            146,
+            787,
+            417
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\eta = \\left(\\frac {1}{2} (1 + \\cos \\left(\\frac {e _ {\\text {c u r}}}{e _ {\\text {m a x}}}\\right) \\pi)\\right) \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            406,
+            417,
+            785,
+            450
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $e_{cur}$  and  $e_{max}$  represent current and maximum number of epochs.",
+        "bbox": [
+            214,
+            455,
+            736,
+            470
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "3.4 Algorithm",
+        "text_level": 1,
+        "bbox": [
+            214,
+            493,
+            346,
+            508
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "By combining above two parts, we can get the total loss function as:",
+        "bbox": [
+            214,
+            518,
+            709,
+            535
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C I B} = \\alpha I (z _ {m}; x _ {\\mathrm {m}}) - I (z; y _ {\\mathrm {o l d}}) \\\\ = \\alpha I \\left(z _ {m}; x _ {\\mathrm {m}}\\right) - \\beta I \\left(z _ {u}; y\\right) - \\gamma I \\left(z _ {m}; y\\right) \\tag {16} \\\\ \\leq \\alpha \\| e \\left(x _ {\\mathrm {m}}\\right) \\| _ {2} ^ {2} + \\beta \\cdot \\eta H \\left(y _ {\\text {o l d}} \\mid z _ {u}\\right) + \\gamma H \\left(y _ {\\text {o l d}} \\mid z _ {m}\\right). \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            307,
+            547,
+            784,
+            602
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The weighting parameters  $\\alpha$ ,  $\\beta$ ,  $\\gamma$  are used to balance the contributions of different components in the overall objective function.",
+        "bbox": [
+            212,
+            612,
+            785,
+            643
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The final objective function comprises three terms: term (1) represents a regularization constraint on the input data, term (2) represents surrogate loss to reflects the influence of the unsampled data; term (3) denotes the cross-entropy between  $z_{m}$  and  $y_{old}$ , this can be seen as the cross-entropy loss function. The aim is to make the learned feature expression fully predict the final label.",
+        "bbox": [
+            212,
+            643,
+            787,
+            718
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Discussion This approach comprises two primary modules: the IBTA module facilitates the learning of new tasks, whereas the IBDS module is utilized post-learning of old tasks to derive features from unsampled data. These features are then integrated as constraints within the training of new tasks, thereby shaping the overall optimization loss function. Our method can be combined with most replay-based strategies. Taking the naive ER method as an example, it randomly selects some samples from the old task and stores them in a buffer, which are trained together with the samples from the new task. Upon finalizing",
+        "bbox": [
+            212,
+            719,
+            787,
+            840
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
+            511,
+            114,
+            730,
+            127
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            774,
+            114,
+            785,
+            126
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/48ef1e08468ed897951a3379377e38bca32a21e4cea047a7fdbf52ad2f8d4678.jpg",
+        "table_caption": [
+            "Table 1: Comparison of the average accuracy (the higher the better) of four split datasets with different buffer sizes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td colspan=\"3\">Split CIFAR-10</td><td colspan=\"3\">Split CIFAR-100</td><td colspan=\"3\">Split ImageNet-100</td><td colspan=\"3\">Split miniImageNet</td></tr><tr><td>Joint</td><td colspan=\"3\">92.38</td><td colspan=\"3\">73.29</td><td colspan=\"3\">80.23</td><td colspan=\"3\">53.55</td></tr><tr><td>FT</td><td colspan=\"3\">19.67</td><td colspan=\"3\">9.29</td><td colspan=\"3\">8.68</td><td colspan=\"3\">9.52</td></tr><tr><td>Buffer size</td><td>100</td><td>200</td><td>500</td><td>200</td><td>500</td><td>2000</td><td>200</td><td>500</td><td>2000</td><td>1000</td><td>2000</td><td>5000</td></tr><tr><td>ER</td><td>36.39</td><td>44.79</td><td>57.74</td><td>14.35</td><td>19.66</td><td>36.76</td><td>13.63</td><td>18.37</td><td>34.25</td><td>8.37</td><td>16.49</td><td>24.17</td></tr><tr><td>+IBCL</td><td>45.43</td><td>51.91</td><td>63.12</td><td>23.98</td><td>28.32</td><td>42.01</td><td>22.72</td><td>28.93</td><td>43.11</td><td>14.79</td><td>22.72</td><td>27.69</td></tr><tr><td>ER-ACE</td><td>53.90</td><td>63.41</td><td>70.53</td><td>26.28</td><td>36.48</td><td>48.41</td><td>24.23</td><td>37.12</td><td>49.55</td><td>17.95</td><td>22.60</td><td>27.92</td></tr><tr><td>+IBCL</td><td>63.85</td><td>70.97</td><td>74.82</td><td>32.12</td><td>40.94</td><td>51.89</td><td>30.72</td><td>41.81</td><td>52.62</td><td>24.77</td><td>27.63</td><td>31.02</td></tr><tr><td>DER++</td><td>57.65</td><td>64.88</td><td>72.70</td><td>25.11</td><td>37.13</td><td>52.08</td><td>26.50</td><td>43.65</td><td>58.05</td><td>18.02</td><td>23.44</td><td>30.43</td></tr><tr><td>+IBCL</td><td>66.41</td><td>72.52</td><td>76.61</td><td>33.82</td><td>44.21</td><td>54.89</td><td>32.63</td><td>46.57</td><td>59.92</td><td>27.72</td><td>31.41</td><td>35.79</td></tr><tr><td>X-DER</td><td>59.29</td><td>65.19</td><td>68.10</td><td>35.34</td><td>44.62</td><td>54.44</td><td>33.21</td><td>46.72</td><td>55.23</td><td>25.24</td><td>26.38</td><td>29.91</td></tr><tr><td>+IBCL</td><td>67.91</td><td>73.82</td><td>74.14</td><td>43.86</td><td>48.72</td><td>55.91</td><td>43.25</td><td>49.62</td><td>56.59</td><td>29.90</td><td>30.21</td><td>32.66</td></tr></table>",
+        "bbox": [
+            222,
+            184,
+            787,
+            359
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "the learning of old task, the sampled data is processed through the old model to yield  $z_{m}$ , and both sampled and unsampled data are processed to extract coupled features  $z$ . Subsequently, by optimizing IBDS, features  $z_{u}$  for each class of unsampled data are obtained. During the training of the new task, IBTA and  $z_{u}$  are combined to optimize the total loss function for learning the new task. Detailed pseudocode of this procedure is provided in the appendix.",
+        "bbox": [
+            212,
+            387,
+            784,
+            479
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
+            215,
+            501,
+            375,
+            518
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will present the datasets and evaluation metrics used in the experiment, and describe the implementation details. Then we describe the experimental results of our method on multiple standard benchmarks. Finally, we conduct an ablation study to illustrate the effectiveness of each module of our method.",
+        "bbox": [
+            212,
+            532,
+            784,
+            608
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.1 Dataset",
+        "text_level": 1,
+        "bbox": [
+            215,
+            631,
+            328,
+            645
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We validate our results on four distinct datasets: CIFAR-10, CIFAR-100, miniImageNet, and ImageNet-100. CIFAR-10 and CIFAR-100 each consist of 50,000 training samples and 10,000 testing samples, with 10 and 100 classes respectively. miniImageNet and ImageNet-100 are subsets of ImageNet, both containing 100 classes. miniImageNet includes 500 images per category for training, while ImageNet-100 includes 1300 images per category for training.",
+        "bbox": [
+            212,
+            656,
+            784,
+            748
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.2 Details",
+        "text_level": 1,
+        "bbox": [
+            215,
+            768,
+            320,
+            782
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "To better compare with other methods, we follow the settings of [46] and [5]. For the CIFAR-10/100 and ImageNet-100 datasets, we adopt ResNet-18, and for the miniImageNet dataset, we adopt EfficientNet-B2. For CIFAR-10/100, we",
+        "bbox": [
+            212,
+            794,
+            784,
+            840
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
+            217,
+            114,
+            235,
+            126
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            126
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/039be141bd4bba34a17cb65083d22e77e756b69b1f0cd790cafd3ca0ed886846.jpg",
+        "table_caption": [
+            "Table 2: Comparison of our method with other regularization methods on three datasets, we use two typical methods DER++ and ER-ACE as benchmarks for comparison."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td colspan=\"3\">Split CIFAR-10</td><td colspan=\"3\">Split CIFAR-100</td><td colspan=\"3\">Split miniImageNet</td></tr><tr><td>Buffer size</td><td>100</td><td>200</td><td>500</td><td>200</td><td>500</td><td>2000</td><td>1000</td><td>2000</td><td>5000</td></tr><tr><td>ER-ACE</td><td>53.90</td><td>63.41</td><td>70.53</td><td>26.28</td><td>36.48</td><td>48.41</td><td>17.95</td><td>22.60</td><td>27.92</td></tr><tr><td>+ sSGD</td><td>56.26</td><td>64.73</td><td>71.45</td><td>28.07</td><td>39.59</td><td>49.70</td><td>18.11</td><td>22.43</td><td>24.12</td></tr><tr><td>+ oEwC</td><td>52.36</td><td>61.09</td><td>68.70</td><td>24.93</td><td>35.06</td><td>45.59</td><td>19.04</td><td>24.32</td><td>29.46</td></tr><tr><td>+ oLAP</td><td>52.76</td><td>63.19</td><td>70.32</td><td>26.42</td><td>36.58</td><td>47.66</td><td>18.34</td><td>23.19</td><td>28.77</td></tr><tr><td>+ OCM</td><td>57.18</td><td>64.65</td><td>70.86</td><td>28.18</td><td>37.74</td><td>49.03</td><td>20.32</td><td>24.32</td><td>28.57</td></tr><tr><td>+ LiDER</td><td>56.08</td><td>65.32</td><td>71.75</td><td>27.94</td><td>38.43</td><td>50.32</td><td>19.69</td><td>24.13</td><td>30.00</td></tr><tr><td>+ DualHSIC</td><td>60.52</td><td>68.08</td><td>73.78</td><td>29.08</td><td>38.94</td><td>50.55</td><td>22.33</td><td>25.41</td><td>30.12</td></tr><tr><td>+ Our</td><td>63.85</td><td>70.97</td><td>74.82</td><td>32.12</td><td>40.94</td><td>51.89</td><td>24.77</td><td>27.63</td><td>31.02</td></tr><tr><td>DER++</td><td>57.65</td><td>64.88</td><td>72.70</td><td>25.11</td><td>37.13</td><td>52.08</td><td>18.02</td><td>23.44</td><td>30.43</td></tr><tr><td>+ sSGD</td><td>55.81</td><td>64.44</td><td>72.05</td><td>24.76</td><td>38.48</td><td>50.74</td><td>16.31</td><td>19.29</td><td>24.24</td></tr><tr><td>+ oEwC</td><td>55.78</td><td>63.02</td><td>71.64</td><td>24.51</td><td>35.22</td><td>51.53</td><td>18.87</td><td>24.53</td><td>31.91</td></tr><tr><td>+ oLAP</td><td>54.86</td><td>62.54</td><td>71.38</td><td>23.26</td><td>34.48</td><td>50.80</td><td>18.91</td><td>25.02</td><td>32.78</td></tr><tr><td>+ OCM</td><td>59.25</td><td>65.81</td><td>73.53</td><td>27.46</td><td>38.94</td><td>52.25</td><td>20.93</td><td>24.75</td><td>31.16</td></tr><tr><td>+ LiDER</td><td>58.43</td><td>66.02</td><td>73.39</td><td>27.32</td><td>39.25</td><td>53.27</td><td>21.58</td><td>28.33</td><td>35.04</td></tr><tr><td>+ DualHSIC</td><td>64.98</td><td>70.28</td><td>75.94</td><td>31.46</td><td>41.86</td><td>53.53</td><td>24.78</td><td>29.37</td><td>34.98</td></tr><tr><td>+ Our</td><td>66.41</td><td>72.52</td><td>76.61</td><td>33.82</td><td>44.21</td><td>54.89</td><td>27.72</td><td>31.41</td><td>35.79</td></tr></table>",
+        "bbox": [
+            228,
+            198,
+            776,
+            478
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "adopt a training epoch of 50 and set the batch size to 32 and 64, respectively. For MiniImageNet and ImageNet-100, we adopt training epochs of 80 and 120, with batch size set to 128 and 64, respectively. In order to better compare the experimental results, we adopt the experimental results reported in [46] and [5], or the hyperparametric design in the original article.",
+        "bbox": [
+            212,
+            508,
+            787,
+            585
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "4.3 Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            215,
+            614,
+            419,
+            630
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We mainly evaluate on class incremental learning scenario. In this setup, each sequential task introduces a distinct set of classes that do not overlap with those from previous tasks. The challenge lies in training a classifier that can effectively classify all classes encountered up to the current stage, without the need for explicit task ids. We evaluate the final performance of the method by average accuracy.",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA C C = \\frac {1}{T} \\sum_ {i = 1} ^ {T} R _ {T, i}, \\tag {17}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where  $R_{T,i}$  denotes the test accuracy on task  $i$  after the model has finished task  $T$ .",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
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+    {
+        "type": "table",
+        "img_path": "images/2d38f47d97a1ae860d0b7e74d5b321446d60c15efb8ed5508636400a0615466f.jpg",
+        "table_caption": [
+            "Table 3: Abalation study of the average accuracy (the higher the better) of split ImageNet-100 and split CIFAR-100 with different buffer sizes."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td colspan=\"3\">Split CIFAR-100</td><td colspan=\"3\">Split ImageNet-100</td></tr><tr><td>Buffer size</td><td>200</td><td>500</td><td>2000</td><td>200</td><td>500</td><td>2000</td></tr><tr><td>ER-ACE</td><td>26.28</td><td>36.48</td><td>48.41</td><td>24.23</td><td>37.12</td><td>49.55</td></tr><tr><td>+ IBTA</td><td>27.36</td><td>37.49</td><td>49.12</td><td>25.63</td><td>37.92</td><td>50.12</td></tr><tr><td>+ IBDS</td><td>30.44</td><td>39.52</td><td>50.91</td><td>29.83</td><td>40.71</td><td>51.85</td></tr><tr><td>+IBCL</td><td>32.12</td><td>40.94</td><td>51.89</td><td>30.72</td><td>41.81</td><td>52.62</td></tr><tr><td>DER++</td><td>25.11</td><td>37.13</td><td>52.08</td><td>26.50</td><td>43.65</td><td>58.05</td></tr><tr><td>+IBTA</td><td>27.88</td><td>38.74</td><td>53.96</td><td>27.39</td><td>45.72</td><td>59.33</td></tr><tr><td>+ IBDS</td><td>31.53</td><td>42.59</td><td>54.33</td><td>29.58</td><td>46.15</td><td>59.70</td></tr><tr><td>+IBCL</td><td>33.82</td><td>44.21</td><td>54.89</td><td>32.63</td><td>46.57</td><td>59.92</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4 Baseline Models",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on multiple state-of-the-art experience replay CL models: ER [10], DER++ [8], X-DER [6], and ER-ACE [9]. In addition to the original loss function based on replay, our method can be considered as a new regularization method. Therefore, we also compare our method with existing regularization-based techniques, including sSGD [32], oEWC [39], oLAP [38], and more recent SOTA methods, OCM [20], LiDER [5] and DualHSIC [46].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.5 Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The comparison results are reported in Table 1. For the method of listing several baselines, our proposed method has improved the model's performance in various datasets and buffer sizes. In addition, we have the following main observations: 1) There has been a significant improvement in basic methods such as ER and DER++, as these two methods adopt more basic methods for sampling. Our method can reduce the bias caused by the sampling process to a certain extent. 2) Our methods have also shown some effectiveness on X-DER and ER-ACE, which take additional measures to alleviate sample imbalance and improve sample utilization, resulting in improved model performance. Our method further enhances the model's capabilities on top of this.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To further demonstrate the effectiveness of our method, we compare our method with other regularization methods, and it can be found that we achieve the best performance, recent methods such as OCM, LiDER and DualHSIC achieve significant progress compared to baseline when the number of buffer is small, and our method further improves the performance when the buffer data is small by considering modeling for the unsampled data.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.6 Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In order to understand the effect of each of the items in the loss function on the performance of the algorithm, an ablation study has been carried out and the",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "12",
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+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/e17b5e35974228cf5ec5776a2af0dda49e6c658d92ad831dc2a12a503c651496.jpg",
+        "image_caption": [
+            "Fig. 4: This figure shows the CKA matrix based on the ER algorithm, FT and incorporating our algorithm. It can be observed from it that due to our modeling of unsampled data, the model shows more information about the old task."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/6c4cc5c7089bf47269767d347ffd7406f8ca2b259b93520de11a4d1a7be87f2c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/305984db984788dc1f90a3b3b41fd0744b949396a47aee300cf03cb7baf59ca2.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "results are shown in Table 3. It is observed that in most of the cases, increasing any of the components has an impact on the performance of the algorithm. However, increasing the IBDS gives a large performance improvement, which indicates that it plays a vital role in the performance of the algorithm. This component represents the loss of substitution of unsampled data, which is necessary for training on new tasks using unsampled data features. Therefore, if this aspect is not well learned, it may negatively affect the subsequent performance of the algorithm. IBTA also has an impact on the performance of the algorithm, the involves regularization constraints on the input features in order to make the model learn enough robust features.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 Characteristic Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We analyze various characteristics of the model to gain insight into the factors contributing to the performance enhancements achieved by our approach.",
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+    },
+    {
+        "type": "text",
+        "text": "5.1 CKA Matrix Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We use Central Kernel Alignment (CKA) [26] in Fig.4, which is an effective tool to measure the similarity of network representations and evaluate the relationships between these backbones. We send the same batch of instances to the ER (2000 buffer size) algorithm model and fine-tuning based model respectively to obtain corresponding feature maps, thus intuitively demonstrating the similarity of algorithm feature maps. Our algorithm can be used in conjunction with the experience replay method to model unsampled data. When the sampled data is 0, i.e. fine-tuning, our method can also get some benefits.",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "header",
+        "text": "IB Based Data Correction in CL",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "13",
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+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/f776ee0a368bf83264a3019df57278fd23a062b9eca311ea385184ae50334934.jpg",
+        "image_caption": [
+            "Initialization"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/9deb011b3e4c1988a3809b8798e4c7015966b38b5352829e6520b0359a26812f.jpg",
+        "image_caption": [
+            "Epoch  $= 20$",
+            "Fig. 5: This image uses TSNE to display the changes in the characteristics of sampled and unsampled data with the number of training epochs of the model. We have shown one class of situation, with a sample data size of 200 and an unsampled data size of 1100."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/e3e5fdfec78084223105586c8257c1a5fb7c74e63c28ad3d3144c282a36632b5.jpg",
+        "image_caption": [
+            "Epoch  $= 50$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "5.2 Feature Decoupling Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "A significant advance of our method is the decoupling of sampled and unsampled data features. We demonstrate this in Fig.5, where we use TSNE technology to visualize the changes in these two features with the increase of network training epochs. We test our method, the ER algorithm, on 200 sampled data and 1100 unsampled data from the ImageNet-100 dataset. As the network training epochs increase, we can observe that the two sets of features begin to separate from their initial coupling, which indicates that our method has achieved decoupling of the two data.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In conclusion, our proposed method is designed to tackle the issue of data bias in continual learning through the application of experience replay. Drawing inspiration from information bottleneck theory, we steer the incorporation of unsampled data information, thereby bolstering the model's capacity to preserve past knowledge while accommodating novel tasks. Our conducted experiments offer empirical validation of the advantages conferred by our approach. While we have presented a method for computing unsampled data, it's important to acknowledge the existence of several alternative strategies for estimating these. This opens up exciting possibilities for continued exploration and innovation in this field.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This work was supported by National Science and Technology Major Project, Grant No.2022ZD0116403, the Youth Innovation Promotion Association CAS and Strategic Priority Research Program of Chinese Academy of Sciences XDA27010300.",
+        "bbox": [
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+        "type": "page_number",
+        "text": "14",
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+    {
+        "type": "header",
+        "text": "S. Chen et al.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            217,
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+            159
+        ],
+        "page_idx": 14
+    },
+    {
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+        ],
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+        "text": "IB Based Data Correction in CL",
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2024/Information Bottleneck Based Data Correction in Continual Learning/6c4e72fe-4072-432b-96c2-9a488daff608_origin.pdf

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2024/Information Bottleneck Based Data Correction in Continual Learning/full.md

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+# Information Bottleneck Based Data Correction in Continual Learning
+
+Shuai Chen $^{1,2}$ , Mingyi Zhang $^{1}$ , Junge Zhang $^{1*}$ , and Kaiqi Huang $^{1,2,3*}$
+
+$^{1}$  CRISE, Institute of Automation, Chinese Academy of Sciences  
+ $^{2}$  School of Artificial Intelligence, University of Chinese Academy of Sciences  
+ $^{3}$  CAS Center for Excellence in Brain Science and Intelligence Technology
+
+Abstract. Continual Learning (CL) requires model to retain previously learned knowledge while learning new tasks. Recently, experience replay-based methods have made significant progress in addressing this challenge. These methods primarily select data from old tasks and store them in a buffer. When learning new task, they train the model using both the current and buffered data. However, the limited number of old data can lead to the model being influenced by new tasks. The repeated replaying of buffer data and the gradual discarding of old task data (un-sampled data) also result in a biased estimation of the model towards the old tasks, causing overfitting issues. All these factors can affect the CL performance. Therefore, we propose a data correction algorithm based on the Information Bottleneck (IBCL) to enhance the performance of the replay-based CL system. This algorithm comprises two components: the Information Bottleneck Task Agnostic Constraints (IBTA), which encourages the buffer data to learn task-relevant features related to the old tasks, thereby reducing the impact of new tasks. The Information Bottleneck Unsampled Data Surrogate (IBDS), which models the information of the unsampled data in the old tasks to alleviate data bias. Our method can be flexibly combined with most existing experience replay methods. We have verified the effectiveness of our method through a series of experiments, demonstrating its potential for improving the performance of CL algorithms.
+
+Keywords: Continual learning  $\cdot$  Incremental learning  $\cdot$  Experience replay
+
+# 1 Introduction
+
+Modern deep learning algorithms have achieved remarkable performance in a diverse range of tasks [48-50]. However, one of their significant limitations is the inability to retain knowledge from previously learned tasks when receiving training on new tasks, known as catastrophic forgetting [18, 25]. Addressing this issue has been a subject of extensive research in the field of continual learning (CL) [12, 36, 52, 53]. Among the proposed methods, the experience replay approaches have received significant attention [11, 13, 31, 54]. These methods aim to
+
+![](images/8085fa4ba7d2799a4275bbe20286b80cd1bdbd100f9f00759e6f7bcdafeea710.jpg)  
+Fig. 1: During the process of CL, when the old task is sampled, there is a consequent discarding of some unsampled data. This leads to bias in the model's estimation of the distribution of the old task.
+
+overcome catastrophic forgetting by selectively storing a subset of data from old tasks in the buffer and then combining buffer data with new task data for joint training. Various replay methods have been investigated from different perspectives to address the challenge of sample selection and balancing the contributions of new and old samples during the replay process [6,14,37].
+
+Despite the progress made in reducing catastrophic forgetting through replay methods, certain limitations still exist. A major issue is that the memory of the buffer is too small, and the model cannot store enough data to restore previously learned knowledge [4, 21, 35]. This will give rise to two significant problems. Firstly, the scarcity of old data will result in an imbalance between the number of new and old tasks, leading to a disruption of knowledge from the old task during the learning process of the new task. Secondly, in the CL process, each time the old task data is sampled, some unsampled data will be discarded, introducing bias in the model's estimation of the old task distribution. Moreover, the repeated replaying of buffer data can contribute to overfitting of this specific data. All of these factors can significantly impact the CL performance. Currently, there are some methods to address the above issues, such as selecting more representative samples [20], increasing the diversity of old samples through data expansion [3], and improving the generalization ability of the model [5].
+
+This work aims to tackle the aforementioned challenges from a different perspective. Regarding the first issue, we propose encouraging the data in the buffer to acquire task agnostic features related to the old task, thereby mitigating the impact of the new task. For the second issue, we focus on an important yet under-investigated question: How can unsampled data effectively contribute to learning new tasks? In Figure 1, we illustrate the cause of model overfitting, which arises because replay-based methods often utilize only a subset of data from old task, leading to biased results. When training on new tasks, we design the objective function as follows:
+
+$$
+\mathcal {L} _ {\text {n e w}} = \frac {1}{N _ {\text {b u f f e r}} + N _ {\text {n e w}}} \sum_ {i = 1} ^ {N _ {n}} \ell_ {i} (\hat {Y}, Y). \tag {1}
+$$
+
+where  $\ell_i(\hat{Y}, Y)$  represents the loss function that takes the true outcome  $Y$  and predicts outcome  $\hat{Y}$  as inputs.  $N_{buffer}$  and  $N_{new}$  denote the numbers of buffer and new task data, respectively.  $N_n$  is the sum of these two quantities. However, this loss function does not provide an unbiased estimate of the loss function for both new and old tasks, as the model gradually loses some data from past tasks during training. The unbiased loss function for new and old tasks should be formulated as follows:
+
+$$
+\mathbb {E} [ \mathcal {L} _ {\text {n e w}} ] \neq \mathcal {L} := \frac {1}{N _ {\text {o l d}} + N _ {\text {n e w}}} \sum_ {i = 1} ^ {N} \ell_ {i} (\hat {Y}, Y). \tag {2}
+$$
+
+where  $N_{old}$  and  $N_{new}$  represent the numbers of old task and new task data, respectively, and  $N$  signifies the sum of these two quantities. To address the bias arising from the discarding of unsampled data from old task, our method aims to estimate the information of the unsampled data using specific strategies. However, unsampled data cannot directly participate in the training of new tasks, we indirectly obtain a surrogate for the information about unsampled data through the relationship between sampled and unsampled data. This information related to the unsampled data serves as a regularization term to constrain the training process of the model, thereby achieving bias correction for the dataset.
+
+Based on the intuition presented above, we propose an Information Bottleneck based data correction algorithm (IBCL). The information bottleneck method is a technique in information theory used to find the best compromise between accuracy and complexity [41]. It is regarded as the theoretical foundation of deep learning and has been applied in many fields, such as robust or invariant representation learning, causal reasoning, and so on [17]. This theory suggests that the model gradually eliminates irrelevant noise information during the learning process, retaining the most relevant feature information to the task. Borrowing the ability of this method, our algorithm mainly consists of two parts: Information Bottleneck Task Agnostic Constraints (IBTA): During the update process of new tasks, we introduce a constraint on the learning process of the buffer data. This constraint encourages the model to learn task agnostic features that are relevant to the old tasks, effectively preventing interference from the new tasks. Information Bottleneck Unsampled Data Surrogate (IBDS): This module is designed to model the information of the unsampled data. As the unsampled data cannot be directly trained, our method decouples the features of the unsampled data from the sampled data after the completion of learning old tasks. This decoupling allows model to leverage the relationship between the two types of data to estimate the surrogate influence of unsampled data. Consequently, this achieves an indirect implementation of the impact of unsampled data on learning new tasks.
+
+Overall, our work makes the following contributions:
+
+- We propose a data correction framework based on information bottleneck to mitigate model bias when the number of old task samples is small.
+
+- To mitigate the problem of the influence of new tasks on old sample features during the learning process, we propose IBTA to encourage the model to learn task agnostic features.
+
+- To counter the issue of overfitting caused by the repeated replay of buffer data and gradual discarding of unsampled data, we propose IBDS to incorporate the information from unsampled data to assist in the training of the new model.
+
+- Our method can be combined with most replay based methods to improve their performance.
+
+# 2 Related Work
+
+# 2.1 Experience Replay Continual Learning
+
+In the context of CL, there are three main approaches to retaining knowledge of past tasks: using a fixed-sized buffer for replaying past samples (replay-based approach) [2, 3, 7, 8, 43], regulating model parameter changes through learning (regularization-based approach) [16, 40, 42], or dynamically expanding model architecture as needed (expansion-based approach) [15, 28, 47]. Despite its simplicity, the replay-based approach has shown promising results in CL settings. Experience Replay (ER) [19] is a widely-used technique, which maintains a fixed-sized buffer to store and replay selected data, helping to mitigate the forgetting of previously learned knowledge. Incremental Classifier and Representation Learning (iCaRL) [37] uses the herding strategy to select a few representative samples. Rainbow Memory [3] proposes a diversity sampling strategy based on per-sample classification uncertainty. However, these methods primarily concentrate on how to choose which old data to store in the buffer, while neglecting the unsampled data. We argue that the unsampled data can also be beneficial in mitigating deviation and should be utilized. To this end, we propose a data correction method that employs the information bottleneck theory to model the information of the unsampled data in the old task, thereby enhancing the performance of several state-of-the-art methods.
+
+# 2.2 Information Bottleneck
+
+Information bottleneck (IB) is a classical concept in information theory, which is used to explain the behavior of deep learning [41]. Furthermore, IB has been extensively utilized in diverse applications, including but not limited to, representation learning decoupling [23, 33], recommendation systems [29, 45], and enhancing model robustness [17]. Recently, there have been some other works that apply information theory to CL, such as [27, 46], but there are fewer works based on the IB theory. The fundamental construct of IB is based on mutual information. In a previous work [20], the maximization of mutual information is employed to learn adequate feature expression. In contrast, our proposed method concentrates on modeling the unsampled data in the previous task.
+
+![](images/ff358228f58fb0907ffd9d15fd833630364b4c1bd2fd93c8aa1a9041b1ec48ae.jpg)  
+Fig. 2: During the updating of new tasks, we constrain the learning process of buffer data, encouraging the model to learn task agnostic features related to the old tasks, thus avoiding the interference of new tasks.
+
+# 3 Method
+
+Our method consists of two key processes: the learning process of new tasks and the processing process after learning old tasks. We introduce IBTA and IBDS separately.
+
+# 3.1 Problem Formulation
+
+In CL scenarios, tasks are introduced one after another and handled separately. We consider a total of  $T$  tasks. Each task  $D_{t} = \{x_{i}^{t},y_{i}^{t}\}_{i = 1}^{n_{t}}$  comprises  $n_t$  input-target pairs  $(x_i^t,y_i^t)$ , which are assumed to be independent and identically distributed (i.i.d.). The aim for each task is to train a model  $f_{\theta}:X\to Y$  with parameters  $\theta$ , capable of predicting the class label  $y$  for a new image  $x$ . In CL algorithms that utilize experience replay, the methods typically store some data from previous task data  $x_{old}$  in a buffer. This stored data is referred to as sampled data  $x_{m}$ , with its features denoted as  $z_{m}$ . The data not selected for storage is called unsampled data  $x_{u}$ , and its features are represented as  $z_{u}$ .
+
+# 3.2 Information Bottleneck Task Agnostic Constraints
+
+During the learning of new tasks, the model focuses on the new task due to the limited data available in the buffer. In order to mitigate the impact of new tasks, our method encourages the buffer data to focus on learning the task-specific features, thus minimizing their influence. In order to compress the information in the dataset into the features of the sampled data as much as possible, the mutual information between the features  $z_{m}$  of the sampled data and the buffer dataset  $x_{m}$  should be minimized; In order to make the feature be able to distinguish well, the feature  $z_{m}$  of the sample needs to predict the label  $y_{old}$  as accurately as possible. The weighting parameters  $\alpha$  is used to balance the contributions of different components in the overall objective function.
+
+$$
+\mathcal {L} _ {I B T A} := \min  \underbrace {\alpha I \left(z _ {m} ; x _ {\mathrm {m}}\right)} _ {(1)} - \underbrace {I \left(z _ {m} ; y _ {\text {o l d}}\right)} _ {(2)}. \tag {3}
+$$
+
+In the given framework, the expression (1) represents a compression component that characterizes the mutual information between the buffer dataset  $x_{m}$  and the sampled data features  $z_{m}$ . This component aims to capture the relevance of  $z_{m}$  to the old dataset  $x_{m}$ . The expression (2) corresponds to an accuracy component that measures the effectiveness of  $z_{m}$  in representing the underlying distribution of the dataset. It aims to ensure that the sampled features  $z_{m}$  preserve sufficient information about the original data. Next, we will proceed to optimize the compression term  $I(z_{m};x_{m})$ . This term can be quantified using the Kullback-Leibler (KL) divergence as follows:
+
+$$
+\begin{array}{l} I (z _ {m}; x _ {\mathrm {m}}) = \mathbb {E} _ {x} \left[ \mathrm {K L} (p (z _ {m} | x _ {\mathrm {m}}) \parallel p (z _ {m})) \right] \\ = \mathbb {E} _ {x} \left[ \int p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \log p \left(z _ {m} \mid x _ {\mathrm {m}}\right) d z - \int p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \log p \left(z _ {m}\right) d z \right]. \tag {4} \\ \end{array}
+$$
+
+Nonetheless, due to the computational complexity involved in calculating  $p(z_{m}) = \int p(z_{m}|x_{m})p(x_{m})dx$ , we resort to the utilization of a variational approximation approach. Instead of using  $p(z_{m})$ , we adopt a variational distribution denoted as  $q(z_{m})$ . Leveraging Gibbs' inequality, we recognize the non-negativity of the Kullback-Leibler (KL) divergence. Thus, we can establish an upper bound for Equation (4),
+
+$$
+\begin{array}{l} - \int p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \log p \left(z _ {m}\right) d z \leq - \int p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \log q \left(z _ {m}\right) d z \tag {5} \\ \Rightarrow \operatorname {K L} \left(p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \| p \left(z _ {m}\right)\right) \leq \operatorname {K L} \left(p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \| q \left(z _ {m}\right)\right). \\ \end{array}
+$$
+
+Similar to prior research [1, 29, 34, 44, 45], we can make the assumption that the posterior distribution  $p(z_{m} \mid x_{m})$  follows a Gaussian distribution and set it  $\mathcal{N}(e(x_m),\mathrm{diag}(\sigma (x_m)))$ . In this context,  $e(x_{m})$  represents the encoded embedding of the variables  $x_{m}$ , and  $\mathrm{diag}(\sigma (x_m))$  indicates the variance in a diagonal matrix form. By employing the reparameterization trick, the embedding  $z_{m}$  can be generated through the formula  $z_{m} = e(x_{m}) + \epsilon \odot \sigma (x_{m})$ , where  $\epsilon \sim \mathcal{N}(0,I)$ . Notably, if we set  $\sigma (x_{m})$  as an all-zero matrix,  $z_{m}$  will effectively become a deterministic embedding. Conversely, the prior distribution  $q(z_{m})$  is assumed to adhere to a standard Gaussian variational distribution, namely  $q(z_{m}) = \mathcal{N}(0,I)$ . Ultimately, the previously mentioned upper bound can be rephrased as follows:
+
+$$
+\operatorname {K L} \left(p \left(z _ {m} \mid x _ {\mathrm {m}}\right) \| q \left(z _ {m}\right)\right) = \| e \left(x _ {\mathrm {m}}\right) \| _ {2} ^ {2} + \sum_ {d} \left(\sigma_ {d} - \frac {1}{2} \log \sigma_ {d} - 1\right). \tag {6}
+$$
+
+where  $\sigma_d$  corresponds to an element within  $\operatorname{diag}\{\sigma(x_m)\}$ . This signifies that for a deterministic embedding  $z_m$ , we can enhance the optimization of this upper bound by directly implementing  $\ell_2$ -norm regularization on the embedding vector  $z_m$ . This process is equivalent to refining the compression term  $I(z_m; x_m)$ . When considering the mutual information  $I(z_m; y_{old})$  within Equation (3), we can express it as  $I(z_m; y_{old}) = H(y_{old}) - H(y_{old} \mid z_m)$ . As  $H(y_{old})$  is a positive constant that can be disregarded, the following inequality holds:
+
+$$
+I \left(z _ {m}; y _ {\text {o l d}}\right) \geq - H \left(y _ {\text {o l d}} \mid z _ {m}\right). \tag {7}
+$$
+
+![](images/65ac90514e9c443546e403e7d5158f0ce4fbb1558b966208a78394fa8412f3ea.jpg)  
+Fig. 3: This module is used to model the information of unsampled data. Because unsampled data cannot be trained directly, our method decouples the features of unsampled data and sampled data after the completion of the old task learning, so that it is convenient to estimate the surrogate loss of unsampled data in the new task by using the relationship between them, and indirectly realize the influence of unsampled data on the new task learning.
+
+This term can be seen as a cross entropy loss function. Therefore, we have implemented the constraint process for learning buffer data. However, the loss function obtained in this way is still biased, as there is missing unsampled data, which means that the contribution to the old task label  $y_{old}$  should be  $I(z; y) = I(z_m, z_u; y)$ , where  $z_u$  is unsampled data feature. During the learning process of the new task, this item cannot be directly calculated. We will calculate it indirectly in the following section.
+
+# 3.3 Information Bottleneck Unsampled Data Surrogate
+
+To estimate the mutual information  $I(z; y) = I(z_{m}, z_{u}; y)$  during the learning process of new task, it becomes essential to obtain  $z_{u}$ . Given that  $x_{u}$  denotes unsampled data, we cannot directly calculate  $z_{u}$  from  $x_{u}$  when learning new task. This necessitates an indirect estimation of  $z_{u}$  from old task model. As shown in Fig.3, during the learning stage of old task, both sampled  $x_{m}$  and unsampled  $x_{u}$  data are involved in the training process. After training completion, the features corresponding to these two parts  $z_{m}$  and  $z_{u}$  are tightly coupled. Consequently, a specific operation is needed after training ends to decouple these two features. If we can decouple the features of sampled and unsampled data by optimizing  $I(z_{m}; z_{u})$ , we can get  $I(z; y) = I(z_{m}; y) + I(z_{u}; y)$ . In this case, the estimate of  $I(z_{u}; y)$  can be used as a surrogate for the unsampled data information during learning new task. The feature  $z_{m}$  of the sampled data and the feature  $z_{u}$  of the unsampled data must maintain as much independence from one another as possible to obtain better discrimination. Drawing on principles from information theory, we are inspired to derive a minimization objective function based on the aforementioned analysis:
+
+$$
+\mathcal {L} _ {I B D S} := \min  I \left(z _ {m}; z _ {u}\right). \tag {8}
+$$
+
+represents a decoupling component, capturing the level of interdependence between  $z_{u}$  and  $z_{m}$ . It aims to minimize the dependence of  $z_{u}$  on  $z_{m}$ , ensuring that  $z_{u}$  provides additional information beyond what is already captured by  $z_{m}$ .
+
+Inspired by previous research work [1, 29, 34, 44, 45], utilizing the chain rule of mutual information, we derive the subsequent equation pertaining to the decoupling component:
+
+$$
+I \left(z _ {m}; z _ {u}\right) = I \left(z _ {m}; y _ {o l d}\right) - I \left(z _ {m}; y _ {o l d} \mid z _ {u}\right) + I \left(z _ {m}; z _ {u} \mid y _ {o l d}\right). \tag {9}
+$$
+
+We proceed to analyze the expression  $I(z_{m};z_{u}\mid y_{old})$  in greater detail. Given that the distribution of  $z_{m}$  exclusively hinges on the variables  $x_{m}$ , and the latter is influenced by  $y_{old}$ , we establish  $H(z_{m}\mid y_{old},z_{u}) = H(z_{m}\mid y_{old})$ , where  $H(\cdot \mid \cdot)$  signifies conditional entropy. By combining the attributes of mutual information, we arrive at the following relationship:
+
+$$
+\begin{array}{l} I (z _ {m}; z _ {u} \mid y _ {\mathrm {o l d}}) = H (z _ {m} \mid y _ {\mathrm {o l d}}) - H (z _ {m} \mid y _ {\mathrm {o l d}}, z _ {u}) \\ = H \left(z _ {m} \mid y _ {\text {o l d}}\right) - H \left(z _ {m} \mid y _ {\text {o l d}}\right) = 0. \tag {10} \\ \end{array}
+$$
+
+By substituting Eq.(9), we have,
+
+$$
+I \left(z _ {m}; z _ {u}\right) = I \left(z _ {m}; y _ {\text {o l d}}\right) - I \left(z _ {m}; y _ {\text {o l d}} \mid z _ {u}\right) \tag {11}
+$$
+
+Since the term  $I(z_{m};y_{old} \mid z_{u})$  in Eq.(11) is still difficult to be calculated, we simplify it further by using the form of conditional entropy:
+
+$$
+\begin{array}{l} I \left(z _ {m}; y _ {\text {o l d}} \mid z _ {u}\right) = H \left(z _ {m} \mid z _ {u}\right) + H \left(y _ {\text {o l d}} \mid z _ {u}\right) - I \left(z _ {m}; y _ {\text {o l d}} \mid z _ {u}\right) \\ = H \left(z _ {m} \mid z _ {u}\right) - H \left(z _ {m} \mid y _ {\text {o l d}}, z _ {u}\right) \tag {12} \\ = H \left(y _ {\text {o l d}} \mid z _ {u}\right) - H \left(y _ {\text {o l d}} \mid z _ {m}, z _ {u}\right) \\ \end{array}
+$$
+
+$$
+I \left(z _ {m}; z _ {u}\right) = I \left(z _ {m}; y _ {o l d}\right) - H \left(y _ {o l d} \mid z _ {u}\right) + H \left(y _ {o l d} \mid z _ {m}, z _ {u}\right). \tag {13}
+$$
+
+Finally, combining Eq.(7) and Eq.(13), we can rewrite the objective function  $\mathcal{L}_{IBDS}$  in Eq.(8) as follows,
+
+$$
+\mathcal {L} _ {I B D S} = - H \left(y _ {o l d} \mid z _ {m}\right) - H \left(y _ {o l d} \mid z _ {u}\right) + H \left(y _ {o l d} \mid z _ {m}, z _ {u}\right). \tag {14}
+$$
+
+By optimizing  $\mathcal{L}_{IBDS}$ , we get the decoupled expression  $z_{u}$ . Now we can compute  $I(z_{u};y)$ , which acts as a surrogate loss to compensate for missing weights due to unsampled data.
+
+During the training process of neural network, the model will encounter the problem of semantic drift [22,24,51], which means that the feature distribution of sampled data will change with the learning of new tasks. This concept highlights a significant challenge: using the fixed features of unsampled data as constraints in the learning of new task becomes problematic. As the model trains on new tasks, the estimation of unsampled data features gradually deviates from their true values, which not only affects the effectiveness of bias correction but also, to some extent, impacts the overall learning process. Just as the "no free lunch"
+
+theorem advocated in machine learning. Once samples are lost, it becomes difficult to perfectly estimate the distribution of unsampled data, the best one can do is to minimize the model's bias when addressing old tasks. To mitigate this impact, it's essential to consider the characteristics of neural networks in CL [9]. Early in the learning of new tasks, gradients undergo significant changes, and the model frequently encounters considerable biases. A viable strategy involves imposing stricter constraints on the new task learning process during the initial stages of model training. This approach instructs the model in reducing biases when learning new tasks. As the training advances, these constraints are gradually relaxed, permitting the model to better adjust to the learning requirements of new tasks during the slower update phases. To address the processing of unsampled data features, a dynamic decay strategy is employed to balance the learning conflicts between old and new tasks, thereby optimizing the model's overall performance. This method allows the model to discover a more balanced learning point between preserving old knowledge and acquiring new tasks, enhancing its learning efficiency and effectiveness. Specifically, inspired by [30], we propose a dynamic cosine annealing factor  $\eta$  for constraint terms when updating unsampled data.
+
+$$
+\eta = \left(\frac {1}{2} (1 + \cos \left(\frac {e _ {\text {c u r}}}{e _ {\text {m a x}}}\right) \pi)\right) \tag {15}
+$$
+
+where  $e_{cur}$  and  $e_{max}$  represent current and maximum number of epochs.
+
+# 3.4 Algorithm
+
+By combining above two parts, we can get the total loss function as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {C I B} = \alpha I (z _ {m}; x _ {\mathrm {m}}) - I (z; y _ {\mathrm {o l d}}) \\ = \alpha I \left(z _ {m}; x _ {\mathrm {m}}\right) - \beta I \left(z _ {u}; y\right) - \gamma I \left(z _ {m}; y\right) \tag {16} \\ \leq \alpha \| e \left(x _ {\mathrm {m}}\right) \| _ {2} ^ {2} + \beta \cdot \eta H \left(y _ {\text {o l d}} \mid z _ {u}\right) + \gamma H \left(y _ {\text {o l d}} \mid z _ {m}\right). \\ \end{array}
+$$
+
+The weighting parameters  $\alpha$ ,  $\beta$ ,  $\gamma$  are used to balance the contributions of different components in the overall objective function.
+
+The final objective function comprises three terms: term (1) represents a regularization constraint on the input data, term (2) represents surrogate loss to reflects the influence of the unsampled data; term (3) denotes the cross-entropy between  $z_{m}$  and  $y_{old}$ , this can be seen as the cross-entropy loss function. The aim is to make the learned feature expression fully predict the final label.
+
+Discussion This approach comprises two primary modules: the IBTA module facilitates the learning of new tasks, whereas the IBDS module is utilized post-learning of old tasks to derive features from unsampled data. These features are then integrated as constraints within the training of new tasks, thereby shaping the overall optimization loss function. Our method can be combined with most replay-based strategies. Taking the naive ER method as an example, it randomly selects some samples from the old task and stores them in a buffer, which are trained together with the samples from the new task. Upon finalizing
+
+Table 1: Comparison of the average accuracy (the higher the better) of four split datasets with different buffer sizes.  
+
+<table><tr><td>Method</td><td colspan="3">Split CIFAR-10</td><td colspan="3">Split CIFAR-100</td><td colspan="3">Split ImageNet-100</td><td colspan="3">Split miniImageNet</td></tr><tr><td>Joint</td><td colspan="3">92.38</td><td colspan="3">73.29</td><td colspan="3">80.23</td><td colspan="3">53.55</td></tr><tr><td>FT</td><td colspan="3">19.67</td><td colspan="3">9.29</td><td colspan="3">8.68</td><td colspan="3">9.52</td></tr><tr><td>Buffer size</td><td>100</td><td>200</td><td>500</td><td>200</td><td>500</td><td>2000</td><td>200</td><td>500</td><td>2000</td><td>1000</td><td>2000</td><td>5000</td></tr><tr><td>ER</td><td>36.39</td><td>44.79</td><td>57.74</td><td>14.35</td><td>19.66</td><td>36.76</td><td>13.63</td><td>18.37</td><td>34.25</td><td>8.37</td><td>16.49</td><td>24.17</td></tr><tr><td>+IBCL</td><td>45.43</td><td>51.91</td><td>63.12</td><td>23.98</td><td>28.32</td><td>42.01</td><td>22.72</td><td>28.93</td><td>43.11</td><td>14.79</td><td>22.72</td><td>27.69</td></tr><tr><td>ER-ACE</td><td>53.90</td><td>63.41</td><td>70.53</td><td>26.28</td><td>36.48</td><td>48.41</td><td>24.23</td><td>37.12</td><td>49.55</td><td>17.95</td><td>22.60</td><td>27.92</td></tr><tr><td>+IBCL</td><td>63.85</td><td>70.97</td><td>74.82</td><td>32.12</td><td>40.94</td><td>51.89</td><td>30.72</td><td>41.81</td><td>52.62</td><td>24.77</td><td>27.63</td><td>31.02</td></tr><tr><td>DER++</td><td>57.65</td><td>64.88</td><td>72.70</td><td>25.11</td><td>37.13</td><td>52.08</td><td>26.50</td><td>43.65</td><td>58.05</td><td>18.02</td><td>23.44</td><td>30.43</td></tr><tr><td>+IBCL</td><td>66.41</td><td>72.52</td><td>76.61</td><td>33.82</td><td>44.21</td><td>54.89</td><td>32.63</td><td>46.57</td><td>59.92</td><td>27.72</td><td>31.41</td><td>35.79</td></tr><tr><td>X-DER</td><td>59.29</td><td>65.19</td><td>68.10</td><td>35.34</td><td>44.62</td><td>54.44</td><td>33.21</td><td>46.72</td><td>55.23</td><td>25.24</td><td>26.38</td><td>29.91</td></tr><tr><td>+IBCL</td><td>67.91</td><td>73.82</td><td>74.14</td><td>43.86</td><td>48.72</td><td>55.91</td><td>43.25</td><td>49.62</td><td>56.59</td><td>29.90</td><td>30.21</td><td>32.66</td></tr></table>
+
+the learning of old task, the sampled data is processed through the old model to yield  $z_{m}$ , and both sampled and unsampled data are processed to extract coupled features  $z$ . Subsequently, by optimizing IBDS, features  $z_{u}$  for each class of unsampled data are obtained. During the training of the new task, IBTA and  $z_{u}$  are combined to optimize the total loss function for learning the new task. Detailed pseudocode of this procedure is provided in the appendix.
+
+# 4 Experiments
+
+In this section, we will present the datasets and evaluation metrics used in the experiment, and describe the implementation details. Then we describe the experimental results of our method on multiple standard benchmarks. Finally, we conduct an ablation study to illustrate the effectiveness of each module of our method.
+
+# 4.1 Dataset
+
+We validate our results on four distinct datasets: CIFAR-10, CIFAR-100, miniImageNet, and ImageNet-100. CIFAR-10 and CIFAR-100 each consist of 50,000 training samples and 10,000 testing samples, with 10 and 100 classes respectively. miniImageNet and ImageNet-100 are subsets of ImageNet, both containing 100 classes. miniImageNet includes 500 images per category for training, while ImageNet-100 includes 1300 images per category for training.
+
+# 4.2 Details
+
+To better compare with other methods, we follow the settings of [46] and [5]. For the CIFAR-10/100 and ImageNet-100 datasets, we adopt ResNet-18, and for the miniImageNet dataset, we adopt EfficientNet-B2. For CIFAR-10/100, we
+
+Table 2: Comparison of our method with other regularization methods on three datasets, we use two typical methods DER++ and ER-ACE as benchmarks for comparison.  
+
+<table><tr><td>Method</td><td colspan="3">Split CIFAR-10</td><td colspan="3">Split CIFAR-100</td><td colspan="3">Split miniImageNet</td></tr><tr><td>Buffer size</td><td>100</td><td>200</td><td>500</td><td>200</td><td>500</td><td>2000</td><td>1000</td><td>2000</td><td>5000</td></tr><tr><td>ER-ACE</td><td>53.90</td><td>63.41</td><td>70.53</td><td>26.28</td><td>36.48</td><td>48.41</td><td>17.95</td><td>22.60</td><td>27.92</td></tr><tr><td>+ sSGD</td><td>56.26</td><td>64.73</td><td>71.45</td><td>28.07</td><td>39.59</td><td>49.70</td><td>18.11</td><td>22.43</td><td>24.12</td></tr><tr><td>+ oEwC</td><td>52.36</td><td>61.09</td><td>68.70</td><td>24.93</td><td>35.06</td><td>45.59</td><td>19.04</td><td>24.32</td><td>29.46</td></tr><tr><td>+ oLAP</td><td>52.76</td><td>63.19</td><td>70.32</td><td>26.42</td><td>36.58</td><td>47.66</td><td>18.34</td><td>23.19</td><td>28.77</td></tr><tr><td>+ OCM</td><td>57.18</td><td>64.65</td><td>70.86</td><td>28.18</td><td>37.74</td><td>49.03</td><td>20.32</td><td>24.32</td><td>28.57</td></tr><tr><td>+ LiDER</td><td>56.08</td><td>65.32</td><td>71.75</td><td>27.94</td><td>38.43</td><td>50.32</td><td>19.69</td><td>24.13</td><td>30.00</td></tr><tr><td>+ DualHSIC</td><td>60.52</td><td>68.08</td><td>73.78</td><td>29.08</td><td>38.94</td><td>50.55</td><td>22.33</td><td>25.41</td><td>30.12</td></tr><tr><td>+ Our</td><td>63.85</td><td>70.97</td><td>74.82</td><td>32.12</td><td>40.94</td><td>51.89</td><td>24.77</td><td>27.63</td><td>31.02</td></tr><tr><td>DER++</td><td>57.65</td><td>64.88</td><td>72.70</td><td>25.11</td><td>37.13</td><td>52.08</td><td>18.02</td><td>23.44</td><td>30.43</td></tr><tr><td>+ sSGD</td><td>55.81</td><td>64.44</td><td>72.05</td><td>24.76</td><td>38.48</td><td>50.74</td><td>16.31</td><td>19.29</td><td>24.24</td></tr><tr><td>+ oEwC</td><td>55.78</td><td>63.02</td><td>71.64</td><td>24.51</td><td>35.22</td><td>51.53</td><td>18.87</td><td>24.53</td><td>31.91</td></tr><tr><td>+ oLAP</td><td>54.86</td><td>62.54</td><td>71.38</td><td>23.26</td><td>34.48</td><td>50.80</td><td>18.91</td><td>25.02</td><td>32.78</td></tr><tr><td>+ OCM</td><td>59.25</td><td>65.81</td><td>73.53</td><td>27.46</td><td>38.94</td><td>52.25</td><td>20.93</td><td>24.75</td><td>31.16</td></tr><tr><td>+ LiDER</td><td>58.43</td><td>66.02</td><td>73.39</td><td>27.32</td><td>39.25</td><td>53.27</td><td>21.58</td><td>28.33</td><td>35.04</td></tr><tr><td>+ DualHSIC</td><td>64.98</td><td>70.28</td><td>75.94</td><td>31.46</td><td>41.86</td><td>53.53</td><td>24.78</td><td>29.37</td><td>34.98</td></tr><tr><td>+ Our</td><td>66.41</td><td>72.52</td><td>76.61</td><td>33.82</td><td>44.21</td><td>54.89</td><td>27.72</td><td>31.41</td><td>35.79</td></tr></table>
+
+adopt a training epoch of 50 and set the batch size to 32 and 64, respectively. For MiniImageNet and ImageNet-100, we adopt training epochs of 80 and 120, with batch size set to 128 and 64, respectively. In order to better compare the experimental results, we adopt the experimental results reported in [46] and [5], or the hyperparametric design in the original article.
+
+# 4.3 Evaluation Metrics
+
+We mainly evaluate on class incremental learning scenario. In this setup, each sequential task introduces a distinct set of classes that do not overlap with those from previous tasks. The challenge lies in training a classifier that can effectively classify all classes encountered up to the current stage, without the need for explicit task ids. We evaluate the final performance of the method by average accuracy.
+
+$$
+A C C = \frac {1}{T} \sum_ {i = 1} ^ {T} R _ {T, i}, \tag {17}
+$$
+
+where  $R_{T,i}$  denotes the test accuracy on task  $i$  after the model has finished task  $T$ .
+
+Table 3: Abalation study of the average accuracy (the higher the better) of split ImageNet-100 and split CIFAR-100 with different buffer sizes.  
+
+<table><tr><td>Method</td><td colspan="3">Split CIFAR-100</td><td colspan="3">Split ImageNet-100</td></tr><tr><td>Buffer size</td><td>200</td><td>500</td><td>2000</td><td>200</td><td>500</td><td>2000</td></tr><tr><td>ER-ACE</td><td>26.28</td><td>36.48</td><td>48.41</td><td>24.23</td><td>37.12</td><td>49.55</td></tr><tr><td>+ IBTA</td><td>27.36</td><td>37.49</td><td>49.12</td><td>25.63</td><td>37.92</td><td>50.12</td></tr><tr><td>+ IBDS</td><td>30.44</td><td>39.52</td><td>50.91</td><td>29.83</td><td>40.71</td><td>51.85</td></tr><tr><td>+IBCL</td><td>32.12</td><td>40.94</td><td>51.89</td><td>30.72</td><td>41.81</td><td>52.62</td></tr><tr><td>DER++</td><td>25.11</td><td>37.13</td><td>52.08</td><td>26.50</td><td>43.65</td><td>58.05</td></tr><tr><td>+IBTA</td><td>27.88</td><td>38.74</td><td>53.96</td><td>27.39</td><td>45.72</td><td>59.33</td></tr><tr><td>+ IBDS</td><td>31.53</td><td>42.59</td><td>54.33</td><td>29.58</td><td>46.15</td><td>59.70</td></tr><tr><td>+IBCL</td><td>33.82</td><td>44.21</td><td>54.89</td><td>32.63</td><td>46.57</td><td>59.92</td></tr></table>
+
+# 4.4 Baseline Models
+
+We conduct experiments on multiple state-of-the-art experience replay CL models: ER [10], DER++ [8], X-DER [6], and ER-ACE [9]. In addition to the original loss function based on replay, our method can be considered as a new regularization method. Therefore, we also compare our method with existing regularization-based techniques, including sSGD [32], oEWC [39], oLAP [38], and more recent SOTA methods, OCM [20], LiDER [5] and DualHSIC [46].
+
+# 4.5 Results
+
+The comparison results are reported in Table 1. For the method of listing several baselines, our proposed method has improved the model's performance in various datasets and buffer sizes. In addition, we have the following main observations: 1) There has been a significant improvement in basic methods such as ER and DER++, as these two methods adopt more basic methods for sampling. Our method can reduce the bias caused by the sampling process to a certain extent. 2) Our methods have also shown some effectiveness on X-DER and ER-ACE, which take additional measures to alleviate sample imbalance and improve sample utilization, resulting in improved model performance. Our method further enhances the model's capabilities on top of this.
+
+To further demonstrate the effectiveness of our method, we compare our method with other regularization methods, and it can be found that we achieve the best performance, recent methods such as OCM, LiDER and DualHSIC achieve significant progress compared to baseline when the number of buffer is small, and our method further improves the performance when the buffer data is small by considering modeling for the unsampled data.
+
+# 4.6 Ablation Study
+
+In order to understand the effect of each of the items in the loss function on the performance of the algorithm, an ablation study has been carried out and the
+
+![](images/e17b5e35974228cf5ec5776a2af0dda49e6c658d92ad831dc2a12a503c651496.jpg)  
+Fig. 4: This figure shows the CKA matrix based on the ER algorithm, FT and incorporating our algorithm. It can be observed from it that due to our modeling of unsampled data, the model shows more information about the old task.
+
+![](images/6c4cc5c7089bf47269767d347ffd7406f8ca2b259b93520de11a4d1a7be87f2c.jpg)
+
+![](images/305984db984788dc1f90a3b3b41fd0744b949396a47aee300cf03cb7baf59ca2.jpg)
+
+results are shown in Table 3. It is observed that in most of the cases, increasing any of the components has an impact on the performance of the algorithm. However, increasing the IBDS gives a large performance improvement, which indicates that it plays a vital role in the performance of the algorithm. This component represents the loss of substitution of unsampled data, which is necessary for training on new tasks using unsampled data features. Therefore, if this aspect is not well learned, it may negatively affect the subsequent performance of the algorithm. IBTA also has an impact on the performance of the algorithm, the involves regularization constraints on the input features in order to make the model learn enough robust features.
+
+# 5 Characteristic Analysis
+
+We analyze various characteristics of the model to gain insight into the factors contributing to the performance enhancements achieved by our approach.
+
+# 5.1 CKA Matrix Analysis
+
+We use Central Kernel Alignment (CKA) [26] in Fig.4, which is an effective tool to measure the similarity of network representations and evaluate the relationships between these backbones. We send the same batch of instances to the ER (2000 buffer size) algorithm model and fine-tuning based model respectively to obtain corresponding feature maps, thus intuitively demonstrating the similarity of algorithm feature maps. Our algorithm can be used in conjunction with the experience replay method to model unsampled data. When the sampled data is 0, i.e. fine-tuning, our method can also get some benefits.
+
+![](images/f776ee0a368bf83264a3019df57278fd23a062b9eca311ea385184ae50334934.jpg)  
+Initialization
+
+![](images/9deb011b3e4c1988a3809b8798e4c7015966b38b5352829e6520b0359a26812f.jpg)  
+Epoch  $= 20$  
+Fig. 5: This image uses TSNE to display the changes in the characteristics of sampled and unsampled data with the number of training epochs of the model. We have shown one class of situation, with a sample data size of 200 and an unsampled data size of 1100.
+
+![](images/e3e5fdfec78084223105586c8257c1a5fb7c74e63c28ad3d3144c282a36632b5.jpg)  
+Epoch  $= 50$
+
+# 5.2 Feature Decoupling Analysis
+
+A significant advance of our method is the decoupling of sampled and unsampled data features. We demonstrate this in Fig.5, where we use TSNE technology to visualize the changes in these two features with the increase of network training epochs. We test our method, the ER algorithm, on 200 sampled data and 1100 unsampled data from the ImageNet-100 dataset. As the network training epochs increase, we can observe that the two sets of features begin to separate from their initial coupling, which indicates that our method has achieved decoupling of the two data.
+
+# 6 Conclusion
+
+In conclusion, our proposed method is designed to tackle the issue of data bias in continual learning through the application of experience replay. Drawing inspiration from information bottleneck theory, we steer the incorporation of unsampled data information, thereby bolstering the model's capacity to preserve past knowledge while accommodating novel tasks. Our conducted experiments offer empirical validation of the advantages conferred by our approach. While we have presented a method for computing unsampled data, it's important to acknowledge the existence of several alternative strategies for estimating these. This opens up exciting possibilities for continued exploration and innovation in this field.
+
+# Acknowledgements
+
+This work was supported by National Science and Technology Major Project, Grant No.2022ZD0116403, the Youth Innovation Promotion Association CAS and Strategic Priority Research Program of Chinese Academy of Sciences XDA27010300.
+
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+        "text": "InsMapper: Exploring Inner-instance Information for Vectorized HD Mapping",
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+        "type": "text",
+        "text": "Zhenhua Xu Kwan-Yee K. Wong Hengshuang Zhao\\*",
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+        "text": "The University of Hong Kong",
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+        "text": "Project webpage: https://tonyxuqq.github.io/InsMapper",
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+        "text": "Abstract. Vectorized high-definition (HD) maps contain detailed information about surrounding road elements, which are crucial for various downstream tasks in modern autonomous vehicles, such as motion planning and vehicle control. Recent works attempt to directly detect the vectorized HD map as a point set prediction task, achieving notable detection performance improvements. However, these methods usually overlook and fail to analyze the important inner-instance correlations between predicted points, impeding further advancements. To address this issue, we investigate the utilization of inner-instance information for vectorized high-definition mapping through transformers, and propose a powerful system named InsMapper, which effectively harnesses inner-instance information with three exquisite designs, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules can better initialize queries for line detection, while the last one refines predicted line instances. InsMapper is highly adaptable and can be seamlessly modified to align with the most recent HD map detection frameworks. Extensive experimental evaluations are conducted on the challenging NuScenes and Argovverse 2 datasets, where InsMapper surpasses the previous state-of-the-art method, demonstrating its effectiveness and generality.",
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+        "type": "text",
+        "text": "Keywords: Autonomous Driving  $\\cdot$  High-definition Map",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
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+        "type": "text",
+        "text": "Vectorized high-definition maps (HD maps) play a critical role in today's autonomous vehicles [6, 23, 27], as they contain detailed information about the road, including the position of road elements (e.g., road boundaries, lane splits, pedestrian crossings, and lane centerlines), connectivity, and topology of the road. Without the assistance of HD maps for perceiving and understanding road elements, unexpected vehicle behaviors may be encountered, such as incorrect path planning results or even vehicle collisions.",
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+    {
+        "type": "text",
+        "text": "Typically, HD maps are created by offline human annotation, which is labor-intensive, inefficient, and expensive. Although there are works proposing to make",
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+    {
+        "type": "page_footnote",
+        "text": "* Corresponding author.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "such an offline process automatic [38, 40, 41], it is not possible to recreate and update the HD map frequently when the road has been modified, such as when a new road is built or an existing road is removed. To address this issue, several recent studies propose to detect local HD maps using an online method [7, 20, 24, 25, 27, 32]. This paper aims to further investigate online HD map detection techniques based on vehicle-mounted sensors (i.e., cameras and LiDARs).",
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+        "text": "Early online HD map detection works consider road element mapping as a semantic segmentation task in bird's-eye view (BEV) [22,30,31], in which road elements are predicted in raster format (i.e., pixel-level semantic segmentation mask). However, rasterized road maps cannot be effectively utilized by downstream tasks of autonomous vehicles, such as motion planning and vehicle control [23,26,27]. Moreover, it is challenging to distinguish instances from the rasterized map, especially when some road elements overlap with each other or when a complicated topology is encountered (e.g., road split or road intersections).",
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+        "type": "text",
+        "text": "To alleviate these problems, HDMap-",
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+    {
+        "type": "text",
+        "text": "Net [20] proposes hand-crafted post-processing algorithms to better obtain road element instances for vectorized HD maps. However, HDMapNet still heavily relies on rasterized results, restricting it from handling complicated urban scenes. Recently, some works have resorted to predicting vectorized HD maps directly [3,24,27,35]. A two-stage hierarchical set prediction method is proposed in VectorMapNet [27]. After predicting key points of road elements in the HD map, VectorMapNet sequentially generates intermediate points. Although VectorMapNet is considered to be the first online vectorized HD map detection work, the sequential operation degrades its efficiency and model performance. MapTR [24] further proposes to use DETR [5, 46] for vectorized HD map detection as a point set prediction problem, and the output point sets are then",
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+        "image_caption": [
+            "Fig.1: Comparison of vectorized HD map detection methods. All solutions are evaluated on the NuScenes validation set. The x-axis represents the mAP results and the y-axis displays topology level correctness [13]. InsMapper is flexible and adaptable, so it can be seamlessly modified to align with multiple existing frameworks. InsMapper is built on MapTR [24].  $\\dagger$  means InsMapper based on more recent framework PivotNet [7], while  $\\ddagger$  indicates InsMapper based on previous SOTA, MapTR-V2 [25]."
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+    {
+        "type": "text",
+        "text": "grouped into road element instances. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance, but it overlooks and fails to utilize the essential inner-instance correlations between points to further boost the performance.",
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+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we focus on investigating the utilization of inner-instance information for vectorized high-definition mapping via transformer, and propose a new framework named InsMapper, which can utilize inner-instance point information for improved online HD map detection via three exquisite designs. First, a hybrid query generation module is introduced to better initialize queries for detection. Then, an inner-instance query fusion module is added before the transformer decoder, which fuses inner-instance object queries to refine the initialized line instances. Finally, a transformer-based inner-instance aggregation module is incorporated to further refine the predicted lines. Extensive experimental evaluations are conducted on the popular and challenging NuScenes [2] and Argoverse 2 [37] datasets. InsMapper is based on MapTR [24], and it can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. No matter what the base framework is, InsMapper harvests state-of-the-art performance, surpassing the previous highest solutions. The intuitive performance comparisons are illustrated in Figure 1, and our main contributions can be summarized as follows:",
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+            "- We analyze the limitations of existing HD map detection algorithms and propose a new framework named InsMapper, which can effectively utilize the easily overlooked inner-instance point correlation information for accurate and generalizable online HD map detection.",
+            "- We incorporate three useful modules to leverage inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules better initialize queries for detection and the last one refines detected line instances.",
+            "- We conduct experiments on the challenging NuScenes and Argoverse 2 datasets. InsMapper outperforms all baselines by a large margin. The achieved state-of-the-art results demonstrate its effectiveness and generality."
+        ],
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+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Vector map detection. Vector maps use vectors to represent road elements, such as road networks, road curbs, and lane lines. A high-definition map (HD map) is a type of vector map, but a vector map may not qualify as an HD map if it lacks sufficient resolution or fails to provide lane-level information, among other factors. Online HD map detection can benefit from insights gained from a broader scope of vector map detection works, including road-network detection [1,14,39, 41], road-curb detection in aerial images [42, 43], and road lane line detection [15, 16], etc. DagMapper [16] aims to detect vectorized lane lines from pre-built point cloud maps using iterations. However, DagMapper only handles simple topology changes of lane lines and struggles to handle complex road intersections. RNGDet++ [41] applies DETR along with an imitation learning algorithm [34] for road-network detection, achieving state-of-the-art performance on multiple datasets. Although these methods achieve satisfactory graph detection accuracy, they suffer from poor efficiency due to their iterative algorithms. Given the",
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+        "page_idx": 2
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+    {
+        "type": "header",
+        "text": "InsMapper",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "stringent real-time requirements of autonomous vehicles, they are not suitable for online HD map detection.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "HD map detection. HD map detection was initially a subtask of BEV detection [21, 22, 28, 30, 31]. Recently, given the importance of HD maps, several works have directly focused on HD map detection [4, 20, 24, 27, 29, 33, 35, 38, 40]. However, most of these works either involve offline HD map creation [12, 38, 40] or only detect one specific road element [3, 4, 33]. HDMapNet [20] is considered to be the first work specifically designed for multiple road element detection. However, HDMapNet outputs rasterized results, requiring complicated handcrafted post-processing to obtain vectorized HD maps. To address this issue, VectorMapNet [27] is believed to be the first work detecting vectorized HD maps in real-time. However, it consists of two stages, and its efficiency is significantly impacted by sequential operations. In contrast, MapTR [24] uses deformable DETR [46] to design an end-to-end vectorized HD map detection model, which greatly simplifies the pipeline and delivers better detection performance. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance on vectorized HD map detection, but it still overlooks and does not investigate the inner-instance correlations between points, limiting further improvements.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Detection by Transformer. DETR [5] is the first end-to-end transformer-based object detection framework. Compared with previous CNN-based methods [8, 10], DETR removes the need for anchor proposals and non-maximum suppression (NMS), making it simpler and more effective. To address the issue of slow convergence, subsequent works propose accelerating DETR training through deformable attention [46], denoising [18], and dynamic query generation [19, 36, 45]. Intuitively, most of these DETR refinements could be adapted to the HD map detection task since our proposed InsMapper relies on DETR. However, unlike typical object detection tasks in which objects are assumed to be independent and identically distributed (i.i.d.), detected points in HD maps have strong correlations, especially among inner-instance points. This inherent difference makes some refined DETR methods unsuitable to our task and additional investigations are required.",
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+    {
+        "type": "text",
+        "text": "3 Point Correlation",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "3.1 Vector Map Decomposition and Sampling",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Let  $G$  denote the original vector map label of the scene, which consists of vertices  $V$  and edges  $E$ . The vector map contains multiple classes of road elements, including pedestrian crossings, road dividers, road boundaries, and lane centerlines. Among them, the first three classes of road elements are simple polylines or polygons without intersection points. While lane centerlines have more complicated topology, such as lane split, lane merge, and lane intersection. To unify all vector elements, the vector map is decomposed into simpler shapes (i.e., polylines and polygons) without intersections. Any vertices in the vector map with degrees larger than two (i.e., intersection vertices) are removed from  $G$ , but",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "incident edges are kept. In this way, a set of simple polylines and polygons without intersections is obtained as  $G^{*} = \\{l_{i}\\}_{i=1}^{N^{*}}$ , where  $G^{*}$  is an undirected graph. Each shape  $l_{i}$  is defined as an instance, and  $N^{*}$  denotes the overall number of instances in a vector map.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following MapTR and MapTR-V2, to enhance the parallelization capacity of the model, each instance is evenly re-sampled with fixed-length points as  $l_{i} = (v_{1},\\dots,v_{j},\\dots,v_{n_{p}})$ .  $l_{i}$  is ordered from  $v_{1}$  to  $v_{n_p}$ , with  $n_p$  being the number of sampled points for each instance. For polygon instances,  $v_{1}$  is equal to  $v_{n_p}$ . Please refer to the supplementary document for the visualization of the pre-processing.",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 Inner-instance Correlation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Unlike conventional object detection tasks, where objects can be approximated as independent and identically distributed (i.i.d.), strong correlations exist between points within the same line instance in the vectorized HD map detection task. Please refer to the supplementary document for the visualization of the point correlation.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inner-instance correlation is crucial for point coordinates prediction. Points within the same instance can collaborate by sharing inner-instance information, leading to smoother and more accurate predictions. Without this collaboration, points of the same instance may produce independent predictions, leading to zig-zag or incorrect instances. The inner-instance correlation can serve as additional constraints to facilitate the query initialization and refinement of predicted lines. In previous methods, the correlation of points is not correctly analyzed and leveraged, limiting further improvement. In subsequent sections, we introduce InsMapper to more effectively utilize point correlations and improve vectorized map detection performance.",
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+    {
+        "type": "text",
+        "text": "4 Methodology",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 Overall Framework",
+        "text_level": 1,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Building on MapTR [24], our proposed InsMapper is an end-to-end trainable framework for online vectorized HD map detection, as illustrated in Figure 2.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "InsMapper is adaptive and can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. Following BEVformer [22], InsMapper first projects perspective view camera images into the bird's-eye-view (BEV). After obtaining the BEV features, InsMapper uses deformable attention layers [46] to process input object queries. Each object query predicts one point, including the object class and the regression point position. To better leverage inner-instance information and further enhance the final detection performance, we introduce three designs in InsMapper: hybrid query generation, which replaces the hierarchical query in MapTR, generating line queries with better diversity; inner-instance query fusion, which fuses generated queries within the same instance based on",
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+    {
+        "type": "header",
+        "text": "InsMapper",
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+    {
+        "type": "page_number",
+        "text": "5",
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+    {
+        "type": "image",
+        "img_path": "images/153f5c94707310daf2c3f6a5c59eb2405a1a7953aa5e3a05b673c0fd415fe27b.jpg",
+        "image_caption": [
+            "Fig. 2: Overall framework. InsMapper is an end-to-end transformer model with an encoder-decoder structure. The transformer encoder projects perspective-view camera images into a bird's-eye view (BEV). Subsequently, the transformer decoder detects vector instances by predicting point sets. To enhance the utilization of inner-instance information, we introduce the following three components: a hybrid query generation scheme (orange module), an inner-instance query fusion module (yellow module), and an inner-instance feature aggregation module (blue module). The first two modules better initialize queries for detection and the final one refines detected line instances."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "inner-instance features to further enhance the quality of initialized line queries; and inner-instance feature aggregation, which adds a new inner-instance self-attention module to decoder layers to further aggregate inner-instance features for line refinement.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Different from past works, which treat queries as independently distributed, InsMapper utilizes inner-instance information to fuse object queries and aggregate intermediate features in deformable transformer decoder layers. Otherwise, adjacent vertices may produce independent position regression results, leading to zigzag or even incorrect instances. With the assistance of inner-instance information, the model can better initialize queries for detection and refine the positions of detected points within an instance, significantly enhancing the final performance, as demonstrated in the experiments section.",
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+    {
+        "type": "text",
+        "text": "4.2 Query Generation",
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+    {
+        "type": "text",
+        "text": "In contrast to traditional object detection tasks, where queries are independent and identically distributed (i.i.d.), the points to be detected in our task exhibit significant correlations. Various methods can be used to generate object queries as input for the transformer decoder, such as the basic scheme, hierar",
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+        "type": "page_number",
+        "text": "6",
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+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2b3026b0a16709faa46790e0f959aea1b377cf19f46caa56809a437cfd9980f5.jpg",
+        "image_caption": [
+            "Fig.3: Query generation schemes. For concise visualization, the number of instances  $N_{I}$  is 2, and the number of points per instance  $n_p$  is 3. The hybrid scheme can initialize lines with both good diversity and quality."
+        ],
+        "image_footnote": [],
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+    },
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+        "img_path": "images/d97ac786feed7392a30d050bc18f5bde601ec124e187d05874aa7cb4d95f00c7.jpg",
+        "image_caption": [
+            "(a) Basic"
+        ],
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+        "type": "image",
+        "img_path": "images/6f3776c816987d234da648677839b80c2689b13c85b31dc2f64d3b1f91713c44.jpg",
+        "image_caption": [
+            "(b) Hierarchical"
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a87f30e0e3d703d02d5300a33ffccd98957e6509fe176317d56eef30638cf4dd.jpg",
+        "image_caption": [
+            "(c) Hybrid",
+            "Fig. 4: Visualization of initialized lines with different query generation schemes. The quality and diversity of initialized lines are crucial for the final performance. Each color represents one initialized line."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "chical scheme, and hybrid scheme. All query generation schemes are illustrated in Figure 3. Initialized queries are organized into line instances. The quality and diversity of the initialized lines are both crucial.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Basic query generation. This method is leveraged in the original DETR [5] for query generation. It assumes that points are i.i.d. and generates queries randomly, without utilizing inner-instance information. Let  $N_{I}$  denote the number of predicted instances, which is obviously larger than  $N^{*}$ . Since each instance contains  $n_p$  points, the basic object queries consist of  $N_{I} \\cdot n_{p}$  randomly generated i.i.d. queries, resulting in irregular line shapes. Due to the lack of constraints on inner-instance points, the initialized line instances are noisy and have poor quality, which leads to degraded performance. MapTR with the basic query scheme is visualized in Figure 4a.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Hierarchical query generation. To address the aforementioned issue of the basic scheme, a hierarchical query generation scheme is proposed in MapTR [24] and MapTR-V2 [25]. Let  $Q_{ins} = \\{q_i^I\\}_{i=1}^{N_I}$  denote instance queries and  $Q_{pts} = \\{q_j^P\\}_{j=1}^{n_p}$  denote point queries. The object queries for HD map detection are then the pairwise addition of  $Q_{ins}$  and  $Q_{pts}$ :",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ = \\left\\{q _ {i, j} = q _ {i} ^ {I} + q _ {j} ^ {P} \\mid q _ {i} ^ {I} \\in Q _ {\\text {i n s}}, q _ {j} ^ {P} \\in Q _ {\\text {p t s}} \\right\\}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            672,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $|Q| = |Q_{ins}| \\cdot |Q_{pts}| = N_I \\cdot n_p$ . For each line instance  $i$ , the instance query  $q_i^I$  denotes its uniqueness. By using  $q_i^I$  as a bridge, object queries within the same instance can better collaborate with each other for point prediction. But all line instances share the same point queries so all initialized lines tend to have quite similar shapes, degrading initialization diversity, which harms the final detection performance. The initialized lines generated by MapTR with the hierarchical query scheme are visualized in Figure 4b.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Hybrid query generation. The basic scheme does not take into account any information exchange between queries, whereas the hierarchical one generates",
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+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "InsMapper",
+        "bbox": [
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+            128
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "repetitive line shapes. To address these issues, this paper presents a hybrid query generation method that mitigates the drawbacks of the aforementioned schemes while maintaining appropriate inner-instance information exchange.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Let the instance queries be  $Q_{ins} = \\{q_i^I\\}_{i=1}^{N_I}$ , and the point queries be  $Q_{pts} = \\{q_j^P\\}_{j=1}^{N_P} = \\{q_j^P\\}_{j=1}^{N_I \\cdot n_p}$ . The point queries are divided into  $N_I$  instance groups, and a point query  $q_j^P$  is assigned to the  $\\lceil \\frac{j}{n_p} \\rceil$ -th instance. Consequently, the final object query is the sum of a point query  $p_j^P$  and its assigned instance query  $p_k^I$ , where  $k = \\lceil \\frac{j}{n_p} \\rceil$ . The object query set can be expressed as:",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ = \\left\\{q _ {k} ^ {I} + q _ {j} ^ {P} \\mid q _ {j} ^ {P} \\in Q _ {p t s} \\right\\} \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where  $|Q| = |Q_{pts}| = N_P = N_I \\cdot n_p$ . In contrast to the hierarchical scheme, each point query in the hybrid scheme is utilized only once to generate the object query, thereby preventing repetitive line shapes. Simultaneously, point queries belonging to the same instance are summed with a shared instance query, establishing the inner-instance connection. The hybrid query generation method can be considered as a combination of the basic and hierarchical schemes, effectively mitigating their respective drawbacks. InsMapper with the hybrid query generation scheme is visualized in Figure 4c.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 Inner-instance Query Fusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The input object queries for the transformer decoder are generated from instance queries and point queries. Although the generated queries can leverage some inner-instance information, this information exchange is indirect and inflexible. The instance query is distributed equally among all inner-instance points, while a more precise point-to-point information exchange cannot be realized. As a result, a query fusion module is introduced to further utilize inner-instance information and refine initialized lines.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Let  $Q_{i} = \\{q_{i,j}\\}_{j=1}^{n_{p}}$  represent the set of object queries belonging to the  $i$ -th instance, and  $q_{i,j}$  denote the  $j$ -th point of the  $i$ -th instance.  $q_{i,j}$  is correlated with all other queries in  $Q_{i}$ . To better fuse inner-instance object queries, each query is updated by a weighted sum of all queries in  $Q_{i}$  as:",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nq _ {i, j} = f \\left(q _ {i, j}, Q _ {i}\\right) = \\sum_ {k = 1} ^ {n _ {p}} w _ {i, j, k} \\phi \\left(q _ {i, k}\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where  $w_{i,j,k}$  demonstrates weights for query fusion.  $f(\\cdot)$  is the fusion function and  $\\phi(\\cdot)$  is the kernel in case nonlinear transformation is needed.  $f(\\cdot)$  could be realized by handcraft weights, fully connected layers, or self-attention. In this work, self-attention is applied as  $f(\\cdot)$ .",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In conventional object detection tasks, object queries are assumed to be independent and identically distributed (i.i.d.), making query fusion unnecessary. However, in the task of HD map detection, the query fusion module effectively aligns the update of queries and enables each point to pay more attention to",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "page_number",
+        "text": "8",
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+        "page_idx": 7
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+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
+            271,
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+            127
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/69c49678df6c7cb8472dd3c690821fde218551d962898247891c2624b3127a37.jpg",
+        "image_caption": [
+            "(a) No fusion"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            225,
+            167,
+            330,
+            325
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/2e3e38d7b3ab1a38ad9f0535c2ec7191e14301154bec10b5aeda39e1526c2965.jpg",
+        "image_caption": [
+            "(b) With fusion"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            352,
+            170,
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+            321
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/4d4a9fcfdb1c5a3058a2349065c04ff2c1c0f86f45216eb70bddfbebe100d8c9.jpg",
+        "image_caption": [
+            "Fig.5: Visualization of the effect of the inner-instance query fusion module. (a) No query fusion. (b) With query fusion. The query fusion module can better refine the initialized lines based on inner-instance information. In this example, the proposed query fusion module significantly enhances the diversity of initialized line instances.",
+            "Fig.6: Decoder of InsMapper. An inner-instance multi-head self-attention module is incorporated into decoder layers. In this module, the attention between points belonging to different instances is blocked (grey grids). Only inner-instance attention is allowed (colored grids). Colored grids are randomly blocked with  $\\epsilon$  probability (set to grey) for robustness. The proposed module can further utilize inner-instance information and refine the predicted lines."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "neighboring points. It can greatly refine the initialized lines for better query initialization, leading to enhanced performance. Without this module, queries within the same instance cannot be aware of each other, rendering them \"blind\". Poor line initialization tends to have degraded detection scores. The effect of the query fusion module is visualized in Figure 5.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4 Inner-instance Feature Aggregation",
+        "text_level": 1,
+        "bbox": [
+            215,
+            630,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In addition to object query manipulation, InsMapper performs inner-instance feature aggregation for predicted line refinement in the transformer decoder layers by incorporating an additional inner-instance self-attention module. Inspired by [9], inner-instance attentions are randomly blocked with probability  $\\epsilon$  for robustness. The decoder layer of InsMapper is depicted in Figure 6.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The inner-instance self-attention module resembles the original self-attention module but features a specially designed attention mask. As illustrated in Figure 6, the attention mask of inner-instance points is set to zero (colored grids), indicating that attention between points within the same instance is allowed. Conversely, for points belonging to different instances (i.e., inter-instance points), the corresponding attention mask values are set to one, blocking attention between them. This method encourages the model to focus more on inner-instance",
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+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "InsMapper",
+        "bbox": [
+            656,
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+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "information, resulting in more consistent predictions. To further enhance the robustness of this module, the inner-instance attention (colored grids) has an  $e$  probability of being blocked.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "An alternative method involves placing the proposed inner-instance attention module before the cross-attention module. However, the self-attention module before cross-attention should not block inter-instance information. Otherwise, some instances may produce duplicate predictions since they cannot \"clearly see\" other instances, which is analyzed in the original DETR [5]. Consequently, implementing inner-instance self attention before the cross-attention module leads to degraded final performance. Thus the proposed inner-instance feature aggregation should be placed after the cross-attention layer. More experiments about the decoder structure are provided in the appendix.",
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5 Experiments",
+        "text_level": 1,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5.1 Experimental Setup",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Datasets. Extensive experiments are conducted on the popular and challenging NuScenes dataset [2] and the Argoverse 2 dataset [37]. These two datasets comprise hundreds of data sequences captured in various autonomous driving scenarios, encompassing diverse weather conditions and time periods. The perception range for the X-axis and Y-axis in the BEV is set to  $[-15m, 15m]$  and  $[-30m, 30m]$ , respectively. The detected vectorized HD map should encompass four types of road elements simultaneously: road boundary, lane split, pedestrian crossing, and lane centerline. Among these, the lane centerline is a crucial element for ensuring effective vehicle planning and control. Detecting lane centerlines poses greater difficulty compared to the other three elements.",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. We perform all the experiments on a machine equipped with 8 RTX-3090 GPUs. During the training phase, all GPUs are utilized, whereas only a single GPU is employed for inference. For our proposed InsMapper, we adopt multiple settings akin to the previous SOTA method, MapTR. All ablation studies are conducted for 24 epochs, with ResNet50 [11] as the backbone. For a fair comparison, except for the proposed modules, we keep the experiment settings exactly the same, such as batch size, network depth, the number of input queries, etc.",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. Models are assessed using two types of metrics. The first metric, average precision (AP), gauges the instance-level detection performance, employing Chamfer distance for matching predictions with ground truth labels. To ensure a fair comparison, we follow previous works to calculate multiple  $\\mathrm{AP}_{\\tau}$  values with  $\\tau \\in \\{0.5, 1.0, 1.5\\}$ , and report the average AP. To measure the topology correctness, the metric TOPO that is widely used in past works [12-14, 41] is reported. For all metrics, a larger value indicates better performance.",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "5.2 Performance Comparison",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare InsMapper with previous state-of-the-art methods using the aforementioned evaluation metrics. The quantitative comparison results",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
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+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
+            271,
+            114,
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+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/a30545cd2c236ff090daae4d43839ad4307e0255bd42faec8e4409d65afc3c0b.jpg",
+        "table_caption": [
+            "Table 1: Quantitative results of comparison experiments on the NuScenes validation set. Colored numbers show differences between InsMapper and the SOTA baseline under the same experiment setting. \"C\" and \"L\" denote camera and LiDAR, respectively. \"-\" denotes that the result is not available. \"V2-99\" and \"Sec\" correspond to VoVNetV2-99 [17] and SECOND [44].  $\\dagger$  represents InsMapper based on PivotNet [7],  $\\ddagger$  indicates InsMapper based on MapTR-V2 [25]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\\(AP_{ped}\\)</td><td>\\(AP_{div}\\)</td><td>\\(AP_{bound}\\)</td><td>\\(AP_{center}\\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>HDMapNet</td><td>30</td><td>Effi-B0</td><td>C</td><td>4.41</td><td>23.73</td><td>58.17</td><td>37.29</td><td>30.90</td><td>29.79</td></tr><tr><td>STSU</td><td>110</td><td>R50</td><td>C</td><td>-</td><td>-</td><td>-</td><td>31.21</td><td>31.21</td><td>32.11</td></tr><tr><td>VectorMapNet</td><td>130</td><td>R50</td><td>C</td><td>28.66</td><td>39.74</td><td>33.06</td><td>34.93</td><td>34.10</td><td>39.90</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.92</td><td>46.25</td><td>50.07</td><td>37.47</td><td>42.93</td><td>46.77</td></tr><tr><td>MapTR</td><td>24</td><td>V2-99</td><td>C</td><td>44.57</td><td>56.25</td><td>60.58</td><td>46.30</td><td>51.92</td><td>55.16</td></tr><tr><td>MapTR</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>49.47</td><td>58.98</td><td>66.72</td><td>44.89</td><td>55.01</td><td>56.77</td></tr><tr><td>MapTR</td><td>110</td><td>R50</td><td>C</td><td>49.16</td><td>59.12</td><td>58.93</td><td>47.26</td><td>53.62</td><td>59.16</td></tr><tr><td>BeMapNet</td><td>24</td><td>R50</td><td>C</td><td>43.59</td><td>54.11</td><td>51.90</td><td>38.60</td><td>47.05</td><td>49.90</td></tr><tr><td>PivotNet</td><td>24</td><td>R50</td><td>C</td><td>42.73</td><td>53.55</td><td>52.01</td><td>42.47</td><td>47.69</td><td>51.04</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>48.20</td><td>54.75</td><td>56.66</td><td>45.86</td><td>51.37</td><td>51.15</td></tr><tr><td>MapTR-V2</td><td>110</td><td>R50</td><td>C</td><td>58.68</td><td>65.72</td><td>67.12</td><td>56.16</td><td>61.92</td><td>63.26</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>44.36</td><td>53.36</td><td>52.77</td><td>42.35</td><td>48.31</td><td>51.58</td></tr><tr><td>InsMapper</td><td>24</td><td>V2-99</td><td>C</td><td>51.16</td><td>63.71</td><td>64.47</td><td>51.40</td><td>57.68</td><td>60.00</td></tr><tr><td>InsMapper</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>56.00</td><td>63.42</td><td>71.61</td><td>52.85</td><td>60.97</td><td>62.51</td></tr><tr><td>InsMapper</td><td>110</td><td>R50</td><td>C</td><td>55.42</td><td>63.87</td><td>65.80</td><td>54.20</td><td>59.40</td><td>66.19</td></tr><tr><td>InsMapper†</td><td>24</td><td>R50</td><td>C</td><td>46.45</td><td>54.91</td><td>54.16</td><td>45.20</td><td>50.18</td><td>53.57</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>49.07</td><td>57.98</td><td>59.84</td><td>47.99</td><td>53.72</td><td>53.00</td></tr><tr><td>InsMapper†</td><td>110</td><td>R50</td><td>C</td><td>62.09</td><td>67.60</td><td>68.15</td><td>58.41</td><td>64.06</td><td>64.72</td></tr></table>",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/ff2567bdaeeaa76a643da0e4ac71e86aea9f272153d40971038885f6761e9c3c.jpg",
+        "table_caption": [
+            "Table 2: Quantitative results of comparison experiments on the Argoverse 2 validation set.  $\\ddagger$  indicates InsMapper based on MapTR-V2 [25]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>APcenter</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>6</td><td>R50</td><td>C</td><td>52.88</td><td>63.68</td><td>61.18</td><td>59.73</td><td>59.37</td><td>75.79</td></tr><tr><td>MapTR-V2</td><td>6</td><td>R50</td><td>C</td><td>57.16</td><td>67.96</td><td>65.25</td><td>63.20</td><td>63.39</td><td>77.94</td></tr><tr><td>InsMapper</td><td>6</td><td>R50</td><td>C</td><td>55.61</td><td>66.60</td><td>62.58</td><td>62.67</td><td>61.87</td><td>77.58</td></tr><tr><td>InsMapper†</td><td>6</td><td>R50</td><td>C</td><td>58.91</td><td>71.35</td><td>66.90</td><td>64.70</td><td>65.46</td><td>79.26</td></tr></table>",
+        "bbox": [
+            215,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/c9cf344cd196342bce229d65f7d6e60b5be68877b7c5f8f400aff0974a95c1ab.jpg",
+        "table_caption": [
+            "Table 3: Quantitative results of comparison experiments on the NuScenes validation set without centerline.  $\\ddagger$  indicates InsMapper based on MapTR-V2 [25]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>mAP</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>46.04</td><td>51.58</td><td>53.08</td><td>50.23</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>59.80</td><td>62.40</td><td>62.40</td><td>61.50</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>48.44</td><td>54.68</td><td>56.92</td><td>53.35</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>61.54</td><td>65.09</td><td>64.62</td><td>63.75</td></tr></table>",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "are reported in Table 1. InsMapper is flexible and adaptive, making it seamless to modify it based on existing transformer frameworks. InsMapper is built on MapTR for experiments, we also report the results of InsMapper with different base frameworks, e.g. InsMapper† is based on PivotNet [7] and InsMapper‡ relies on the previous SOTA method MapTR-V2 [25]. Compared to the previous methods, InsMapper improves the AP of all road elements by around 2. The topological metric also sees an improvement of around 1.5. The inference FPS of",
+        "bbox": [
+            212,
+            734,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "header",
+        "text": "InsMapper",
+        "bbox": [
+            656,
+            114,
+            730,
+            128
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
+        "bbox": [
+            767,
+            114,
+            782,
+            126
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/e4dd68f52ddfa6eba12b27b688195bd1fd82907b204c2b159d06cf9d783dc2dc.jpg",
+        "table_caption": [
+            "Table 4: Quantitative results of comparison experiments on the NuScenes validation set. Centerlines are directed graphs in this table.  $\\ddagger$  indicates InsMapper based on MapTR-V2 [25]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\\(AP_{ped}\\)</td><td>\\(AP_{div}\\)</td><td>\\(AP_{bound}\\)</td><td>\\(AP_{center}\\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.39</td><td>46.61</td><td>50.69</td><td>37.22</td><td>42.98</td><td>46.98</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>49.53</td><td>55.46</td><td>58.48</td><td>53.82</td><td>54.32</td><td>54.90</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>43.24</td><td>53.77</td><td>53.89</td><td>43.22</td><td>48.53</td><td>52.09</td></tr><tr><td>\\(InsMapper^{\\dagger}\\)</td><td>24</td><td>R50</td><td>C</td><td>51.62</td><td>57.88</td><td>60.90</td><td>56.52</td><td>56.73</td><td>56.01</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "MapTR and InsMapper are 8.5 and 7.5, respectively. The evaluation outcomes on the Argoverse 2 dataset [37] can be found in Table 2. InsMapper outperforms past works with notable enhancements. Table 3 presents the results without centerlines. InsMapper with different bases attains an improvement of more than  $2\\mathrm{mAP}$ . In the aforementioned experiments, all road elements are treated as undirected graphs. Table 4 shows the results when centerlines are represented as directed graphs. Based on the results, InsMapper still presents superior results than past works for directed HD map detection. Furthermore, we illustrate the qualitative visualizations in Figure 7. Owing to the effective employment of inner-instance information, InsMapper generates smoother and more precise HD maps compared to previous works.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Consequently, InsMapper demonstrates superior performance compared to prior approaches across multiple datasets, exhibiting outstanding detection outcomes. Concurrently, InsMapper maintains a comparable inference speed to the previous state-of-the-art method. These exceptional experimental results strongly demonstrate the effectiveness and generality of the proposed designs.",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "5.3 Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Key component designs. We conduct several ablation study experiments to confirm the necessity of the proposed modules. Initially, we incorporate these modules into the previous state-of-the-art baseline model incrementally, and the results are presented in Table 5. It is evident that all three modules contribute to performance improvements, thereby validating their necessity. To further investigate the impact of each module's design, we perform comprehensive ablation studies in the following paragraphs.",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Hybrid query generation. Compared to basic or hierarchical query generation schemes, the proposed hybrid query generation scheme generates queries with better quality and diversity, due to effectively utilizing inner-instance correlation. The evaluation results of the different query generation schemes are presented in Table 6. These results reveal that the hybrid query generation scheme outperforms its counterparts, thereby demonstrating the soundness of this design.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Inner-instance query fusion. Query fusion is proposed to leverage the correlation between inner-instance queries to enhance prediction performance. Various methods can be employed for fusing queries, including mean fusing (i.e.,",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "page_number",
+        "text": "12",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
+            271,
+            114,
+            349,
+            126
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/9e81c143736942d0d6a4bb29a6b7d0ab832ae314d6a85d767761e8c8af2a39bd.jpg",
+        "image_caption": [
+            "Fig. 7: Qualitative visualization. The predicted map contains four classes, i.e., road boundaries (green), lane splits (red), pedestrian crossing (blue), and lane centerlines (pink). InsMapper presents better detection results compared with the past work."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            217,
+            143,
+            571,
+            558
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/503858f18474dde558d326dc82abed08358b72a575badea6db98b137a2268064.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "each query is summed with the mean of all queries of the same instance), fusion by the feed-forward network, and fusion by self-attention. The evaluation results are presented in Table 7. The outcomes of the query fusion methods vary significantly, with self-attention-based query fusion achieving the best results. Consequently, self-attention query fusion is incorporated into InsMapper.",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Inner-instance feature aggregation. In InsMapper, the inner-instance self-attention module is incorporated into the decoder layers following the cross-attention module. We evaluate InsMapper under four different conditions: without the inner-instance self-attention module (no attention), replace the inner-instance self-attention module with a vanilla self-attention module (vanilla attention), without the random blocking (no random blocking, i.e.,  $\\epsilon = 0$ ), and with the module placed before the cross-attention (change position). The results are shown in Table 8. The outcomes reveal that removing or altering the proposed",
+        "bbox": [
+            212,
+            719,
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+            840
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "header",
+        "text": "InsMapper",
+        "bbox": [
+            656,
+            114,
+            730,
+            128
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "page_number",
+        "text": "13",
+        "bbox": [
+            767,
+            114,
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+            126
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/e76427544833258e5817c6b9646dc499e0eff9fb340dd6cda978a54ee2d6b268.jpg",
+        "table_caption": [
+            "Table 5: Ablation studies on key component designs. \"QG\", \"QF\" and \"FA\" represent hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>QG</td><td>QF</td><td>FA</td><td>mAP</td><td>TOPO</td></tr><tr><td></td><td></td><td></td><td>42.93</td><td>46.77</td></tr><tr><td>✓</td><td>✓</td><td></td><td>45.42(↑2.49)</td><td>49.19(↑2.42)</td></tr><tr><td>✓</td><td></td><td>✓</td><td>45.45(↑2.52)</td><td>48.54(↑1.77)</td></tr><tr><td></td><td>✓</td><td>✓</td><td>46.93(↑4.00)</td><td>50.16(↑3.39)</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>48.31(↑5.38)</td><td>51.58(↑4.81)</td></tr></table>",
+        "bbox": [
+            218,
+            226,
+            488,
+            325
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/3d6ac60e8cc309f99b6c5c8c3caaa76cf6819ecd289a029b00aa3a6401118bff.jpg",
+        "table_caption": [
+            "Table 6: Ablation studies on inner-instance query generation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Query Scheme</td><td>mAP</td><td>TOPO</td></tr><tr><td>InsMapper-basic</td><td>46.62</td><td>49.39</td></tr><tr><td>InsMapper-hierarchical</td><td>46.93</td><td>50.16</td></tr><tr><td>InsMapper-hybrid</td><td>48.31</td><td>51.58</td></tr></table>",
+        "bbox": [
+            217,
+            364,
+            491,
+            438
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/60467ad1dcabcde060cf7384529273568e4ffcd11675ff327319086a3e8335c4.jpg",
+        "table_caption": [
+            "Table 7: Ablation studies on inner-instance query fusion."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Query Fusion</td><td>mAP</td><td>TOPO</td></tr><tr><td>No fusion</td><td>45.45</td><td>48.54</td></tr><tr><td>Mean</td><td>43.34</td><td>46.00</td></tr><tr><td>Feed-Forward</td><td>47.80</td><td>50.93</td></tr><tr><td>Self-attention</td><td>48.31</td><td>51.58</td></tr></table>",
+        "bbox": [
+            509,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/44be73fd04a7f1432fe73293e2e9318887cb5e9b550adfa2643f738220674af7.jpg",
+        "table_caption": [
+            "Table 8: Ablation studies on inner-instance feature aggregation. Multiple designs of the incorporated inner-instance self-attention layers are examined."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>mAP</td><td>TOPO</td></tr><tr><td>No attention</td><td>45.42</td><td>49.19</td></tr><tr><td>Vanilla attention</td><td>46.23</td><td>49.51</td></tr><tr><td>No random blocking</td><td>47.67</td><td>51.49</td></tr><tr><td>Change position</td><td>45.24</td><td>48.16</td></tr><tr><td>InsMapper</td><td>48.31</td><td>51.58</td></tr></table>",
+        "bbox": [
+            513,
+            338,
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+            436
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "module can impair model performance. This observation confirms the effectiveness of the proposed module design.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion",
+        "text_level": 1,
+        "bbox": [
+            215,
+            544,
+            359,
+            561
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduced InsMapper, an end-to-end transformer-based model for on-the-fly vectorized HD map detection. InsMapper surpasses previous works by effectively leveraging inner-instance information to improve detection outcomes. Three exquisite designs have been proposed to utilize inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules improve the quality of initialized line instances for detection, while the last module effectively refines the detected lines. The superiority of InsMapper is well exhibited through experiments on the challenging NuScenes and Argoverse 2 datasets. The evaluation results demonstrate the effectiveness and generality of InsMapper, making it a promising solution for the vectorized HD map detection task. In the future, InsMapper will be further enhanced for temporal-consistent vector map detection, making it more suitable for real-world applications.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. This work is supported by the National Natural Science Foundation of China (No. 62201484), HKU Startup Fund, and HKU Seed Fund for Basic Research.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "page_number",
+        "text": "14",
+        "bbox": [
+            217,
+            114,
+            235,
+            126
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "header",
+        "text": "Z. Xu et al.",
+        "bbox": [
+            271,
+            114,
+            351,
+            127
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            215,
+            143,
+            323,
+            159
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "2. Caesar, H., Bankiti, V., Lang, A.H., Vora, S., Liong, V.E., Xu, Q., Krishnan, A., Pan, Y., Baldan, G., Beijbom, O.: nuscenes: A multimodal dataset for autonomous driving. In: CVPR (2020) 3, 10",
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2024/InsMapper_ Exploring Inner-instance Information for Vectorized HD Mapping/703739e6-709f-487f-9515-53b438aabcdc_model.json

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+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "InsMapper: Exploring Inner-instance Information for Vectorized HD Mapping"
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+            "bbox": [
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+            "angle": 0,
+            "content": "Zhenhua Xu Kwan-Yee K. Wong Hengshuang Zhao\\*"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "The University of Hong Kong"
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+            "angle": 0,
+            "content": "Project webpage: https://tonyxuqq.github.io/InsMapper"
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+            "bbox": [
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+            "content": "Abstract. Vectorized high-definition (HD) maps contain detailed information about surrounding road elements, which are crucial for various downstream tasks in modern autonomous vehicles, such as motion planning and vehicle control. Recent works attempt to directly detect the vectorized HD map as a point set prediction task, achieving notable detection performance improvements. However, these methods usually overlook and fail to analyze the important inner-instance correlations between predicted points, impeding further advancements. To address this issue, we investigate the utilization of inner-instance information for vectorized high-definition mapping through transformers, and propose a powerful system named InsMapper, which effectively harnesses inner-instance information with three exquisite designs, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules can better initialize queries for line detection, while the last one refines predicted line instances. InsMapper is highly adaptable and can be seamlessly modified to align with the most recent HD map detection frameworks. Extensive experimental evaluations are conducted on the challenging NuScenes and Argovverse 2 datasets, where InsMapper surpasses the previous state-of-the-art method, demonstrating its effectiveness and generality."
+        },
+        {
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+            "angle": 0,
+            "content": "Keywords: Autonomous Driving \\(\\cdot\\) High-definition Map"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "1 Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Vectorized high-definition maps (HD maps) play a critical role in today's autonomous vehicles [6, 23, 27], as they contain detailed information about the road, including the position of road elements (e.g., road boundaries, lane splits, pedestrian crossings, and lane centerlines), connectivity, and topology of the road. Without the assistance of HD maps for perceiving and understanding road elements, unexpected vehicle behaviors may be encountered, such as incorrect path planning results or even vehicle collisions."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Typically, HD maps are created by offline human annotation, which is labor-intensive, inefficient, and expensive. Although there are works proposing to make"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "* Corresponding author."
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
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+                0.23,
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+            "angle": 0,
+            "content": "2"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
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+                0.352,
+                0.128
+            ],
+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.147,
+                0.788,
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+            ],
+            "angle": 0,
+            "content": "such an offline process automatic [38, 40, 41], it is not possible to recreate and update the HD map frequently when the road has been modified, such as when a new road is built or an existing road is removed. To address this issue, several recent studies propose to detect local HD maps using an online method [7, 20, 24, 25, 27, 32]. This paper aims to further investigate online HD map detection techniques based on vehicle-mounted sensors (i.e., cameras and LiDARs)."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Early online HD map detection works consider road element mapping as a semantic segmentation task in bird's-eye view (BEV) [22,30,31], in which road elements are predicted in raster format (i.e., pixel-level semantic segmentation mask). However, rasterized road maps cannot be effectively utilized by downstream tasks of autonomous vehicles, such as motion planning and vehicle control [23,26,27]. Moreover, it is challenging to distinguish instances from the rasterized map, especially when some road elements overlap with each other or when a complicated topology is encountered (e.g., road split or road intersections)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
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+            "angle": 0,
+            "content": "To alleviate these problems, HDMap-"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Net [20] proposes hand-crafted post-processing algorithms to better obtain road element instances for vectorized HD maps. However, HDMapNet still heavily relies on rasterized results, restricting it from handling complicated urban scenes. Recently, some works have resorted to predicting vectorized HD maps directly [3,24,27,35]. A two-stage hierarchical set prediction method is proposed in VectorMapNet [27]. After predicting key points of road elements in the HD map, VectorMapNet sequentially generates intermediate points. Although VectorMapNet is considered to be the first online vectorized HD map detection work, the sequential operation degrades its efficiency and model performance. MapTR [24] further proposes to use DETR [5, 46] for vectorized HD map detection as a point set prediction problem, and the output point sets are then"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Fig.1: Comparison of vectorized HD map detection methods. All solutions are evaluated on the NuScenes validation set. The x-axis represents the mAP results and the y-axis displays topology level correctness [13]. InsMapper is flexible and adaptable, so it can be seamlessly modified to align with multiple existing frameworks. InsMapper is built on MapTR [24]. \\(\\dagger\\) means InsMapper based on more recent framework PivotNet [7], while \\(\\ddagger\\) indicates InsMapper based on previous SOTA, MapTR-V2 [25]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.78,
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+            "angle": 0,
+            "content": "grouped into road element instances. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance, but it overlooks and fails to utilize the essential inner-instance correlations between points to further boost the performance."
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "InsMapper"
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+        {
+            "type": "page_number",
+            "bbox": [
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "In this work, we focus on investigating the utilization of inner-instance information for vectorized high-definition mapping via transformer, and propose a new framework named InsMapper, which can utilize inner-instance point information for improved online HD map detection via three exquisite designs. First, a hybrid query generation module is introduced to better initialize queries for detection. Then, an inner-instance query fusion module is added before the transformer decoder, which fuses inner-instance object queries to refine the initialized line instances. Finally, a transformer-based inner-instance aggregation module is incorporated to further refine the predicted lines. Extensive experimental evaluations are conducted on the popular and challenging NuScenes [2] and Argoverse 2 [37] datasets. InsMapper is based on MapTR [24], and it can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. No matter what the base framework is, InsMapper harvests state-of-the-art performance, surpassing the previous highest solutions. The intuitive performance comparisons are illustrated in Figure 1, and our main contributions can be summarized as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.226,
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+            "angle": 0,
+            "content": "- We analyze the limitations of existing HD map detection algorithms and propose a new framework named InsMapper, which can effectively utilize the easily overlooked inner-instance point correlation information for accurate and generalizable online HD map detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.226,
+                0.464,
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+            "angle": 0,
+            "content": "- We incorporate three useful modules to leverage inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules better initialize queries for detection and the last one refines detected line instances."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We conduct experiments on the challenging NuScenes and Argoverse 2 datasets. InsMapper outperforms all baselines by a large margin. The achieved state-of-the-art results demonstrate its effectiveness and generality."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+            "bbox": [
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+            "angle": 0,
+            "content": "2 Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
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+            "angle": 0,
+            "content": "Vector map detection. Vector maps use vectors to represent road elements, such as road networks, road curbs, and lane lines. A high-definition map (HD map) is a type of vector map, but a vector map may not qualify as an HD map if it lacks sufficient resolution or fails to provide lane-level information, among other factors. Online HD map detection can benefit from insights gained from a broader scope of vector map detection works, including road-network detection [1,14,39, 41], road-curb detection in aerial images [42, 43], and road lane line detection [15, 16], etc. DagMapper [16] aims to detect vectorized lane lines from pre-built point cloud maps using iterations. However, DagMapper only handles simple topology changes of lane lines and struggles to handle complex road intersections. RNGDet++ [41] applies DETR along with an imitation learning algorithm [34] for road-network detection, achieving state-of-the-art performance on multiple datasets. Although these methods achieve satisfactory graph detection accuracy, they suffer from poor efficiency due to their iterative algorithms. Given the"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
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+            "angle": 0,
+            "content": "4"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
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+                0.351,
+                0.127
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+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.147,
+                0.784,
+                0.176
+            ],
+            "angle": 0,
+            "content": "stringent real-time requirements of autonomous vehicles, they are not suitable for online HD map detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.178,
+                0.787,
+                0.433
+            ],
+            "angle": 0,
+            "content": "HD map detection. HD map detection was initially a subtask of BEV detection [21, 22, 28, 30, 31]. Recently, given the importance of HD maps, several works have directly focused on HD map detection [4, 20, 24, 27, 29, 33, 35, 38, 40]. However, most of these works either involve offline HD map creation [12, 38, 40] or only detect one specific road element [3, 4, 33]. HDMapNet [20] is considered to be the first work specifically designed for multiple road element detection. However, HDMapNet outputs rasterized results, requiring complicated handcrafted post-processing to obtain vectorized HD maps. To address this issue, VectorMapNet [27] is believed to be the first work detecting vectorized HD maps in real-time. However, it consists of two stages, and its efficiency is significantly impacted by sequential operations. In contrast, MapTR [24] uses deformable DETR [46] to design an end-to-end vectorized HD map detection model, which greatly simplifies the pipeline and delivers better detection performance. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance on vectorized HD map detection, but it still overlooks and does not investigate the inner-instance correlations between points, limiting further improvements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
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+            ],
+            "angle": 0,
+            "content": "Detection by Transformer. DETR [5] is the first end-to-end transformer-based object detection framework. Compared with previous CNN-based methods [8, 10], DETR removes the need for anchor proposals and non-maximum suppression (NMS), making it simpler and more effective. To address the issue of slow convergence, subsequent works propose accelerating DETR training through deformable attention [46], denoising [18], and dynamic query generation [19, 36, 45]. Intuitively, most of these DETR refinements could be adapted to the HD map detection task since our proposed InsMapper relies on DETR. However, unlike typical object detection tasks in which objects are assumed to be independent and identically distributed (i.i.d.), detected points in HD maps have strong correlations, especially among inner-instance points. This inherent difference makes some refined DETR methods unsuitable to our task and additional investigations are required."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.652,
+                0.424,
+                0.667
+            ],
+            "angle": 0,
+            "content": "3 Point Correlation"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.681,
+                0.607,
+                0.697
+            ],
+            "angle": 0,
+            "content": "3.1 Vector Map Decomposition and Sampling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.705,
+                0.787,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Let \\( G \\) denote the original vector map label of the scene, which consists of vertices \\( V \\) and edges \\( E \\). The vector map contains multiple classes of road elements, including pedestrian crossings, road dividers, road boundaries, and lane centerlines. Among them, the first three classes of road elements are simple polylines or polygons without intersection points. While lane centerlines have more complicated topology, such as lane split, lane merge, and lane intersection. To unify all vector elements, the vector map is decomposed into simpler shapes (i.e., polylines and polygons) without intersections. Any vertices in the vector map with degrees larger than two (i.e., intersection vertices) are removed from \\( G \\), but"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.657,
+                0.115,
+                0.732,
+                0.129
+            ],
+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.775,
+                0.117,
+                0.785,
+                0.127
+            ],
+            "angle": 0,
+            "content": "5"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.147,
+                0.784,
+                0.207
+            ],
+            "angle": 0,
+            "content": "incident edges are kept. In this way, a set of simple polylines and polygons without intersections is obtained as \\( G^{*} = \\{l_{i}\\}_{i=1}^{N^{*}} \\), where \\( G^{*} \\) is an undirected graph. Each shape \\( l_{i} \\) is defined as an instance, and \\( N^{*} \\) denotes the overall number of instances in a vector map."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.208,
+                0.785,
+                0.284
+            ],
+            "angle": 0,
+            "content": "Following MapTR and MapTR-V2, to enhance the parallelization capacity of the model, each instance is evenly re-sampled with fixed-length points as \\( l_{i} = (v_{1},\\dots,v_{j},\\dots,v_{n_{p}}) \\). \\( l_{i} \\) is ordered from \\( v_{1} \\) to \\( v_{n_p} \\), with \\( n_p \\) being the number of sampled points for each instance. For polygon instances, \\( v_{1} \\) is equal to \\( v_{n_p} \\). Please refer to the supplementary document for the visualization of the pre-processing."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.307,
+                0.48,
+                0.321
+            ],
+            "angle": 0,
+            "content": "3.2 Inner-instance Correlation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.333,
+                0.784,
+                0.408
+            ],
+            "angle": 0,
+            "content": "Unlike conventional object detection tasks, where objects can be approximated as independent and identically distributed (i.i.d.), strong correlations exist between points within the same line instance in the vectorized HD map detection task. Please refer to the supplementary document for the visualization of the point correlation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.41,
+                0.785,
+                0.56
+            ],
+            "angle": 0,
+            "content": "Inner-instance correlation is crucial for point coordinates prediction. Points within the same instance can collaborate by sharing inner-instance information, leading to smoother and more accurate predictions. Without this collaboration, points of the same instance may produce independent predictions, leading to zig-zag or incorrect instances. The inner-instance correlation can serve as additional constraints to facilitate the query initialization and refinement of predicted lines. In previous methods, the correlation of points is not correctly analyzed and leveraged, limiting further improvement. In subsequent sections, we introduce InsMapper to more effectively utilize point correlations and improve vectorized map detection performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.585,
+                0.381,
+                0.603
+            ],
+            "angle": 0,
+            "content": "4 Methodology"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.618,
+                0.421,
+                0.632
+            ],
+            "angle": 0,
+            "content": "4.1 Overall Framework"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.643,
+                0.784,
+                0.673
+            ],
+            "angle": 0,
+            "content": "Building on MapTR [24], our proposed InsMapper is an end-to-end trainable framework for online vectorized HD map detection, as illustrated in Figure 2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.675,
+                0.785,
+                0.84
+            ],
+            "angle": 0,
+            "content": "InsMapper is adaptive and can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. Following BEVformer [22], InsMapper first projects perspective view camera images into the bird's-eye-view (BEV). After obtaining the BEV features, InsMapper uses deformable attention layers [46] to process input object queries. Each object query predicts one point, including the object class and the regression point position. To better leverage inner-instance information and further enhance the final detection performance, we introduce three designs in InsMapper: hybrid query generation, which replaces the hierarchical query in MapTR, generating line queries with better diversity; inner-instance query fusion, which fuses generated queries within the same instance based on"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
+                0.116,
+                0.23,
+                0.127
+            ],
+            "angle": 0,
+            "content": "6"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
+                0.115,
+                0.352,
+                0.128
+            ],
+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.223,
+                0.146,
+                0.788,
+                0.393
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.214,
+                0.406,
+                0.788,
+                0.518
+            ],
+            "angle": 0,
+            "content": "Fig. 2: Overall framework. InsMapper is an end-to-end transformer model with an encoder-decoder structure. The transformer encoder projects perspective-view camera images into a bird's-eye view (BEV). Subsequently, the transformer decoder detects vector instances by predicting point sets. To enhance the utilization of inner-instance information, we introduce the following three components: a hybrid query generation scheme (orange module), an inner-instance query fusion module (yellow module), and an inner-instance feature aggregation module (blue module). The first two modules better initialize queries for detection and the final one refines detected line instances."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.548,
+                0.788,
+                0.607
+            ],
+            "angle": 0,
+            "content": "inner-instance features to further enhance the quality of initialized line queries; and inner-instance feature aggregation, which adds a new inner-instance self-attention module to decoder layers to further aggregate inner-instance features for line refinement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.608,
+                0.788,
+                0.73
+            ],
+            "angle": 0,
+            "content": "Different from past works, which treat queries as independently distributed, InsMapper utilizes inner-instance information to fuse object queries and aggregate intermediate features in deformable transformer decoder layers. Otherwise, adjacent vertices may produce independent position regression results, leading to zigzag or even incorrect instances. With the assistance of inner-instance information, the model can better initialize queries for detection and refine the positions of detected points within an instance, significantly enhancing the final performance, as demonstrated in the experiments section."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.753,
+                0.414,
+                0.769
+            ],
+            "angle": 0,
+            "content": "4.2 Query Generation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.78,
+                0.788,
+                0.842
+            ],
+            "angle": 0,
+            "content": "In contrast to traditional object detection tasks, where queries are independent and identically distributed (i.i.d.), the points to be detected in our task exhibit significant correlations. Various methods can be used to generate object queries as input for the transformer decoder, such as the basic scheme, hierar"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.657,
+                0.115,
+                0.732,
+                0.129
+            ],
+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.775,
+                0.116,
+                0.785,
+                0.127
+            ],
+            "angle": 0,
+            "content": "7"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.218,
+                0.175,
+                0.486,
+                0.282
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.215,
+                0.293,
+                0.487,
+                0.378
+            ],
+            "angle": 0,
+            "content": "Fig.3: Query generation schemes. For concise visualization, the number of instances \\(N_{I}\\) is 2, and the number of points per instance \\(n_p\\) is 3. The hybrid scheme can initialize lines with both good diversity and quality."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.507,
+                0.151,
+                0.593,
+                0.277
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.522,
+                0.284,
+                0.579,
+                0.296
+            ],
+            "angle": 0,
+            "content": "(a) Basic"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.604,
+                0.149,
+                0.692,
+                0.277
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.603,
+                0.283,
+                0.697,
+                0.296
+            ],
+            "angle": 0,
+            "content": "(b) Hierarchical"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.708,
+                0.15,
+                0.788,
+                0.279
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.717,
+                0.284,
+                0.781,
+                0.296
+            ],
+            "angle": 0,
+            "content": "(c) Hybrid"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.307,
+                0.8,
+                0.377
+            ],
+            "angle": 0,
+            "content": "Fig. 4: Visualization of initialized lines with different query generation schemes. The quality and diversity of initialized lines are crucial for the final performance. Each color represents one initialized line."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.407,
+                0.785,
+                0.451
+            ],
+            "angle": 0,
+            "content": "chical scheme, and hybrid scheme. All query generation schemes are illustrated in Figure 3. Initialized queries are organized into line instances. The quality and diversity of the initialized lines are both crucial."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.453,
+                0.788,
+                0.588
+            ],
+            "angle": 0,
+            "content": "Basic query generation. This method is leveraged in the original DETR [5] for query generation. It assumes that points are i.i.d. and generates queries randomly, without utilizing inner-instance information. Let \\( N_{I} \\) denote the number of predicted instances, which is obviously larger than \\( N^{*} \\). Since each instance contains \\( n_p \\) points, the basic object queries consist of \\( N_{I} \\cdot n_{p} \\) randomly generated i.i.d. queries, resulting in irregular line shapes. Due to the lack of constraints on inner-instance points, the initialized line instances are noisy and have poor quality, which leads to degraded performance. MapTR with the basic query scheme is visualized in Figure 4a."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.215,
+                0.589,
+                0.788,
+                0.666
+            ],
+            "angle": 0,
+            "content": "Hierarchical query generation. To address the aforementioned issue of the basic scheme, a hierarchical query generation scheme is proposed in MapTR [24] and MapTR-V2 [25]. Let \\( Q_{ins} = \\{q_i^I\\}_{i=1}^{N_I} \\) denote instance queries and \\( Q_{pts} = \\{q_j^P\\}_{j=1}^{n_p} \\) denote point queries. The object queries for HD map detection are then the pairwise addition of \\( Q_{ins} \\) and \\( Q_{pts} \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.346,
+                0.674,
+                0.787,
+                0.695
+            ],
+            "angle": 0,
+            "content": "\\[\nQ = \\left\\{q _ {i, j} = q _ {i} ^ {I} + q _ {j} ^ {P} \\mid q _ {i} ^ {I} \\in Q _ {\\text {i n s}}, q _ {j} ^ {P} \\in Q _ {\\text {p t s}} \\right\\}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.704,
+                0.788,
+                0.81
+            ],
+            "angle": 0,
+            "content": "where \\( |Q| = |Q_{ins}| \\cdot |Q_{pts}| = N_I \\cdot n_p \\). For each line instance \\( i \\), the instance query \\( q_i^I \\) denotes its uniqueness. By using \\( q_i^I \\) as a bridge, object queries within the same instance can better collaborate with each other for point prediction. But all line instances share the same point queries so all initialized lines tend to have quite similar shapes, degrading initialization diversity, which harms the final detection performance. The initialized lines generated by MapTR with the hierarchical query scheme are visualized in Figure 4b."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.215,
+                0.81,
+                0.788,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Hybrid query generation. The basic scheme does not take into account any information exchange between queries, whereas the hierarchical one generates"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
+                0.116,
+                0.23,
+                0.127
+            ],
+            "angle": 0,
+            "content": "8"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
+                0.115,
+                0.352,
+                0.128
+            ],
+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.147,
+                0.784,
+                0.192
+            ],
+            "angle": 0,
+            "content": "repetitive line shapes. To address these issues, this paper presents a hybrid query generation method that mitigates the drawbacks of the aforementioned schemes while maintaining appropriate inner-instance information exchange."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.192,
+                0.785,
+                0.284
+            ],
+            "angle": 0,
+            "content": "Let the instance queries be \\( Q_{ins} = \\{q_i^I\\}_{i=1}^{N_I} \\), and the point queries be \\( Q_{pts} = \\{q_j^P\\}_{j=1}^{N_P} = \\{q_j^P\\}_{j=1}^{N_I \\cdot n_p} \\). The point queries are divided into \\( N_I \\) instance groups, and a point query \\( q_j^P \\) is assigned to the \\( \\lceil \\frac{j}{n_p} \\rceil \\)-th instance. Consequently, the final object query is the sum of a point query \\( p_j^P \\) and its assigned instance query \\( p_k^I \\), where \\( k = \\lceil \\frac{j}{n_p} \\rceil \\). The object query set can be expressed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.413,
+                0.295,
+                0.786,
+                0.314
+            ],
+            "angle": 0,
+            "content": "\\[\nQ = \\left\\{q _ {k} ^ {I} + q _ {j} ^ {P} \\mid q _ {j} ^ {P} \\in Q _ {p t s} \\right\\} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.318,
+                0.785,
+                0.44
+            ],
+            "angle": 0,
+            "content": "where \\( |Q| = |Q_{pts}| = N_P = N_I \\cdot n_p \\). In contrast to the hierarchical scheme, each point query in the hybrid scheme is utilized only once to generate the object query, thereby preventing repetitive line shapes. Simultaneously, point queries belonging to the same instance are summed with a shared instance query, establishing the inner-instance connection. The hybrid query generation method can be considered as a combination of the basic and hierarchical schemes, effectively mitigating their respective drawbacks. InsMapper with the hybrid query generation scheme is visualized in Figure 4c."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.463,
+                0.498,
+                0.479
+            ],
+            "angle": 0,
+            "content": "4.3 Inner-instance Query Fusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.489,
+                0.785,
+                0.594
+            ],
+            "angle": 0,
+            "content": "The input object queries for the transformer decoder are generated from instance queries and point queries. Although the generated queries can leverage some inner-instance information, this information exchange is indirect and inflexible. The instance query is distributed equally among all inner-instance points, while a more precise point-to-point information exchange cannot be realized. As a result, a query fusion module is introduced to further utilize inner-instance information and refine initialized lines."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.595,
+                0.785,
+                0.657
+            ],
+            "angle": 0,
+            "content": "Let \\( Q_{i} = \\{q_{i,j}\\}_{j=1}^{n_{p}} \\) represent the set of object queries belonging to the \\( i \\)-th instance, and \\( q_{i,j} \\) denote the \\( j \\)-th point of the \\( i \\)-th instance. \\( q_{i,j} \\) is correlated with all other queries in \\( Q_{i} \\). To better fuse inner-instance object queries, each query is updated by a weighted sum of all queries in \\( Q_{i} \\) as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.379,
+                0.669,
+                0.786,
+                0.709
+            ],
+            "angle": 0,
+            "content": "\\[\nq _ {i, j} = f \\left(q _ {i, j}, Q _ {i}\\right) = \\sum_ {k = 1} ^ {n _ {p}} w _ {i, j, k} \\phi \\left(q _ {i, k}\\right) \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.72,
+                0.784,
+                0.78
+            ],
+            "angle": 0,
+            "content": "where \\( w_{i,j,k} \\) demonstrates weights for query fusion. \\( f(\\cdot) \\) is the fusion function and \\( \\phi(\\cdot) \\) is the kernel in case nonlinear transformation is needed. \\( f(\\cdot) \\) could be realized by handcraft weights, fully connected layers, or self-attention. In this work, self-attention is applied as \\( f(\\cdot) \\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.781,
+                0.785,
+                0.841
+            ],
+            "angle": 0,
+            "content": "In conventional object detection tasks, object queries are assumed to be independent and identically distributed (i.i.d.), making query fusion unnecessary. However, in the task of HD map detection, the query fusion module effectively aligns the update of queries and enables each point to pay more attention to"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.657,
+                0.115,
+                0.732,
+                0.129
+            ],
+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.775,
+                0.116,
+                0.787,
+                0.127
+            ],
+            "angle": 0,
+            "content": "9"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.227,
+                0.169,
+                0.331,
+                0.326
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.239,
+                0.337,
+                0.319,
+                0.349
+            ],
+            "angle": 0,
+            "content": "(a) No fusion"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.354,
+                0.171,
+                0.452,
+                0.323
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.357,
+                0.337,
+                0.45,
+                0.349
+            ],
+            "angle": 0,
+            "content": "(b) With fusion"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.482,
+                0.148,
+                0.79,
+                0.346
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.214,
+                0.36,
+                0.465,
+                0.498
+            ],
+            "angle": 0,
+            "content": "Fig.5: Visualization of the effect of the inner-instance query fusion module. (a) No query fusion. (b) With query fusion. The query fusion module can better refine the initialized lines based on inner-instance information. In this example, the proposed query fusion module significantly enhances the diversity of initialized line instances."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.475,
+                0.36,
+                0.794,
+                0.499
+            ],
+            "angle": 0,
+            "content": "Fig.6: Decoder of InsMapper. An inner-instance multi-head self-attention module is incorporated into decoder layers. In this module, the attention between points belonging to different instances is blocked (grey grids). Only inner-instance attention is allowed (colored grids). Colored grids are randomly blocked with \\(\\epsilon\\) probability (set to grey) for robustness. The proposed module can further utilize inner-instance information and refine the predicted lines."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.53,
+                0.788,
+                0.607
+            ],
+            "angle": 0,
+            "content": "neighboring points. It can greatly refine the initialized lines for better query initialization, leading to enhanced performance. Without this module, queries within the same instance cannot be aware of each other, rendering them \"blind\". Poor line initialization tends to have degraded detection scores. The effect of the query fusion module is visualized in Figure 5."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.631,
+                0.555,
+                0.646
+            ],
+            "angle": 0,
+            "content": "4.4 Inner-instance Feature Aggregation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.659,
+                0.787,
+                0.735
+            ],
+            "angle": 0,
+            "content": "In addition to object query manipulation, InsMapper performs inner-instance feature aggregation for predicted line refinement in the transformer decoder layers by incorporating an additional inner-instance self-attention module. Inspired by [9], inner-instance attentions are randomly blocked with probability \\(\\epsilon\\) for robustness. The decoder layer of InsMapper is depicted in Figure 6."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.735,
+                0.788,
+                0.84
+            ],
+            "angle": 0,
+            "content": "The inner-instance self-attention module resembles the original self-attention module but features a specially designed attention mask. As illustrated in Figure 6, the attention mask of inner-instance points is set to zero (colored grids), indicating that attention between points within the same instance is allowed. Conversely, for points belonging to different instances (i.e., inter-instance points), the corresponding attention mask values are set to one, blocking attention between them. This method encourages the model to focus more on inner-instance"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
+                0.116,
+                0.236,
+                0.127
+            ],
+            "angle": 0,
+            "content": "10"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
+                0.115,
+                0.351,
+                0.127
+            ],
+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.147,
+                0.784,
+                0.192
+            ],
+            "angle": 0,
+            "content": "information, resulting in more consistent predictions. To further enhance the robustness of this module, the inner-instance attention (colored grids) has an \\( e \\) probability of being blocked."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.193,
+                0.785,
+                0.329
+            ],
+            "angle": 0,
+            "content": "An alternative method involves placing the proposed inner-instance attention module before the cross-attention module. However, the self-attention module before cross-attention should not block inter-instance information. Otherwise, some instances may produce duplicate predictions since they cannot \"clearly see\" other instances, which is analyzed in the original DETR [5]. Consequently, implementing inner-instance self attention before the cross-attention module leads to degraded final performance. Thus the proposed inner-instance feature aggregation should be placed after the cross-attention layer. More experiments about the decoder structure are provided in the appendix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.347,
+                0.377,
+                0.364
+            ],
+            "angle": 0,
+            "content": "5 Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.374,
+                0.429,
+                0.39
+            ],
+            "angle": 0,
+            "content": "5.1 Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.394,
+                0.785,
+                0.546
+            ],
+            "angle": 0,
+            "content": "Datasets. Extensive experiments are conducted on the popular and challenging NuScenes dataset [2] and the Argoverse 2 dataset [37]. These two datasets comprise hundreds of data sequences captured in various autonomous driving scenarios, encompassing diverse weather conditions and time periods. The perception range for the X-axis and Y-axis in the BEV is set to \\([-15m, 15m]\\) and \\([-30m, 30m]\\), respectively. The detected vectorized HD map should encompass four types of road elements simultaneously: road boundary, lane split, pedestrian crossing, and lane centerline. Among these, the lane centerline is a crucial element for ensuring effective vehicle planning and control. Detecting lane centerlines poses greater difficulty compared to the other three elements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.546,
+                0.794,
+                0.666
+            ],
+            "angle": 0,
+            "content": "Implementation details. We perform all the experiments on a machine equipped with 8 RTX-3090 GPUs. During the training phase, all GPUs are utilized, whereas only a single GPU is employed for inference. For our proposed InsMapper, we adopt multiple settings akin to the previous SOTA method, MapTR. All ablation studies are conducted for 24 epochs, with ResNet50 [11] as the backbone. For a fair comparison, except for the proposed modules, we keep the experiment settings exactly the same, such as batch size, network depth, the number of input queries, etc."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.667,
+                0.787,
+                0.773
+            ],
+            "angle": 0,
+            "content": "Evaluation metrics. Models are assessed using two types of metrics. The first metric, average precision (AP), gauges the instance-level detection performance, employing Chamfer distance for matching predictions with ground truth labels. To ensure a fair comparison, we follow previous works to calculate multiple \\(\\mathrm{AP}_{\\tau}\\) values with \\(\\tau \\in \\{0.5, 1.0, 1.5\\}\\), and report the average AP. To measure the topology correctness, the metric TOPO that is widely used in past works [12-14, 41] is reported. For all metrics, a larger value indicates better performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.215,
+                0.79,
+                0.473,
+                0.805
+            ],
+            "angle": 0,
+            "content": "5.2 Performance Comparison"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.81,
+                0.785,
+                0.84
+            ],
+            "angle": 0,
+            "content": "In this section, we compare InsMapper with previous state-of-the-art methods using the aforementioned evaluation metrics. The quantitative comparison results"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.657,
+                0.115,
+                0.732,
+                0.129
+            ],
+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.769,
+                0.116,
+                0.784,
+                0.127
+            ],
+            "angle": 0,
+            "content": "11"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.214,
+                0.145,
+                0.788,
+                0.229
+            ],
+            "angle": 0,
+            "content": "Table 1: Quantitative results of comparison experiments on the NuScenes validation set. Colored numbers show differences between InsMapper and the SOTA baseline under the same experiment setting. \"C\" and \"L\" denote camera and LiDAR, respectively. \"-\" denotes that the result is not available. \"V2-99\" and \"Sec\" correspond to VoVNetV2-99 [17] and SECOND [44]. \\(\\dagger\\) represents InsMapper based on PivotNet [7], \\(\\ddagger\\) indicates InsMapper based on MapTR-V2 [25]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.217,
+                0.24,
+                0.787,
+                0.459
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\\(AP_{ped}\\)</td><td>\\(AP_{div}\\)</td><td>\\(AP_{bound}\\)</td><td>\\(AP_{center}\\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>HDMapNet</td><td>30</td><td>Effi-B0</td><td>C</td><td>4.41</td><td>23.73</td><td>58.17</td><td>37.29</td><td>30.90</td><td>29.79</td></tr><tr><td>STSU</td><td>110</td><td>R50</td><td>C</td><td>-</td><td>-</td><td>-</td><td>31.21</td><td>31.21</td><td>32.11</td></tr><tr><td>VectorMapNet</td><td>130</td><td>R50</td><td>C</td><td>28.66</td><td>39.74</td><td>33.06</td><td>34.93</td><td>34.10</td><td>39.90</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.92</td><td>46.25</td><td>50.07</td><td>37.47</td><td>42.93</td><td>46.77</td></tr><tr><td>MapTR</td><td>24</td><td>V2-99</td><td>C</td><td>44.57</td><td>56.25</td><td>60.58</td><td>46.30</td><td>51.92</td><td>55.16</td></tr><tr><td>MapTR</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>49.47</td><td>58.98</td><td>66.72</td><td>44.89</td><td>55.01</td><td>56.77</td></tr><tr><td>MapTR</td><td>110</td><td>R50</td><td>C</td><td>49.16</td><td>59.12</td><td>58.93</td><td>47.26</td><td>53.62</td><td>59.16</td></tr><tr><td>BeMapNet</td><td>24</td><td>R50</td><td>C</td><td>43.59</td><td>54.11</td><td>51.90</td><td>38.60</td><td>47.05</td><td>49.90</td></tr><tr><td>PivotNet</td><td>24</td><td>R50</td><td>C</td><td>42.73</td><td>53.55</td><td>52.01</td><td>42.47</td><td>47.69</td><td>51.04</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>48.20</td><td>54.75</td><td>56.66</td><td>45.86</td><td>51.37</td><td>51.15</td></tr><tr><td>MapTR-V2</td><td>110</td><td>R50</td><td>C</td><td>58.68</td><td>65.72</td><td>67.12</td><td>56.16</td><td>61.92</td><td>63.26</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>44.36</td><td>53.36</td><td>52.77</td><td>42.35</td><td>48.31</td><td>51.58</td></tr><tr><td>InsMapper</td><td>24</td><td>V2-99</td><td>C</td><td>51.16</td><td>63.71</td><td>64.47</td><td>51.40</td><td>57.68</td><td>60.00</td></tr><tr><td>InsMapper</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>56.00</td><td>63.42</td><td>71.61</td><td>52.85</td><td>60.97</td><td>62.51</td></tr><tr><td>InsMapper</td><td>110</td><td>R50</td><td>C</td><td>55.42</td><td>63.87</td><td>65.80</td><td>54.20</td><td>59.40</td><td>66.19</td></tr><tr><td>InsMapper†</td><td>24</td><td>R50</td><td>C</td><td>46.45</td><td>54.91</td><td>54.16</td><td>45.20</td><td>50.18</td><td>53.57</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>49.07</td><td>57.98</td><td>59.84</td><td>47.99</td><td>53.72</td><td>53.00</td></tr><tr><td>InsMapper†</td><td>110</td><td>R50</td><td>C</td><td>62.09</td><td>67.60</td><td>68.15</td><td>58.41</td><td>64.06</td><td>64.72</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.214,
+                0.473,
+                0.785,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Table 2: Quantitative results of comparison experiments on the Argoverse 2 validation set. \\(\\ddagger\\) indicates InsMapper based on MapTR-V2 [25]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.217,
+                0.513,
+                0.787,
+                0.582
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>APcenter</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>6</td><td>R50</td><td>C</td><td>52.88</td><td>63.68</td><td>61.18</td><td>59.73</td><td>59.37</td><td>75.79</td></tr><tr><td>MapTR-V2</td><td>6</td><td>R50</td><td>C</td><td>57.16</td><td>67.96</td><td>65.25</td><td>63.20</td><td>63.39</td><td>77.94</td></tr><tr><td>InsMapper</td><td>6</td><td>R50</td><td>C</td><td>55.61</td><td>66.60</td><td>62.58</td><td>62.67</td><td>61.87</td><td>77.58</td></tr><tr><td>InsMapper†</td><td>6</td><td>R50</td><td>C</td><td>58.91</td><td>71.35</td><td>66.90</td><td>64.70</td><td>65.46</td><td>79.26</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.214,
+                0.596,
+                0.785,
+                0.625
+            ],
+            "angle": 0,
+            "content": "Table 3: Quantitative results of comparison experiments on the NuScenes validation set without centerline. \\(\\ddagger\\) indicates InsMapper based on MapTR-V2 [25]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.217,
+                0.637,
+                0.787,
+                0.706
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>mAP</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>46.04</td><td>51.58</td><td>53.08</td><td>50.23</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>59.80</td><td>62.40</td><td>62.40</td><td>61.50</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>48.44</td><td>54.68</td><td>56.92</td><td>53.35</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>61.54</td><td>65.09</td><td>64.62</td><td>63.75</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.735,
+                0.788,
+                0.841
+            ],
+            "angle": 0,
+            "content": "are reported in Table 1. InsMapper is flexible and adaptive, making it seamless to modify it based on existing transformer frameworks. InsMapper is built on MapTR for experiments, we also report the results of InsMapper with different base frameworks, e.g. InsMapper† is based on PivotNet [7] and InsMapper‡ relies on the previous SOTA method MapTR-V2 [25]. Compared to the previous methods, InsMapper improves the AP of all road elements by around 2. The topological metric also sees an improvement of around 1.5. The inference FPS of"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
+                0.116,
+                0.236,
+                0.127
+            ],
+            "angle": 0,
+            "content": "12"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
+                0.115,
+                0.351,
+                0.127
+            ],
+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.216,
+                0.145,
+                0.788,
+                0.187
+            ],
+            "angle": 0,
+            "content": "Table 4: Quantitative results of comparison experiments on the NuScenes validation set. Centerlines are directed graphs in this table. \\(\\ddagger\\) indicates InsMapper based on MapTR-V2 [25]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.217,
+                0.199,
+                0.789,
+                0.269
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\\(AP_{ped}\\)</td><td>\\(AP_{div}\\)</td><td>\\(AP_{bound}\\)</td><td>\\(AP_{center}\\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.39</td><td>46.61</td><td>50.69</td><td>37.22</td><td>42.98</td><td>46.98</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>49.53</td><td>55.46</td><td>58.48</td><td>53.82</td><td>54.32</td><td>54.90</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>43.24</td><td>53.77</td><td>53.89</td><td>43.22</td><td>48.53</td><td>52.09</td></tr><tr><td>\\(InsMapper^{\\dagger}\\)</td><td>24</td><td>R50</td><td>C</td><td>51.62</td><td>57.88</td><td>60.90</td><td>56.52</td><td>56.73</td><td>56.01</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.298,
+                0.789,
+                0.463
+            ],
+            "angle": 0,
+            "content": "MapTR and InsMapper are 8.5 and 7.5, respectively. The evaluation outcomes on the Argoverse 2 dataset [37] can be found in Table 2. InsMapper outperforms past works with notable enhancements. Table 3 presents the results without centerlines. InsMapper with different bases attains an improvement of more than \\(2\\mathrm{mAP}\\). In the aforementioned experiments, all road elements are treated as undirected graphs. Table 4 shows the results when centerlines are represented as directed graphs. Based on the results, InsMapper still presents superior results than past works for directed HD map detection. Furthermore, we illustrate the qualitative visualizations in Figure 7. Owing to the effective employment of inner-instance information, InsMapper generates smoother and more precise HD maps compared to previous works."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.465,
+                0.789,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Consequently, InsMapper demonstrates superior performance compared to prior approaches across multiple datasets, exhibiting outstanding detection outcomes. Concurrently, InsMapper maintains a comparable inference speed to the previous state-of-the-art method. These exceptional experimental results strongly demonstrate the effectiveness and generality of the proposed designs."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.568,
+                0.403,
+                0.582
+            ],
+            "angle": 0,
+            "content": "5.3 Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.597,
+                0.789,
+                0.703
+            ],
+            "angle": 0,
+            "content": "Key component designs. We conduct several ablation study experiments to confirm the necessity of the proposed modules. Initially, we incorporate these modules into the previous state-of-the-art baseline model incrementally, and the results are presented in Table 5. It is evident that all three modules contribute to performance improvements, thereby validating their necessity. To further investigate the impact of each module's design, we perform comprehensive ablation studies in the following paragraphs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.704,
+                0.789,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Hybrid query generation. Compared to basic or hierarchical query generation schemes, the proposed hybrid query generation scheme generates queries with better quality and diversity, due to effectively utilizing inner-instance correlation. The evaluation results of the different query generation schemes are presented in Table 6. These results reveal that the hybrid query generation scheme outperforms its counterparts, thereby demonstrating the soundness of this design."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.795,
+                0.789,
+                0.843
+            ],
+            "angle": 0,
+            "content": "Inner-instance query fusion. Query fusion is proposed to leverage the correlation between inner-instance queries to enhance prediction performance. Various methods can be employed for fusing queries, including mean fusing (i.e.,"
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
+                0.657,
+                0.115,
+                0.732,
+                0.129
+            ],
+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.769,
+                0.116,
+                0.786,
+                0.127
+            ],
+            "angle": 0,
+            "content": "13"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.218,
+                0.144,
+                0.573,
+                0.559
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.575,
+                0.144,
+                0.784,
+                0.559
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.216,
+                0.568,
+                0.788,
+                0.611
+            ],
+            "angle": 0,
+            "content": "Fig. 7: Qualitative visualization. The predicted map contains four classes, i.e., road boundaries (green), lane splits (red), pedestrian crossing (blue), and lane centerlines (pink). InsMapper presents better detection results compared with the past work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.643,
+                0.788,
+                0.718
+            ],
+            "angle": 0,
+            "content": "each query is summed with the mean of all queries of the same instance), fusion by the feed-forward network, and fusion by self-attention. The evaluation results are presented in Table 7. The outcomes of the query fusion methods vary significantly, with self-attention-based query fusion achieving the best results. Consequently, self-attention query fusion is incorporated into InsMapper."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.72,
+                0.789,
+                0.841
+            ],
+            "angle": 0,
+            "content": "Inner-instance feature aggregation. In InsMapper, the inner-instance self-attention module is incorporated into the decoder layers following the cross-attention module. We evaluate InsMapper under four different conditions: without the inner-instance self-attention module (no attention), replace the inner-instance self-attention module with a vanilla self-attention module (vanilla attention), without the random blocking (no random blocking, i.e., \\(\\epsilon = 0\\)), and with the module placed before the cross-attention (change position). The results are shown in Table 8. The outcomes reveal that removing or altering the proposed"
+        }
+    ],
+    [
+        {
+            "type": "page_number",
+            "bbox": [
+                0.218,
+                0.116,
+                0.236,
+                0.127
+            ],
+            "angle": 0,
+            "content": "14"
+        },
+        {
+            "type": "header",
+            "bbox": [
+                0.272,
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+            "angle": 0,
+            "content": "Z. Xu et al."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.216,
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+            "angle": 0,
+            "content": "Table 5: Ablation studies on key component designs. \"QG\", \"QF\" and \"FA\" represent hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation, respectively."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>QG</td><td>QF</td><td>FA</td><td>mAP</td><td>TOPO</td></tr><tr><td></td><td></td><td></td><td>42.93</td><td>46.77</td></tr><tr><td>✓</td><td>✓</td><td></td><td>45.42(↑2.49)</td><td>49.19(↑2.42)</td></tr><tr><td>✓</td><td></td><td>✓</td><td>45.45(↑2.52)</td><td>48.54(↑1.77)</td></tr><tr><td></td><td>✓</td><td>✓</td><td>46.93(↑4.00)</td><td>50.16(↑3.39)</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>48.31(↑5.38)</td><td>51.58(↑4.81)</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.217,
+                0.338,
+                0.492,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Table 6: Ablation studies on inner-instance query generation."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.218,
+                0.366,
+                0.493,
+                0.439
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Query Scheme</td><td>mAP</td><td>TOPO</td></tr><tr><td>InsMapper-basic</td><td>46.62</td><td>49.39</td></tr><tr><td>InsMapper-hierarchical</td><td>46.93</td><td>50.16</td></tr><tr><td>InsMapper-hybrid</td><td>48.31</td><td>51.58</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.509,
+                0.158,
+                0.786,
+                0.185
+            ],
+            "angle": 0,
+            "content": "Table 7: Ablation studies on inner-instance query fusion."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.511,
+                0.186,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Query Fusion</td><td>mAP</td><td>TOPO</td></tr><tr><td>No fusion</td><td>45.45</td><td>48.54</td></tr><tr><td>Mean</td><td>43.34</td><td>46.00</td></tr><tr><td>Feed-Forward</td><td>47.80</td><td>50.93</td></tr><tr><td>Self-attention</td><td>48.31</td><td>51.58</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.509,
+                0.282,
+                0.786,
+                0.337
+            ],
+            "angle": 0,
+            "content": "Table 8: Ablation studies on inner-instance feature aggregation. Multiple designs of the incorporated inner-instance self-attention layers are examined."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.514,
+                0.339,
+                0.784,
+                0.438
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>mAP</td><td>TOPO</td></tr><tr><td>No attention</td><td>45.42</td><td>49.19</td></tr><tr><td>Vanilla attention</td><td>46.23</td><td>49.51</td></tr><tr><td>No random blocking</td><td>47.67</td><td>51.49</td></tr><tr><td>Change position</td><td>45.24</td><td>48.16</td></tr><tr><td>InsMapper</td><td>48.31</td><td>51.58</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.473,
+                0.784,
+                0.504
+            ],
+            "angle": 0,
+            "content": "module can impair model performance. This observation confirms the effectiveness of the proposed module design."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.216,
+                0.545,
+                0.36,
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+            ],
+            "angle": 0,
+            "content": "6 Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.595,
+                0.788,
+                0.793
+            ],
+            "angle": 0,
+            "content": "In this paper, we introduced InsMapper, an end-to-end transformer-based model for on-the-fly vectorized HD map detection. InsMapper surpasses previous works by effectively leveraging inner-instance information to improve detection outcomes. Three exquisite designs have been proposed to utilize inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules improve the quality of initialized line instances for detection, while the last module effectively refines the detected lines. The superiority of InsMapper is well exhibited through experiments on the challenging NuScenes and Argoverse 2 datasets. The evaluation results demonstrate the effectiveness and generality of InsMapper, making it a promising solution for the vectorized HD map detection task. In the future, InsMapper will be further enhanced for temporal-consistent vector map detection, making it more suitable for real-world applications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.214,
+                0.795,
+                0.787,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Acknowledgement. This work is supported by the National Natural Science Foundation of China (No. 62201484), HKU Startup Fund, and HKU Seed Fund for Basic Research."
+        }
+    ],
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "InsMapper"
+        },
+        {
+            "type": "page_number",
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+            "content": "15"
+        },
+        {
+            "type": "title",
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+            "angle": 0,
+            "content": "References"
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+        }
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2024/InsMapper_ Exploring Inner-instance Information for Vectorized HD Mapping/703739e6-709f-487f-9515-53b438aabcdc_origin.pdf

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2024/InsMapper_ Exploring Inner-instance Information for Vectorized HD Mapping/full.md

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+# InsMapper: Exploring Inner-instance Information for Vectorized HD Mapping
+
+Zhenhua Xu Kwan-Yee K. Wong Hengshuang Zhao\*
+
+The University of Hong Kong
+
+Project webpage: https://tonyxuqq.github.io/InsMapper
+
+Abstract. Vectorized high-definition (HD) maps contain detailed information about surrounding road elements, which are crucial for various downstream tasks in modern autonomous vehicles, such as motion planning and vehicle control. Recent works attempt to directly detect the vectorized HD map as a point set prediction task, achieving notable detection performance improvements. However, these methods usually overlook and fail to analyze the important inner-instance correlations between predicted points, impeding further advancements. To address this issue, we investigate the utilization of inner-instance information for vectorized high-definition mapping through transformers, and propose a powerful system named InsMapper, which effectively harnesses inner-instance information with three exquisite designs, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules can better initialize queries for line detection, while the last one refines predicted line instances. InsMapper is highly adaptable and can be seamlessly modified to align with the most recent HD map detection frameworks. Extensive experimental evaluations are conducted on the challenging NuScenes and Argovverse 2 datasets, where InsMapper surpasses the previous state-of-the-art method, demonstrating its effectiveness and generality.
+
+Keywords: Autonomous Driving  $\cdot$  High-definition Map
+
+# 1 Introduction
+
+Vectorized high-definition maps (HD maps) play a critical role in today's autonomous vehicles [6, 23, 27], as they contain detailed information about the road, including the position of road elements (e.g., road boundaries, lane splits, pedestrian crossings, and lane centerlines), connectivity, and topology of the road. Without the assistance of HD maps for perceiving and understanding road elements, unexpected vehicle behaviors may be encountered, such as incorrect path planning results or even vehicle collisions.
+
+Typically, HD maps are created by offline human annotation, which is labor-intensive, inefficient, and expensive. Although there are works proposing to make
+
+such an offline process automatic [38, 40, 41], it is not possible to recreate and update the HD map frequently when the road has been modified, such as when a new road is built or an existing road is removed. To address this issue, several recent studies propose to detect local HD maps using an online method [7, 20, 24, 25, 27, 32]. This paper aims to further investigate online HD map detection techniques based on vehicle-mounted sensors (i.e., cameras and LiDARs).
+
+Early online HD map detection works consider road element mapping as a semantic segmentation task in bird's-eye view (BEV) [22,30,31], in which road elements are predicted in raster format (i.e., pixel-level semantic segmentation mask). However, rasterized road maps cannot be effectively utilized by downstream tasks of autonomous vehicles, such as motion planning and vehicle control [23,26,27]. Moreover, it is challenging to distinguish instances from the rasterized map, especially when some road elements overlap with each other or when a complicated topology is encountered (e.g., road split or road intersections).
+
+To alleviate these problems, HDMap-
+
+Net [20] proposes hand-crafted post-processing algorithms to better obtain road element instances for vectorized HD maps. However, HDMapNet still heavily relies on rasterized results, restricting it from handling complicated urban scenes. Recently, some works have resorted to predicting vectorized HD maps directly [3,24,27,35]. A two-stage hierarchical set prediction method is proposed in VectorMapNet [27]. After predicting key points of road elements in the HD map, VectorMapNet sequentially generates intermediate points. Although VectorMapNet is considered to be the first online vectorized HD map detection work, the sequential operation degrades its efficiency and model performance. MapTR [24] further proposes to use DETR [5, 46] for vectorized HD map detection as a point set prediction problem, and the output point sets are then
+
+![](images/7eb90e49242fce19ab9f25d5d0a95a1d9ee8ba290014cdd3d56266bab7472bd0.jpg)  
+Fig.1: Comparison of vectorized HD map detection methods. All solutions are evaluated on the NuScenes validation set. The x-axis represents the mAP results and the y-axis displays topology level correctness [13]. InsMapper is flexible and adaptable, so it can be seamlessly modified to align with multiple existing frameworks. InsMapper is built on MapTR [24].  $\dagger$  means InsMapper based on more recent framework PivotNet [7], while  $\ddagger$  indicates InsMapper based on previous SOTA, MapTR-V2 [25].
+
+grouped into road element instances. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance, but it overlooks and fails to utilize the essential inner-instance correlations between points to further boost the performance.
+
+In this work, we focus on investigating the utilization of inner-instance information for vectorized high-definition mapping via transformer, and propose a new framework named InsMapper, which can utilize inner-instance point information for improved online HD map detection via three exquisite designs. First, a hybrid query generation module is introduced to better initialize queries for detection. Then, an inner-instance query fusion module is added before the transformer decoder, which fuses inner-instance object queries to refine the initialized line instances. Finally, a transformer-based inner-instance aggregation module is incorporated to further refine the predicted lines. Extensive experimental evaluations are conducted on the popular and challenging NuScenes [2] and Argoverse 2 [37] datasets. InsMapper is based on MapTR [24], and it can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. No matter what the base framework is, InsMapper harvests state-of-the-art performance, surpassing the previous highest solutions. The intuitive performance comparisons are illustrated in Figure 1, and our main contributions can be summarized as follows:
+
+- We analyze the limitations of existing HD map detection algorithms and propose a new framework named InsMapper, which can effectively utilize the easily overlooked inner-instance point correlation information for accurate and generalizable online HD map detection.  
+- We incorporate three useful modules to leverage inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules better initialize queries for detection and the last one refines detected line instances.  
+- We conduct experiments on the challenging NuScenes and Argoverse 2 datasets. InsMapper outperforms all baselines by a large margin. The achieved state-of-the-art results demonstrate its effectiveness and generality.
+
+# 2 Related Work
+
+Vector map detection. Vector maps use vectors to represent road elements, such as road networks, road curbs, and lane lines. A high-definition map (HD map) is a type of vector map, but a vector map may not qualify as an HD map if it lacks sufficient resolution or fails to provide lane-level information, among other factors. Online HD map detection can benefit from insights gained from a broader scope of vector map detection works, including road-network detection [1,14,39, 41], road-curb detection in aerial images [42, 43], and road lane line detection [15, 16], etc. DagMapper [16] aims to detect vectorized lane lines from pre-built point cloud maps using iterations. However, DagMapper only handles simple topology changes of lane lines and struggles to handle complex road intersections. RNGDet++ [41] applies DETR along with an imitation learning algorithm [34] for road-network detection, achieving state-of-the-art performance on multiple datasets. Although these methods achieve satisfactory graph detection accuracy, they suffer from poor efficiency due to their iterative algorithms. Given the
+
+stringent real-time requirements of autonomous vehicles, they are not suitable for online HD map detection.
+
+HD map detection. HD map detection was initially a subtask of BEV detection [21, 22, 28, 30, 31]. Recently, given the importance of HD maps, several works have directly focused on HD map detection [4, 20, 24, 27, 29, 33, 35, 38, 40]. However, most of these works either involve offline HD map creation [12, 38, 40] or only detect one specific road element [3, 4, 33]. HDMapNet [20] is considered to be the first work specifically designed for multiple road element detection. However, HDMapNet outputs rasterized results, requiring complicated handcrafted post-processing to obtain vectorized HD maps. To address this issue, VectorMapNet [27] is believed to be the first work detecting vectorized HD maps in real-time. However, it consists of two stages, and its efficiency is significantly impacted by sequential operations. In contrast, MapTR [24] uses deformable DETR [46] to design an end-to-end vectorized HD map detection model, which greatly simplifies the pipeline and delivers better detection performance. Some recent works further improve the performance of MapTR [7, 25, 32]. Among them, MapTR-V2 achieves state-of-the-art performance on vectorized HD map detection, but it still overlooks and does not investigate the inner-instance correlations between points, limiting further improvements.
+
+Detection by Transformer. DETR [5] is the first end-to-end transformer-based object detection framework. Compared with previous CNN-based methods [8, 10], DETR removes the need for anchor proposals and non-maximum suppression (NMS), making it simpler and more effective. To address the issue of slow convergence, subsequent works propose accelerating DETR training through deformable attention [46], denoising [18], and dynamic query generation [19, 36, 45]. Intuitively, most of these DETR refinements could be adapted to the HD map detection task since our proposed InsMapper relies on DETR. However, unlike typical object detection tasks in which objects are assumed to be independent and identically distributed (i.i.d.), detected points in HD maps have strong correlations, especially among inner-instance points. This inherent difference makes some refined DETR methods unsuitable to our task and additional investigations are required.
+
+# 3 Point Correlation
+
+# 3.1 Vector Map Decomposition and Sampling
+
+Let  $G$  denote the original vector map label of the scene, which consists of vertices  $V$  and edges  $E$ . The vector map contains multiple classes of road elements, including pedestrian crossings, road dividers, road boundaries, and lane centerlines. Among them, the first three classes of road elements are simple polylines or polygons without intersection points. While lane centerlines have more complicated topology, such as lane split, lane merge, and lane intersection. To unify all vector elements, the vector map is decomposed into simpler shapes (i.e., polylines and polygons) without intersections. Any vertices in the vector map with degrees larger than two (i.e., intersection vertices) are removed from  $G$ , but
+
+incident edges are kept. In this way, a set of simple polylines and polygons without intersections is obtained as  $G^{*} = \{l_{i}\}_{i=1}^{N^{*}}$ , where  $G^{*}$  is an undirected graph. Each shape  $l_{i}$  is defined as an instance, and  $N^{*}$  denotes the overall number of instances in a vector map.
+
+Following MapTR and MapTR-V2, to enhance the parallelization capacity of the model, each instance is evenly re-sampled with fixed-length points as  $l_{i} = (v_{1},\dots,v_{j},\dots,v_{n_{p}})$ .  $l_{i}$  is ordered from  $v_{1}$  to  $v_{n_p}$ , with  $n_p$  being the number of sampled points for each instance. For polygon instances,  $v_{1}$  is equal to  $v_{n_p}$ . Please refer to the supplementary document for the visualization of the pre-processing.
+
+# 3.2 Inner-instance Correlation
+
+Unlike conventional object detection tasks, where objects can be approximated as independent and identically distributed (i.i.d.), strong correlations exist between points within the same line instance in the vectorized HD map detection task. Please refer to the supplementary document for the visualization of the point correlation.
+
+Inner-instance correlation is crucial for point coordinates prediction. Points within the same instance can collaborate by sharing inner-instance information, leading to smoother and more accurate predictions. Without this collaboration, points of the same instance may produce independent predictions, leading to zig-zag or incorrect instances. The inner-instance correlation can serve as additional constraints to facilitate the query initialization and refinement of predicted lines. In previous methods, the correlation of points is not correctly analyzed and leveraged, limiting further improvement. In subsequent sections, we introduce InsMapper to more effectively utilize point correlations and improve vectorized map detection performance.
+
+# 4 Methodology
+
+# 4.1 Overall Framework
+
+Building on MapTR [24], our proposed InsMapper is an end-to-end trainable framework for online vectorized HD map detection, as illustrated in Figure 2.
+
+InsMapper is adaptive and can be seamlessly modified based on the latest frameworks with more enhanced performance, such as PivotNet [7] and MapTR-V2 [25]. Following BEVformer [22], InsMapper first projects perspective view camera images into the bird's-eye-view (BEV). After obtaining the BEV features, InsMapper uses deformable attention layers [46] to process input object queries. Each object query predicts one point, including the object class and the regression point position. To better leverage inner-instance information and further enhance the final detection performance, we introduce three designs in InsMapper: hybrid query generation, which replaces the hierarchical query in MapTR, generating line queries with better diversity; inner-instance query fusion, which fuses generated queries within the same instance based on
+
+![](images/153f5c94707310daf2c3f6a5c59eb2405a1a7953aa5e3a05b673c0fd415fe27b.jpg)  
+Fig. 2: Overall framework. InsMapper is an end-to-end transformer model with an encoder-decoder structure. The transformer encoder projects perspective-view camera images into a bird's-eye view (BEV). Subsequently, the transformer decoder detects vector instances by predicting point sets. To enhance the utilization of inner-instance information, we introduce the following three components: a hybrid query generation scheme (orange module), an inner-instance query fusion module (yellow module), and an inner-instance feature aggregation module (blue module). The first two modules better initialize queries for detection and the final one refines detected line instances.
+
+inner-instance features to further enhance the quality of initialized line queries; and inner-instance feature aggregation, which adds a new inner-instance self-attention module to decoder layers to further aggregate inner-instance features for line refinement.
+
+Different from past works, which treat queries as independently distributed, InsMapper utilizes inner-instance information to fuse object queries and aggregate intermediate features in deformable transformer decoder layers. Otherwise, adjacent vertices may produce independent position regression results, leading to zigzag or even incorrect instances. With the assistance of inner-instance information, the model can better initialize queries for detection and refine the positions of detected points within an instance, significantly enhancing the final performance, as demonstrated in the experiments section.
+
+# 4.2 Query Generation
+
+In contrast to traditional object detection tasks, where queries are independent and identically distributed (i.i.d.), the points to be detected in our task exhibit significant correlations. Various methods can be used to generate object queries as input for the transformer decoder, such as the basic scheme, hierar
+
+![](images/2b3026b0a16709faa46790e0f959aea1b377cf19f46caa56809a437cfd9980f5.jpg)  
+Fig.3: Query generation schemes. For concise visualization, the number of instances  $N_{I}$  is 2, and the number of points per instance  $n_p$  is 3. The hybrid scheme can initialize lines with both good diversity and quality.
+
+![](images/d97ac786feed7392a30d050bc18f5bde601ec124e187d05874aa7cb4d95f00c7.jpg)  
+(a) Basic
+
+![](images/6f3776c816987d234da648677839b80c2689b13c85b31dc2f64d3b1f91713c44.jpg)  
+(b) Hierarchical
+
+![](images/a87f30e0e3d703d02d5300a33ffccd98957e6509fe176317d56eef30638cf4dd.jpg)  
+(c) Hybrid  
+Fig. 4: Visualization of initialized lines with different query generation schemes. The quality and diversity of initialized lines are crucial for the final performance. Each color represents one initialized line.
+
+chical scheme, and hybrid scheme. All query generation schemes are illustrated in Figure 3. Initialized queries are organized into line instances. The quality and diversity of the initialized lines are both crucial.
+
+Basic query generation. This method is leveraged in the original DETR [5] for query generation. It assumes that points are i.i.d. and generates queries randomly, without utilizing inner-instance information. Let  $N_{I}$  denote the number of predicted instances, which is obviously larger than  $N^{*}$ . Since each instance contains  $n_p$  points, the basic object queries consist of  $N_{I} \cdot n_{p}$  randomly generated i.i.d. queries, resulting in irregular line shapes. Due to the lack of constraints on inner-instance points, the initialized line instances are noisy and have poor quality, which leads to degraded performance. MapTR with the basic query scheme is visualized in Figure 4a.
+
+Hierarchical query generation. To address the aforementioned issue of the basic scheme, a hierarchical query generation scheme is proposed in MapTR [24] and MapTR-V2 [25]. Let  $Q_{ins} = \{q_i^I\}_{i=1}^{N_I}$  denote instance queries and  $Q_{pts} = \{q_j^P\}_{j=1}^{n_p}$  denote point queries. The object queries for HD map detection are then the pairwise addition of  $Q_{ins}$  and  $Q_{pts}$ :
+
+$$
+Q = \left\{q _ {i, j} = q _ {i} ^ {I} + q _ {j} ^ {P} \mid q _ {i} ^ {I} \in Q _ {\text {i n s}}, q _ {j} ^ {P} \in Q _ {\text {p t s}} \right\}, \tag {1}
+$$
+
+where  $|Q| = |Q_{ins}| \cdot |Q_{pts}| = N_I \cdot n_p$ . For each line instance  $i$ , the instance query  $q_i^I$  denotes its uniqueness. By using  $q_i^I$  as a bridge, object queries within the same instance can better collaborate with each other for point prediction. But all line instances share the same point queries so all initialized lines tend to have quite similar shapes, degrading initialization diversity, which harms the final detection performance. The initialized lines generated by MapTR with the hierarchical query scheme are visualized in Figure 4b.
+
+Hybrid query generation. The basic scheme does not take into account any information exchange between queries, whereas the hierarchical one generates
+
+repetitive line shapes. To address these issues, this paper presents a hybrid query generation method that mitigates the drawbacks of the aforementioned schemes while maintaining appropriate inner-instance information exchange.
+
+Let the instance queries be  $Q_{ins} = \{q_i^I\}_{i=1}^{N_I}$ , and the point queries be  $Q_{pts} = \{q_j^P\}_{j=1}^{N_P} = \{q_j^P\}_{j=1}^{N_I \cdot n_p}$ . The point queries are divided into  $N_I$  instance groups, and a point query  $q_j^P$  is assigned to the  $\lceil \frac{j}{n_p} \rceil$ -th instance. Consequently, the final object query is the sum of a point query  $p_j^P$  and its assigned instance query  $p_k^I$ , where  $k = \lceil \frac{j}{n_p} \rceil$ . The object query set can be expressed as:
+
+$$
+Q = \left\{q _ {k} ^ {I} + q _ {j} ^ {P} \mid q _ {j} ^ {P} \in Q _ {p t s} \right\} \tag {2}
+$$
+
+where  $|Q| = |Q_{pts}| = N_P = N_I \cdot n_p$ . In contrast to the hierarchical scheme, each point query in the hybrid scheme is utilized only once to generate the object query, thereby preventing repetitive line shapes. Simultaneously, point queries belonging to the same instance are summed with a shared instance query, establishing the inner-instance connection. The hybrid query generation method can be considered as a combination of the basic and hierarchical schemes, effectively mitigating their respective drawbacks. InsMapper with the hybrid query generation scheme is visualized in Figure 4c.
+
+# 4.3 Inner-instance Query Fusion
+
+The input object queries for the transformer decoder are generated from instance queries and point queries. Although the generated queries can leverage some inner-instance information, this information exchange is indirect and inflexible. The instance query is distributed equally among all inner-instance points, while a more precise point-to-point information exchange cannot be realized. As a result, a query fusion module is introduced to further utilize inner-instance information and refine initialized lines.
+
+Let  $Q_{i} = \{q_{i,j}\}_{j=1}^{n_{p}}$  represent the set of object queries belonging to the  $i$ -th instance, and  $q_{i,j}$  denote the  $j$ -th point of the  $i$ -th instance.  $q_{i,j}$  is correlated with all other queries in  $Q_{i}$ . To better fuse inner-instance object queries, each query is updated by a weighted sum of all queries in  $Q_{i}$  as:
+
+$$
+q _ {i, j} = f \left(q _ {i, j}, Q _ {i}\right) = \sum_ {k = 1} ^ {n _ {p}} w _ {i, j, k} \phi \left(q _ {i, k}\right) \tag {3}
+$$
+
+where  $w_{i,j,k}$  demonstrates weights for query fusion.  $f(\cdot)$  is the fusion function and  $\phi(\cdot)$  is the kernel in case nonlinear transformation is needed.  $f(\cdot)$  could be realized by handcraft weights, fully connected layers, or self-attention. In this work, self-attention is applied as  $f(\cdot)$ .
+
+In conventional object detection tasks, object queries are assumed to be independent and identically distributed (i.i.d.), making query fusion unnecessary. However, in the task of HD map detection, the query fusion module effectively aligns the update of queries and enables each point to pay more attention to
+
+![](images/69c49678df6c7cb8472dd3c690821fde218551d962898247891c2624b3127a37.jpg)  
+(a) No fusion
+
+![](images/2e3e38d7b3ab1a38ad9f0535c2ec7191e14301154bec10b5aeda39e1526c2965.jpg)  
+(b) With fusion
+
+![](images/4d4a9fcfdb1c5a3058a2349065c04ff2c1c0f86f45216eb70bddfbebe100d8c9.jpg)  
+Fig.5: Visualization of the effect of the inner-instance query fusion module. (a) No query fusion. (b) With query fusion. The query fusion module can better refine the initialized lines based on inner-instance information. In this example, the proposed query fusion module significantly enhances the diversity of initialized line instances.  
+Fig.6: Decoder of InsMapper. An inner-instance multi-head self-attention module is incorporated into decoder layers. In this module, the attention between points belonging to different instances is blocked (grey grids). Only inner-instance attention is allowed (colored grids). Colored grids are randomly blocked with  $\epsilon$  probability (set to grey) for robustness. The proposed module can further utilize inner-instance information and refine the predicted lines.
+
+neighboring points. It can greatly refine the initialized lines for better query initialization, leading to enhanced performance. Without this module, queries within the same instance cannot be aware of each other, rendering them "blind". Poor line initialization tends to have degraded detection scores. The effect of the query fusion module is visualized in Figure 5.
+
+# 4.4 Inner-instance Feature Aggregation
+
+In addition to object query manipulation, InsMapper performs inner-instance feature aggregation for predicted line refinement in the transformer decoder layers by incorporating an additional inner-instance self-attention module. Inspired by [9], inner-instance attentions are randomly blocked with probability  $\epsilon$  for robustness. The decoder layer of InsMapper is depicted in Figure 6.
+
+The inner-instance self-attention module resembles the original self-attention module but features a specially designed attention mask. As illustrated in Figure 6, the attention mask of inner-instance points is set to zero (colored grids), indicating that attention between points within the same instance is allowed. Conversely, for points belonging to different instances (i.e., inter-instance points), the corresponding attention mask values are set to one, blocking attention between them. This method encourages the model to focus more on inner-instance
+
+information, resulting in more consistent predictions. To further enhance the robustness of this module, the inner-instance attention (colored grids) has an  $e$  probability of being blocked.
+
+An alternative method involves placing the proposed inner-instance attention module before the cross-attention module. However, the self-attention module before cross-attention should not block inter-instance information. Otherwise, some instances may produce duplicate predictions since they cannot "clearly see" other instances, which is analyzed in the original DETR [5]. Consequently, implementing inner-instance self attention before the cross-attention module leads to degraded final performance. Thus the proposed inner-instance feature aggregation should be placed after the cross-attention layer. More experiments about the decoder structure are provided in the appendix.
+
+# 5 Experiments
+
+# 5.1 Experimental Setup
+
+Datasets. Extensive experiments are conducted on the popular and challenging NuScenes dataset [2] and the Argoverse 2 dataset [37]. These two datasets comprise hundreds of data sequences captured in various autonomous driving scenarios, encompassing diverse weather conditions and time periods. The perception range for the X-axis and Y-axis in the BEV is set to  $[-15m, 15m]$  and  $[-30m, 30m]$ , respectively. The detected vectorized HD map should encompass four types of road elements simultaneously: road boundary, lane split, pedestrian crossing, and lane centerline. Among these, the lane centerline is a crucial element for ensuring effective vehicle planning and control. Detecting lane centerlines poses greater difficulty compared to the other three elements.
+
+Implementation details. We perform all the experiments on a machine equipped with 8 RTX-3090 GPUs. During the training phase, all GPUs are utilized, whereas only a single GPU is employed for inference. For our proposed InsMapper, we adopt multiple settings akin to the previous SOTA method, MapTR. All ablation studies are conducted for 24 epochs, with ResNet50 [11] as the backbone. For a fair comparison, except for the proposed modules, we keep the experiment settings exactly the same, such as batch size, network depth, the number of input queries, etc.
+
+Evaluation metrics. Models are assessed using two types of metrics. The first metric, average precision (AP), gauges the instance-level detection performance, employing Chamfer distance for matching predictions with ground truth labels. To ensure a fair comparison, we follow previous works to calculate multiple  $\mathrm{AP}_{\tau}$  values with  $\tau \in \{0.5, 1.0, 1.5\}$ , and report the average AP. To measure the topology correctness, the metric TOPO that is widely used in past works [12-14, 41] is reported. For all metrics, a larger value indicates better performance.
+
+# 5.2 Performance Comparison
+
+In this section, we compare InsMapper with previous state-of-the-art methods using the aforementioned evaluation metrics. The quantitative comparison results
+
+Table 1: Quantitative results of comparison experiments on the NuScenes validation set. Colored numbers show differences between InsMapper and the SOTA baseline under the same experiment setting. "C" and "L" denote camera and LiDAR, respectively. "-" denotes that the result is not available. "V2-99" and "Sec" correspond to VoVNetV2-99 [17] and SECOND [44].  $\dagger$  represents InsMapper based on PivotNet [7],  $\ddagger$  indicates InsMapper based on MapTR-V2 [25].  
+
+<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\(AP_{ped}\)</td><td>\(AP_{div}\)</td><td>\(AP_{bound}\)</td><td>\(AP_{center}\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>HDMapNet</td><td>30</td><td>Effi-B0</td><td>C</td><td>4.41</td><td>23.73</td><td>58.17</td><td>37.29</td><td>30.90</td><td>29.79</td></tr><tr><td>STSU</td><td>110</td><td>R50</td><td>C</td><td>-</td><td>-</td><td>-</td><td>31.21</td><td>31.21</td><td>32.11</td></tr><tr><td>VectorMapNet</td><td>130</td><td>R50</td><td>C</td><td>28.66</td><td>39.74</td><td>33.06</td><td>34.93</td><td>34.10</td><td>39.90</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.92</td><td>46.25</td><td>50.07</td><td>37.47</td><td>42.93</td><td>46.77</td></tr><tr><td>MapTR</td><td>24</td><td>V2-99</td><td>C</td><td>44.57</td><td>56.25</td><td>60.58</td><td>46.30</td><td>51.92</td><td>55.16</td></tr><tr><td>MapTR</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>49.47</td><td>58.98</td><td>66.72</td><td>44.89</td><td>55.01</td><td>56.77</td></tr><tr><td>MapTR</td><td>110</td><td>R50</td><td>C</td><td>49.16</td><td>59.12</td><td>58.93</td><td>47.26</td><td>53.62</td><td>59.16</td></tr><tr><td>BeMapNet</td><td>24</td><td>R50</td><td>C</td><td>43.59</td><td>54.11</td><td>51.90</td><td>38.60</td><td>47.05</td><td>49.90</td></tr><tr><td>PivotNet</td><td>24</td><td>R50</td><td>C</td><td>42.73</td><td>53.55</td><td>52.01</td><td>42.47</td><td>47.69</td><td>51.04</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>48.20</td><td>54.75</td><td>56.66</td><td>45.86</td><td>51.37</td><td>51.15</td></tr><tr><td>MapTR-V2</td><td>110</td><td>R50</td><td>C</td><td>58.68</td><td>65.72</td><td>67.12</td><td>56.16</td><td>61.92</td><td>63.26</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>44.36</td><td>53.36</td><td>52.77</td><td>42.35</td><td>48.31</td><td>51.58</td></tr><tr><td>InsMapper</td><td>24</td><td>V2-99</td><td>C</td><td>51.16</td><td>63.71</td><td>64.47</td><td>51.40</td><td>57.68</td><td>60.00</td></tr><tr><td>InsMapper</td><td>24</td><td>R50&amp;Sec</td><td>C&amp;L</td><td>56.00</td><td>63.42</td><td>71.61</td><td>52.85</td><td>60.97</td><td>62.51</td></tr><tr><td>InsMapper</td><td>110</td><td>R50</td><td>C</td><td>55.42</td><td>63.87</td><td>65.80</td><td>54.20</td><td>59.40</td><td>66.19</td></tr><tr><td>InsMapper†</td><td>24</td><td>R50</td><td>C</td><td>46.45</td><td>54.91</td><td>54.16</td><td>45.20</td><td>50.18</td><td>53.57</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>49.07</td><td>57.98</td><td>59.84</td><td>47.99</td><td>53.72</td><td>53.00</td></tr><tr><td>InsMapper†</td><td>110</td><td>R50</td><td>C</td><td>62.09</td><td>67.60</td><td>68.15</td><td>58.41</td><td>64.06</td><td>64.72</td></tr></table>
+
+Table 2: Quantitative results of comparison experiments on the Argoverse 2 validation set.  $\ddagger$  indicates InsMapper based on MapTR-V2 [25].  
+
+<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>APcenter</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>6</td><td>R50</td><td>C</td><td>52.88</td><td>63.68</td><td>61.18</td><td>59.73</td><td>59.37</td><td>75.79</td></tr><tr><td>MapTR-V2</td><td>6</td><td>R50</td><td>C</td><td>57.16</td><td>67.96</td><td>65.25</td><td>63.20</td><td>63.39</td><td>77.94</td></tr><tr><td>InsMapper</td><td>6</td><td>R50</td><td>C</td><td>55.61</td><td>66.60</td><td>62.58</td><td>62.67</td><td>61.87</td><td>77.58</td></tr><tr><td>InsMapper†</td><td>6</td><td>R50</td><td>C</td><td>58.91</td><td>71.35</td><td>66.90</td><td>64.70</td><td>65.46</td><td>79.26</td></tr></table>
+
+Table 3: Quantitative results of comparison experiments on the NuScenes validation set without centerline.  $\ddagger$  indicates InsMapper based on MapTR-V2 [25].  
+
+<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>APped</td><td>APdiv</td><td>APbound</td><td>mAP</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>46.04</td><td>51.58</td><td>53.08</td><td>50.23</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>59.80</td><td>62.40</td><td>62.40</td><td>61.50</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>48.44</td><td>54.68</td><td>56.92</td><td>53.35</td></tr><tr><td>InsMapper‡</td><td>24</td><td>R50</td><td>C</td><td>61.54</td><td>65.09</td><td>64.62</td><td>63.75</td></tr></table>
+
+are reported in Table 1. InsMapper is flexible and adaptive, making it seamless to modify it based on existing transformer frameworks. InsMapper is built on MapTR for experiments, we also report the results of InsMapper with different base frameworks, e.g. InsMapper† is based on PivotNet [7] and InsMapper‡ relies on the previous SOTA method MapTR-V2 [25]. Compared to the previous methods, InsMapper improves the AP of all road elements by around 2. The topological metric also sees an improvement of around 1.5. The inference FPS of
+
+Table 4: Quantitative results of comparison experiments on the NuScenes validation set. Centerlines are directed graphs in this table.  $\ddagger$  indicates InsMapper based on MapTR-V2 [25].  
+
+<table><tr><td>Methods</td><td>Epochs</td><td>Backbone</td><td>Modality</td><td>\(AP_{ped}\)</td><td>\(AP_{div}\)</td><td>\(AP_{bound}\)</td><td>\(AP_{center}\)</td><td>mAP</td><td>TOPO</td></tr><tr><td>MapTR</td><td>24</td><td>R50</td><td>C</td><td>37.39</td><td>46.61</td><td>50.69</td><td>37.22</td><td>42.98</td><td>46.98</td></tr><tr><td>MapTR-V2</td><td>24</td><td>R50</td><td>C</td><td>49.53</td><td>55.46</td><td>58.48</td><td>53.82</td><td>54.32</td><td>54.90</td></tr><tr><td>InsMapper</td><td>24</td><td>R50</td><td>C</td><td>43.24</td><td>53.77</td><td>53.89</td><td>43.22</td><td>48.53</td><td>52.09</td></tr><tr><td>\(InsMapper^{\dagger}\)</td><td>24</td><td>R50</td><td>C</td><td>51.62</td><td>57.88</td><td>60.90</td><td>56.52</td><td>56.73</td><td>56.01</td></tr></table>
+
+MapTR and InsMapper are 8.5 and 7.5, respectively. The evaluation outcomes on the Argoverse 2 dataset [37] can be found in Table 2. InsMapper outperforms past works with notable enhancements. Table 3 presents the results without centerlines. InsMapper with different bases attains an improvement of more than  $2\mathrm{mAP}$ . In the aforementioned experiments, all road elements are treated as undirected graphs. Table 4 shows the results when centerlines are represented as directed graphs. Based on the results, InsMapper still presents superior results than past works for directed HD map detection. Furthermore, we illustrate the qualitative visualizations in Figure 7. Owing to the effective employment of inner-instance information, InsMapper generates smoother and more precise HD maps compared to previous works.
+
+Consequently, InsMapper demonstrates superior performance compared to prior approaches across multiple datasets, exhibiting outstanding detection outcomes. Concurrently, InsMapper maintains a comparable inference speed to the previous state-of-the-art method. These exceptional experimental results strongly demonstrate the effectiveness and generality of the proposed designs.
+
+# 5.3 Ablation Studies
+
+Key component designs. We conduct several ablation study experiments to confirm the necessity of the proposed modules. Initially, we incorporate these modules into the previous state-of-the-art baseline model incrementally, and the results are presented in Table 5. It is evident that all three modules contribute to performance improvements, thereby validating their necessity. To further investigate the impact of each module's design, we perform comprehensive ablation studies in the following paragraphs.
+
+Hybrid query generation. Compared to basic or hierarchical query generation schemes, the proposed hybrid query generation scheme generates queries with better quality and diversity, due to effectively utilizing inner-instance correlation. The evaluation results of the different query generation schemes are presented in Table 6. These results reveal that the hybrid query generation scheme outperforms its counterparts, thereby demonstrating the soundness of this design.
+
+Inner-instance query fusion. Query fusion is proposed to leverage the correlation between inner-instance queries to enhance prediction performance. Various methods can be employed for fusing queries, including mean fusing (i.e.,
+
+![](images/9e81c143736942d0d6a4bb29a6b7d0ab832ae314d6a85d767761e8c8af2a39bd.jpg)  
+Fig. 7: Qualitative visualization. The predicted map contains four classes, i.e., road boundaries (green), lane splits (red), pedestrian crossing (blue), and lane centerlines (pink). InsMapper presents better detection results compared with the past work.
+
+![](images/503858f18474dde558d326dc82abed08358b72a575badea6db98b137a2268064.jpg)
+
+each query is summed with the mean of all queries of the same instance), fusion by the feed-forward network, and fusion by self-attention. The evaluation results are presented in Table 7. The outcomes of the query fusion methods vary significantly, with self-attention-based query fusion achieving the best results. Consequently, self-attention query fusion is incorporated into InsMapper.
+
+Inner-instance feature aggregation. In InsMapper, the inner-instance self-attention module is incorporated into the decoder layers following the cross-attention module. We evaluate InsMapper under four different conditions: without the inner-instance self-attention module (no attention), replace the inner-instance self-attention module with a vanilla self-attention module (vanilla attention), without the random blocking (no random blocking, i.e.,  $\epsilon = 0$ ), and with the module placed before the cross-attention (change position). The results are shown in Table 8. The outcomes reveal that removing or altering the proposed
+
+Table 5: Ablation studies on key component designs. "QG", "QF" and "FA" represent hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation, respectively.  
+
+<table><tr><td>QG</td><td>QF</td><td>FA</td><td>mAP</td><td>TOPO</td></tr><tr><td></td><td></td><td></td><td>42.93</td><td>46.77</td></tr><tr><td>✓</td><td>✓</td><td></td><td>45.42(↑2.49)</td><td>49.19(↑2.42)</td></tr><tr><td>✓</td><td></td><td>✓</td><td>45.45(↑2.52)</td><td>48.54(↑1.77)</td></tr><tr><td></td><td>✓</td><td>✓</td><td>46.93(↑4.00)</td><td>50.16(↑3.39)</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>48.31(↑5.38)</td><td>51.58(↑4.81)</td></tr></table>
+
+Table 6: Ablation studies on inner-instance query generation.  
+
+<table><tr><td>Query Scheme</td><td>mAP</td><td>TOPO</td></tr><tr><td>InsMapper-basic</td><td>46.62</td><td>49.39</td></tr><tr><td>InsMapper-hierarchical</td><td>46.93</td><td>50.16</td></tr><tr><td>InsMapper-hybrid</td><td>48.31</td><td>51.58</td></tr></table>
+
+Table 7: Ablation studies on inner-instance query fusion.  
+
+<table><tr><td>Query Fusion</td><td>mAP</td><td>TOPO</td></tr><tr><td>No fusion</td><td>45.45</td><td>48.54</td></tr><tr><td>Mean</td><td>43.34</td><td>46.00</td></tr><tr><td>Feed-Forward</td><td>47.80</td><td>50.93</td></tr><tr><td>Self-attention</td><td>48.31</td><td>51.58</td></tr></table>
+
+Table 8: Ablation studies on inner-instance feature aggregation. Multiple designs of the incorporated inner-instance self-attention layers are examined.  
+
+<table><tr><td>Method</td><td>mAP</td><td>TOPO</td></tr><tr><td>No attention</td><td>45.42</td><td>49.19</td></tr><tr><td>Vanilla attention</td><td>46.23</td><td>49.51</td></tr><tr><td>No random blocking</td><td>47.67</td><td>51.49</td></tr><tr><td>Change position</td><td>45.24</td><td>48.16</td></tr><tr><td>InsMapper</td><td>48.31</td><td>51.58</td></tr></table>
+
+module can impair model performance. This observation confirms the effectiveness of the proposed module design.
+
+# 6 Conclusion
+
+In this paper, we introduced InsMapper, an end-to-end transformer-based model for on-the-fly vectorized HD map detection. InsMapper surpasses previous works by effectively leveraging inner-instance information to improve detection outcomes. Three exquisite designs have been proposed to utilize inner-instance information, including hybrid query generation, inner-instance query fusion, and inner-instance feature aggregation. The first two modules improve the quality of initialized line instances for detection, while the last module effectively refines the detected lines. The superiority of InsMapper is well exhibited through experiments on the challenging NuScenes and Argoverse 2 datasets. The evaluation results demonstrate the effectiveness and generality of InsMapper, making it a promising solution for the vectorized HD map detection task. In the future, InsMapper will be further enhanced for temporal-consistent vector map detection, making it more suitable for real-world applications.
+
+Acknowledgement. This work is supported by the National Natural Science Foundation of China (No. 62201484), HKU Startup Fund, and HKU Seed Fund for Basic Research.
+
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+        "text": "Aditya Jain<sup>1*</sup>, Fagner Cunha<sup>2*</sup>, Michael James Bunsen<sup>1*</sup>, Juan Sebastián Canas<sup>1</sup>, Léonard Pasi<sup>1</sup>, Nathan Pinoy<sup>3</sup>, Flemming Helsing<sup>3</sup>, JoAnne Russo<sup>4</sup>, Marc Botham<sup>5</sup>, Michael Sabourin<sup>6</sup>, Jonathan Fréchette<sup>12</sup>, Alexandre Anctil<sup>7</sup>, Yacksecari Lopez<sup>8</sup>, Eduardo Navarro<sup>8</sup>, Filonila Perez Pimentel<sup>8</sup>, Ana Cecilia Zamora<sup>8</sup>, José Alejandro Ramirez Silva<sup>8</sup>, Jonathan Gagnon<sup>12</sup>, Tom August<sup>5</sup>, Kim Bjerge<sup>3</sup>, Alba Gomez Segura<sup>5</sup>, Marc Bélisle<sup>9</sup>, Yves Basset<sup>8</sup>, Kent P. McFarland<sup>4</sup>, David Roy<sup>5</sup>, Toke Thomas Hoye<sup>3</sup>, Maxim Larrivée<sup>10</sup>, and David Rolnick<sup>1,11</sup>",
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+        "text": "<sup>1</sup> Mila - Quebec AI Institute",
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+        "text": "2 Federal University of Amazonas",
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+        "text": "3 Aarhus University",
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+        "text": "4 Vermont Center for Ecostudies",
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+        "text": "7 Centre de données sur le patrimoine naturel du Québec",
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+        "text": "Smithsonian Tropical Research Institute",
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+        "text": "<sup>9</sup> Université de Sherbrooke",
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+    {
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+        "text": "10 Montreal Insectarium",
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+        "text": "11 McGill University",
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+    {
+        "type": "text",
+        "text": "$^{12}$  Independent Researcher",
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+        "type": "text",
+        "text": "Abstract. Insects represent half of all global biodiversity, yet many of the world's insects are disappearing, with severe implications for ecosystems and agriculture. Despite this crisis, data on insect diversity and abundance remain woefully inadequate, due to the scarcity of human experts and the lack of scalable tools for monitoring. Ecologists have started to adopt camera traps to record and study insects, and have proposed computer vision algorithms as an answer for scalable data processing. However, insect monitoring in the wild poses unique challenges that have not yet been addressed within computer vision, including the combination of long-tailed data, extremely similar classes, and significant distribution shifts. We provide the first large-scale machine learning benchmarks for fine-grained insect recognition, designed to match real-world tasks faced by ecologists. Our contributions include a curated dataset of images from citizen science platforms and museums, and an expert-annotated dataset drawn from automated camera traps across multiple continents, designed to test out-of-distribution generalization under field conditions. We train and evaluate a variety of baseline algorithms and introduce a combination of data augmentation techniques that enhance generalization across geographies and hardware setups. The dataset is made publicly available<sup>1</sup>.",
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+    {
+        "type": "page_footnote",
+        "text": "* Denotes equal contribution. Correspondence to: moth-ai@mila.quebec",
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+        "type": "page_footnote",
+        "text": "$^{1}$  https://github.com/RolnickLab/ami-dataset",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Computer vision algorithms for species identification have become important tools in studying and protecting the Earth's wildlife. Biodiversity applications have also been beneficial to computer vision, serving as a fruitful source of new benchmarks and algorithms [11,23,68,75]. However, research in computer vision for biodiversity has often focused on large animals, not reflecting the full set of challenges faced in ecology and conservation.",
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+        "type": "text",
+        "text": "There are over a million known species of insects on Earth, representing nearly one half of all known organisms (by comparison, there are only 10,000 species of birds, and even fewer mammals) [51,62]. Insects play essential roles in nearly all terrestrial ecosystems, as well as providing ecosystem services such as pollination that are critical for humanity [60], yet a looming \"insect apocalyptic\" threatens both their abundance and diversity [72]. Despite the crisis, data on insect populations is shockingly sparse [27], as a result of less resources, a plethora of species, and the high level of expertise typically required to study insects. Amid this data gap, computer vision tools for automated monitoring have the potential to radically reshape the study and conservation of insects. In particular, recent breakthroughs in camera traps for insects have made it possible to automatically photograph large numbers of individuals in the wild [38,41,58], opening up the the potential for image-processing algorithms to parse this raw data.",
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+        "text": "Species recognition from camera traps is a well-studied problem in the computer vision community [55], with common challenges including poor lighting, occlusion of individuals, camouflage, and blur [14]. However, working with insects presents distinct challenges from those faced in traditional camera traps, which are often designed for large animals. For example, while traditional camera trap images may only rarely contain a target species, almost every image from an insect camera trap includes insects – often hundreds of them. Where traditional camera traps may have a short list of species of interest, insect monitoring requires considering thousands of species at any given location, with many of them being extremely similar, and most with very little labeled data.",
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+        "type": "text",
+        "text": "While recent authors have proposed the use of computer vision tools for detecting and identifying insects in camera trap data [8, 17, 20, 32, 43, 63], such studies have involved small datasets with only a few species represented. There has to date been no work assessing the performance of algorithms in identifying large number of insect species, or addressing the challenges of generalization across in-the-wild deployments. Our work here offers the following contributions:",
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+        "text": "- We introduce the AMI (Automated Monitoring of Insects) dataset, consisting of two parts: 1) AMI-GBIF, a dataset of  $\\sim 2.5\\mathrm{M}$  human-captured images curated from citizen science platforms and museum collections, 2) AMI-Traps, an expert-annotated dataset of 2,893 insect camera trap images (representing 52,948 labeled insects) collected from a global network of automated camera traps, designed to test in-the-wild performance (Fig. 1).",
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+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "header",
+        "text": "A. Jain et al.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/00003212e95be6e5dd272b91109bf82f0a6193888b5755b4b1ef396d96a576bc.jpg",
+        "image_caption": [
+            "Fig. 1: Illustration of the difference between insect species identification from human-captured images and in the wild. On left are shown images of three moth species from our AMI-GBIF dataset, curated from citizen science data and museum collections. On right are shown images of the same species (along with other insects) within a photograph taken by an automated camera trap in the wild from our AMI-Traps dataset. One of the challenges of the AMI dataset is generalizing from AMI-GBIF to AMI-Traps without additional labeled data."
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+            "- We frame the problem of practical insect monitoring in the field as a set of computer vision tasks, entailing very fine-grained classification from long-tailed data, with the additional challenge of generalization across multiple kinds of imagery.",
+            "- We test a variety of strong baseline models for the proposed tasks, including a combination of data augmentation approaches that significantly improve performance under field conditions."
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+        "text": "2 Related Work",
+        "text_level": 1,
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+    {
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+        "text": "Biodiversity Image Datasets. Advancements in computer vision have been closely intertwined with the creation of curated datasets such as ImageNet [26, 59], Pascal VOC [30], Open Images [44], and MS-COCO [46]. In recent years, the computer vision and machine learning communities have increasingly directed their focus towards addressing pressing human threats, including biodiversity loss [68] and climate change [57]. These domains not only hold significant potential for societal impact but also offer fertile ground for exploring intriguing machine learning questions such as domain generalization [77], long-tailed distributions [71], and fine-grained classification [74]. Such challenges have found especially fruitful testbeds in the classification of species, where datasets such as iNaturalist [70] have proven useful for both the computer vision and ecology communities. While some challenges have considered plant identification [15, 45, 53, 56], the majority have focused on animals, including datasets focused on birds [16, 69, 73], mammals [9, 14, 64], and fish [22, 25, 39, 40]. Such datasets have often leveraged concurrent advancements in sensor technology, including in satellite imagery and drones. In particular, camera traps have been widely adopted by biologists as an in situ and cost-effective means of wildlife",
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+        "text": "Insect Identification in the Wild",
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+    {
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+        "image_caption": [
+            "(a) Incomplete"
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+            "(b) Overlapping",
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+        "image_caption": [
+            "Fig. 2: Examples of challenges in the AMI-Traps dataset. (a) Incomplete: In some occasions, the body of an insect is incomplete due to its position in the automatically taken image. (b) Overlapping: Sometimes insects occlude each other. (c) Motion: Moving insects can be blurred and hard to classify. (d) Lighting: The lighting and camera exposure of the images is variable and can lead to poor contrast that masks some or all detail. (e) Resolution: Some insects are very small, leading to low-resolution images. (f) Perspective: While insects are generally positioned at a fixed distance, sometimes insects appear in the air or perched on the camera itself. Additionally, unexpected objects such as spider webs, dirt, and vegetation can be captured by the cameras and may be confused with objects of interest."
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+            "(d) Lighting",
+            "(e) Resolution"
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+        "text": "monitoring [55], and have in turn presented fascinating challenges for the computer vision community [14], including in classification [12, 29], object detection [13,31], out-of-distribution generalization [34,42,50], and active learning [54]. Such algorithms have to date, however, been designed mostly for large animals such as mammals.",
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+    {
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+        "text": "Insect Image Datasets. As algorithms and datasets for species recognition have proliferated, insects have traditionally been underrepresented. Within ImageNet1k [59], only 27 classes depicted insects, as compared to 57 for birds and 93 classes for wild mammals [49]. Some popular fine-grained classification datasets such as NABirds and CUB have focused exclusively on birds [69, 73], while camera trap datasets such as iWildCam have been focused on mammals [12]. The iNat2017 dataset [70] included 1,021 classes of insects out of 5,089 total classes in the dataset. By largely focusing on other taxonomic groups, prior works have neglected the challenges posed by insect data, such as extremely similar classes (reflecting far greater diversity than any other group of organisms), small size, hyperabundance, etc. In recent years, however, some works have introduced insect-focused benchmark datasets. The newly released BIOSCAN-1M dataset includes images and DNA sequences, with a focus on fly identification [33]. Despite the very large size of the dataset (1.1 million datapoints), the number of object classes involved is relatively small, with the focus being to distinguish between 40 taxonomic families of flies, reflecting the challenging nature of insect identification. Other recent datasets for computer vision include one focused on 8 classes of pollinators across Europe [61], and the Indian Butterflies dataset,",
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+    {
+        "type": "page_number",
+        "text": "4",
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+    {
+        "type": "header",
+        "text": "A. Jain et al.",
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+    {
+        "type": "text",
+        "text": "encompassing 30k images of butterflies from India across 315 species [67]. A variety of publications have used computer vision algorithms for detection of pest insects in specific agricultural applications [10, 52, 66].",
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+    {
+        "type": "text",
+        "text": "Insect Camera Traps. The use of camera traps for studying insect biodiversity is relatively recent. Geissmann et al. [32] introduced the Sticky Pi device, which uses sticky cards to capture (and kill) insects, which are then automatically photographed. Bjerge et al. [21] introduced an automated camera trap using UV light to attract and photograph moths and other insects (without killing them), which was built on by subsequent works [18, 20]. A similar approach focused on diurnal pollinators via a camera trap installed above flowers [17, 19]. These works also propose deep learning methods for processing the resulting images, considering both object detection and classification of a small number of insect categories. The lack of fine-grained classification is largely due to the time required to annotate images from the traps, making it difficult to obtain a large enough labeled dataset from trap data alone.",
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+    {
+        "type": "text",
+        "text": "3 Benchmark Design",
+        "text_level": 1,
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+        "text": "In this paper, we propose a benchmark dataset for insect species identification that addresses the challenges faced in real-world use cases. These include both (1) challenges that distinguish insect identification from other kinds of species identification, notably the massive diversity of often-similar species, and (2) the particular challenges associated with deploying these algorithms \"in the wild\".",
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+        "type": "text",
+        "text": "To address the first family of challenges, we introduce a dataset for fine-grained insect classification that (to our knowledge) is by far the largest yet released, with  $\\sim 2.5\\mathrm{M}$  images across over 5,000 classes. We concentrate on moths, which are readily drawn to UV camera traps and can often be visually identified to species (unlike some other insects) [21].",
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+    {
+        "type": "text",
+        "text": "The second family of challenges is more complex - involving the gap between field conditions and the high-quality images typically used for training species identification algorithms. Figure 2 illustrates some of the challenges that computer vision algorithms face on data from automated insect camera traps, in contrast to images taken by humans. Insects may occlude each other or be partially \"out of frame\". Motion blur and lighting issues may occur, along with objects in unexpected positions. The resolution of images may be very low, owing to the small size of insects at a stereotyped distance from the camera. Also, insect camera traps typically use webcams and PCB camera modules due to their cost and software integration capabilities, and the resulting images are often both structurally different and overall lower quality than those taken by human photographers.",
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+    {
+        "type": "text",
+        "text": "As described in the preceding section, previous authors working with insect camera traps have addressed the problem of challenging camera trap data by training algorithms on annotated data from the particular camera trap in question. However, manual annotation is extremely time-intensive, since it must be performed by expert entomologists, of whom there are very few in any given",
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+    {
+        "type": "header",
+        "text": "Insect Identification in the Wild",
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+    {
+        "type": "page_number",
+        "text": "5",
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+    {
+        "type": "text",
+        "text": "region. Insect species vary greatly across regions, meaning that fine-grained annotations in one location are generally not useful in another. Furthermore, the hardware used in insect camera traps also varies greatly (with considerable differences in lighting and background, as well as image sharpness, contrast, noise reduction settings, and compression artifacts, which are exacerbated on small scale crops), meaning that even two datasets from the same region may not be comparable.",
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+        "type": "text",
+        "text": "In this paper, we remove the problem of annotation by solving a more challenging computer vision problem. Namely, we propose to train algorithms on abundant labeled images of insects taken by human photographers, then use these algorithms on out-of-distribution camera trap images. Our benchmark dataset is designed to test this functionality, by including both a large training set of curated photographs taken by humans and an out-of-distribution test set drawn from a geographically diverse set of insect camera traps.",
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+        "type": "text",
+        "text": "The AMI dataset is therefore designed to test fine-grained classification of moth species both in in-distribution and out-of-distribution contexts. It also includes the task of binary classification of insects as moth or non-moth, which is a prerequisite for camera traps since moths are not the only insects to appear. Note that we do not consider the task of object detection, which in applications is a precursor to insect identification. This is because object detection against a relatively plain background is a simpler task, where good results have already been obtained in the insect camera trap literature [18,20,21,32].",
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+    {
+        "type": "text",
+        "text": "4 The AMI Dataset",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we describe the construction of the datasets that we release in this work: AMI-Traps and AMI-GBIF. For AMI-Traps, we collected insect camera trap data by field deployments in three regions: NE-America (Northeast of North America), which includes data from Quebec in Canada and Vermont in the USA; W-Europe (Western Europe), which includes data from the UK and Denmark; and C-America (Central America), comprising data from Panama. For AMI-GBIF, we compiled public data for the same three regions using the Global Biodiversity Information Facility (GBIF) [7]. The GBIF platform provides access to biodiversity data aggregated from multiple sources, such as museums, research institutions, and citizen science platforms such as iNaturalist [4], Observation.org [5], and BugGuide [1]. For brevity, we sometimes refer to AMI-Traps and AMI-GBIF as AMI-T and AMI-G, respectively. Figure 3 shows examples of images from the two datasets and Tab. 1 compares the number of images and coverage of classes at different taxonomic levels.",
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+        "type": "text",
+        "text": "4.1 AMI-Traps Dataset",
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+        "type": "text",
+        "text": "Data Collection. The source images in the AMI-Traps dataset were collected from a variety of different insect camera traps deployed across 22 monitoring stations in the three regions previously described. The cameras were configured",
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+        "text": "6",
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+    {
+        "type": "header",
+        "text": "A. Jain et al.",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/6d3d09004541e7bbf9f29d11bdc159376009b17c5cc75bd7e740c4a592d92ee7.jpg",
+        "image_caption": [
+            "Fig. 3: Sample images from the AMI Dataset. The AMI Dataset is composed of (1) AMI-GBIF, curated from a number of sources with imagery from citizen science and museum collections, and (2) AMI-Traps, drawn from automated camera traps for insects across five countries in three regions. The number of individual insects annotated per sub-dataset is denoted in parentheses."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "to be motion-sensitive, as well as taking photos on a fixed interval of 10 minutes; we selected a subset of images for annotation so as to avoid highly similar images. In total, 2,893 trap images were sampled from all cameras and made available on the Label Studio annotation platform (see Appendix B for more details).",
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+        "text": "Annotation Process. Images were annotated by entomologists with expertise in the species of the particular region. Labeling was conducted according a three-step process. 1) We designed a custom object detection model to suggest boxes around objects in the image (refer to Appendix B for details on this model), to save annotators time. Annotators were asked to correct errors in the proposed boxes as well as drawing any missing boxes. Insects appearing smaller than 1 centimeter were ignored. 2) Annotators were asked to label image crops according to one of three coarse categories: moth, non-moth, or unidentifiable. Some insects could not be labeled due to motion blur, occlusion, or other factors. 3) For insects labeled as moths, annotators were asked to select the narrowest taxonomic group that could be determined from the image - identifying moths to species where possible, if not species then genus, and if not genus then family.",
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+    {
+        "type": "text",
+        "text": "Data Statistics. 2,893 source images from the traps were annotated (see Tab. B.2 in the supplementary for further details) which includes Vermont (900), Denmark (892), Quebec (533), UK (446), and Panama (122). A total of 52,948 insects were labeled within these images, including 37,105  $(70.08\\%)$  non-moths,",
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+    {
+        "type": "header",
+        "text": "Insect Identification in the Wild",
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+    {
+        "type": "page_number",
+        "text": "7",
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+    {
+        "type": "text",
+        "text": "14,105 (26.64%) moths, and 1,738 (3.28%) unidentifiable. Out of the 14,105 moth crops, 10,854 (76.95%), 7,065 (50.09%) and 5,374 (38.10%) crops were labeled at the family, genus, and species level respectively.",
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+    {
+        "type": "text",
+        "text": "4.2 AMI-GBIF Dataset",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "AMI-GBIF has two sub-datasets: binary and fine-grained classification. The fine-grained classification dataset contains images for moth species in each of the regions covered by AMI-Traps. The binary classification dataset contains images of moths aggregated across all regions and non-moths from anywhere on earth.",
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+        "type": "text",
+        "text": "Dataset Construction. First, in collaboration with regional moth specialists, we created \"checklists\" of species that could occur in each of the three regions of interest. It is worth noting that some species are included in more than one checklist, though most are unique to a single region. Next, we compared the checklists against the GBIF taxonomic backbone [2], merged synonym names (since some species have multiple accepted names), and manually investigated doubtful or unmatched names. Following that, we used the GBIF occurrence search tool to download metadata for all observations from the order Lepidoptera with images, which returned 15.1 million observations [3]. We then fetched images from observations in which the species is included in our regional checklists. The number of training images per species were limited to 1,000, though for many species it was considerably lower due to the long-tailed nature of the data. All images were resized to have the smallest dimension of 450px and packaged using the WebDataset format [6].",
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+    {
+        "type": "text",
+        "text": "Quality Control. After downloading the images, we applied a set of cleaning steps to ensure the quality of the dataset. First, we removed duplicate URLs, i.e., images linked to more than one observation. This may occur when an image contains multiple individual insects, or when a placeholder is used for an observation (for example, Fig. A.1b in Appendix A shows a picture used as a placeholder for more than 100,000 observations). Next, we excluded images from specific datasets (refer to Tab. A.1 in Appendix A)) that we found to have a high percentage of images unsuitable for training our models, for instance, images of body parts or text only. Another issue we identified is that some observations contained thumbnail images that are too small to provide sufficient information to train our models; we removed all images with a width or height less than 64 pixels. Finally, as our dataset targets only adult insects, we removed images containing non-adult individuals such as eggs and caterpillars. For observations where the life stage was reported by the observer, approximately  $60\\%$  of the cases, we removed all occurrences tagged as non-adult. For the remaining images with a missing life stage tag, we designed a classification model to predict the life stage (refer to Appendix A for details about this model) and removed all images classified as non-adult.",
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+    {
+        "type": "text",
+        "text": "Dataset Split. Each GBIF observation may contain more than one image, but each image is considered an independent instance of the species. However, as images belonging to the same observation may be very similar, we keep images from the same observation in the same data split. To do so, we split the dataset",
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+    {
+        "type": "page_number",
+        "text": "8",
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+    },
+    {
+        "type": "header",
+        "text": "A. Jain et al.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "using the observation ID as reference, with the proportion of  $70\\%$ ,  $10\\%$ , and  $20\\%$  for the train, validation and test sets respectively. We apply a stratified split, i.e., we guarantee that this proportion is also maintained at the species level. We exclude species with fewer than 5 images, so the minimum number of images for a species in the training set is 4, and in the test set is one. Due to the data split based on observation ID, the validation set might lack images for some species. As some species may belong to multiple checklists, we keep the train/val/test splits consistent across the regions to prevent data leakage when training a unified model for all regions.",
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+        "text": "Binary Classification. Since moths are not the only insects that appear on the camera trap screen, for our proposed benchmark task of binary classification, we curate a dataset comprising 350,000 images for each of the moth and non-moth categories. The moth class consists of adult moth images randomly sampled from the AMI-GBIF dataset. For the non-moth category, we leveraged expert knowledge of the taxonomic groups likely to appear on the screen, fetching images of adult individuals from GBIF of the following groups: Diptera (85,474), Hemiptera (75,053), Odonata (68,770), Coleoptera (45,954), Araneae (21,321), Orthoptera (21,261), Formicidae (12,206), Ichneumonidae (6,581), Trichoptera (5,316), Neuroptera (4,880), Opiliones (1,880), Ephemeroptera (1,304) — this includes mostly insects, with some Arachnids. The dataset is split into train, validation, and test sets with proportions of  $70\\%$ ,  $10\\%$ , and  $20\\%$ , respectively. Specifically for the moth category, the splits are kept consistent with the splits for the fine-grained species classification task.",
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+        "type": "text",
+        "text": "Statistics. The final dataset contains  $\\sim 2.5\\mathrm{M}$  images from 5,364 species, 1,734 genera and 77 families of moths, along with 350,000 additional images of non-moth groups. The binary dataset contains 700,000 images, composed of 350,000 moth images and the 350,000 non-moth images. The fine-grained dataset contains 2,564,392 moth images, and Tab. 1 shows the number of images and species for each region. Though species are selected based on their presence in regions of interest, we include all GBIF observations of these species from anywhere on Earth (see Fig. A.2 in supplementary for the global distribution of images). As in other biodiversity datasets, the number of images per species in AMI-GBIF follows a long-tailed distribution (see Fig. C.3 in supplementary). Specifically, only 3,099 species have more than 100 images and are considered under the \"many-shot\" bucket, 1,358 species contains between 20 and 100 images and are considered \"medium-shot\", and there are 907 species with less than 20 training images, considered as \"few-shot\" categories.",
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+    {
+        "type": "text",
+        "text": "5 Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we describe the methods used to assess the difficulty of the proposed benchmark tasks. We evaluate a variety of high-performing image classification architectures and use extensive data augmentation to address the challenges of domain shift between the two datasets. Motivated by the particular structure of the AMI-Traps dataset, we add a mixed-resolution (MixRes) data",
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+    {
+        "type": "header",
+        "text": "Insect Identification in the Wild",
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+    },
+    {
+        "type": "page_number",
+        "text": "9",
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+    {
+        "type": "table",
+        "img_path": "images/cf4692da1b0ca236aaa7751bf606018707568c1a42204c55a51125fd9061c300.jpg",
+        "table_caption": [
+            "Table 1: Comparison between the AMI-GBIF and AMI-Traps dataset for the fine-grained classification task. Images for the traps dataset denote the individual insect crops and not the raw trap images. The last three rows show the unique classes for each of the three taxonomic levels for the two datasets for different regions. It is also important to note that regions have species in common."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">All Regions</td><td colspan=\"2\">NE-America</td><td colspan=\"2\">W-Europe</td><td colspan=\"2\">C-America</td></tr><tr><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td></tr><tr><td>Images</td><td>2,564,392</td><td>14,105</td><td>1,179,943</td><td>9,066</td><td>1,579,333</td><td>4,066</td><td>99,405</td><td>973</td></tr><tr><td>Families</td><td>77</td><td>43</td><td>68</td><td>34</td><td>65</td><td>26</td><td>27</td><td>11</td></tr><tr><td>Genera</td><td>1,734</td><td>344</td><td>887</td><td>204</td><td>957</td><td>192</td><td>385</td><td>12</td></tr><tr><td>Species</td><td>5,364</td><td>516</td><td>2,497</td><td>277</td><td>2,603</td><td>244</td><td>636</td><td>6</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "augmentation technique. As we describe in the following section, our approaches perform quite well, with MixRes leading to an especially significant performance improvement.",
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+    {
+        "type": "text",
+        "text": "Models. We work with five computer vision models widely used in identification of wildlife: ResNet50 [35], MobileNetV3-Large [37], ConvNeXt-T [47], ConvNeXt-B [47], and ViT-B/16 [28]. We select ResNet50 because it is the most popular backbone used as a baseline for almost any computer vision task. Considering the possibility that the trained models may need to run on hardware with limited resources, such as edge devices and personal computers, for in-field predictions, we choose MobileNetV3Large as a lightweight model alternative. Furthermore, considering that vision transformers have surpassed convolutional neural networks and become the state-of-the-art models for image classification, we select the ViT-B/16 model to provide a baseline from this family of architectures. Finally, for representing modern convolutional neural networks, we choose the recently introduced ConvNeXt architecture, which has proven to be competitive with transformers using only standard ConvNet modules. From this family of models, we select two versions: the base version (ConvNeXt-B) and, considering lightweight usage scenarios, we also include the tiny version (ConvNeXt-T). Unless otherwise stated, we use a default input resolution of 128x128 for all models.",
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+    {
+        "type": "text",
+        "text": "Data Augmentation Approaches. One characteristic of the in-the-wild images is the large variety of crops due to the diversity of insect sizes. A considerable number of them have small resolutions, below  $64 \\times 64$ . At this scale, some important visual features that the model may have learned from high-resolution GBIF images might not be identifiable, leading to inaccurate predictions. This issue can be further amplified when these low-resolution crops are scaled up to the input model size. To compel the model to learn features for low-resolution inputs and avoid bias towards visual features only distinguishable in high-resolution images from other domains, we use a data augmentation technique we refer to as Mixed Resolution (MixRes) that simulates this low-resolution input during training (see Fig. D.4 in supplementary). This approach consists of randomly resizing the training input image to  $25\\%$  or  $50\\%$  of the model input size with a",
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+    {
+        "type": "page_number",
+        "text": "10",
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+    },
+    {
+        "type": "header",
+        "text": "A. Jain et al.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "probability  $\\rho$  for each case. In our experiments  $\\rho$  is set to 0.25, maintaining the original input size with probability 0.5. We employ MixRes in all experiments unless otherwise stated.",
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In addition to MixRes, we also use a set of standard data augmentation operations: random resize crop with scale of 0.3 to 1.0 and an aspect ratio between  $3/4$  and  $4/3$ , random horizontal flip with  $50\\%$  probability, and RandAugment [24] with  $N = 2$  operations and magnitude  $M = 9$ . Finally, the image is normalized using the mean and standard deviation of ImageNet and scaled to the input network size.",
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. We train all models with the AMI-GBIF training sets using the ImageNet-1K pretrained weights from the timm library [76] (for ConvNext and ViT we used ImageNet-22K weights). Each model is trained with a batch size of 128 and the AdamW optimizer [48] for 30 epochs. The initial learning rate is set to 0.001, with a weight decay of 1e-5. The learning rate is linearly warmed up from 0 to the initial value for 2 epochs and then decayed using cosine scheduling [36]. We also apply label smoothing [65] with a value of 0.1.",
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+    },
+    {
+        "type": "text",
+        "text": "Inference Settings. At test time, the insect crops from AMI-Traps are padded with black pixels to make them square, preventing the distortion of the shape of the insect before prediction. Next, the images are normalized with the mean and standard deviation of ImageNet and, finally, resized to the model input size. No padding is done for the test images from AMI-GBIF.",
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Higher Taxonomic Rank Prediction. We consider the accuracy of our baseline models both with respect to the exact insect species predicted and with respect to higher level taxonomic groups such as genus and family. Indeed some images in our dataset cannot be labeled at the species level at all due to the quality or perspective of the image, and our annotators instead provided labels at the genus or family level. In our experiments, to make predictions at a higher taxonomic level, we simply sum together species-level predictions to get genus results, and similarly, the genus predictions are grouped together to get family predictions.",
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+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. During the binary classification step, it is important to achieve high precision by filtering out as many non-moths as possible to prevent the propagation of errors in the pipeline. At the same time, it is also important to assess recall because if too many moths are discarded at this step, it may impact the utility of the data for ecological studies. Therefore, for the binary classification task, along with accuracy, we also consider precision, recall, and F1-score as evaluation metrics. For the fine-grained classification task, we evaluate the model in terms of micro- and macro-averaged accuracy at the species, genus and family levels. Micro-averaging aggregates all class samples to calculate the accuracy while the macro-average is the average of per-class accuracy. Unless otherwise stated, the reported accuracy is micro-averaged. We conduct each experiment for three independent runs and report the mean and standard deviation.",
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+    {
+        "type": "header",
+        "text": "Insect Identification in the Wild",
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+    },
+    {
+        "type": "page_number",
+        "text": "11",
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+    {
+        "type": "text",
+        "text": "6 Experiments and Results",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Binary Classification Results. This task involves distinguishing moths from non-moths. Here we train a ResNet50 model on the AMI-GBIF dataset and evaluate performance both on the AMI-GBIF held-out test set and on the entirety of the AMI-Traps dataset. On AMI-GBIF (in-distribution), the model achieves a test accuracy of  $97.77\\% \\pm 0.02\\%$ . Table 2 shows the results for the AMI-Traps dataset in more detail. We observe that the model has a high recall but a lower precision, which means it is over-predicting the moth class. Also, the bigger the image crop, the better the accuracy of the insect classification; many non-moths where the model errs are extremely small and are therefore highly blurred in the trap images. Table E.3 in the supplementary illustrates the improvement in model performance when crops are square padded (our default at inference time) versus an ablation where padding is not performed.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8650a1fd72c60892336133d2d9c26a31e49babb0317771eb2b06cb36c8805ad4.jpg",
+        "table_caption": [
+            "Table 2: Binary classification model evaluation results on the AMI-Traps dataset after training on AMI-GBIF, showing that recall is high throughout, while precision drops on very small insects, which are predominantly non-moths. Crops  $>100\\mathrm{px}$  or  $>150\\mathrm{px}$  represent that atleast one side of the box is greater than the threshold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Moths</td><td>Non-moths</td><td>Total</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1-score</td></tr><tr><td>All crops</td><td>14,105</td><td>37,105</td><td>51,120</td><td>86.48±1.00</td><td>68.31±1.70</td><td>95.03±0.39</td><td>79.48±1.27</td></tr><tr><td>Crops &gt; 100px</td><td>11,630</td><td>16,534</td><td>28,164</td><td>88.39±0.97</td><td>79.46±1.43</td><td>96.99±0.20</td><td>87.35±0.94</td></tr><tr><td>Crops &gt; 150px</td><td>6,446</td><td>5,961</td><td>12,407</td><td>92.95±0.22</td><td>89.83±0.43</td><td>97.48±0.12</td><td>93.70±0.30</td></tr></table>",
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+        "text": "Fine-grained Classification Results. The fine-grained classification task aims to identify moths to the species level (and secondarily to genus or family level). In our experiments, we train models on AMI-GBIF data for each of the three regions of the AMI dataset, evaluating both on AMI-GBIF (in-distribution) and AMI-Traps (out-of-distribution) data (see Tab. 3). Not all moth species present in a region appear regularly at camera traps; hence, the list of species in AMI-Traps is a subset of species in AMI-GBIF for a given area (see Tab. 1). Therefore, we also evaluate the models on an in-distribution subset  $(\\mathrm{Test}\\ddagger)$  from AMI-GBIF containing only the species present in AMI-Traps. Meanwhile, for AMI-Traps, there are 16 species not present in AMI-GBIF that were removed during our evaluation procedure (these represent unexpected species not included in the regional checklists used to define AMI-GBIF). Overall, the best model at the species level is ConvNeXt-B for both AMI-GBIF and AMI-traps. For C-America, annotations are mostly provided at the genus or family level, due to the challenging nature of visual identification of moths in this biodiversity-rich region. Furthermore, while the genus and family accuracies are similar between N-America and W-Europe, they are much lower for C-America. This can be attributed to the fact that there are 10 times fewer images in the training set for this region. Note that for genus and family evaluation, there are some cases where the accuracy is lower than the species level. This occurs because those",
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+    {
+        "type": "page_number",
+        "text": "12",
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+    {
+        "type": "header",
+        "text": "A. Jain et al.",
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+    {
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+        "table_caption": [
+            "Table 3: Accuracy results for the fine-grained classification task. Overall, ConvNeXt-B achieves the best results for both AMI-GBIF and AMI-traps, with ViT-B/16 achieving slightly better results for some cases at the genus and family levels. Test‡ represents a subset of the AMI-GBIF test set, containing only the species present in AMI-Traps. Species-level results on AMI-Traps for the C-America region are not available since most annotations were provided only at higher taxonomic levels."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Region</td><td rowspan=\"3\">Model</td><td colspan=\"2\">AMI-GBIF</td><td colspan=\"6\">AMI-Traps</td></tr><tr><td colspan=\"2\">Species</td><td colspan=\"2\">Species</td><td colspan=\"2\">Genus</td><td colspan=\"2\">Family</td></tr><tr><td>Micro Test</td><td>Micro Test‡</td><td>Micro Top1</td><td>Macro Top1</td><td>Micro Top1</td><td>Macro Top1</td><td>Micro Top1</td><td>Macro Top1</td></tr><tr><td rowspan=\"5\">NE-America</td><td>ResNet50</td><td>87.56±0.12</td><td>89.39±0.14</td><td>71.86±1.02</td><td>64.96±2.00</td><td>80.07±0.49</td><td>74.66±0.35</td><td>90.44±0.41</td><td>69.30±4.15</td></tr><tr><td>MBNetV3L</td><td>83.73±0.17</td><td>85.80±0.29</td><td>67.41±0.72</td><td>61.21±1.20</td><td>74.83±1.30</td><td>71.20±2.47</td><td>89.31±0.62</td><td>64.48±1.87</td></tr><tr><td>ConvNeXt-T</td><td>89.81±0.05</td><td>91.21±0.06</td><td>74.89±0.05</td><td>68.00±0.76</td><td>83.26±1.22</td><td>77.26±0.85</td><td>90.61±0.53</td><td>74.60±0.64</td></tr><tr><td>ConvNeXt-B</td><td>90.45±0.03</td><td>91.66±0.03</td><td>76.75±1.52</td><td>68.56±0.62</td><td>85.46±0.83</td><td>78.28±0.14</td><td>91.07±0.29</td><td>76.87±1.10</td></tr><tr><td>ViT-B/16</td><td>86.39±0.05</td><td>87.94±0.10</td><td>77.43±0.79</td><td>68.02±0.34</td><td>85.57±0.98</td><td>78.97±0.72</td><td>91.45±0.34</td><td>73.66±1.49</td></tr><tr><td rowspan=\"5\">W-Europe</td><td>ResNet50</td><td>86.45±0.08</td><td>90.25±0.03</td><td>79.39±0.39</td><td>72.84±0.21</td><td>78.95±0.26</td><td>73.22±0.60</td><td>89.13±0.42</td><td>75.24±1.85</td></tr><tr><td>MBNetV3L</td><td>82.20±0.05</td><td>86.47±0.13</td><td>76.30±1.29</td><td>70.35±0.93</td><td>76.35±1.19</td><td>72.88±1.28</td><td>88.33±0.47</td><td>72.21±0.38</td></tr><tr><td>ConvNeXt-T</td><td>88.82±0.03</td><td>92.05±0.05</td><td>82.44±0.89</td><td>74.59±0.62</td><td>81.86±0.79</td><td>74.15±0.59</td><td>90.08±0.59</td><td>74.58±2.93</td></tr><tr><td>ConvNeXt-B</td><td>89.35±0.01</td><td>92.48±0.05</td><td>82.87±0.39</td><td>76.41±0.50</td><td>82.45±0.44</td><td>75.98±1.05</td><td>91.27±0.60</td><td>79.39±2.70</td></tr><tr><td>ViT-B/16</td><td>85.45±0.03</td><td>89.22±0.11</td><td>82.44±0.36</td><td>75.25±0.98</td><td>83.01±0.26</td><td>75.96±0.35</td><td>91.68±0.17</td><td>75.81±0.79</td></tr><tr><td rowspan=\"5\">C-America</td><td>ResNet50</td><td>87.46±0.23</td><td>95.92±0.68</td><td>-</td><td>-</td><td>47.44±1.11</td><td>66.59±0.60</td><td>69.18±0.24</td><td>42.40±0.31</td></tr><tr><td>MBNetV3L</td><td>83.68±0.24</td><td>92.89±0.27</td><td>-</td><td>-</td><td>41.03±2.22</td><td>59.32±1.18</td><td>68.34±1.69</td><td>41.42±2.98</td></tr><tr><td>ConvNeXt-T</td><td>87.65±0.11</td><td>95.46±0.46</td><td>-</td><td>-</td><td>55.77±3.33</td><td>70.68±1.58</td><td>69.46±0.42</td><td>45.35±0.67</td></tr><tr><td>ConvNeXt-B</td><td>88.62±0.09</td><td>96.22±0.26</td><td>-</td><td>-</td><td>51.92±3.85</td><td>68.63±1.94</td><td>72.24±1.47</td><td>44.31±1.32</td></tr><tr><td>ViT-B/16</td><td>79.80±0.26</td><td>88.36±1.02</td><td>-</td><td>-</td><td>47.44±4.44</td><td>64.70±4.07</td><td>69.87±1.51</td><td>42.00±3.60</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "higher taxonomic levels include crops that have labels only at higher levels. In the supplementary material, we include additional results for AMI-GBIF long-tail accuracies (Tab. E.4), a pre-training ablation study (Tab. E.5), and a study analyzing classification accuracy as a function of prediction confidence (Fig. E.5).",
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+    {
+        "type": "text",
+        "text": "Data augmentation approaches. To assess the effectiveness of the mixed resolution data augmentation technique, we conduct an ablation study using ResNet50 for the NE-America region. As the effects of MixRes could already be covered by other data augmentation operations used in our preprocessing, such as random resize crop or one of the operations of RandAugment, we analyze multiple combinations of these operations. Additionally, we evaluate a higher input resolution, using the original 224 input size of ResNet50, to determine whether this leads to better predictions. Table 4 shows the results. While applying MixRes results in a slight decrease in accuracy within the in-distribution AMI-GBIF test set, for the in-the-wild AMI-Traps test set there is a substantial improvement, ranging between  $4\\%$  and  $7\\%$  when compared to models not trained with MixRes. Another important observation is that, although RandAugment and random resize together contribute to an overall improvement of around  $16\\%$ , MixRes remains additionally beneficial. Finally, despite an increase of more than  $4\\%$  in accuracy within the original domain when using a higher resolution, there is a marginal decrease in the accuracy of the in-the-wild results.",
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+    {
+        "type": "text",
+        "text": "7 Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Many ecological applications require species-level image classification to meet their goals. Despite advances in computer vision, there remain challenges in",
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+    {
+        "type": "header",
+        "text": "Insect Identification in the Wild",
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+    },
+    {
+        "type": "page_number",
+        "text": "13",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f6c860a8441da95dff8cbccbac4a26ab243dad7232acb9d117ff1fd7b9021d02.jpg",
+        "table_caption": [
+            "Table 4: Ablation study on data augmentation techniques using a ResNet50 for the NE-America region evaluated on micro-averaged top-1 species accuracy. \"RandAug\" denotes the combination of the RandAugment and random resize crop data augmentation techniques. AMI-GBIF† test set contains only the species present in AMI-Traps."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Resolution</td><td>RandAug</td><td>MixRes</td><td>AMI-GBIF‡</td><td>AMI-Traps</td></tr><tr><td>128</td><td>×</td><td>×</td><td>89.18±0.08</td><td>51.46±2.73</td></tr><tr><td>128</td><td>✓</td><td>×</td><td>89.71±0.16</td><td>67.88±1.27</td></tr><tr><td>128</td><td>×</td><td>✓</td><td>87.41±0.06</td><td>58.41±0.30</td></tr><tr><td>128</td><td>✓</td><td>✓</td><td>89.39±0.14</td><td>71.86±1.02</td></tr><tr><td>224</td><td>✓</td><td>✓</td><td>92.97±0.17</td><td>68.41±1.06</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "implementing fine-grained classification that is effective in real-world scenarios. Here we outline the challenges of insect identification in the wild and propose a benchmark dataset to tackle them. We present AMI-GBIF, a dataset with 2.5 million labeled photographs of 5,000 moth species. We also introduce AMI-Traps, a dataset of images captured by automated insect monitoring systems across five countries, labeled by regional experts. We evaluate multiple classification models both on the AMI-GBIF dataset and in out-of-distribution generalization to AMI-Traps, with ConvNeXt-B generally performing the best. We also evaluate a range of data augmentation techniques, finding that a combination of simple approaches, notably mixed-resolution augmentation, considerably improves generalization under field conditions.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Several limitations of this work should be noted. First, while annotating AMI-Traps already occupied a considerable time for expert entomologists, further expanding it to a greater number of species and geographic regions would be helpful in further stress-testing field deployments of fine-grained classification algorithms. Second, while we focus on camera traps for nocturnal insects, it would be useful also to consider diurnal insect camera traps, for example those aimed at pollinators, which pose some additional challenges, such as multiple perspectives and a diversity of backgrounds. We hope furthermore that future works will consider more sophisticated domain adaptation approaches building on the baselines we present here.",
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+    },
+    {
+        "type": "text",
+        "text": "This work represents a step towards computer vision algorithms for species recognition that are effective in the ultra-challenging regime of insect identification and work effectively in field conditions. The approach we propose should make it possible in particular to generalize algorithms for insect camera traps rapidly and cost-effectively across different hardware setups and regions of interest. We hope that the datasets, challenges and strategies presented here will propel further research in computer vision for insects and help accelerate initiatives to understand and protect our planet's biodiversity.",
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+    {
+        "type": "page_number",
+        "text": "14",
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+    },
+    {
+        "type": "header",
+        "text": "A. Jain et al.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We thank Annie-Shan Morin, Anna Viklund, and Jamie Alison for their helpful input and support to the project.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This research was generously funded by Mila Quebec AI Institute and Ministère de l'Économie, de l'Innovation et de l'Energie. The work was additionally supported in part by the Canada CIFAR AI Chairs program (NSERC 585136), the Global Climate Center on AI and Biodiversity Change (ABC) (NSF OISE2330423), the Montreal Insectarium, the Coordenação de Aperfeçoamento de Pessoal de Nível Superior - Brasil (CAPES-PROEX) - Finance Code 001, the Amazonas State Research Support Foundation - FAPEAM - through the POSGRAD project 2024/2025, the AMBER project funded by the abrdn Charitable Foundation, the Aage V. Jensen Naturfond grant no. N2024-0013, the European Union's Horizon Europe Research and Innovation programme under grant agreement no. 101060639 (MAMBO), and a Discovery Grant by NSERC. The computing resources were provided by Mila Quebec AI Institute, the Digital Research Alliance of Canada, and NVIDIA Corporation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A.J., F.C., and M.J.B. led dataset creation and experiments. J.S.C. and L.P. contributed to machine learning pipeline development. N.P., F.H, J.R., M.B., M.S., J.F., A.A., Y.L., E.N., F.P.P., A.C.Z., J.A.R.S., and J.G. performed insect identification for the AMI-Traps dataset. T.A, K.B., A.G.S., M.B., Y.B., K.P.M, D. Roy, T.T.H., M.L., and D. Rolnick guided and advised the project.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            215,
+            502,
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+            517
+        ],
+        "page_idx": 14
+    },
+    {
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+        ],
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2024/Insect Identification in the Wild_ The AMI Dataset/deef9d64-c259-4177-ab17-679ea66a461f_origin.pdf

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+# Insect Identification in the Wild: The AMI Dataset
+
+Aditya Jain<sup>1*</sup>, Fagner Cunha<sup>2*</sup>, Michael James Bunsen<sup>1*</sup>, Juan Sebastián Canas<sup>1</sup>, Léonard Pasi<sup>1</sup>, Nathan Pinoy<sup>3</sup>, Flemming Helsing<sup>3</sup>, JoAnne Russo<sup>4</sup>, Marc Botham<sup>5</sup>, Michael Sabourin<sup>6</sup>, Jonathan Fréchette<sup>12</sup>, Alexandre Anctil<sup>7</sup>, Yacksecari Lopez<sup>8</sup>, Eduardo Navarro<sup>8</sup>, Filonila Perez Pimentel<sup>8</sup>, Ana Cecilia Zamora<sup>8</sup>, José Alejandro Ramirez Silva<sup>8</sup>, Jonathan Gagnon<sup>12</sup>, Tom August<sup>5</sup>, Kim Bjerge<sup>3</sup>, Alba Gomez Segura<sup>5</sup>, Marc Bélisle<sup>9</sup>, Yves Basset<sup>8</sup>, Kent P. McFarland<sup>4</sup>, David Roy<sup>5</sup>, Toke Thomas Hoye<sup>3</sup>, Maxim Larrivée<sup>10</sup>, and David Rolnick<sup>1,11</sup>
+
+<sup>1</sup> Mila - Quebec AI Institute
+
+2 Federal University of Amazonas
+
+3 Aarhus University
+
+4 Vermont Center for Ecostudies
+
+UK Centre for Ecology & Hydrology
+
+McGuire Center
+
+7 Centre de données sur le patrimoine naturel du Québec
+
+Smithsonian Tropical Research Institute
+
+<sup>9</sup> Université de Sherbrooke
+
+10 Montreal Insectarium
+
+11 McGill University
+
+$^{12}$  Independent Researcher
+
+Abstract. Insects represent half of all global biodiversity, yet many of the world's insects are disappearing, with severe implications for ecosystems and agriculture. Despite this crisis, data on insect diversity and abundance remain woefully inadequate, due to the scarcity of human experts and the lack of scalable tools for monitoring. Ecologists have started to adopt camera traps to record and study insects, and have proposed computer vision algorithms as an answer for scalable data processing. However, insect monitoring in the wild poses unique challenges that have not yet been addressed within computer vision, including the combination of long-tailed data, extremely similar classes, and significant distribution shifts. We provide the first large-scale machine learning benchmarks for fine-grained insect recognition, designed to match real-world tasks faced by ecologists. Our contributions include a curated dataset of images from citizen science platforms and museums, and an expert-annotated dataset drawn from automated camera traps across multiple continents, designed to test out-of-distribution generalization under field conditions. We train and evaluate a variety of baseline algorithms and introduce a combination of data augmentation techniques that enhance generalization across geographies and hardware setups. The dataset is made publicly available<sup>1</sup>.
+
+# 1 Introduction
+
+Computer vision algorithms for species identification have become important tools in studying and protecting the Earth's wildlife. Biodiversity applications have also been beneficial to computer vision, serving as a fruitful source of new benchmarks and algorithms [11,23,68,75]. However, research in computer vision for biodiversity has often focused on large animals, not reflecting the full set of challenges faced in ecology and conservation.
+
+There are over a million known species of insects on Earth, representing nearly one half of all known organisms (by comparison, there are only 10,000 species of birds, and even fewer mammals) [51,62]. Insects play essential roles in nearly all terrestrial ecosystems, as well as providing ecosystem services such as pollination that are critical for humanity [60], yet a looming "insect apocalyptic" threatens both their abundance and diversity [72]. Despite the crisis, data on insect populations is shockingly sparse [27], as a result of less resources, a plethora of species, and the high level of expertise typically required to study insects. Amid this data gap, computer vision tools for automated monitoring have the potential to radically reshape the study and conservation of insects. In particular, recent breakthroughs in camera traps for insects have made it possible to automatically photograph large numbers of individuals in the wild [38,41,58], opening up the the potential for image-processing algorithms to parse this raw data.
+
+Species recognition from camera traps is a well-studied problem in the computer vision community [55], with common challenges including poor lighting, occlusion of individuals, camouflage, and blur [14]. However, working with insects presents distinct challenges from those faced in traditional camera traps, which are often designed for large animals. For example, while traditional camera trap images may only rarely contain a target species, almost every image from an insect camera trap includes insects – often hundreds of them. Where traditional camera traps may have a short list of species of interest, insect monitoring requires considering thousands of species at any given location, with many of them being extremely similar, and most with very little labeled data.
+
+While recent authors have proposed the use of computer vision tools for detecting and identifying insects in camera trap data [8, 17, 20, 32, 43, 63], such studies have involved small datasets with only a few species represented. There has to date been no work assessing the performance of algorithms in identifying large number of insect species, or addressing the challenges of generalization across in-the-wild deployments. Our work here offers the following contributions:
+
+- We introduce the AMI (Automated Monitoring of Insects) dataset, consisting of two parts: 1) AMI-GBIF, a dataset of  $\sim 2.5\mathrm{M}$  human-captured images curated from citizen science platforms and museum collections, 2) AMI-Traps, an expert-annotated dataset of 2,893 insect camera trap images (representing 52,948 labeled insects) collected from a global network of automated camera traps, designed to test in-the-wild performance (Fig. 1).
+
+![](images/00003212e95be6e5dd272b91109bf82f0a6193888b5755b4b1ef396d96a576bc.jpg)  
+Fig. 1: Illustration of the difference between insect species identification from human-captured images and in the wild. On left are shown images of three moth species from our AMI-GBIF dataset, curated from citizen science data and museum collections. On right are shown images of the same species (along with other insects) within a photograph taken by an automated camera trap in the wild from our AMI-Traps dataset. One of the challenges of the AMI dataset is generalizing from AMI-GBIF to AMI-Traps without additional labeled data.
+
+- We frame the problem of practical insect monitoring in the field as a set of computer vision tasks, entailing very fine-grained classification from long-tailed data, with the additional challenge of generalization across multiple kinds of imagery.  
+- We test a variety of strong baseline models for the proposed tasks, including a combination of data augmentation approaches that significantly improve performance under field conditions.
+
+# 2 Related Work
+
+Biodiversity Image Datasets. Advancements in computer vision have been closely intertwined with the creation of curated datasets such as ImageNet [26, 59], Pascal VOC [30], Open Images [44], and MS-COCO [46]. In recent years, the computer vision and machine learning communities have increasingly directed their focus towards addressing pressing human threats, including biodiversity loss [68] and climate change [57]. These domains not only hold significant potential for societal impact but also offer fertile ground for exploring intriguing machine learning questions such as domain generalization [77], long-tailed distributions [71], and fine-grained classification [74]. Such challenges have found especially fruitful testbeds in the classification of species, where datasets such as iNaturalist [70] have proven useful for both the computer vision and ecology communities. While some challenges have considered plant identification [15, 45, 53, 56], the majority have focused on animals, including datasets focused on birds [16, 69, 73], mammals [9, 14, 64], and fish [22, 25, 39, 40]. Such datasets have often leveraged concurrent advancements in sensor technology, including in satellite imagery and drones. In particular, camera traps have been widely adopted by biologists as an in situ and cost-effective means of wildlife
+
+![](images/c8422f237016fb6a7084b360cb3732bc8a7d1c35b2e6e6375849c53ca34a5014.jpg)
+
+![](images/c8d7dee1236803f8056af0ee0b3845fd33dd3d277603922e0f9d64c8b7e2393e.jpg)  
+(a) Incomplete
+
+![](images/ff4a585ec332620364206eefd14b9081a9fe36e330ff7b5f7ca3df710832ddc0.jpg)  
+(b) Overlapping  
+(c) Motion
+
+![](images/d9d2b1c95c7f02a1d8fca63c3d025a0f755d16b8d30d32f621e88939ab03b5e2.jpg)
+
+![](images/2107424f9c29b4c8e3cc810131011b20ef05a0ea9a3822c40be081770f90c764.jpg)  
+Fig. 2: Examples of challenges in the AMI-Traps dataset. (a) Incomplete: In some occasions, the body of an insect is incomplete due to its position in the automatically taken image. (b) Overlapping: Sometimes insects occlude each other. (c) Motion: Moving insects can be blurred and hard to classify. (d) Lighting: The lighting and camera exposure of the images is variable and can lead to poor contrast that masks some or all detail. (e) Resolution: Some insects are very small, leading to low-resolution images. (f) Perspective: While insects are generally positioned at a fixed distance, sometimes insects appear in the air or perched on the camera itself. Additionally, unexpected objects such as spider webs, dirt, and vegetation can be captured by the cameras and may be confused with objects of interest.
+
+![](images/d25edc3113fff52e6dd677f6c5d7786b8f7aa6715e2d2171963f3f77c8b59014.jpg)
+
+![](images/afdce32fb78a285bbb6342f87374635c6e7ed62ef5730bc0ab098be0a2df700b.jpg)
+
+![](images/4b7b837aeb3abd3c022276d253d1d6aa0761af1fe5cfe8d7f98afd06b4869868.jpg)
+
+![](images/bde0083e1d7e69c0259918e0346dc0eff44e7c7ad1adc146b61a2226a13e5f33.jpg)  
+(d) Lighting  
+(e) Resolution
+
+![](images/65f593ddb7b468337474b2dd8a2f838564d7358c5ba6be8132ef0e21091b0f05.jpg)  
+(f) Perspective
+
+monitoring [55], and have in turn presented fascinating challenges for the computer vision community [14], including in classification [12, 29], object detection [13,31], out-of-distribution generalization [34,42,50], and active learning [54]. Such algorithms have to date, however, been designed mostly for large animals such as mammals.
+
+Insect Image Datasets. As algorithms and datasets for species recognition have proliferated, insects have traditionally been underrepresented. Within ImageNet1k [59], only 27 classes depicted insects, as compared to 57 for birds and 93 classes for wild mammals [49]. Some popular fine-grained classification datasets such as NABirds and CUB have focused exclusively on birds [69, 73], while camera trap datasets such as iWildCam have been focused on mammals [12]. The iNat2017 dataset [70] included 1,021 classes of insects out of 5,089 total classes in the dataset. By largely focusing on other taxonomic groups, prior works have neglected the challenges posed by insect data, such as extremely similar classes (reflecting far greater diversity than any other group of organisms), small size, hyperabundance, etc. In recent years, however, some works have introduced insect-focused benchmark datasets. The newly released BIOSCAN-1M dataset includes images and DNA sequences, with a focus on fly identification [33]. Despite the very large size of the dataset (1.1 million datapoints), the number of object classes involved is relatively small, with the focus being to distinguish between 40 taxonomic families of flies, reflecting the challenging nature of insect identification. Other recent datasets for computer vision include one focused on 8 classes of pollinators across Europe [61], and the Indian Butterflies dataset,
+
+encompassing 30k images of butterflies from India across 315 species [67]. A variety of publications have used computer vision algorithms for detection of pest insects in specific agricultural applications [10, 52, 66].
+
+Insect Camera Traps. The use of camera traps for studying insect biodiversity is relatively recent. Geissmann et al. [32] introduced the Sticky Pi device, which uses sticky cards to capture (and kill) insects, which are then automatically photographed. Bjerge et al. [21] introduced an automated camera trap using UV light to attract and photograph moths and other insects (without killing them), which was built on by subsequent works [18, 20]. A similar approach focused on diurnal pollinators via a camera trap installed above flowers [17, 19]. These works also propose deep learning methods for processing the resulting images, considering both object detection and classification of a small number of insect categories. The lack of fine-grained classification is largely due to the time required to annotate images from the traps, making it difficult to obtain a large enough labeled dataset from trap data alone.
+
+# 3 Benchmark Design
+
+In this paper, we propose a benchmark dataset for insect species identification that addresses the challenges faced in real-world use cases. These include both (1) challenges that distinguish insect identification from other kinds of species identification, notably the massive diversity of often-similar species, and (2) the particular challenges associated with deploying these algorithms "in the wild".
+
+To address the first family of challenges, we introduce a dataset for fine-grained insect classification that (to our knowledge) is by far the largest yet released, with  $\sim 2.5\mathrm{M}$  images across over 5,000 classes. We concentrate on moths, which are readily drawn to UV camera traps and can often be visually identified to species (unlike some other insects) [21].
+
+The second family of challenges is more complex - involving the gap between field conditions and the high-quality images typically used for training species identification algorithms. Figure 2 illustrates some of the challenges that computer vision algorithms face on data from automated insect camera traps, in contrast to images taken by humans. Insects may occlude each other or be partially "out of frame". Motion blur and lighting issues may occur, along with objects in unexpected positions. The resolution of images may be very low, owing to the small size of insects at a stereotyped distance from the camera. Also, insect camera traps typically use webcams and PCB camera modules due to their cost and software integration capabilities, and the resulting images are often both structurally different and overall lower quality than those taken by human photographers.
+
+As described in the preceding section, previous authors working with insect camera traps have addressed the problem of challenging camera trap data by training algorithms on annotated data from the particular camera trap in question. However, manual annotation is extremely time-intensive, since it must be performed by expert entomologists, of whom there are very few in any given
+
+region. Insect species vary greatly across regions, meaning that fine-grained annotations in one location are generally not useful in another. Furthermore, the hardware used in insect camera traps also varies greatly (with considerable differences in lighting and background, as well as image sharpness, contrast, noise reduction settings, and compression artifacts, which are exacerbated on small scale crops), meaning that even two datasets from the same region may not be comparable.
+
+In this paper, we remove the problem of annotation by solving a more challenging computer vision problem. Namely, we propose to train algorithms on abundant labeled images of insects taken by human photographers, then use these algorithms on out-of-distribution camera trap images. Our benchmark dataset is designed to test this functionality, by including both a large training set of curated photographs taken by humans and an out-of-distribution test set drawn from a geographically diverse set of insect camera traps.
+
+The AMI dataset is therefore designed to test fine-grained classification of moth species both in in-distribution and out-of-distribution contexts. It also includes the task of binary classification of insects as moth or non-moth, which is a prerequisite for camera traps since moths are not the only insects to appear. Note that we do not consider the task of object detection, which in applications is a precursor to insect identification. This is because object detection against a relatively plain background is a simpler task, where good results have already been obtained in the insect camera trap literature [18,20,21,32].
+
+# 4 The AMI Dataset
+
+In this section, we describe the construction of the datasets that we release in this work: AMI-Traps and AMI-GBIF. For AMI-Traps, we collected insect camera trap data by field deployments in three regions: NE-America (Northeast of North America), which includes data from Quebec in Canada and Vermont in the USA; W-Europe (Western Europe), which includes data from the UK and Denmark; and C-America (Central America), comprising data from Panama. For AMI-GBIF, we compiled public data for the same three regions using the Global Biodiversity Information Facility (GBIF) [7]. The GBIF platform provides access to biodiversity data aggregated from multiple sources, such as museums, research institutions, and citizen science platforms such as iNaturalist [4], Observation.org [5], and BugGuide [1]. For brevity, we sometimes refer to AMI-Traps and AMI-GBIF as AMI-T and AMI-G, respectively. Figure 3 shows examples of images from the two datasets and Tab. 1 compares the number of images and coverage of classes at different taxonomic levels.
+
+# 4.1 AMI-Traps Dataset
+
+Data Collection. The source images in the AMI-Traps dataset were collected from a variety of different insect camera traps deployed across 22 monitoring stations in the three regions previously described. The cameras were configured
+
+![](images/6d3d09004541e7bbf9f29d11bdc159376009b17c5cc75bd7e740c4a592d92ee7.jpg)  
+Fig. 3: Sample images from the AMI Dataset. The AMI Dataset is composed of (1) AMI-GBIF, curated from a number of sources with imagery from citizen science and museum collections, and (2) AMI-Traps, drawn from automated camera traps for insects across five countries in three regions. The number of individual insects annotated per sub-dataset is denoted in parentheses.
+
+to be motion-sensitive, as well as taking photos on a fixed interval of 10 minutes; we selected a subset of images for annotation so as to avoid highly similar images. In total, 2,893 trap images were sampled from all cameras and made available on the Label Studio annotation platform (see Appendix B for more details).
+
+Annotation Process. Images were annotated by entomologists with expertise in the species of the particular region. Labeling was conducted according a three-step process. 1) We designed a custom object detection model to suggest boxes around objects in the image (refer to Appendix B for details on this model), to save annotators time. Annotators were asked to correct errors in the proposed boxes as well as drawing any missing boxes. Insects appearing smaller than 1 centimeter were ignored. 2) Annotators were asked to label image crops according to one of three coarse categories: moth, non-moth, or unidentifiable. Some insects could not be labeled due to motion blur, occlusion, or other factors. 3) For insects labeled as moths, annotators were asked to select the narrowest taxonomic group that could be determined from the image - identifying moths to species where possible, if not species then genus, and if not genus then family.
+
+Data Statistics. 2,893 source images from the traps were annotated (see Tab. B.2 in the supplementary for further details) which includes Vermont (900), Denmark (892), Quebec (533), UK (446), and Panama (122). A total of 52,948 insects were labeled within these images, including 37,105  $(70.08\%)$  non-moths,
+
+14,105 (26.64%) moths, and 1,738 (3.28%) unidentifiable. Out of the 14,105 moth crops, 10,854 (76.95%), 7,065 (50.09%) and 5,374 (38.10%) crops were labeled at the family, genus, and species level respectively.
+
+# 4.2 AMI-GBIF Dataset
+
+AMI-GBIF has two sub-datasets: binary and fine-grained classification. The fine-grained classification dataset contains images for moth species in each of the regions covered by AMI-Traps. The binary classification dataset contains images of moths aggregated across all regions and non-moths from anywhere on earth.
+
+Dataset Construction. First, in collaboration with regional moth specialists, we created "checklists" of species that could occur in each of the three regions of interest. It is worth noting that some species are included in more than one checklist, though most are unique to a single region. Next, we compared the checklists against the GBIF taxonomic backbone [2], merged synonym names (since some species have multiple accepted names), and manually investigated doubtful or unmatched names. Following that, we used the GBIF occurrence search tool to download metadata for all observations from the order Lepidoptera with images, which returned 15.1 million observations [3]. We then fetched images from observations in which the species is included in our regional checklists. The number of training images per species were limited to 1,000, though for many species it was considerably lower due to the long-tailed nature of the data. All images were resized to have the smallest dimension of 450px and packaged using the WebDataset format [6].
+
+Quality Control. After downloading the images, we applied a set of cleaning steps to ensure the quality of the dataset. First, we removed duplicate URLs, i.e., images linked to more than one observation. This may occur when an image contains multiple individual insects, or when a placeholder is used for an observation (for example, Fig. A.1b in Appendix A shows a picture used as a placeholder for more than 100,000 observations). Next, we excluded images from specific datasets (refer to Tab. A.1 in Appendix A)) that we found to have a high percentage of images unsuitable for training our models, for instance, images of body parts or text only. Another issue we identified is that some observations contained thumbnail images that are too small to provide sufficient information to train our models; we removed all images with a width or height less than 64 pixels. Finally, as our dataset targets only adult insects, we removed images containing non-adult individuals such as eggs and caterpillars. For observations where the life stage was reported by the observer, approximately  $60\%$  of the cases, we removed all occurrences tagged as non-adult. For the remaining images with a missing life stage tag, we designed a classification model to predict the life stage (refer to Appendix A for details about this model) and removed all images classified as non-adult.
+
+Dataset Split. Each GBIF observation may contain more than one image, but each image is considered an independent instance of the species. However, as images belonging to the same observation may be very similar, we keep images from the same observation in the same data split. To do so, we split the dataset
+
+using the observation ID as reference, with the proportion of  $70\%$ ,  $10\%$ , and  $20\%$  for the train, validation and test sets respectively. We apply a stratified split, i.e., we guarantee that this proportion is also maintained at the species level. We exclude species with fewer than 5 images, so the minimum number of images for a species in the training set is 4, and in the test set is one. Due to the data split based on observation ID, the validation set might lack images for some species. As some species may belong to multiple checklists, we keep the train/val/test splits consistent across the regions to prevent data leakage when training a unified model for all regions.
+
+Binary Classification. Since moths are not the only insects that appear on the camera trap screen, for our proposed benchmark task of binary classification, we curate a dataset comprising 350,000 images for each of the moth and non-moth categories. The moth class consists of adult moth images randomly sampled from the AMI-GBIF dataset. For the non-moth category, we leveraged expert knowledge of the taxonomic groups likely to appear on the screen, fetching images of adult individuals from GBIF of the following groups: Diptera (85,474), Hemiptera (75,053), Odonata (68,770), Coleoptera (45,954), Araneae (21,321), Orthoptera (21,261), Formicidae (12,206), Ichneumonidae (6,581), Trichoptera (5,316), Neuroptera (4,880), Opiliones (1,880), Ephemeroptera (1,304) — this includes mostly insects, with some Arachnids. The dataset is split into train, validation, and test sets with proportions of  $70\%$ ,  $10\%$ , and  $20\%$ , respectively. Specifically for the moth category, the splits are kept consistent with the splits for the fine-grained species classification task.
+
+Statistics. The final dataset contains  $\sim 2.5\mathrm{M}$  images from 5,364 species, 1,734 genera and 77 families of moths, along with 350,000 additional images of non-moth groups. The binary dataset contains 700,000 images, composed of 350,000 moth images and the 350,000 non-moth images. The fine-grained dataset contains 2,564,392 moth images, and Tab. 1 shows the number of images and species for each region. Though species are selected based on their presence in regions of interest, we include all GBIF observations of these species from anywhere on Earth (see Fig. A.2 in supplementary for the global distribution of images). As in other biodiversity datasets, the number of images per species in AMI-GBIF follows a long-tailed distribution (see Fig. C.3 in supplementary). Specifically, only 3,099 species have more than 100 images and are considered under the "many-shot" bucket, 1,358 species contains between 20 and 100 images and are considered "medium-shot", and there are 907 species with less than 20 training images, considered as "few-shot" categories.
+
+# 5 Methods
+
+In this section, we describe the methods used to assess the difficulty of the proposed benchmark tasks. We evaluate a variety of high-performing image classification architectures and use extensive data augmentation to address the challenges of domain shift between the two datasets. Motivated by the particular structure of the AMI-Traps dataset, we add a mixed-resolution (MixRes) data
+
+Table 1: Comparison between the AMI-GBIF and AMI-Traps dataset for the fine-grained classification task. Images for the traps dataset denote the individual insect crops and not the raw trap images. The last three rows show the unique classes for each of the three taxonomic levels for the two datasets for different regions. It is also important to note that regions have species in common.  
+
+<table><tr><td rowspan="2"></td><td colspan="2">All Regions</td><td colspan="2">NE-America</td><td colspan="2">W-Europe</td><td colspan="2">C-America</td></tr><tr><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td><td>AMI-G</td><td>AMI-T</td></tr><tr><td>Images</td><td>2,564,392</td><td>14,105</td><td>1,179,943</td><td>9,066</td><td>1,579,333</td><td>4,066</td><td>99,405</td><td>973</td></tr><tr><td>Families</td><td>77</td><td>43</td><td>68</td><td>34</td><td>65</td><td>26</td><td>27</td><td>11</td></tr><tr><td>Genera</td><td>1,734</td><td>344</td><td>887</td><td>204</td><td>957</td><td>192</td><td>385</td><td>12</td></tr><tr><td>Species</td><td>5,364</td><td>516</td><td>2,497</td><td>277</td><td>2,603</td><td>244</td><td>636</td><td>6</td></tr></table>
+
+augmentation technique. As we describe in the following section, our approaches perform quite well, with MixRes leading to an especially significant performance improvement.
+
+Models. We work with five computer vision models widely used in identification of wildlife: ResNet50 [35], MobileNetV3-Large [37], ConvNeXt-T [47], ConvNeXt-B [47], and ViT-B/16 [28]. We select ResNet50 because it is the most popular backbone used as a baseline for almost any computer vision task. Considering the possibility that the trained models may need to run on hardware with limited resources, such as edge devices and personal computers, for in-field predictions, we choose MobileNetV3Large as a lightweight model alternative. Furthermore, considering that vision transformers have surpassed convolutional neural networks and become the state-of-the-art models for image classification, we select the ViT-B/16 model to provide a baseline from this family of architectures. Finally, for representing modern convolutional neural networks, we choose the recently introduced ConvNeXt architecture, which has proven to be competitive with transformers using only standard ConvNet modules. From this family of models, we select two versions: the base version (ConvNeXt-B) and, considering lightweight usage scenarios, we also include the tiny version (ConvNeXt-T). Unless otherwise stated, we use a default input resolution of 128x128 for all models.
+
+Data Augmentation Approaches. One characteristic of the in-the-wild images is the large variety of crops due to the diversity of insect sizes. A considerable number of them have small resolutions, below  $64 \times 64$ . At this scale, some important visual features that the model may have learned from high-resolution GBIF images might not be identifiable, leading to inaccurate predictions. This issue can be further amplified when these low-resolution crops are scaled up to the input model size. To compel the model to learn features for low-resolution inputs and avoid bias towards visual features only distinguishable in high-resolution images from other domains, we use a data augmentation technique we refer to as Mixed Resolution (MixRes) that simulates this low-resolution input during training (see Fig. D.4 in supplementary). This approach consists of randomly resizing the training input image to  $25\%$  or  $50\%$  of the model input size with a
+
+probability  $\rho$  for each case. In our experiments  $\rho$  is set to 0.25, maintaining the original input size with probability 0.5. We employ MixRes in all experiments unless otherwise stated.
+
+In addition to MixRes, we also use a set of standard data augmentation operations: random resize crop with scale of 0.3 to 1.0 and an aspect ratio between  $3/4$  and  $4/3$ , random horizontal flip with  $50\%$  probability, and RandAugment [24] with  $N = 2$  operations and magnitude  $M = 9$ . Finally, the image is normalized using the mean and standard deviation of ImageNet and scaled to the input network size.
+
+Implementation Details. We train all models with the AMI-GBIF training sets using the ImageNet-1K pretrained weights from the timm library [76] (for ConvNext and ViT we used ImageNet-22K weights). Each model is trained with a batch size of 128 and the AdamW optimizer [48] for 30 epochs. The initial learning rate is set to 0.001, with a weight decay of 1e-5. The learning rate is linearly warmed up from 0 to the initial value for 2 epochs and then decayed using cosine scheduling [36]. We also apply label smoothing [65] with a value of 0.1.
+
+Inference Settings. At test time, the insect crops from AMI-Traps are padded with black pixels to make them square, preventing the distortion of the shape of the insect before prediction. Next, the images are normalized with the mean and standard deviation of ImageNet and, finally, resized to the model input size. No padding is done for the test images from AMI-GBIF.
+
+Higher Taxonomic Rank Prediction. We consider the accuracy of our baseline models both with respect to the exact insect species predicted and with respect to higher level taxonomic groups such as genus and family. Indeed some images in our dataset cannot be labeled at the species level at all due to the quality or perspective of the image, and our annotators instead provided labels at the genus or family level. In our experiments, to make predictions at a higher taxonomic level, we simply sum together species-level predictions to get genus results, and similarly, the genus predictions are grouped together to get family predictions.
+
+Evaluation Metrics. During the binary classification step, it is important to achieve high precision by filtering out as many non-moths as possible to prevent the propagation of errors in the pipeline. At the same time, it is also important to assess recall because if too many moths are discarded at this step, it may impact the utility of the data for ecological studies. Therefore, for the binary classification task, along with accuracy, we also consider precision, recall, and F1-score as evaluation metrics. For the fine-grained classification task, we evaluate the model in terms of micro- and macro-averaged accuracy at the species, genus and family levels. Micro-averaging aggregates all class samples to calculate the accuracy while the macro-average is the average of per-class accuracy. Unless otherwise stated, the reported accuracy is micro-averaged. We conduct each experiment for three independent runs and report the mean and standard deviation.
+
+# 6 Experiments and Results
+
+Binary Classification Results. This task involves distinguishing moths from non-moths. Here we train a ResNet50 model on the AMI-GBIF dataset and evaluate performance both on the AMI-GBIF held-out test set and on the entirety of the AMI-Traps dataset. On AMI-GBIF (in-distribution), the model achieves a test accuracy of  $97.77\% \pm 0.02\%$ . Table 2 shows the results for the AMI-Traps dataset in more detail. We observe that the model has a high recall but a lower precision, which means it is over-predicting the moth class. Also, the bigger the image crop, the better the accuracy of the insect classification; many non-moths where the model errs are extremely small and are therefore highly blurred in the trap images. Table E.3 in the supplementary illustrates the improvement in model performance when crops are square padded (our default at inference time) versus an ablation where padding is not performed.
+
+Table 2: Binary classification model evaluation results on the AMI-Traps dataset after training on AMI-GBIF, showing that recall is high throughout, while precision drops on very small insects, which are predominantly non-moths. Crops  $>100\mathrm{px}$  or  $>150\mathrm{px}$  represent that atleast one side of the box is greater than the threshold.  
+
+<table><tr><td></td><td>Moths</td><td>Non-moths</td><td>Total</td><td>Accuracy</td><td>Precision</td><td>Recall</td><td>F1-score</td></tr><tr><td>All crops</td><td>14,105</td><td>37,105</td><td>51,120</td><td>86.48±1.00</td><td>68.31±1.70</td><td>95.03±0.39</td><td>79.48±1.27</td></tr><tr><td>Crops &gt; 100px</td><td>11,630</td><td>16,534</td><td>28,164</td><td>88.39±0.97</td><td>79.46±1.43</td><td>96.99±0.20</td><td>87.35±0.94</td></tr><tr><td>Crops &gt; 150px</td><td>6,446</td><td>5,961</td><td>12,407</td><td>92.95±0.22</td><td>89.83±0.43</td><td>97.48±0.12</td><td>93.70±0.30</td></tr></table>
+
+Fine-grained Classification Results. The fine-grained classification task aims to identify moths to the species level (and secondarily to genus or family level). In our experiments, we train models on AMI-GBIF data for each of the three regions of the AMI dataset, evaluating both on AMI-GBIF (in-distribution) and AMI-Traps (out-of-distribution) data (see Tab. 3). Not all moth species present in a region appear regularly at camera traps; hence, the list of species in AMI-Traps is a subset of species in AMI-GBIF for a given area (see Tab. 1). Therefore, we also evaluate the models on an in-distribution subset  $(\mathrm{Test}\ddagger)$  from AMI-GBIF containing only the species present in AMI-Traps. Meanwhile, for AMI-Traps, there are 16 species not present in AMI-GBIF that were removed during our evaluation procedure (these represent unexpected species not included in the regional checklists used to define AMI-GBIF). Overall, the best model at the species level is ConvNeXt-B for both AMI-GBIF and AMI-traps. For C-America, annotations are mostly provided at the genus or family level, due to the challenging nature of visual identification of moths in this biodiversity-rich region. Furthermore, while the genus and family accuracies are similar between N-America and W-Europe, they are much lower for C-America. This can be attributed to the fact that there are 10 times fewer images in the training set for this region. Note that for genus and family evaluation, there are some cases where the accuracy is lower than the species level. This occurs because those
+
+Table 3: Accuracy results for the fine-grained classification task. Overall, ConvNeXt-B achieves the best results for both AMI-GBIF and AMI-traps, with ViT-B/16 achieving slightly better results for some cases at the genus and family levels. Test‡ represents a subset of the AMI-GBIF test set, containing only the species present in AMI-Traps. Species-level results on AMI-Traps for the C-America region are not available since most annotations were provided only at higher taxonomic levels.  
+
+<table><tr><td rowspan="3">Region</td><td rowspan="3">Model</td><td colspan="2">AMI-GBIF</td><td colspan="6">AMI-Traps</td></tr><tr><td colspan="2">Species</td><td colspan="2">Species</td><td colspan="2">Genus</td><td colspan="2">Family</td></tr><tr><td>Micro Test</td><td>Micro Test‡</td><td>Micro Top1</td><td>Macro Top1</td><td>Micro Top1</td><td>Macro Top1</td><td>Micro Top1</td><td>Macro Top1</td></tr><tr><td rowspan="5">NE-America</td><td>ResNet50</td><td>87.56±0.12</td><td>89.39±0.14</td><td>71.86±1.02</td><td>64.96±2.00</td><td>80.07±0.49</td><td>74.66±0.35</td><td>90.44±0.41</td><td>69.30±4.15</td></tr><tr><td>MBNetV3L</td><td>83.73±0.17</td><td>85.80±0.29</td><td>67.41±0.72</td><td>61.21±1.20</td><td>74.83±1.30</td><td>71.20±2.47</td><td>89.31±0.62</td><td>64.48±1.87</td></tr><tr><td>ConvNeXt-T</td><td>89.81±0.05</td><td>91.21±0.06</td><td>74.89±0.05</td><td>68.00±0.76</td><td>83.26±1.22</td><td>77.26±0.85</td><td>90.61±0.53</td><td>74.60±0.64</td></tr><tr><td>ConvNeXt-B</td><td>90.45±0.03</td><td>91.66±0.03</td><td>76.75±1.52</td><td>68.56±0.62</td><td>85.46±0.83</td><td>78.28±0.14</td><td>91.07±0.29</td><td>76.87±1.10</td></tr><tr><td>ViT-B/16</td><td>86.39±0.05</td><td>87.94±0.10</td><td>77.43±0.79</td><td>68.02±0.34</td><td>85.57±0.98</td><td>78.97±0.72</td><td>91.45±0.34</td><td>73.66±1.49</td></tr><tr><td rowspan="5">W-Europe</td><td>ResNet50</td><td>86.45±0.08</td><td>90.25±0.03</td><td>79.39±0.39</td><td>72.84±0.21</td><td>78.95±0.26</td><td>73.22±0.60</td><td>89.13±0.42</td><td>75.24±1.85</td></tr><tr><td>MBNetV3L</td><td>82.20±0.05</td><td>86.47±0.13</td><td>76.30±1.29</td><td>70.35±0.93</td><td>76.35±1.19</td><td>72.88±1.28</td><td>88.33±0.47</td><td>72.21±0.38</td></tr><tr><td>ConvNeXt-T</td><td>88.82±0.03</td><td>92.05±0.05</td><td>82.44±0.89</td><td>74.59±0.62</td><td>81.86±0.79</td><td>74.15±0.59</td><td>90.08±0.59</td><td>74.58±2.93</td></tr><tr><td>ConvNeXt-B</td><td>89.35±0.01</td><td>92.48±0.05</td><td>82.87±0.39</td><td>76.41±0.50</td><td>82.45±0.44</td><td>75.98±1.05</td><td>91.27±0.60</td><td>79.39±2.70</td></tr><tr><td>ViT-B/16</td><td>85.45±0.03</td><td>89.22±0.11</td><td>82.44±0.36</td><td>75.25±0.98</td><td>83.01±0.26</td><td>75.96±0.35</td><td>91.68±0.17</td><td>75.81±0.79</td></tr><tr><td rowspan="5">C-America</td><td>ResNet50</td><td>87.46±0.23</td><td>95.92±0.68</td><td>-</td><td>-</td><td>47.44±1.11</td><td>66.59±0.60</td><td>69.18±0.24</td><td>42.40±0.31</td></tr><tr><td>MBNetV3L</td><td>83.68±0.24</td><td>92.89±0.27</td><td>-</td><td>-</td><td>41.03±2.22</td><td>59.32±1.18</td><td>68.34±1.69</td><td>41.42±2.98</td></tr><tr><td>ConvNeXt-T</td><td>87.65±0.11</td><td>95.46±0.46</td><td>-</td><td>-</td><td>55.77±3.33</td><td>70.68±1.58</td><td>69.46±0.42</td><td>45.35±0.67</td></tr><tr><td>ConvNeXt-B</td><td>88.62±0.09</td><td>96.22±0.26</td><td>-</td><td>-</td><td>51.92±3.85</td><td>68.63±1.94</td><td>72.24±1.47</td><td>44.31±1.32</td></tr><tr><td>ViT-B/16</td><td>79.80±0.26</td><td>88.36±1.02</td><td>-</td><td>-</td><td>47.44±4.44</td><td>64.70±4.07</td><td>69.87±1.51</td><td>42.00±3.60</td></tr></table>
+
+higher taxonomic levels include crops that have labels only at higher levels. In the supplementary material, we include additional results for AMI-GBIF long-tail accuracies (Tab. E.4), a pre-training ablation study (Tab. E.5), and a study analyzing classification accuracy as a function of prediction confidence (Fig. E.5).
+
+Data augmentation approaches. To assess the effectiveness of the mixed resolution data augmentation technique, we conduct an ablation study using ResNet50 for the NE-America region. As the effects of MixRes could already be covered by other data augmentation operations used in our preprocessing, such as random resize crop or one of the operations of RandAugment, we analyze multiple combinations of these operations. Additionally, we evaluate a higher input resolution, using the original 224 input size of ResNet50, to determine whether this leads to better predictions. Table 4 shows the results. While applying MixRes results in a slight decrease in accuracy within the in-distribution AMI-GBIF test set, for the in-the-wild AMI-Traps test set there is a substantial improvement, ranging between  $4\%$  and  $7\%$  when compared to models not trained with MixRes. Another important observation is that, although RandAugment and random resize together contribute to an overall improvement of around  $16\%$ , MixRes remains additionally beneficial. Finally, despite an increase of more than  $4\%$  in accuracy within the original domain when using a higher resolution, there is a marginal decrease in the accuracy of the in-the-wild results.
+
+# 7 Conclusion
+
+Many ecological applications require species-level image classification to meet their goals. Despite advances in computer vision, there remain challenges in
+
+Table 4: Ablation study on data augmentation techniques using a ResNet50 for the NE-America region evaluated on micro-averaged top-1 species accuracy. "RandAug" denotes the combination of the RandAugment and random resize crop data augmentation techniques. AMI-GBIF† test set contains only the species present in AMI-Traps.  
+
+<table><tr><td>Resolution</td><td>RandAug</td><td>MixRes</td><td>AMI-GBIF‡</td><td>AMI-Traps</td></tr><tr><td>128</td><td>×</td><td>×</td><td>89.18±0.08</td><td>51.46±2.73</td></tr><tr><td>128</td><td>✓</td><td>×</td><td>89.71±0.16</td><td>67.88±1.27</td></tr><tr><td>128</td><td>×</td><td>✓</td><td>87.41±0.06</td><td>58.41±0.30</td></tr><tr><td>128</td><td>✓</td><td>✓</td><td>89.39±0.14</td><td>71.86±1.02</td></tr><tr><td>224</td><td>✓</td><td>✓</td><td>92.97±0.17</td><td>68.41±1.06</td></tr></table>
+
+implementing fine-grained classification that is effective in real-world scenarios. Here we outline the challenges of insect identification in the wild and propose a benchmark dataset to tackle them. We present AMI-GBIF, a dataset with 2.5 million labeled photographs of 5,000 moth species. We also introduce AMI-Traps, a dataset of images captured by automated insect monitoring systems across five countries, labeled by regional experts. We evaluate multiple classification models both on the AMI-GBIF dataset and in out-of-distribution generalization to AMI-Traps, with ConvNeXt-B generally performing the best. We also evaluate a range of data augmentation techniques, finding that a combination of simple approaches, notably mixed-resolution augmentation, considerably improves generalization under field conditions.
+
+Several limitations of this work should be noted. First, while annotating AMI-Traps already occupied a considerable time for expert entomologists, further expanding it to a greater number of species and geographic regions would be helpful in further stress-testing field deployments of fine-grained classification algorithms. Second, while we focus on camera traps for nocturnal insects, it would be useful also to consider diurnal insect camera traps, for example those aimed at pollinators, which pose some additional challenges, such as multiple perspectives and a diversity of backgrounds. We hope furthermore that future works will consider more sophisticated domain adaptation approaches building on the baselines we present here.
+
+This work represents a step towards computer vision algorithms for species recognition that are effective in the ultra-challenging regime of insect identification and work effectively in field conditions. The approach we propose should make it possible in particular to generalize algorithms for insect camera traps rapidly and cost-effectively across different hardware setups and regions of interest. We hope that the datasets, challenges and strategies presented here will propel further research in computer vision for insects and help accelerate initiatives to understand and protect our planet's biodiversity.
+
+# Acknowledgements
+
+We thank Annie-Shan Morin, Anna Viklund, and Jamie Alison for their helpful input and support to the project.
+
+This research was generously funded by Mila Quebec AI Institute and Ministère de l'Économie, de l'Innovation et de l'Energie. The work was additionally supported in part by the Canada CIFAR AI Chairs program (NSERC 585136), the Global Climate Center on AI and Biodiversity Change (ABC) (NSF OISE2330423), the Montreal Insectarium, the Coordenação de Aperfeçoamento de Pessoal de Nível Superior - Brasil (CAPES-PROEX) - Finance Code 001, the Amazonas State Research Support Foundation - FAPEAM - through the POSGRAD project 2024/2025, the AMBER project funded by the abrdn Charitable Foundation, the Aage V. Jensen Naturfond grant no. N2024-0013, the European Union's Horizon Europe Research and Innovation programme under grant agreement no. 101060639 (MAMBO), and a Discovery Grant by NSERC. The computing resources were provided by Mila Quebec AI Institute, the Digital Research Alliance of Canada, and NVIDIA Corporation.
+
+A.J., F.C., and M.J.B. led dataset creation and experiments. J.S.C. and L.P. contributed to machine learning pipeline development. N.P., F.H, J.R., M.B., M.S., J.F., A.A., Y.L., E.N., F.P.P., A.C.Z., J.A.R.S., and J.G. performed insect identification for the AMI-Traps dataset. T.A, K.B., A.G.S., M.B., Y.B., K.P.M, D. Roy, T.T.H., M.L., and D. Rolnick guided and advised the project.
+
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2024/InstaStyle_ Inversion Noise of a Stylized Image is Secretly a Style Adviser/938fb53e-3bec-4f8a-bc7e-f5b36dd7b576_origin.pdf

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2024/InstaStyle_ Inversion Noise of a Stylized Image is Secretly a Style Adviser/full.md

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+# INSTASTYLE: Inversion Noise of a Stylized Image is Secretly a Style Adviser
+
+Xing Cui $^{1}$  Zekun Li $^{2}$  Peipei Li $^{1\star}$  Huaibo Huang $^{3}$  Xuannan Liu $^{1}$  Zhaofeng He $^{1}$
+
+<sup>1</sup> Beijing University of Posts and Telecommunications
+
+<sup>2</sup> University of California, Santa Barbara
+
+$^{3}$  MAIS & NLPR, Institute of Automation, Chinese Academy of Sciences
+
+{cuixing, lipeipei, liuxuannan, zhaofenghe}@bupt.edu.cn
+
+zekunli@cs.ucsb.edu huaibo.huang@cripac.ia.ac.cn
+
+https://cuixing100876.github.io/instastyle.github.io/
+
+![](images/1e63eab505223bc53f6724f12ef348ed063d982a0d5eed9da5777533207015f9.jpg)  
+(a) Stylized image generation
+
+![](images/169ca768357d38194f2bb25e7bf82d15cb71c2e183bd28dbc4ac52b090739872.jpg)
+
+![](images/69cb3e298b998b86a6927958978f4559c255977f7d7a973f04cf3751e19c297d.jpg)
+
+![](images/84c629f341a3fd09e2ee3f6cd287e8f9f227a9693baefa5afcb66f43fc32c2af.jpg)
+
+![](images/b473543400ab34673d2adfbf995d8edb1c31fb93a1762a0942448bb5d951a3dc.jpg)  
+(b) Combination of two styles
+
+![](images/1c4d6b7cda07a19095eb7c0f005b26060b39492853b3c4481b232b0aab1effce.jpg)
+
+![](images/97529d597569d6ed5e4480cfb297ad0f2af082ea4440564d09051db94f66be3f.jpg)
+
+![](images/9330de21c23d5472d0ff22763d378e135a93505a0d1b824f021dedc8d5609c02.jpg)  
+Fig.1: Visualization of INSTASTYLE. (a) Our method excels at capturing style details and distinguishing between similar styles. (b) The first and third columns show images styled with reference to style 1 and style 2, respectively. The middle column shows images in a combined style. (c) Our method supports adjusting the degree of two styles during combination, dynamically ranging from one style to another.
+
+![](images/907bae5c8e0dc894846f9e6f17ff37fd2c55f8afe2aa130360b62c3694a522a6.jpg)  
+(c) Smooth style combination between two styles
+
+![](images/55ba7284fe8c72a89735b12aa9a149385830693aae246f036db71da7804d6512.jpg)
+
+![](images/267eaa01b35a34ab943f9ada63666182b2a808ac49138da21b5861ffa48e9bce.jpg)
+
+![](images/c07f653d646e4259d232a88b8f4c396b95f600fd4f1138d064b6859e612e65a8.jpg)
+
+![](images/8f12bad59ba600af0c00a833e3d7ab06fdbc0c2280cf101b86b5e6ab0fce7cc1.jpg)
+
+![](images/4bcbdf770e23e41f3ada368e2fd9598647f1c8198b5ab2243a224d827bbd285c.jpg)  
+Style 2
+
+Abstract. Stylized text-to-image generation focuses on creating images from textual descriptions while adhering to a style specified by reference images. However, subtle style variations within different reference images can hinder the model from accurately learning the target style. In this paper, we propose INSTASTYLE, a novel approach that excels in generating high-fidelity stylized images with only a single reference image. Our approach is based on the finding that the inversion noise from a stylized reference image inherently carries the style signal, as evidenced by their non-zero signal-to-noise ratio. We employ DDIM inversion to extract this noise from the reference image and leverage a
+
+diffusion model to generate new stylized images from the "style" noise. Additionally, the inherent ambiguity and bias of textual prompts impede the precise conveying of style during image inversion. To address this, we devise prompt refinement, which learns a style token assisted by human feedback. Qualitative and quantitative experimental results demonstrate that INSTASTYLE achieves superior performance compared to current benchmarks. Furthermore, our approach also showcases its capability in the creative task of style combination with mixed inversion noise.
+
+Keywords: Stylized image generation  $\cdot$  Inversion noise  $\cdot$  Signal-to-noise ratio  $\cdot$  Prompt refinement
+
+# 1 Introduction
+
+Recently, the advent of DDPMs [16, 51] has ushered in a new era of image generation. Existing text-to-image generation methods [5, 43, 45, 46] can generate images in coarse-grained styles by incorporating style descriptions in the textual prompt. However, the textual prompt is ambiguous which makes it hard to express style precisely [11]. Recently, personalized generation [10,48,63] has been introduced to generate novel concepts, which can be utilized for stylized generation by viewing the reference style as a new concept. These approaches typically necessitate mul
+
+tiple images as references. However, the subtle style variations in these multiple images present a challenge for the model to accurately learn and replicate the intended style. As shown in the first column of Fig. 1 (a), although the reference image Houses at Auvers (top) and Thatched Cottages by a Hill (bottom) are all Van Gogh's artworks, the differences in terms of color and texture [2] pose a significant challenge. Some recent approaches [3,53,69] are designed to more accurately describe the target style during generation. However, they may ignore the fine-grained style information in the reference images.
+
+In this paper, we propose INSTASTYLE (Inversion Noise of a Stylized Image is Secretly a Style Adviser) based on the observation that the inversion noise from a stylized reference image inherently contains the style signal. Specifically, our approach only requires a single reference image, which is transformed into a noise via DDIM inversion. The inversion noise, which preserves the style signal, is then used to generate stylized images by utilizing diffusion models. To shed light on this phenomenon, we demonstrate that the inversion noise maintains
+
+![](images/c6e36f47eb5ca9567d1b717d049362c833b3659b33beacdc9ab7cb5b91e60c4c.jpg)  
+Fig. 2: Motivation. Sampling from the inversion noise of a reference image can generate stylized images. However, the optimal style token varies for each case among human-written style tokens. Our learnable style token, i.e., "<style1>", shows greater universality across various scenarios.
+
+a non-zero signal-to-noise ratio in Sec. 3.2, indicating that it retains essential information (including the style signal) from the reference image.
+
+Nevertheless, directly using human-written prompts to describe styles for inverting the reference image often encounters challenges due to the inherent ambiguity of natural language. For instance, specific style descriptors like "ink painting" don't always work effectively with various objects. As shown in Fig. 2, the style "ink painting" might suit an object like a "chair" but not as well with a "boy". This inconsistency can arise because "ink painting" is typically associated with landscapes and might not yield optimal results for human subjects. Conversely, when using vague descriptors like "specific style", they may fail to provide enough information, leading to unpredictable generation quality (see the second row in Fig. 2). To address this, we propose Prompt Refinement to learn a style token with the assistance of human feedback. As illustrated in the last row of Fig. 2, the style information is boosted by using the learned style token in the noising process to obtain a better "style" noise. Therefore, our prompt refinement stands apart from previous methods [3, 53, 69], where style tokens are utilized in the denoising process to generate target images. During prompt refinement, we first collect images via human feedback. Then we optimize the embedding of the style token and the key and value projection matrices in the cross-attention layers of the diffusion model.
+
+As shown in Fig. 1 (a), our approach can effectively retain the fine-grained style in the reference image as well as generate new objects in high fidelity. Furthermore, our method supports the creative generation of style combination (Fig. 1 (b) and (c)) and allows adjusting the degree of two styles dynamically (Fig. 1 (c)). To sum up, our contributions are as follows:
+
+- We find that the inversion noise of a reference image via DDIM inversion potentially retains style information and evidence this observation by the non-zero signal-to-noise ratio of the inversion noise.  
+- We propose INSTASTYLE based on our observation, which leverages the style signal in inversion noise. Additionally, to better represent the style during inversion, a prompt refinement scheme is designed to learn the style token. Human feedback is also introduced to enhance model alignment with human preferences during prompt refinement.  
+- Qualitative and quantitative experimental results show the superiority of our INSTASTYLE in generating high-quality stylized images. Moreover, it exhibits promising potential in creative scenarios like style combinations.
+
+# 2 Related Work
+
+# 2.1 Text-to-image Synthesis
+
+Image synthesis is an essential subject in computer vision [7,23,41,56]. Previous works are based on variational auto-encoder [29, 33] or generative adversarial networks [5,14,32,35,57]. With the advance of pretrained vison-language models [44,61] and diffusion models [34,54,73], text-to-image generation [4,8,43,45,
+
+[60] has been widely studied and shown remarkable generalization ability. Recently, Lin et al. [36] have pointed out that the noise of the last step during noisering in the training process has a non-zero signal-to-noise ratio (SNR), i.e., there exists a signal leak. This results in a misalignment between the training and inference process. Therefore, some works [36, 50] propose to train diffusion models by enforcing the SNR to zero to avoid the signal leak. On the contrary, our approach leverages the leaked signal, which potentially includes the style details, from the reference image for the stylized generation.
+
+As these methods ignore the concepts that do not appear in the training set [10], some works [10,48,49] study personalized text-to-image generation which aims to adapt text-to-image models to new concepts given several reference images. For example, Textual Inversion [10] introduces and optimizes a word vector for each new concept. Subsequent works [1,63,74] further enhance the flexibility and adaptiveness of the learning strategy. Some methods [20, 48, 49] propose to finetune the original diffusion model, showing more satisfactory results. However, maintaining fine-grained style while simultaneously generating new objects remains a challenge for current personalized generation methods [52].
+
+# 2.2 Stylized Image Generation
+
+Stylized image generation is a new paradigm for image generation which aims to generate content in a specific style given a few reference images. Although it is similar to the neural style transfer task [12, 13, 22, 27, 37, 59] which generates stylized images as well, they are fundamentally different. Style transfer solves an image translation task, focusing on translating a content image to target style [15, 21, 24, 28, 62, 64, 67, 68, 70]. For example, some works explore the global and local information to preserve the content of the source image [6, 18, 25, 26, 55, 65, 71, 75]. On the contrary, stylized image generation is geared towards generating a new image in specific style conditioned on a text. For example, ZDAIS [53] views stylized image generation as a domain adaptive task, where each style belongs to a domain. It learns disentangled prompts to adapt the model to new domains. Some approaches [9, 52] fine-tune the model to capture style properties. Our work differs from theirs by proposing a framework based on our observation that inversion noise contains style information.
+
+# 3 Method
+
+As shown in Fig. 3, our proposed method involves two main stages. In the first stage, we employ DDIM inversion to transform the reference image into noise. Notably, the inversion noise exhibits a non-zero signal-to-noise ratio, suggesting the presence of style signals from the reference image. Subsequently, we generate  $M$  stylized images from the inversion noise conditioned on the given textual prompts. Due to the inherent ambiguity of the textual prompts that describe the style, it is challenging to precisely convey the desired style. Addressing this,
+
+![](images/eb3fe407cfbedfbac602427d450029f373f0a543a3e1a5fda5646613d6d87ca0.jpg)  
+Fig. 3: The training process of INSTASTYLE. (a) The first stage is initial stylized image generation. The reference image is inverted to noise conditioned on a prompt via DDIM Inversion. Then the inversion noise is utilized to generate initial stylized images. (b) The second stage is prompt refinement which leverages the selected high-quality initial stylized images to learn a style token.
+
+the second stage involves the incorporation of human feedback to select  $N$  high-quality generated images from the first stage. The selected images are then used to learn a style token via prompt refinement.
+
+# 3.1 Preliminaries
+
+We begin by reviewing the fundamental diffusion model. Subsequently, we introduce Stable Diffusion [46], a key component of our framework. Finally, we discuss both DDIM and DDIM inversion. In our method, DDIM serves the purpose of denoising a noise to generate new images. Concurrently, DDIM inversion is utilized to transform the reference image into a corresponding "style" noise.
+
+Diffusion models. Diffusion models [16, 51] contain a forward process and a backward process. The forward process adds noise to the data according to a predetermined, non-learned variance schedule  $\beta_{1},\ldots,\beta_{T}$ :
+
+$$
+q \left(z _ {t} \mid z _ {t - 1}\right) := \mathcal {N} \left(z _ {t}; \sqrt {1 - \beta_ {t}} z _ {t - 1}, \beta_ {t} \mathbf {I}\right). \tag {1}
+$$
+
+An important property of the forward process is that we can obtain the latent variable  $z_{t}$  directly based on  $z_{0}$ :
+
+$$
+z _ {t} = \sqrt {\alpha_ {t}} z _ {0} + \sqrt {1 - \alpha_ {t}} \varepsilon , \tag {2}
+$$
+
+where  $\varepsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ ,  $\alpha_{t}\coloneqq \prod_{i = 1}^{t}(1 - \beta_{i})$ . Diffusion models restore the information by learning the backward process:
+
+$$
+p _ {\theta} \left(z _ {t - 1} \mid z _ {t}\right) := \mathcal {N} \left(z _ {t - 1}; \mu_ {\theta} \left(z _ {t}, t\right), \Sigma_ {\theta} \left(z _ {t}, t\right)\right). \tag {3}
+$$
+
+Stable Diffusion. In Stable Diffusion, the diffusion process happens in latent space [46]. It utilizes a pretrained autoencoder which consists of an encoder and a decoder. The encoder  $\mathcal{E}(\cdot)$  maps an image  $x$  into a latent code  $z$  and the decoder  $\mathcal{D}(\cdot)$  transforms the latent code back into an image. The denoising model  $\varepsilon_{\theta}(\cdot)$
+
+is an Unet [47]. During training, artificial noise is added to the sampled data  $z_0$  according to timestamp  $t$  based on Eq. (2), resulting in a noised sample  $z_t$ . Denoising model starts with  $z_t$  and is trained to predict the artificial noise:
+
+$$
+\min  _ {\theta} E _ {z _ {0}, \varepsilon \sim N (0, I), t \sim \operatorname {U n i f o r m} (1, T)} \| \varepsilon - \varepsilon_ {\theta} \left(z _ {t}, t, \mathcal {C}\right) \| _ {2} ^ {2}, \tag {4}
+$$
+
+where  $\mathcal{C} = \psi (\mathcal{P})$  is the embedding of text condition  $\mathcal{P}$
+
+DDIM. In inference time, given a noise vector  $z_{T}$ , the noise is gradually removed by sequentially predicting the added noise for  $T$  steps. DDIM [54] is one of the denoising approaches with a deterministic process:
+
+$$
+z _ {t - 1} = \sqrt {\frac {\alpha_ {t - 1}}{\alpha_ {t}}} z _ {t} + \left(\sqrt {\frac {1}{\alpha_ {t - 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \cdot \tilde {\varepsilon} _ {\theta}, \qquad (5)
+$$
+
+where  $\tilde{\varepsilon}_{\theta}$  is the estimated noise.
+
+DDIM inversion [42, 54] transforms an image to a noise conditioned on a prompt. The diffusion process is performed in the reverse direction, i.e.,  $z_0 \to z_T$ :
+
+$$
+z _ {t + 1} = \sqrt {\frac {\alpha_ {t + 1}}{\alpha_ {t}}} z _ {t} + \left(\sqrt {\frac {1}{\alpha_ {t + 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \cdot \tilde {\varepsilon} _ {\theta}. \tag {6}
+$$
+
+# 3.2 Initial Stylized Image Generation
+
+As shown in Fig. 3 (a), the first stage of our INSTASTYLE involves obtaining the inversion noise via DDIM inversion and sampling images via DDIM.
+
+In DDIM inversion, the added noise for each step is calculated conditioned on a prompt and gradually incorporated into the reference image following Eq. (6). Specifically, we set the learnable style token as a human-written style description in this stage. We demonstrate that the inversion noise from a stylized reference image inherently carries the style signal from the perspective of the signal-to-noise ratio. As the estimated noise  $\varepsilon_{\theta}(z_t,t,\mathcal{C})$  is trained to approximate the artificial noise  $\varepsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , we assume that  $\varepsilon_{\theta}(z_t,t,\mathcal{C}) \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ . According to Eq. (6),  $z_{t + 1}$  can be approximated in a closed form:
+
+$$
+z _ {t + 1} = \sqrt {\frac {\alpha_ {t + 1}}{\alpha_ {0}}} z _ {0} + \sqrt {\sum_ {i = 0} ^ {t} \frac {\alpha_ {t + 1}}{\alpha_ {i + 1}} \left(\sqrt {\frac {1}{\alpha_ {i + 1}} - 1} - \sqrt {\frac {1}{\alpha_ {i}} - 1}\right) ^ {2}} \cdot \bar {\varepsilon} _ {0}, \tag {7}
+$$
+
+where  $\bar{\varepsilon}_0\sim \mathcal{N}(\mathbf{0},\mathbf{I})$
+
+Signal-to-Noise ratio. Signal-to-noise ratio (SNR) is introduced to measure the ratio of signals from the original image preserved in the noise [36,46]. The SNR of the inversion noise can be calculated as:
+
+$$
+\operatorname {S N R} (t) := \frac {1}{\sum_ {i = 0} ^ {t} \frac {\alpha_ {0}}{\alpha_ {i + 1}} \left(\sqrt {\frac {1}{\alpha_ {i + 1}} - 1} - \sqrt {\frac {1}{\alpha_ {i}} - 1}\right) ^ {2}}. \tag {8}
+$$
+
+We present detailed derivations in Sec. B in Supplementary Material. In Stable Diffusion [46], the predetermined variance schedule  $\beta_{t} = (\sqrt{0.00085}\cdot (1 - j) + \sqrt{0.012}\cdot j)^{2}$ , where  $j = \frac{t - 1}{T - 1}$ . At the terminal timestep  $T = 1000$ , the
+
+$SNR(T) = 0.015144$ , i.e.,  $z_{T}$  has a none-zero signal-to-noise ratio. This nonzero signal-to-noise ratio suggests that the noise obtained via DDIM inversion still retains information from the reference image and deviates from white noise. Besides, we conduct qualitative experiments and observe that style information can consistently be preserved at the terminal timestep (refer to Sec. C.3 in Supplementary Material). Therefore, we can generate target stylized images by sampling from the inversion noise based on Eq. (5).
+
+# 3.3 Prompt Refinement
+
+As the natural language prompts may not precisely convey the style (Fig. 2), we propose Prompt Refinement to learn the style tokens as shown in Fig. 3 (b). We utilize the generated stylized images in the first stage to constitute the training data for prompt refinement learning. While these generated images may not always be precise, we observe that most of them successfully retain the style information alongside appropriate content. We manually select images that distinctly embody the reference style and the target object to build the dataset.
+
+Specifically, we introduce a new token, i.e., “<style1>” to represent the style descriptor and learn its embedding. In practice, we initialize the new token with the embeddings of the textual style descriptor of the reference image. The text condition is input to the model via two projection matrices in the cross-attention block of diffusion model  $\varepsilon_{\theta}$ , i.e.,  $W^{k} \in \mathbb{R}^{d \times d'}$  and  $W^{v} \in \mathbb{R}^{d \times d'}$ . Therefore, we also fine-tune these two projection matrices. The text feature  $\mathbf{c} \in \mathbb{R}^{s \times d}$  is projected to key  $K = \mathbf{c}W^{k}$  and value  $V = \mathbf{c}W^{v}$ . The query matrix  $W^{q} \in \mathbb{R}^{l \times d'}$  projects the latent image feature  $\mathbf{f} \in \mathbb{R}^{(h \times w) \times l}$  into query feature  $Q = \mathbf{f}W^{q}$ . Then the cross-attention [58] is calculated as:
+
+$$
+\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {S o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d ^ {\prime}}}\right) V. \tag {9}
+$$
+
+We utilize the LoRA [20] for model fine-tuning. Specifically, for a projection matrix  $W \in \mathbb{R}^{d \times d'}$  (i.e.,  $W = W^k$  or  $W = W^v$ ) to be fine-tuned, we update a low-rank residual rather than directly fine-tuning  $W$ . Formally, we denote the fine-tuned projection matrix as  $W' = W + BA$ , where  $B \in \mathbb{R}^{d \times r}$ ,  $A \in \mathbb{R}^{r \times d'}$ , and the rank  $r \ll \min(d, d')$ . During training, only  $A$  and  $B$  are learnable. For  $y = Wx$ , the modified forward pass is  $y = Wx + BAx$ . Putting the two stages together, our full algorithm is shown in Algorithm 1.
+
+# 3.4 Inference
+
+Stylized image generation. For stylized image generation, we first learn the style token "<style1>" to describe the style in the reference image. During inference, the learned style token is integrated into the prompt that inverts image and the prompt that generates the target image. Besides, the diffusion model  $\varepsilon_{\theta}$  is utilized as the backbone of DDIM inversion and DDIM. Specifically, the reference image is first inverted to a noise  $z_{T}$  via DDIM inversion conditioned
+
+1. Input: A source prompt embedding  $\mathcal{C} = \psi(\mathcal{P})$  and a reference image  $\mathcal{I}$ . Initial style token embedding  $v$  is included in the prompt embedding  $\mathcal{C}$ .  
+2 Output: Optimized style token embedding  $v^{*}$  and diffusion model  $\varepsilon_{\theta}^{*}$ .
+
+// Initial Stylized Image Generation
+
+3 Compute the inversion noise  $z_{T}$  using DDIM inversion over  $\mathcal{I}$  conditioned on  $\mathcal{C}$  based on Eq. (6);  
+4 Generate  $M$  images conditioned on a predefined prompt set based on Eq. (5); // Prompt Refinement  
+5 Select  $N$  images from  $M$  images with human feedback as the training dataset  $q(\mathbf{x}_0, c)$ ;
+
+6 repeat
+
+Algorithm 1: INSTASTYLE  
+```txt
+7  $\mathbf{x}_0,c\sim q(\mathbf{x}_0,c)$    
+8  $z_{0} = \mathcal{E}(\mathbf{x}_{0})$    
+9  $t\sim \mathrm{Uniform}(\{1,\dots ,T\})$    
+10  $\varepsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$    
+11  $z_{t} = \sqrt{\alpha_{t}} z_{0} + \sqrt{1 - \alpha_{t}}\varepsilon$    
+12 Take gradient step on  $\nabla_{\theta ,v}\| \varepsilon -\varepsilon_{\theta}(z_t,t,c)\| _2^2;$
+```
+
+13 until converged;  
+14 Return  $v^{*}$ ,  $\varepsilon_{\theta}^{*}$
+
+on a prompt containing the learned style token. Then we sample from the inversion noise conditioned on a target prompt which contains the target content and the learned style token via DDIM. Specifically, the estimated noise is calculated based on the classifier-free guidance [17]:
+
+$$
+\tilde {\varepsilon} _ {\theta} \left(z _ {t}, t, \mathcal {C}, \varnothing\right) = \varepsilon_ {\theta} \left(z _ {t}, t, \varnothing\right) + w \cdot \left(\varepsilon_ {\theta} \left(z _ {t}, t, \mathcal {C}\right) - \varepsilon_ {\theta} \left(z _ {t}, t, \varnothing\right)\right), \tag {10}
+$$
+
+where  $\varnothing = \psi(")$  is the embedding of a null text.  $\varepsilon_{\theta}(z_t, t, \mathcal{C})$  represents the conditional predictions.  $w$  is the guidance scale parameter.
+
+Combination of two styles. To combine two styles, we learn style tokens for each style, i.e., “<style1>” and “<style2>”. Specifically, we use the selected images of both styles to constitute the training set. Then we jointly optimize the embeddings of the style tokens and fine-tune the key projection and value projection in the cross-attention block. During inference, we individually transform two reference images into their corresponding inversion noise  $z_{t1} \in \mathbb{R}^{H \times W \times C}$  and  $z_{t2} \in \mathbb{R}^{H \times W \times C}$  via DDIM inversion conditioned on a prompt containing their learned style token. As the style can be described by both the “style” noise and style token, we combine the styles from these two perspectives. For the “style” noise, the combined inversion noise  $z_{t}$  is obtained based on a masking strategy:
+
+$$
+z _ {t} = (\mathbf {1} - \mathbf {M}) \odot z _ {t 1} + \mathbf {M} \odot z _ {t 2}, \tag {11}
+$$
+
+where  $\odot$  is element-wise multiplication and  $\mathbf{1}$  is a binary mask filled with ones.  $\mathbf{M} \in \{0, 1\}^{H \times W}$  denotes a random binary mask indicating where to drop out and fill in from two inversion noises. The noise mix ratio between two inversion
+
+noises is  $\alpha$ , representing the percent of  $\mathbf{M}$  that is set to 1 (the rest is set to 0). Finally, we utilize a composed guidance mechanism [38] to estimate the noise:
+
+$$
+\begin{array}{l} \tilde {\varepsilon} _ {\theta} \left(z _ {t}, t, \mathcal {C}, \varnothing\right) = \varepsilon_ {\theta} \left(z _ {t}, t, \varnothing\right) \\ + w \cdot (1 - \beta) \cdot \left(\varepsilon_ {\theta} \left(z _ {t}, t, \mathcal {C} _ {1}\right) - \varepsilon_ {\theta} \left(z _ {t}, t, \varnothing\right)\right) \tag {12} \\ + w \cdot \beta \cdot \left(\varepsilon_ {\theta} \left(z _ {t}, t, \mathcal {C} _ {2}\right) - \varepsilon_ {\theta} \left(z _ {t}, t, \varnothing\right)\right), \\ \end{array}
+$$
+
+where  $\beta$  is a prompt mix ratio.  $\mathcal{C}_1$  and  $\mathcal{C}_2$  are the embeddings of the target prompts for the two styles, respectively. Denote the target object as  $<\mathrm{obj}>$ , they can be formulated as  $\mathcal{C}_1 = \psi("A < \mathrm{obj}>$  in the style of  $<\mathrm{style}1>$ ) and  $\mathcal{C}_2 = \psi("A < \mathrm{obj}>$  in the style of  $<\mathrm{style}2>$ ).
+
+# 4 Experiment
+
+# 4.1 Experimental Setting
+
+We collect 60 images as the reference style dataset. The complete information on these images is listed in Tab. 2 in the Supplementary Material. Our method is implemented using PyTorch and executed on a single NVIDIA GeForce RTX 3090 GPU. The training procedure consists of 500 iterations, employing the Adam optimizer with a learning rate of  $1 \times 10^{-5}$ . During sampling, we set the guidance scale  $w = 2.5$ . The number of generated images  $M$  in the first stage is 15 whose details are shown in Sec. C.1 in the Supplementary Material. The number of selected images  $N$  in the second stage is set to 5.
+
+![](images/c80cd58cfac2a6c96bc4d5b69f6c86d483da87d9c4e1d3427d3057bcb40f2567.jpg)
+
+![](images/62bb4229f8af2972e988e022ba0d231ef3ad458bc58eb5fedee8e8358b7441be.jpg)
+
+![](images/bd86b46287db8e57f5d00d11245aa8a8a3df65f210ac82d2bf536f74c6df529a.jpg)
+
+![](images/f76010f551154aba616b502ebb7632c7ed8a8dc21e847c25fe407ec728079064.jpg)  
+Reference
+
+![](images/7da6a41e381c596b65db7c7f3decaf9953cc2a7dd0161b4941397773a727d28a.jpg)
+
+![](images/ad889a0748d7d4b91bc4e81feab077c629a9fff69edfcd9d34d3c23ae55d6273.jpg)
+
+![](images/ec16abb08643cb1c6a287e592936c53702e6390106467c49c48455a9c122504f.jpg)
+
+![](images/a4f917a9ca3a35ce6227ed953403d9a6a49b24239d416c7cadfd7b3ae105b922.jpg)  
+(a)InstaStyle(Ours)
+
+![](images/820c13bc6a331fdd56672ae44865209d89456ea7e66cc8269458d290bf5066b3.jpg)
+
+![](images/f4ea39848124db46872acc74bb26bef845260cfadd46797d37f9938aa2eb0ba4.jpg)
+
+![](images/f30cfcc739e5c8d127bd62253d7bf6fd9854cea2b82a4bef23f836be27277f2a.jpg)
+
+![](images/55ceaa9fe7cd17f7c80fc91b8bafb11df3a9528725f082866ec54ca2184e4fcc.jpg)  
+(b) StyleDrop
+
+![](images/a44d63fc11adf0886ed91375a8e74f7fae3953358ce775aa66cefe1ac9d7695e.jpg)
+
+![](images/4674897d31eeb69fbacd88345437a172ba213fbd74048934bf294f05392867fb.jpg)
+
+![](images/0107c43360cc799d70b54fe3f4e7e4e8b60c9f736ad4ba37ad6fb88f2ea1bc34.jpg)
+
+![](images/cedd09f2c56d58e9316e4c472b9610fbbd96ec4b0292eeb9a36619ac9f8bb852.jpg)  
+(c) DreamBooth  
+Fig. 4: Qualitative comparison of stylized image generation on various styles. Objects for synthesis are Bicycle, Sunflowers and Chair. Our method excels at capturing fine-grained style information, such as color, textures, and brushstrokes.
+
+![](images/002147886c24b0ab81221df2673671661e13f714c9273a98d253f706318af2ce.jpg)
+
+![](images/653565d4528b7c0528cf9491e47b6acdccc83b98af0dc302b7a61fafab4ca3fe.jpg)
+
+![](images/6983507207ecd7191875b40ee1de1704c34080d70e3b1344588e9ce3ba303710.jpg)
+
+![](images/83b87eac91516065c091178a75e7d91cba991330dfc8b756dcd910b4ccddb590.jpg)  
+(d) Custom Diffusion
+
+![](images/40a69f8153fe9d2dbf1fbe2c7145211952e9bf6c2a33c76174eb41e0829690d7.jpg)
+
+![](images/88421700aef09d80582a937676a89610ad3f6f07859c37df56059aa7ebbfea5e.jpg)
+
+![](images/79e448d2d647579d093015077ce84c9df2da00dec33a313e6c9974613d4136ee.jpg)
+
+![](images/d5b43c83b2a50bb2f1d961f2fb79cdcb39838166256d1b4b070d8709d0b2ca67.jpg)  
+(e) Textual Inversion
+
+![](images/93a947d27a8f62ea37793f74e43126f818fb863980e76daf4c312e7d6151b1a3.jpg)
+
+![](images/e723e52182e240f95fbbe1b7a875a9b19283d0e8e74851d803ff4d831ec3d572.jpg)
+
+![](images/49116d4c68b22b28a783b598b4d337418063adbb1b2519c0a2bf9d78da5f3f88.jpg)
+
+![](images/6c1a1cdaf0f6f75b8d8923bfa18fd5b89f2d51c76d7d7dc52e08972b08ca6aa6.jpg)
+
+![](images/a8d3e58b66bc7a859d63d2473cbdf9c7094fcc83fa576d996983b959fa348831.jpg)  
+Reference
+
+![](images/6308999419633e125169ded48e8b7eff36ed76541bc56a75a94058289b96d5f0.jpg)  
+Elephant
+
+![](images/edc3f3da5f4238def5eac7a6ed55fdab14f7825f302830fd0521a3e20a4fd899.jpg)  
+Castle
+
+![](images/dd8c65a113b26c9d1a7ab6c21cd6573ca34f853337ef4a1d7a5000375691bd2a.jpg)
+
+![](images/de7afc33523f9555c9b8ce501cbfdd3109d3fbc90863b3439ab6346959c63a42.jpg)
+
+![](images/d7c07f514c16acc211d896020f09eae1047f00ab72e06c84dd7ccecb71e2a852.jpg)  
+InstaStyle (Ours) AsePA-Net
+
+![](images/1f685ed8d931e04fcb720f28c5e00c1b0b51feb446af776d043f685b254cc413.jpg)
+
+![](images/330ec054cd93cdd9ed17ca7eb53fd48bddd2eef517b06bc473b1e77534e8c038.jpg)
+
+![](images/ef77012026b7637a45a696c5a90362734f2fbf4bd85a431bdbf604570b051001.jpg)
+
+![](images/206cfea526225d6930e12f88a1c78d4df1041164ce2bd67524b1ba578a9e2a94.jpg)
+
+![](images/d10c581de5238462787cc8f7fff64353771ac95d9828003356f85a3eb8091a98.jpg)
+
+AsePA-Net
+
+![](images/73463e740a620daeeb15fcfe9c403a856ba19fd6a67bb97c6da8d3d443e15c3e.jpg)
+
+![](images/95bfccb1ea87ba82468c96b26daec57cc902ad2b653de2bcfeef06fd6fa3ecd4.jpg)
+
+![](images/35d60c178be4da672a7f060d94fa71e8479354998dd926f364096d7bbe1c0838.jpg)
+
+![](images/cbfcc14075106e7f94a26eb32d48e078074cd840d83d012f91adf7a93a083600.jpg)
+
+![](images/d7180e1caddb0d3a86177ba9e3e5d782cb58390549923bd61eaf4ac902533446.jpg)  
+QuantArt
+
+![](images/05598e7175a982d5487822da50fa43e462e996653c5f4523c0726f50f9d32d62.jpg)
+
+![](images/0c9d46d1c3d0bcf4267c7bd4f59bbb1cc89b6f4ff181b89666d1784bd8fc38dc.jpg)
+
+![](images/e264bcef2f9453325657db6676fb1edfdc9e33fc03bf384f5a8ea86c94ee7706.jpg)
+
+![](images/1476c31bfcbc733e327d103cc8148e8bbc300b1968115dddab1c68d7bf80e6f0.jpg)
+
+![](images/4b93159d2c873695fdb64eed844b3e72c22c4070dca0151e1897340a52c97462.jpg)  
+StyTr2  
+Fig. 5: Qualitative comparison with style transfer methods. For style transfer methods, content images are employed (shown in the bottom right). Despite our method relying solely on text for content, we achieve comparable performance in the fidelity of the content. Furthermore, we excel in preserving style details.
+
+![](images/e41ca3e62ebe14a9808eafe31303259a8263db9d06de58c81dded567f3601f4f.jpg)
+
+![](images/34009c2c215c55995462b4dc78ce439822f400a8f47f02ecc3754b8173f441ae.jpg)
+
+![](images/1fd7c27b9d3cedce90590f2b1b794c1f6ebdb3bb91f09bbe58e630c76a928466.jpg)
+
+![](images/8fdcbdce0135afb31df927f694a23fd3910a085c92de7df6dc37827d04698ab6.jpg)
+
+![](images/3487069969ff08a784ccbb60e4c46f118026d63ab2069534411f7daec87421b4.jpg)  
+CCPL
+
+![](images/987a6b0916c64ccabaa92e53be4572161cd6d477426dc4baa3004fb4e22a8d70.jpg)
+
+![](images/045f44cf9b34091bb737841c03f6264b59476797cef469c95c02a9fd0615060d.jpg)
+
+![](images/02fba50679b86a7063d59cd655d216a36378a742a971c229f1341e5ac30046a6.jpg)
+
+![](images/48e2922a4116385d9a72fd20ddb187d0dce8e687c4feb90b5859d93d60c78ee6.jpg)
+
+![](images/bfb1dcd8741518b7e4e125fd298e9295f0816ec4af33087a11432480483cff82.jpg)  
+CAST
+
+![](images/b45d1cc9e7ae0b014b3310e82ec8e6e580f41351184793f9912aa37b1e52385c.jpg)
+
+![](images/b0c9100974743ffa73e09a8c2b364963320cdada2537265b94bb012071077003.jpg)
+
+![](images/c88c1c8132436e21e819713e6a68af7e3b7ca7f87a3da6c7d55f384e05abaa90.jpg)
+
+![](images/026dc34338163e68aa922611d253adf77f91015dfa3e6afaaf49b935b3859adb.jpg)
+
+![](images/cc3dfe80fe84d7125c55048fa26b61828e98d962b7edeca00acce1a79438501d.jpg)  
+AdaAttn
+
+# 4.2 Stylized Image Synthesis
+
+We conduct comparisons of INSTASTYLE against four recent methods following the open-sourced code $^{4,5}$ , i.e., StyleDrop [52], DreamBooth [48], Custom Diffusion [31], and Textual Inversion [10]. Besides, following [53], we also make a comparison with style transfer methods [6,19,21,39,66,72] to further illustrate the superiority of our approach. Notably, the style transfer task takes images as content input, in contrast to our task which only utilizes text prompts for content. To make a comparison between the two tasks, we additionally generate content images based on text prompts for style transfer methods. Although we can compare the two tasks under this setting, the comparison is unfair to our approach because the content images utilized by style transfer methods may provide additional content information compared to our text prompts.
+
+Qualitative results. As shown in Fig. 4, textual Inversion and Custom Diffusion often yield an unsatisfactory style. Taking the well-known Van Gogh painting style (e.g., row 3 and row 4) as an example, they fail to capture fine-grained style information in the reference image. The fine-tuning-based methods, i.e., DreamBooth and StyleDrop, result in distorted content. For example, they gen
+
+Table 1: (a) Quantitative comparison regarding the style consistency score and content fidelity score. (b) User study. The results show the percentage of votes where the comparison method is preferred over ours, ties with ours and is inferior to ours. We use the abbreviation (ST) to represent approaches for style transfer tasks.  
+(a)  
+
+<table><tr><td>Method</td><td>Style (↑)</td><td>Content (↑)</td></tr><tr><td>(ST) AdaAttN [39]</td><td>0.587</td><td>0.287</td></tr><tr><td>(ST) CCPL [66]</td><td>0.542</td><td>0.286</td></tr><tr><td>(ST) StyTr2 [6]</td><td>0.560</td><td>0.282</td></tr><tr><td>(ST) CAST [72]</td><td>0.594</td><td>0.285</td></tr><tr><td>(ST) QuantArt [21]</td><td>0.554</td><td>0.289</td></tr><tr><td>(ST) AesPA-Net [19]</td><td>0.604</td><td>0.284</td></tr><tr><td>Textual Inversion [10]</td><td>0.562</td><td>0.278</td></tr><tr><td>Custom Diffusion [31]</td><td>0.611</td><td>0.280</td></tr><tr><td>DreamBooth [48]</td><td>0.561</td><td>0.244</td></tr><tr><td>StyleDrop [52]</td><td>0.602</td><td>0.248</td></tr><tr><td>Ours (INSTSTYLE)</td><td>0.655</td><td>0.294</td></tr></table>
+
+(b)  
+
+<table><tr><td>Method</td><td>Preference</td><td>Tie</td><td>Ours</td></tr><tr><td>(ST) AdaAttN [39]</td><td>0.26</td><td>0.13</td><td>0.61</td></tr><tr><td>(ST) CCPL [66]</td><td>0.30</td><td>0.23</td><td>0.47</td></tr><tr><td>(ST) StyTr2 [6]</td><td>0.27</td><td>0.20</td><td>0.53</td></tr><tr><td>(ST) CAST [72]</td><td>0.31</td><td>0.26</td><td>0.43</td></tr><tr><td>(ST) QuantArt [21]</td><td>0.12</td><td>0.23</td><td>0.65</td></tr><tr><td>(ST) AesPA-nNet [19]</td><td>0.23</td><td>0.22</td><td>0.55</td></tr><tr><td>Textual Inversion [10]</td><td>0.09</td><td>0.13</td><td>0.78</td></tr><tr><td>Custom Diffusion [31]</td><td>0.09</td><td>0.15</td><td>0.76</td></tr><tr><td>DreamBooth [48]</td><td>0.24</td><td>0.17</td><td>0.56</td></tr><tr><td>StyleDrop [52]</td><td>0.27</td><td>0.26</td><td>0.47</td></tr></table>
+
+erate bicycles with leaked content from the reference image in the last row. In contrast, benefiting from the style signal in the inversion noise, our INSTASTYLE can generate stylized images with fine-grained style details and higher fidelity. Take the bicycle in Fig. 4 as an example, our method can better preserve the color, textures, and brushstroke. Besides, the generated bicycle is more accurate. Fig. 5 presents the qualitative comparisons with style transfer methods. Despite the inherent challenge of utilizing text as content input in contrast to style transfer methods that use the content image as input, our INSTASTYLE demonstrates comparable performance in content fidelity. Additionally, our INSTASTYLE exhibits superior performance in preserving the style details of the reference image, notably in terms of color and brushstroke characteristics. More qualitative results are shown in Figs. 9 to 13 in the Supplementary Material.
+
+Quantitative results. We follow evaluation measures in prior works [10,52]. We utilize 100 objects in CIFAR100 [30] as the target objects. The generated images are evaluated from two aspects. For style consistency, we calculate the CLIP score [44] between the generated image and the reference image. For content fidelity, CLIP score [44] is calculated between the image and the prompt.
+
+As shown in Tab. 1 (a), INSTASTYLE achieves the highest style consistency and content fidelity, indicating that the images generated by INSTASTYLE exhibit a consistent style with the reference image while retaining its generation capability. For the comparison methods, Textual Inversion and Custom Diffusion have a lower style consistency, falling short of INSTASTYLE in style preservation. As for DreamBooth and StyleDrop, our approach surpasses them in generating target objects with a higher content score. We also compare with style transfer methods [6,19,21,39,66,72] which utilize content images as input. Notably, our approach diverges by only employing text prompts as content input. This brings challenges in terms of generating high-quality content as text prompts contain less information than content images. Despite this distinction, we achieve an
+
+improved content score. Additionally, our approach excels in preserving style details, exhibiting a higher style consistency score.
+
+User study. Given the highly subjective nature of stylized generation and the inherent biases in content alignment and style consistency, we conduct a user study following previous works [6, 52]. Each question presents participants with a pair of images: one stylized image generated by our approach and another produced by a selected comparison method. To avoid bias, the images are anonymized and randomized for each question. Participants are tasked with evaluating which result they believed exhibited better stylization effects and content structures. To ensure robustness and reliability, we invite 20 participants for the user study. We compare our method with 10 existing methods, including the style transfer methods [6, 18, 21, 39, 66, 72] and current comparable methods [10, 31, 48, 52]. For each method, 30 generated image pairs are randomly selected. Finally, each participant completed 300 rounds of comparisons, resulting in a total of 6,000 votes across all methods. We count the votes and show the statistical results in Tab. 1 (b). Our approach obtains a higher preference, underscoring its superiority over competitors in both style preservation and content generation.
+
+![](images/ddc98eed017386d9aacf4897124584d45d4e45043821f6481d8d2ab6a5cd0cd3.jpg)  
+Fig. 6: Visualization of the combination of two styles. In each case, we show our combination results (the biggest image). For better comparison, we also present the stylized generation results of style1 and style2 in the top left (blue box) and bottom left (red box), respectively. Objects for synthesis are Boat, Truck, Horse, Elephant, Pear, Lion, Plate, Pot, Helicopter, Bicycle, Palace, and Motorcycle.
+
+![](images/08c824084edf5b72d9e5b220c3f1e0e1226b1893a8afded2055c0d8853171490.jpg)
+
+![](images/f8d2d26bed1296db83e55389e0b19a7c9fcceefb533625c708b4b4e8069954c2.jpg)
+
+![](images/82e18b05baf7c9fa1db32c84e3cca3ae22b7db7774eaf5f6ed4e8a03996ea6cb.jpg)
+
+![](images/9fbc5de0087b186f10f8abda4b9334c6691931f27bdd6402aaa9477563c972a1.jpg)
+
+# 4.3 Combination of Two Styles
+
+We present style combination results in Fig. 6, where we set  $\alpha = 0.5$  and  $\beta = 0.5$  to illustrate a more obvious effect of style combination. Specifically, in each case, we also show the stylized generation results of style 1 (the top left) and style 2 (bottom left), respectively. The biggest image on the right is our combination
+
+![](images/90e0317c5d4ede5d33bd0924b11ddf8f1f3121ebb4d02ac49c021304b98895c4.jpg)  
+Fig. 7: Visualization of the combination of two styles. The style can be controlled via the noise mix ratio and the prompt mix ratio. Our approach enables continuous style combinations, demonstrating its flexibility and diversity.
+
+results, showing the powerful style combination ability of our approach. More visualizations are shown in. Figs. 14 and 15 in Supplementary Material.
+
+As introduced in Sec. 3.4, both the noise mix ratio  $\alpha$  and the prompt mix ratio  $\beta$  can affect the style. Fig. 7 illustrates the impact of the two parameters, where each row shows a different noise mix ratio ( $\alpha = 0.1, 0.3, 0.5, 0.7, 0.9$ ) and each column shows a different prompt mix ratio ( $\beta = 0.1, 0.3, 0.5, 0.7, 0.9$ ). The style is mainly influenced by the noise and the prompt further improves the style details, showing that our approach is flexible and can generate diverse results.
+
+# 4.4 Ablation Study
+
+Our approach achieves stylized generation from two perspectives. One is the "style" noise obtained via DDIM inversion, which is utilized as the initial noise during inference to provide fine-grained style information. The other is the style token, which is learned via prompt refinement tuning to describe the style precisely. In this section, we conduct the ablation study. The visualization results and quantitative results are shown in Fig. 8 (a) and Fig. 8 (b), respectively. Specifically, each point in Fig. 8 (b) presents the average style consistency score and content fidelity score of 100 generated images for a reference style.
+
+Impact of inversion noise. A prominent advantage of our INSTASTYLE is that we utilize the inversion noise as the initial image during inference time to preserve the fine-grained style information. Thereby, we first conduct an ablation study by replacing the inversion "style" noise with random noise. As shown in
+
+![](images/27548266a07c0e682ddb7c8380909a1d562657bb15c4fac7d54b7559f5a08dc2.jpg)  
+Fig. 8: Ablation study. (a) Visualization of ablation study. The reference style image is shown in the bottom right corner. Objects for synthesis are *Dinosaur*, *Bicycle*, *Bee*, and *Boy*, respectively. Without the inversion noise, the stylized performance is seriously degraded. Prompt refinement can further improve style details. (b) Quantitative results of ablation study. Our method lies further along the top right corner, showing better style preservation and content generation capability.
+
+Fig. 8 (a) (second row), without the inversion noise, the stylized performance is seriously degraded. The quantitative results in Fig. 8 (b) further illustrate that ablating the "style" noise (blue dots) will result in a lower style consistency score, harming the style of the generated image.
+
+Impact of prompt refinement tuning. We ablate the prompt refinement stage to show the necessity of learning a style token to avoid ambiguity and bias in human-writing textual style tokens. Fig. 8 (a) (third row) reveals that our learnable style token can better describe the style without harming the generation ability. The quantitative results in Fig. 8 (b) show that ablating the prompt refinement (green dots) will result in a lower content fidelity score and style score, further proving the importance of the learnable style token.
+
+# 5 Conclusion
+
+Our research solves the task of stylized generation by exploring the fine-grained style information in the reference image. Through extensive analysis and empirical investigation, we find that the initial noise with a non-zero signal-to-noise ratio in the diffusion model leans toward a particular style. Therefore, DDIM inversion is introduced to obtain an initial noise containing fine-grained style information. Furthermore, we highlight the challenge caused by the internal bias in textual style tokens and propose to learn a style token adaptively to better describe the style without bias. Our approach produces satisfactory stylized generation results and supports the combination of two styles. Extensive qualitative and quantitative comparisons demonstrate the superiority of our method.
+
+Acknowledgement This research is sponsored by National Natural Science Foundation of China (Grant No. 62306041, U21B2045, 62176025), Beijing Nova Program (Grant No. Z211100002121106, 20230484488, 20230484276), Youth Innovation Promotion Association CAS (Grant No.2022132), and Beijing Municipal Science & Technology Commission (Z231100007423015).
+
+# References
+
+1. Alaluf, Y., Richardson, E., Metzer, G., Cohen-Or, D.: A neural space-time representation for text-to-image personalization. ACM TOG (2023)  
+2. Chen, H., Zhao, L., Wang, Z., Zhang, H., Zuo, Z., Li, A., Xing, W., Lu, D.: Dualast: Dual style-learning networks for artistic style transfer. In: CVPR (2021)  
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+        "type": "text",
+        "text": "Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation",
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+        "text": "Arpit Garg<sup>1</sup>, Cuong Nguyen<sup>3</sup>, Rafael Felix<sup>1</sup>, Thanh-Toan Do<sup>2</sup>, and Gustavo Carneiro<sup>3</sup>",
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+        "text": "$^{1}$  Australian Institute for Machine Learning, University of Adelaide, SA, Australia  $^{2}$  Department of Data Science and AI, Monash University, Australia",
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+        "type": "text",
+        "text": "3 Centre for Vision, Speech and Signal Processing, University of Surrey, UK",
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+    {
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+        "text": "Abstract. Deep learning faces a formidable challenge when handling noisy labels, as models tend to overfit samples affected by label noise. This challenge is further compounded by the presence of instance-dependent noise (IDN), a realistic form of label noise arising from ambiguous sample information. To address IDN, Label Noise Learning (LNL) incorporates a sample selection stage to differentiate clean and noisy-label samples. This stage uses an arbitrary criterion and a pre-defined curriculum that initially selects most samples as noisy and gradually decreases this selection rate during training. Such curriculum is sub-optimal since it does not consider the actual label noise rate in the training set. This paper addresses this issue with a new noise-rate estimation method that is easily integrated with most state-of-the-art (SOTA) LNL methods to produce a more effective curriculum. Synthetic and real-world benchmarks' results demonstrate that integrating our approach with SOTA LNL methods improves accuracy in most cases. $^4$",
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+    {
+        "type": "text",
+        "text": "Keywords: Noisy-labels  $\\cdot$  Instance-dependent noise  $\\cdot$  Label noise Learning",
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+    },
+    {
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+        "text": "Deep neural networks (DNNs) have demonstrated their effectiveness in various domains, including vision [47], language [42], and medicine [37]. However, its efficacy is largely dependent on high-quality training data, which can be resource-intensive to obtain [43]. Although cost-effective labelling techniques, such as data mining [11] and crowdsourcing [39], offer cheaper alternatives, they often compromise label quality [39]. Consequently, this can lead to erroneous labels in real-world datasets [21]. This is a relevant issue because even slight inaccuracies in the labels can significantly affect the performance of DNN due to their inherent memorisation capabilities [34, 53]. This has prompted the development of algorithms resilient to noisy-label learning, with the aim of training models",
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+        "text": "$^{4}$  Code is available at https://github.com/arpit2412/NoiseRateLearning. Supported by the Engineering and Physical Sciences Research Council (EPSRC) through grant EP/Y018036/1 and the Australian Research Council (ARC) through grant FT190100525.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "despite inaccuracies in training data labels. Although various strategies exist, our work uniquely proposes an approach centered on the estimation of the label noise rate from the training data, which is notably absent from current methodologies.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "There are two types of label noise, namely instance-independent noise (IIN) [16] and instance-dependent noise (IDN) [44]. Such type of label noise typically influences the design principles of noisy-label learning algorithms. For example, IIN focuses on mislabellings that are independent of sample information [16], where estimating the underlying label transition matrix is a common way of handling this type of noise [51]. On the other hand, in the more realistic IDN, mislabelling is due to both sample information and true class labels [44], which generally require the combination of many label noise learning techniques, such as robust loss functions [28, 56], and noisy-label sample selection [26, 58]. Of the strategies mentioned above, sample selection approaches that classify training data into clean and noisy samples have produced competitive results on many benchmarks [9, 11, 15, 21, 26]. Such sample selection techniques require the definition of a classification criterion and a selection curriculum. Many studies on this topic focus on developing new sample selection criteria, such as the small-loss hypothesis [26], which states that noisy-label samples have higher loss values than clean-label samples, particularly at the early stage of training [1]. Another criterion type is the feature-based one. An example of such criterion is FINE [21] that discriminates clean and noisy-label samples via the distance to class-specific eigenvectors. In this technique, clean-label samples tend to lie closer to the class-specific dominant eigenvector of the latent representations than noisy-label samples. Another type of criterion is proposed in SSR [11], which introduces a selection criterion based on the K-nearest-neighbor (KNN) classification in the feature space. Furthermore, CC [58] uses a two-stage sampling procedure, including class-level feature clustering followed by a consistency score. An equally important problem in sample selection is the definition of the curriculum for selecting clean training samples, but it has received comparatively less attention.",
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+        "type": "text",
+        "text": "The sample selection curriculum defines a threshold to be used with one of the criteria listed above to classify the training samples as clean or noisy at each training epoch [45]. For example, the threshold can be fixed to an arbitrary clustering score that separates clean and noisy samples [26], but this strategy does not account for the proportion of label noise in the training set, nor does it consider the dynamics of the selection of noisy-label samples during the training. The consideration of such dynamics has been studied in [16, 49], which defined a curriculum of the noisy-label sampling rate  $R(t)$  as a function of the training epoch  $t \\in \\{1, \\dots, T\\}$ . The curriculum  $R(t)$  defines a sampling rate close to  $100\\%$  of the training set at the beginning of the training, which is then reduced to arbitrarily low rates at the end of the training. In practice, the function  $R(t)$  is predefined [16] or learned by weighting a set of basis functions [49].",
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+        "type": "text",
+        "text": "Although generally effective, these techniques do not consider the label noise rate estimated from the training set, making them vulnerable to over-fitting (if too many noisy-label samples are classified as clean) or under-fitting (if informative clean-label samples are classified as noisy). It can be argued that the estimation",
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+        "text": "2",
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+    {
+        "type": "header",
+        "text": "A. Garg et al.",
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+    {
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+        "img_path": "images/a180e75bd1f43c8f3c626a7caf5e2fc0fcf82f6c0d858ceb5e6d660de8757ded.jpg",
+        "image_caption": [
+            "(a) Motivation"
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
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+    {
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+        "image_caption": [
+            "(b) Proposed Graphical Model",
+            "Fig. 1: (a) Comparison of test accuracy  $\\%$  (as a function of training epoch) between the original DivideMix [26] (solid, blue curve) and our modified DivideMix (dashed, red curve) that selects the clean and noisy data based on a fixed noise rate  $R(t) = 1 - \\epsilon = 50\\%$  using the small-loss criterion on CIFAR100 [22] at 0.5 IDN [44]; (b) The proposed probabilistic graphical model that generates noisy-label  $\\hat{Y}$  conditioned on the image  $X$ , the latent clean-label  $Y$  and noise rate  $\\epsilon$ , where forward pass (solid lines) is parameterised by  $\\theta_y, \\theta_{\\hat{y}}$  and  $\\epsilon$  representing the generation step, and the backward pass (dashed lines) is parameterised by  $\\rho$ ."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "of the label transition matrix [6,7,48,51] aims to recover the noise rate affecting pairwise label transitions. However, label transition matrix techniques follow a quite different strategy compared to sample selection methods, where their main challenge is the general underconstrained aspect of the matrix estimation, making them sensitive to large noise rates and not scalable to a high number of classes [39]. Although several methods address label noise, none estimates the label noise rate directly from the training data to guide sample selection. Addressing this gap is the primary challenge of our study.",
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+    {
+        "type": "text",
+        "text": "To underscore the importance of using the noise rate for sample selection during training, we experiment with CIFAR100 [22] at an IDN rate  $\\epsilon = 50\\%$  [44] (noise rate specifications and other details are explained in Sec. 4). We use DivideMix [26] and replace its sample selection (based on an arbitrary clustering score [10,32,41]) by a thresholding process that classifies the  $R(t) = 1 - \\epsilon = 50\\%$  largest loss samples as noisy, and the remaining ones as clean in all training epochs  $t \\in \\{1, \\dots, T\\}$ . This sample selection is used for the semi-supervised learning of DivideMix [26]. As shown in Fig. 1a, the new sample selection approach based on the \"manually provided\" noise rate (dashed red curve) improves  $6\\%$  in terms of prediction accuracy compared to the original DivideMix [26] (solid blue curve) which relies on arbitrary thresholding. Similar conclusions can be achieved with other methods that apply sample selection strategies to address the noisy-label learning problem, as shown in the experiments.",
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+    {
+        "type": "text",
+        "text": "In this paper, we introduce a new sample selection strategy centered on estimating the label noise rate of the training set. Our strategy is based on our novel noisy-label learning graphical model illustrated in Fig. 1b. This model can be",
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+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
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+        "image_caption": [
+            "(a) Curriculum function  $R(t)$"
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+        "image_caption": [
+            "(b) Accuracy Comparison",
+            "Fig. 2: (a) Visual comparison of different  $R(t)$  on CIFAR100 [22] at 0.5 IDN [44]: (i) Co-teaching [16] with curriculum based on hyper-parameter  $T_{k} \\in \\{5,10\\}$ , where  $R(t) = 1 - \\tau \\cdot \\min(t / T_{k}, 1)$  with  $\\tau = \\epsilon = 0.5$  being manually set; (ii) S2E [49], where  $R(t)$  is estimated with a bi-level optimisation; (iii) SSR [11], where  $R(t)$  is based on a relabelling pattern, (iv) CC [58] following the small-loss hypothesis [26] and cosine similarity for  $R(t)$ ; and (v) ours. (b) Accuracy of noisy-label learning methods on CIFAR100 [22] at 0.5 IDN [44], including DivideMix [26], FINE [21] and InstanceGM [15], without (left, blue) and (right, orange) integration of our proposed graphical model for estimating the noise rate  $\\epsilon$  and sample selection rate based on  $\\epsilon$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "seamlessly integrated with state-of-the-art (SOTA) noisy-label learning techniques, providing them with a precise noise rate estimate and subsequently refining the sample selection curriculum. In particular, our model's curriculum is not restrained by predefined  $R(t)$  functions [16, 49], but rather relies on a dynamically estimated noise rate sourced directly from the training set, as depicted in Fig. 2a. Our method dynamically estimates training set noise rates to mitigate overfitting and underfitting, seamlessly integrates with existing algorithms, and serves as a robust foundation for future noisy-label learning research. To summarise, our main contributions include:",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- An innovative noisy-label learning graphical model, shown in Fig. 1b, that not only estimates but also leverages the noise rate from the training dataset to produce a refined sample selection curriculum for SOTA LNL methods.",
+            "- A simple and synergistic integration strategy of our novel graphical model with several SOTA noisy-label learning algorithms, such as DivideMix [26] and SSR [11], to improve their sample selection effectiveness, leading to an increased test accuracy, as shown in Fig. 2b."
+        ],
+        "bbox": [
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+            616,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Empirical evaluations show the role of our proposed sample selection methodology in improving the efficacy of leading noisy-label learning algorithms across various synthetic and real-world IDN benchmarks. Although our primary focus lies in addressing IDN problems, because of its more challenging and realistic nature, we have also applied our model to IIN problems, with detailed results in Tab. 6 and discussion in Appendix 3 of the supplementary material. With our innovative approach, we aim to improve the accuracy of SOTA LNL methods.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "A. Garg et al.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "It is well-known that DNNs suffer from overfitting when trained with noisy-labels [52], resulting in poor generalisation [28, 55]. To mitigate the problems related to noisy-label learning, several techniques have been developed, including noise-robust loss functions [30], noise-label sample selection [21, 26, 40, 58, 59], meta-learning [57], and re-labeling followed by sample selection [11]. These techniques can handle many types of label noise (e.g., symmetric and asymmetric), but the most challenging type, i.e., IDN [39], tends to be successfully addressed with methods that have a training stage based on sample selection techniques [21, 26, 40, 58, 59]. These sample selection techniques separate clean and noisy-label samples, where clean samples are treated as labelled, and noisy samples are discarded [8, 16, 18, 49] or treated as unlabeled samples [9, 15, 26, 35, 59] for semi-supervised learning [3]. Another solution consists of aligning clean and noisy samples with an information fusion method [19]. A major limitation of these approaches is the overly simplistic design of the curriculum to select clean and noisy-label samples during training. It is either predetermined [16, 18] or learned from a set of predetermined basis functions [49]. We argue that the design of a curriculum based on an estimated noise rate would benefit such methods, as motivated by Fig. 1a, but to the best of our knowledge, such estimation has not been explored by previous methods. The closest idea explored is based on the estimation of the type of noise instead of the noise rate [45]. It is possible to argue that the estimation of the label transition matrices [5, 7, 44, 60], composed of the learned noise rate that affects the transition between pairs of labels, is a way to estimate the label noise rate. However, they portray results of comparatively lower accuracy for large real-world datasets or for IDN problems [39, 44]. A possible reason for these poorer results is that label transition approaches suffer from identifiability issues [14], where any clean-label distribution assignment is acceptable as long as the distribution of observed labels can be reconstructed [13]. This makes the identification of the actual underlying clean-labels challenging. One solution is to consider the use of multiple annotations per sample to help analyse agreements and disagreements for improved identification of clean patterns [14, 31]. However, the annotation of datasets with a single label per training sample is already challenging; the complexity is significantly larger to acquire multiple labels per sample.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "An alternative technique to handle IDN problems is based on graphical models that represent the relationship between various observed and latent variables [15,45,50]. The approaches in [15,50] use graphical models that rely on a generative approach to produce noisy-labels from the respective image features and latent clean-labels. However, previous graphical models do not take into account the underlying noise rate parameter during modeling. Our work is the first graphical model approach to estimate the noise rate of the dataset. In addition, a close examination of existing literature reveals a trend: when traditional graphical models are integrated with SOTA noisy-label learning methods, the outcomes often fall short of expectations in terms of accuracy [2,15,50]. This observation underscores a strong point of our work. Our approach is uniquely tailored for",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
+        "bbox": [
+            397,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "easy integration with current SOTA noisy-label learning methods for sample selection, which, in turn, improves over the SOTA classification accuracy.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we present our new graphical model that estimates the noise rate, which will be used in the sample selection process. Let  $\\mathcal{D} = \\{(x_i,\\hat{y}_i)\\}_{i = 1}^N$  be the noisy-label training set containing  $d$ -dimensional data vector  $x_{i}\\in \\mathcal{X}\\subseteq \\mathbb{R}^{d}$  and its respective  $C$ -dimensional one-hot encoded observed (potentially corrupted) label  $\\hat{y}_i\\in \\hat{\\mathcal{V}} = \\{\\hat{y}:\\hat{y}\\in \\{0,1\\} ^C\\wedge \\mathbf{1}_C^\\top \\hat{y} = 1\\}$ , where  $\\mathbf{1}_C$  is a vector of ones with  $C$  dimensions. The aim is to estimate the label noise rate  $\\epsilon$ , used for the generation of noisy-label training data from the observed training dataset  $\\mathcal{D}$  and integrate this label noise rate into the sample selection strategy.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1 Graphical Model",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We portray the generation of noisy-label via the probabilistic graphical model shown in Fig. 1b. The observed random variables, denoted by shaded circles, are data  $X$  and the corresponding noisy-label  $\\hat{Y}$ . We also have one latent variable, namely: the clean-label  $Y$ . Under our proposed modeling assumption, a noisy-label of a data instance can be generated as follows:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- sample an instance from  $p(X)$ , i.e.:  $x \\sim p(X)$",
+            "- sample a clean-label from the clean-label distribution:"
+        ],
+        "bbox": [
+            225,
+            486,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny \\sim \\operatorname {C a t e g o r i c a l} (Y; f _ {\\theta_ {y}} (x))\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            243,
+            517,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "- sample a noisy-label from the noisy-label distribution:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {y} \\sim \\operatorname {C a t e g o r i c a l} (\\hat {Y}; \\epsilon \\times f _ {\\theta_ {\\hat {y}}} (x, f _ {\\theta_ {y}} (x)) + (1 - \\epsilon) \\times y),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            546,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\text{Categorical}()$  denotes a categorical distribution,  $f_{\\theta_y}: \\mathcal{X} \\to \\Delta_{C-1}$  and  $f_{\\theta_{\\hat{y}}}: \\mathcal{X} \\times \\Delta_{C-1} \\to \\Delta_{C-1}$  denote two classifiers for the clean-label  $Y$  and noisy-label  $\\hat{Y}$ , respectively, with  $\\Delta_{C-1} = \\{s : s \\in [0,1]^C \\wedge \\mathbf{1}_C^\\top s = 1\\}$  being the  $(C-1)$ -dimensional probability simplex. According to the data generation process shown in Fig. 1b,  $\\epsilon$  corresponds to  $\\mathbb{E}_{(x,\\hat{y}) \\sim p(X,\\hat{Y})}[P(\\hat{y} \\neq y|x)]$ , which is the label noise rate of the training dataset of interest. Our aim is to infer the parameters  $\\theta_y, \\theta_{\\hat{y}}$  and  $\\epsilon$  from a noisy-label dataset  $\\mathcal{D}$  by maximising the following log-likelihood:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\max  _ {\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon} \\mathbb {E} _ {(x _ {i}, \\hat {y} _ {i}) \\sim \\mathcal {D}} [ \\ln p (\\hat {y} _ {i} | x _ {i}; \\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon) ] = \\max  _ {\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon} \\mathbb {E} _ {(x _ {i}, \\hat {y} _ {i}) \\sim \\mathcal {D}} [ \\ln \\sum_ {y _ {i}} p (\\hat {y} _ {i}, y _ {i} | x _ {i}; \\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon) ]. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Due to the presence of the clean-label  $y_{i}$ , it is difficult to directly evaluate the log-likelihood in Eq. (1). Therefore, we employ the expectation-maximisation (EM) algorithm [10] to maximise the log-likelihood. The main idea of the EM algorithm is to (i) construct a tight lower bound of the likelihood in Eq. (1) by estimating the posterior of the latent variable  $Y$  (known as expectation step) and (ii) maximise that lower bound (known as maximisation step). Formally, let",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "A. Garg et al.",
+        "bbox": [
+            271,
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+            128
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "$q(y_{i}|x,\\hat{y};\\rho)$  be an arbitrary distribution over a clean-label  $y_{i}$ . The evidence lower bound (ELBO) of the log-likelihood in Eq. (1) can be obtained through Jensen's inequality and is presented as follows:",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} Q \\left(\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon , \\rho\\right) = \\mathbb {E} _ {\\left(x _ {i}, \\hat {y} _ {i}\\right) \\sim \\mathcal {D}} \\left[ \\mathbb {E} _ {q \\left(y _ {i} \\mid x _ {i}; \\hat {y} _ {i}; \\rho\\right)} \\left[ \\ln p \\left(\\hat {y} _ {i} \\mid x _ {i}, y _ {i}; \\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon\\right) \\right] \\right. \\\\ - \\operatorname {K L} \\left[ q \\left(y _ {i} \\mid x _ {i}, \\hat {y} _ {i}; \\rho\\right) \\| p \\left(y _ {i} \\mid x _ {i}; \\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon\\right) \\right] \\\\ = \\mathbb {E} _ {\\left(x _ {i}, \\hat {y} _ {i}\\right) \\sim \\mathcal {D}} \\left[ \\mathbb {E} _ {q \\left(y _ {i} \\mid x _ {i}; \\hat {y} _ {i}; \\rho\\right)} \\left[ \\ln p \\left(\\hat {y} _ {i} \\mid x _ {i}, y _ {i}; \\theta_ {\\hat {y}}, \\epsilon\\right) \\right. \\right. \\\\ \\left. + \\ln p \\left(y _ {i} \\mid x _ {i}; \\theta_ {y}\\right) \\right] + \\mathbb {H} \\left[ q \\left(y _ {i} \\mid x _ {i}, \\hat {y} _ {i}; \\rho\\right) \\right], \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{KL}[q\\| p]$  is the Kullback - Leibler divergence between distributions  $q$  and  $p$  and  $\\mathbb{H}(q)$  is the entropy of the distribution  $q$ . The EM algorithm is then carried out iteratively by alternating the following two steps:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "E step: we maximise the ELBO in (2) w.r.t.  $q(y_{i}|x_{i},\\hat{y}_{i};\\rho)$ . Theoretically, such an optimisation results in KL  $[q(y_{i}|x_{i},\\hat{y}_{i};\\rho)\\| p(y_{i}|x_{i},\\hat{y}_{i})] = 0$  or  $q(y_{i}|x_{i},\\hat{y}_{i};\\rho) = p(y_{i}|x_{i},\\hat{y}_{i})$ . This is equivalent to estimating the posterior of the clean-label  $y_{i}$  given noisy-label data  $(x_{i},\\hat{y}_{i})$ . Obtaining the posterior  $p(y_{i}|x_{i},\\hat{y}_{i})$  is, however, intractable for most deep-learning models. To mitigate such an issue, we follow the variational EM approach [33] by employing an approximate posterior  $q(y_{i}|x_{i},\\hat{y}_{i};\\rho^{(t)})$  that is the closest to the true posterior  $p(y_{i}|x_{i},\\hat{y}_{i})$ , where:",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\rho^ {(t)} = \\arg \\max _ {\\rho} Q \\left(\\theta_ {y} ^ {(t)}, \\theta_ {\\hat {y}} ^ {(t)}, \\epsilon^ {(t)}, \\rho\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "with the superscript  ${}^{(t)}$  denoting the parameters at the  $t$ -th iteration. Although this results in a non-tight lower bound of the log-likelihood in Eq. (1), it does increase the variational bound  $Q$ .",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "M step: we maximise the ELBO in Eq. (2) w.r.t.  $\\theta_y, \\theta_{\\hat{y}}$  and  $\\epsilon$  given  $\\rho^{(t)}$  obtained in the E step:",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\theta_ {y} ^ {(t + 1)}, \\theta_ {\\hat {y}} ^ {(t + 1)}, \\epsilon^ {(t + 1)} = \\arg \\max  _ {\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon} Q (\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon , \\rho^ {(t)}). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The estimated noise rate  $\\epsilon$  can then be integrated into certain noisy-label algorithms to train the models of interest as mentioned in Sec. 1. In addition, the inference of noise rate  $\\epsilon$  might be associated with the identifiability issue when estimating the clean-label  $Y$  [29], i.e., there exists multiple sets of  $\\rho$  and  $\\theta_y$ , where each set can explain the observed noisy-label data equally well. Such issues are addressed in the following subsection.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.2 Sample Selection",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The identifiability issue when inferring the clean-label  $Y$  from noisy-label data  $(X, \\hat{Y})$  can be mitigated either by acquiring multiple noisy-labels [29] or introducing additional constraints, such as small loss hypothesis [16] or FINE [21]. Since requesting additional noisy-labels per training sample is not always possible, we",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
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+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Proposed noisy-label learning that relies on the estimation of noise rate  $\\epsilon$  to build a sample selection curriculum."
+        ],
+        "code_body": "1: procedure NOISE RATE ESTIMATION AND INTEGRATION(D,T,λ)  \n2:  $\\triangleright$ $\\mathcal{D} = \\{(x_i,\\hat{y}_i)\\}_{i = 1}^N$  training set with noisy-label data  \n3:  $\\triangleright$  T: number of epochs  \n4:  $\\triangleright$  λ: a hyper-parameter  \n5:  $\\triangleright$  Notation:  $\\Theta^{(t)} = (\\theta_y^{(t)},\\theta_{\\hat{y}}^{(t)},\\epsilon^{(t)})$   \n6: Initialise  $\\theta_y^{(1)},\\theta_{\\hat{y}}^{(1)},\\epsilon^{(1)}$  and  $\\rho^{(0)}$   \n7:  $\\theta_y^{(1)}\\gets \\mathrm{WARM~UP}(\\mathcal{D},\\theta_y^{(1)})$   \n8:  $t\\gets 0$   \n9: for  $n_{\\mathrm{epoch}} = 1:T$  do  \n10: for each mini-batch  $\\mathcal{S}$  in SHUFFLE(D) do  \n11:  $t\\gets t + 1$   \n12:  $\\mathcal{S}_{\\mathrm{clean}},\\mathcal{S}_{\\mathrm{noisy}}\\gets \\mathrm{SAMPLE~SELECTION}(\\mathcal{S},\\theta_y^{(t)},\\epsilon^{(t)})$   \n13:  $\\triangleright$  Variational E-step as in Eq. (3)  \n14:  $\\rho^{(t)}\\gets \\mathrm{E~STEP}(\\mathcal{S},\\theta_y^{(t)},\\theta_{\\hat{y}}^{(t)},\\epsilon^{(t)},\\rho^{(t - 1)})$   \n15:  $\\triangleright$  M-step as in Eq. (8)  \n16:  $\\theta_y^{(t + 1)},\\theta_{\\hat{y}}^{(t + 1)},\\epsilon^{(t + 1)}\\gets \\mathrm{M~STEP}(\\mathcal{S}_{\\mathrm{clean}},\\mathcal{S}_{\\mathrm{noisy}},\\theta_y^{(t)},\\theta_{\\hat{y}}^{(t)},\\epsilon^{(t)},\\rho^{(t)},\\lambda)$   \n17: return  $\\theta_y$   \n1 parameter of the clean-label classifier",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "follow the latter approach by imposing a constraint (scoring term), denoted as  $L(\\theta_y, \\epsilon^{(t)})$ , over  $\\theta_y$  in the M step via a sample selection approach based on the estimated noise rate  $\\epsilon^{(t)}$ . Formally, we propose a new curriculum when selecting samples as follows:",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR (t) = 1 - \\epsilon^ {(t)}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In the simplest case, such as Co-teaching [16] or FINE [21], the constraint for  $\\theta_y$  can be written as:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL \\left(\\theta_ {y}, \\epsilon^ {(t)}\\right) = \\sum_ {\\left(x _ {i}, \\hat {y} _ {i}\\right) \\in \\mathcal {S} _ {\\text {c l e a n}}} \\operatorname {K L} \\left[ \\operatorname {C a t e g o r i c a l} (Y; \\hat {y}) \\| \\operatorname {C a t e g o r i c a l} \\left(Y; f _ {\\theta_ {y}} \\left(x _ {i}\\right)\\right) \\right], \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "where:",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {\\text {c l e a n}} = \\left\\{\\left(x _ {i}, \\hat {y} _ {i}\\right): \\left(x _ {i}, \\hat {y} _ {i}\\right) \\in \\mathcal {D} \\wedge z \\left(x _ {i}, y _ {i}\\right) \\leq m \\right\\},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm \\in \\{m: \\Pr (z \\left(x _ {i}, y _ {i}\\right) \\leq m) \\geq R (t) \\wedge \\Pr (z \\left(x _ {i}, y _ {i}\\right) \\geq m) \\geq 1 - R (t) \\},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            256,
+            718,
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+            734
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} _ {\\text {n o i s y}} = \\mathcal {D} \\backslash \\mathcal {S} _ {\\text {c l e a n}}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            256,
+            737,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "with  $R(t)$  defined in (5), and  $z(x,y)$  representing the score of a criterion (e.g., loss [26, 58, 59], distance to the largest eigenvectors [21], or KNN scores [11]). Intuitively, the loss in Eq. (6) is simply the cross-entropy loss on the  $\\lfloor R(t)\\times N\\rfloor$  samples that have smallest scores (with  $\\lfloor .\\rfloor$  being the floor function). One can also extend to other SOTA models by replacing the loss  $L$  accordingly. For example,",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
+            217,
+            114,
+            228,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "A. Garg et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            128
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/08c3a57bb884bedf5284bacc78cd61a6a3ead553af3eb4a53130280ac377ba00.jpg",
+        "image_caption": [
+            "Fig. 3: Our training algorithm uses an existing noisy-label classifier (e.g., DivideMix [26]) parameterised by  $\\theta_y$  as the clean-label model  $p(Y|X;\\theta_y)$ . The generation of noisy-label (given  $X$  and  $Y$ ) is carried out by a model parameterised by noise rate  $\\epsilon$  and  $\\theta_{\\tilde{y}}$ . The noisy-label classifier is based on a sample-selection mechanism that uses a curriculum  $R(t) = 1 - \\epsilon^{(t)}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            233,
+            143,
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+            316
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "if DivideMix [26] is used as a base model to constrain  $\\theta_y$ ,  $L$  will include two additional terms: loss on un-labeled data and regularisation using mixup [54].",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "3.3 Training and Testing",
+        "text_level": 1,
+        "bbox": [
+            215,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Given the sample selection approach in Sec. 3.2, the M step in Eq. (4) is slightly modified by integrating the constraint in Eq. (6), which can be written as",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\theta_ {y} ^ {(t + 1)}, \\theta_ {\\hat {y}} ^ {(t + 1)}, \\epsilon^ {(t + 1)} = \\arg \\max  _ {\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon} Q (\\theta_ {y}, \\theta_ {\\hat {y}}, \\epsilon , \\rho^ {(t)}) - \\lambda L (\\theta_ {y}, \\epsilon^ {(t)}), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            264,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  is a hyper-parameter and  $L$  is defined in Eq. (6). The training procedure is summarised in Algorithm 1 and visualised in Fig. 3. In the implementation, we integrate the proposed method into existing models, such as DivideMix [26] or FINE [21]. Note that the clean-label classifier  $f_{\\theta_y}(.)$  is also the clean classifier of the base model.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We show extensive experiments in several noisy-label synthetic benchmarks with CIFAR100 [22], and real-world benchmarks, including CNWL's red mini-ImageNet [17], Clothing1M [45] and mini-WebVision [27]. Sec. 4.2 describes implementation details. We evaluate our approach by plugging SOTA models into  $p(y|x;\\theta_y)$ , defined in Sec. 3, with results being shown in Sec. 4.3, and ablation studies in Sec. 4.4.",
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+    },
+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.1 Dataset Descriptions",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We follow the existing literature to generate the IDN labels [44] for CIFAR100 [22]. The dataset contains 50,000 training images and 10,000 testing images of shape  $32 \\times 32 \\times 3$ . The dataset is class-balanced with 100 different categories and the IDN rates considered are 0.2, 0.3, 0.4 and 0.5 [44]. Another important IDN benchmark dataset is the red mini-ImageNet, a real-world dataset from CNWL [17]. In this dataset, there are 100 distinct classes, with each class containing 600 images. The images and their corresponding noisy-labels have been crawled from the internet at various controllable label noise rates. For a fair comparison with the existing literature [9, 15, 46], we have resized the images to  $32 \\times 32$  pixels from the  $84 \\times 84$  original pixel settings. We show results with  $40\\%$ ,  $60\\%$  and  $60\\%$  noise rates on this dataset. Clothing1M [45] is a real-world clothing classification dataset that contains 1 million images with an estimated noise rate of  $38.5\\%$ . The dataset contains 14 different categories, and the labels are generated from surrounding texts. Images in this dataset are of different sizes, and we follow the resize structure suggested in [21, 26]. This dataset also contains  $50k$  manually validated clean training images,  $14k$  images for the validation set, and  $10k$  testing images. We have not used the clean training, validation set, or any extra training images while training. Only the testing set is used for evaluation. Mini-WebVision [26] contains 65,944 images with their respective labels from the 50 different initial categories from the WebVision [27], with image size of  $256 \\times 256$  pixels. Following the evaluation process commonly used in this benchmark, 50 categories from the ILSVRC12 [23] dataset are also used for testing.",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "4.2 Implementation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "All methods are implemented in Pytorch [36] and use one NVIDIA RTX 3090 card for training and testing. As mentioned in the original papers, hyperparameter settings are kept the same for the baselines used in the proposed algorithm. All classifier architectures are also kept the same as the baseline models. A random initialisation of noise rate parameter  $\\epsilon$  with the sigmoid as its activation function is employed for all experiments to maintain the fairness of the comparisons with other approaches. The value of  $\\lambda$  in Eq. (8) is set to 1 for all the cases. We integrate many SOTA approaches [11, 15, 21, 26, 58, 59] into our graphical model, as explained in Sec. 3.3. For CIFAR100 [22] with IDN [44], we integrate DivideMix [26], C2D [59], CC [58], and InstanceGM [15] into our model, given their superior performance across various noise rates. Additionally, we also use F-Dividemix from FINE [21], as shown in Fig. 2b. For red mini-ImageNet [17], we test our proposed approach with and without DINO self-supervision [4]. For the implementation without self-supervision, we use DivideMix [26] and InstanceGM [15], and for the self-supervised version, we only use InstanceGM [15]. The models for Clothing1M [45] and mini-WebVision [26] (validation on ImageNet [23]) are trained using DivideMix [26], SSR [11], C2D [59] and CC [58]. Additional implementation details, empirical analysis, and computational analysis are presented in the supplementary material in Appendices 1, 2 and 4, respectively.",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
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+            114,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "A. Garg et al.",
+        "bbox": [
+            271,
+            114,
+            364,
+            128
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/4bfd87feb77d72e512e4ee274f0c31901970f3e0ba53f7122e3fe8f58099bdec.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Noise Rates - IDN</td></tr><tr><td>0.2</td><td>0.3</td><td>0.4</td><td>0.5</td></tr><tr><td>CE [50]</td><td>30.42</td><td>24.15</td><td>21.45</td><td>14.42</td></tr><tr><td>PartT [44]</td><td>65.33</td><td>64.56</td><td>59.73</td><td>56.80</td></tr><tr><td>kMEIDTM [7]</td><td>69.16</td><td>66.76</td><td>63.46</td><td>59.18</td></tr><tr><td>DivideMix [26]</td><td>77.03</td><td>76.33</td><td>70.80</td><td>58.61</td></tr><tr><td>DivideMix-Ours</td><td>77.42</td><td>77.21</td><td>72.41</td><td>64.02</td></tr><tr><td></td><td>(+0.39)</td><td>(+0.88)</td><td>(+1.61)</td><td>(+5.41)</td></tr><tr><td>C2D [59]</td><td>78.61</td><td>78.18</td><td>72.89</td><td>63.19</td></tr><tr><td>C2D-Ours</td><td>79.07</td><td>78.59</td><td>73.31</td><td>65.28</td></tr><tr><td></td><td>(+0.46)</td><td>(+0.41)</td><td>(+0.42)</td><td>(+2.09)</td></tr><tr><td>CC [58]</td><td>79.61</td><td>77.56</td><td>76.58</td><td>63.19</td></tr><tr><td>CC-Ours</td><td>79.72</td><td>78.71</td><td>77.38</td><td>67.53</td></tr><tr><td></td><td>(+0.11)</td><td>(+1.15)</td><td>(+0.80)</td><td>(+4.34)</td></tr><tr><td>InstanceGM [15]</td><td>79.69</td><td>79.21</td><td>78.47</td><td>77.19</td></tr><tr><td>InstanceGM-Ours</td><td>79.61</td><td>79.40</td><td>79.52</td><td>78.21</td></tr><tr><td></td><td>(-0.08)</td><td>(+0.19)</td><td>(+1.05)</td><td>(+1.02)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2d58fde9424dd3cccf214c591423fbdd0f7123c4d8ff348a89bcb2192a7e5c3.jpg",
+        "table_caption": [
+            "Table 1: Test accuracy % on (left) CIFAR100 [22] under different IDN [45], and (right) red mini-ImageNet [17]. Other models' results are from [7, 15, 46]. Here, we integrate DivideMix [26], C2D [59], CC [58] and InstanceGM [15] into our proposed model for CIFAR100 [22]. For red mini-ImageNet [17], we present the results with and without self-supervision [4]. We integrate DivideMix [26] and InstanceGM [15] into our model, with the latter tested with and without self-supervision."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Noise rate</td></tr><tr><td>0.4</td><td>0.6</td><td>0.8</td></tr><tr><td>CE [46]</td><td>42.70</td><td>37.30</td><td>29.76</td></tr><tr><td>MixUp [54]</td><td>46.40</td><td>40.58</td><td>33.58</td></tr><tr><td>MentorMix [17]</td><td>47.14</td><td>43.80</td><td>33.46</td></tr><tr><td>FaMUS [46]</td><td>51.42</td><td>45.10</td><td>35.50</td></tr><tr><td>DivideMix [26]</td><td>46.72</td><td>43.14</td><td>34.50</td></tr><tr><td>DivideMix-Ours</td><td>50.70</td><td>45.11</td><td>37.44</td></tr><tr><td></td><td>(+3.98)</td><td>(+1.97)</td><td>(+2.94)</td></tr><tr><td>InstanceGM [15]</td><td>52.24</td><td>47.96</td><td>39.62</td></tr><tr><td>InstanceGM-Ours</td><td>56.61</td><td>51.40</td><td>43.83</td></tr><tr><td></td><td>(+4.37)</td><td>(+3.44)</td><td>(+4.21)</td></tr><tr><td colspan=\"4\">With self-supervised learning</td></tr><tr><td>PropMix [9]</td><td>56.22</td><td>52.84</td><td>43.42</td></tr><tr><td>InstanceGM-SS [15]</td><td>56.37</td><td>53.21</td><td>44.03</td></tr><tr><td>InstanceGM-SS-Ours</td><td>58.29</td><td>53.60</td><td>45.47</td></tr><tr><td></td><td>(+1.92)</td><td>(+0.39)</td><td>(+1.44)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/284a65786cefd4bf552f156bc2186dde2912e47a7aaa070cc230f159a079983e.jpg",
+        "table_caption": [
+            "Table 2: Final estimated noise rate  $\\epsilon$  for the Tab. 1, (left) CIFAR100 [22] under various IDN [44], and (right) red mini-ImageNet [17] with and without self-supervision."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"5\">Estimated noise rates</td></tr><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Actual noise rate</td></tr><tr><td>0.2</td><td>0.3</td><td>0.4</td><td>0.5</td></tr><tr><td>DivideMix-Ours</td><td>0.18</td><td>0.34</td><td>0.47</td><td>0.53</td></tr><tr><td>C2D-Ours</td><td>0.19</td><td>0.33</td><td>0.38</td><td>0.52</td></tr><tr><td>CC-Ours</td><td>0.21</td><td>0.34</td><td>0.41</td><td>0.54</td></tr><tr><td>InstanceGM-Ours</td><td>0.23</td><td>0.37</td><td>0.42</td><td>0.47</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/d433bbea64944dfbb523ed9b62d1e29215db162b39b2c3d74b086baa83a95672.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Estimated noise rates</td></tr><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">Actual noise rate</td></tr><tr><td>0.4</td><td>0.6</td></tr><tr><td>DivideMix-Ours</td><td>0.39</td><td>0.58</td></tr><tr><td>InstanceGM-Ours</td><td>0.38</td><td>0.55</td></tr><tr><td>InstanceGM-SS-Ours</td><td>0.48</td><td>0.53</td></tr><tr><td></td><td></td><td>0.73</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.3 Comparison with SOTA",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This section compares our approach with SOTA methods on datasets with the IDN settings and noisy real-world settings. The bold text in tables indicate SOTA results, and our results are in the greyed rows.",
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+    },
+    {
+        "type": "text",
+        "text": "Synthetic Instance-Dependent Noise The comparison between various baselines and our proposed method on CIFAR100 [22] with IDN [44] is shown in Tab. 1 (left) with the noise rate ranging from 0.2 to 0.5. It is worth noting that using our proposed model with DivideMix [26], C2D [59], CC [58] and InstanceGM [15] improve their performance in almost all cases, particularly with large noise rates. Tab. 2 (left) also shows the final noise rate  $\\epsilon$  estimated by our model which is reasonably close to the simulated noise rate displayed in the table's header.",
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+        "page_idx": 10
+    },
+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "table",
+        "img_path": "images/0332020760bcfb9fed8e6553408cbb4a0a7b58c2587196643a6ee2d8aa30f5c8.jpg",
+        "table_caption": [
+            "Table 3: Test accuracy (\\%) of competing methods, and final estimated noise rate  $\\epsilon$  on Clothing1M [45]. Also, we have not considered competing models that rely on a clean or validation set whilst training. We integrate DivideMix [26], C2D [59], SSR [11] and CC [58] into our model. DivideMix [26] and CC [58] shows the locally reproduced results. Mentioned noise rate by [45] is 0.385."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Test accuracy (%)</td><td>Estimated noise rate</td></tr><tr><td>OT-Filter [12]</td><td>74.50</td><td></td></tr><tr><td>ELR+ with C2D [59]</td><td>74.58</td><td></td></tr><tr><td>AugDesc [35]</td><td>75.11</td><td></td></tr><tr><td>NCE [25]</td><td>75.30</td><td></td></tr><tr><td>DivideMix [26]</td><td>74.32</td><td></td></tr><tr><td>DivideMix-Ours</td><td>74.41 (+0.09)</td><td>0.41</td></tr><tr><td>C2D [59]</td><td>74.58</td><td></td></tr><tr><td>C2D-Ours</td><td>74.71 (+0.13)</td><td>0.41</td></tr><tr><td>SSR (class-imbalance) [11]</td><td>74.12</td><td></td></tr><tr><td>SSR-Ours</td><td>74.20 (+0.08)</td><td>0.42</td></tr><tr><td>CC [58]</td><td>75.24</td><td></td></tr><tr><td>CC-Ours</td><td>75.31 (+0.07)</td><td>0.41</td></tr></table>",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Real-World Noise We also evaluate our proposed method on various real-world noisy settings regarding test accuracy and estimated noise rates  $\\epsilon$  in Tabs. 1 to 4. Similarly to the synthetic IDN in Tab. 1 (left), the results show that existing noisy-label robust methods can be easily integrated with our model to outperform current SOTA results for real-world noisy-label datasets. Tabs. 1 and 2 (right) shows the results on red mini-ImageNet using two configurations, including cases without self-supervision (top part of the table) and with self-supervision (bottom part of the table). The self-supervision DINO pre-training [4] relies only on images from red mini-ImageNet to enable a fair comparison with existing baselines [9, 15]. Results from Tab. 1 (right) demonstrate that our approach improves the performance of SOTA methods by a considerable margin in all cases. In fact, using estimated noise rate  $\\epsilon$  (Tab. 2 (right)) while training InstanceGM [15] without self-supervision shows better performance than existing self-supervised baselines at 0.4 noise rate. Moreover, DivideMix [26], C2D [59], SSR [11], and CC [58] are used as a baselines for Clothing1M [45] as shown in Tab. 3, with results showing slight improvements with the use of our method. For mini-WebVision [26] (validation on ImageNet [23]), we use DivideMix [26], C2D [59], SSR [11], and CC [58] as baselines (Tab. 4). It is worth noting that our results are better than the SOTA for all settings in Tab. 4.",
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+        "type": "text",
+        "text": "4.4 Ablation",
+        "text_level": 1,
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+        "text": "We show an ablation study with testing accuracy (top) and training time (bottom) of our approach in Tab. 5 (left) on CIFAR100 [22] at 0.3 and 0.5 IDN [44] using DivideMix [26] as baseline. Detailed complexity analysis is shown in the supplementary material, Tab. 10. Initially, the accuracy result of baseline DivideMix [26] is  $76.33\\%$ ,  $58.61\\%$  for 0.3 and 0.5 IDN, respectively. In the second row, we fix the noise rate  $\\epsilon$  at 0.3 and 0.5 for DivideMix's sample selection, as explained in Sec. 3.3 (without updating  $\\epsilon$ ), then the results improved to  $78.14\\%$  and  $64.44\\%$ ,",
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+        "type": "page_number",
+        "text": "12",
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+        "type": "header",
+        "text": "A. Garg et al.",
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+        "img_path": "images/3964453370a30ed11490097d59e6764282009b9af482a1587051d72fc2d23f24.jpg",
+        "table_caption": [
+            "Table 4: Test accuracy (\\%) and final estimated noise rate  $\\epsilon$  on mini-WebVision [26] and validation on ImageNet [23]. We integrate DivideMix [26], Contrast-to-Divide (C2D) [59], SSR [11] and CC [58] into our model, whilst models suffixed with -Ours denotes our proposed approach. ImageNet [23] is only considered for validation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"2\">mini-WebVision</td><td colspan=\"2\">ImageNet</td><td rowspan=\"2\">Estimated noise rate</td></tr><tr><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td></tr><tr><td>BtR [38]</td><td>80.88</td><td>92.76</td><td>75.96</td><td>92.20</td><td></td></tr><tr><td>NCE [25]</td><td>79.50</td><td>93.80</td><td>76.30</td><td>94.10</td><td></td></tr><tr><td>DivideMix [26]</td><td>77.32</td><td>91.64</td><td>75.20</td><td>91.64</td><td></td></tr><tr><td>DivideMix-Ours</td><td>78.51</td><td>92.03</td><td>76.11</td><td>93.24</td><td>0.43</td></tr><tr><td></td><td>(+1.19)</td><td>(+0.39)</td><td>(+0.91)</td><td>(+1.60)</td><td></td></tr><tr><td>C2D [59]</td><td>79.42</td><td>92.32</td><td>78.57</td><td>93.04</td><td></td></tr><tr><td>C2D-Ours</td><td>80.20</td><td>92.82</td><td>79.16</td><td>93.12</td><td>0.43</td></tr><tr><td></td><td>(+0.78)</td><td>(+0.50)</td><td>(+0.59)</td><td>(+0.08)</td><td></td></tr><tr><td>SSR [11]</td><td>80.92</td><td>92.80</td><td>75.76</td><td>91.76</td><td></td></tr><tr><td>SSR-Ours</td><td>81.68</td><td>93.80</td><td>76.91</td><td>93.05</td><td>0.43</td></tr><tr><td></td><td>(+0.76)</td><td>(+1.00)</td><td>(+1.15)</td><td>(+1.29)</td><td></td></tr><tr><td>CC [58]</td><td>79.36</td><td>93.64</td><td>76.08</td><td>93.86</td><td>-</td></tr><tr><td>CC-Ours</td><td>80.01</td><td>93.79</td><td>77.11</td><td>94.21</td><td>0.44</td></tr><tr><td></td><td>(+0.65)</td><td>(+0.15)</td><td>(+1.03)</td><td>(+0.35)</td><td></td></tr></table>",
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+        "table_caption": [
+            "Table 5: (left) Ablation results on CIFAR100 at 0.3 and 0.5 IDN. We display accuracy results under different configurations and compare the training time of our approach against DivideMix [26]. The implementation settings and detailed computational analysis are described in Sec. 4.2 and Appendix 4 respectively. (right above) Ablation results for initialisation with different  $\\epsilon$  values on CIFAR100 [22] at a synthetic noise rate of 0.5 IDN [44] with DivideMix-Ours. (right below) Ablation graph showing the learning pattern of the noise rate parameter estimation under different initialisation values, i.e.,  $\\epsilon = 0.001$  (blue),  $\\epsilon = 0.1$  (orange),  $\\epsilon = 0.9$  (red), when trained on DivideMix-ours case at 0.5 IDN [44] on CIFAR100 [22]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Models</td><td colspan=\"2\">Accuracy (%)</td></tr><tr><td>0.3</td><td>0.5</td></tr><tr><td>DivideMix [26]</td><td>76.33</td><td>58.61</td></tr><tr><td>DivideMix with fixed ε</td><td>78.14</td><td>64.44</td></tr><tr><td>Our method with pre-trained DivideMix</td><td>75.01</td><td>52.31</td></tr><tr><td>Our method with original DivideMix (no ε)</td><td>76.20</td><td>56.30</td></tr><tr><td>DivideMix-Ours</td><td>77.21</td><td>64.02</td></tr><tr><td colspan=\"3\">Training Time (GPU-hours)</td></tr><tr><td>DivideMix [26]</td><td colspan=\"2\">7.20</td></tr><tr><td>DivideMix-Ours</td><td colspan=\"2\">8.50</td></tr><tr><td>DivideMix-Ours (Mixed Precision)</td><td colspan=\"2\">6.10</td></tr></table>",
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+    {
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+        "type": "text",
+        "text": "which is the ideal case (i.e., a perfect noise rate estimation) that motivated our work. In the third case, we use the proposed graphical model with pre-trained DivideMix [26] that shows accuracy of  $75.01\\%$  and  $52.31\\%$ . In the next case, the proposed graphical model is trained together with DivideMix [26] without considering the estimated noise rate  $\\epsilon$  for sample selection, which results in accuracy of  $76.20\\%$  and  $56.30\\%$ . In the last row, we show the training of the proposed model with DivideMix [26], together with the estimation of noise rate  $\\epsilon$ , and the",
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+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
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+    {
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+        "text": "13",
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+    {
+        "type": "text",
+        "text": "selection of samples based on that, with  $\\approx 1\\%$  and  $\\approx 8\\%$  accuracy improvement to 0.3 and 0.5 IDN, which is quite close to our ideal case (second row). We also study the effect that the initialisation of the noise rate parameter  $\\epsilon$  plays in our method. As described in Sec. 4.2, we randomly initialise  $\\epsilon$  within the range  $(0,1)$ . To test the robustness of our method to this initialisation, we perform an ablation study by initialising  $\\epsilon$  with three different values, namely: 0.001, 0.1, and 0.9 on CIFAR100 [24] at 0.5 IDN [44] using the DivideMix-ours approach. Our results, presented in Tab. 5 (right above and below), demonstrate that the initial value of  $\\epsilon$  has a limited effect on the model's performance, highlighting the stability of our method across different initialisation of  $\\epsilon$ . In the supplementary material, Tab. 7 (left) presents comparative analyses of our model against PartT [44] and SSR [11] on CIFAR100 [22] at 0.5 IDN [44], while Tab. 7 (right) showcases similar comparisons with baselines DivideMix [26] and InstanceGM [15] at a higher noise rate of 0.6 IDN [44]. Additionally, Tab. 8 provides further insights into the performance of DivideMix [26] on red mini-ImageNet [17] at lower noise rates of 0.1, 0.2 and 0.3. Tab. 9 illustrates noise rate estimation with standard deviation for our model integrated with DivideMix [26] and InstanceGM [15] on CIFAR100 [22] under IDN [44] settings at 0.2, 0.3, 0.4, and 0.5. Further statistical analysis is detailed in Appendix 5 with confidence interval presented in Tab. 12. Performance analysis with various architectures (Tab. 13) and lambda values (Tab. 14) are mentioned in Appendix 6. Threshold-based comparisons are in Appendix 7 and Tab. 15.",
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+    {
+        "type": "text",
+        "text": "5 Discussion and Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this work, we proposed an innovative graphical model for IDN noisy-label learning, focusing on the estimation of the label noise rate that is leveraged to introduce a robust sample selection curriculum. Given that SOTA IDN noisy-label learning approaches tend to rely on sample selection methods, our method can be seamlessly integrated to them to improve their performance in many synthetic and real-world benchmarks, including CIFAR100 [22], red mini-ImageNet [17], Clothing1M [45], mini-WebVision [26], and ImageNet [23].",
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+    {
+        "type": "text",
+        "text": "From a societal perspective, our methodology offers a positive impact by mitigating biases inherent in noisy data, thereby promoting more fair and accurate machine learning outcomes. It also opens the door to future research avenues, including exploring advanced noise rate estimation methodologies and investigating noise-robust loss functions such as GCE [56] and ELR [28] with it. Our choice of using the same network architecture for clean and noisy labels enables compatibility with co-teaching techniques [16,26]. However, investigating different network structures for clean and noisy labels remains a potential avenue for future research. Moreover, we aim to delve into its dynamics, uncovering substantial improvements for certain models while observing more marginal enhancements for others. For more detailed information, please refer to Appendix 8. Our approach also hints at potential breakthroughs in streamlining data annotation challenges.",
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+        "text": "14",
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+    {
+        "type": "header",
+        "text": "A. Garg et al.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+    {
+        "type": "header",
+        "text": "Noisy-Label Learning with Noise-Rate Estimation",
+        "bbox": [
+            397,
+            114,
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+        "page_idx": 16
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+    {
+        "type": "page_number",
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+    {
+        "type": "list",
+        "sub_type": "ref_text",
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+        "bbox": [
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+    }
+]

2024/Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation/8698146c-3791-42ec-912e-34881bbacb25_origin.pdf

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2024/Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation/full.md

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+# Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation
+
+Arpit Garg<sup>1</sup>, Cuong Nguyen<sup>3</sup>, Rafael Felix<sup>1</sup>, Thanh-Toan Do<sup>2</sup>, and Gustavo Carneiro<sup>3</sup>
+
+$^{1}$  Australian Institute for Machine Learning, University of Adelaide, SA, Australia  $^{2}$  Department of Data Science and AI, Monash University, Australia
+
+3 Centre for Vision, Speech and Signal Processing, University of Surrey, UK
+
+Abstract. Deep learning faces a formidable challenge when handling noisy labels, as models tend to overfit samples affected by label noise. This challenge is further compounded by the presence of instance-dependent noise (IDN), a realistic form of label noise arising from ambiguous sample information. To address IDN, Label Noise Learning (LNL) incorporates a sample selection stage to differentiate clean and noisy-label samples. This stage uses an arbitrary criterion and a pre-defined curriculum that initially selects most samples as noisy and gradually decreases this selection rate during training. Such curriculum is sub-optimal since it does not consider the actual label noise rate in the training set. This paper addresses this issue with a new noise-rate estimation method that is easily integrated with most state-of-the-art (SOTA) LNL methods to produce a more effective curriculum. Synthetic and real-world benchmarks' results demonstrate that integrating our approach with SOTA LNL methods improves accuracy in most cases. $^4$
+
+Keywords: Noisy-labels  $\cdot$  Instance-dependent noise  $\cdot$  Label noise Learning
+
+# 1 Introduction
+
+Deep neural networks (DNNs) have demonstrated their effectiveness in various domains, including vision [47], language [42], and medicine [37]. However, its efficacy is largely dependent on high-quality training data, which can be resource-intensive to obtain [43]. Although cost-effective labelling techniques, such as data mining [11] and crowdsourcing [39], offer cheaper alternatives, they often compromise label quality [39]. Consequently, this can lead to erroneous labels in real-world datasets [21]. This is a relevant issue because even slight inaccuracies in the labels can significantly affect the performance of DNN due to their inherent memorisation capabilities [34, 53]. This has prompted the development of algorithms resilient to noisy-label learning, with the aim of training models
+
+despite inaccuracies in training data labels. Although various strategies exist, our work uniquely proposes an approach centered on the estimation of the label noise rate from the training data, which is notably absent from current methodologies.
+
+There are two types of label noise, namely instance-independent noise (IIN) [16] and instance-dependent noise (IDN) [44]. Such type of label noise typically influences the design principles of noisy-label learning algorithms. For example, IIN focuses on mislabellings that are independent of sample information [16], where estimating the underlying label transition matrix is a common way of handling this type of noise [51]. On the other hand, in the more realistic IDN, mislabelling is due to both sample information and true class labels [44], which generally require the combination of many label noise learning techniques, such as robust loss functions [28, 56], and noisy-label sample selection [26, 58]. Of the strategies mentioned above, sample selection approaches that classify training data into clean and noisy samples have produced competitive results on many benchmarks [9, 11, 15, 21, 26]. Such sample selection techniques require the definition of a classification criterion and a selection curriculum. Many studies on this topic focus on developing new sample selection criteria, such as the small-loss hypothesis [26], which states that noisy-label samples have higher loss values than clean-label samples, particularly at the early stage of training [1]. Another criterion type is the feature-based one. An example of such criterion is FINE [21] that discriminates clean and noisy-label samples via the distance to class-specific eigenvectors. In this technique, clean-label samples tend to lie closer to the class-specific dominant eigenvector of the latent representations than noisy-label samples. Another type of criterion is proposed in SSR [11], which introduces a selection criterion based on the K-nearest-neighbor (KNN) classification in the feature space. Furthermore, CC [58] uses a two-stage sampling procedure, including class-level feature clustering followed by a consistency score. An equally important problem in sample selection is the definition of the curriculum for selecting clean training samples, but it has received comparatively less attention.
+
+The sample selection curriculum defines a threshold to be used with one of the criteria listed above to classify the training samples as clean or noisy at each training epoch [45]. For example, the threshold can be fixed to an arbitrary clustering score that separates clean and noisy samples [26], but this strategy does not account for the proportion of label noise in the training set, nor does it consider the dynamics of the selection of noisy-label samples during the training. The consideration of such dynamics has been studied in [16, 49], which defined a curriculum of the noisy-label sampling rate  $R(t)$  as a function of the training epoch  $t \in \{1, \dots, T\}$ . The curriculum  $R(t)$  defines a sampling rate close to  $100\%$  of the training set at the beginning of the training, which is then reduced to arbitrarily low rates at the end of the training. In practice, the function  $R(t)$  is predefined [16] or learned by weighting a set of basis functions [49].
+
+Although generally effective, these techniques do not consider the label noise rate estimated from the training set, making them vulnerable to over-fitting (if too many noisy-label samples are classified as clean) or under-fitting (if informative clean-label samples are classified as noisy). It can be argued that the estimation
+
+![](images/a180e75bd1f43c8f3c626a7caf5e2fc0fcf82f6c0d858ceb5e6d660de8757ded.jpg)  
+(a) Motivation
+
+![](images/7d25d80cae29bd7cfecbfdbad32f62383c9de642ce5c58d654608ce8e8055e3e.jpg)  
+(b) Proposed Graphical Model  
+Fig. 1: (a) Comparison of test accuracy  $\%$  (as a function of training epoch) between the original DivideMix [26] (solid, blue curve) and our modified DivideMix (dashed, red curve) that selects the clean and noisy data based on a fixed noise rate  $R(t) = 1 - \epsilon = 50\%$  using the small-loss criterion on CIFAR100 [22] at 0.5 IDN [44]; (b) The proposed probabilistic graphical model that generates noisy-label  $\hat{Y}$  conditioned on the image  $X$ , the latent clean-label  $Y$  and noise rate  $\epsilon$ , where forward pass (solid lines) is parameterised by  $\theta_y, \theta_{\hat{y}}$  and  $\epsilon$  representing the generation step, and the backward pass (dashed lines) is parameterised by  $\rho$ .
+
+of the label transition matrix [6,7,48,51] aims to recover the noise rate affecting pairwise label transitions. However, label transition matrix techniques follow a quite different strategy compared to sample selection methods, where their main challenge is the general underconstrained aspect of the matrix estimation, making them sensitive to large noise rates and not scalable to a high number of classes [39]. Although several methods address label noise, none estimates the label noise rate directly from the training data to guide sample selection. Addressing this gap is the primary challenge of our study.
+
+To underscore the importance of using the noise rate for sample selection during training, we experiment with CIFAR100 [22] at an IDN rate  $\epsilon = 50\%$  [44] (noise rate specifications and other details are explained in Sec. 4). We use DivideMix [26] and replace its sample selection (based on an arbitrary clustering score [10,32,41]) by a thresholding process that classifies the  $R(t) = 1 - \epsilon = 50\%$  largest loss samples as noisy, and the remaining ones as clean in all training epochs  $t \in \{1, \dots, T\}$ . This sample selection is used for the semi-supervised learning of DivideMix [26]. As shown in Fig. 1a, the new sample selection approach based on the "manually provided" noise rate (dashed red curve) improves  $6\%$  in terms of prediction accuracy compared to the original DivideMix [26] (solid blue curve) which relies on arbitrary thresholding. Similar conclusions can be achieved with other methods that apply sample selection strategies to address the noisy-label learning problem, as shown in the experiments.
+
+In this paper, we introduce a new sample selection strategy centered on estimating the label noise rate of the training set. Our strategy is based on our novel noisy-label learning graphical model illustrated in Fig. 1b. This model can be
+
+![](images/c2fc73a33c98dface34ed4f3415f9bc7caaa303299e41de6b32bf051a54fe249.jpg)  
+(a) Curriculum function  $R(t)$
+
+![](images/d989ee52eda15970afc13f9f66dc0f90d99152f959141d0db19c6b74d4948716.jpg)  
+(b) Accuracy Comparison  
+Fig. 2: (a) Visual comparison of different  $R(t)$  on CIFAR100 [22] at 0.5 IDN [44]: (i) Co-teaching [16] with curriculum based on hyper-parameter  $T_{k} \in \{5,10\}$ , where  $R(t) = 1 - \tau \cdot \min(t / T_{k}, 1)$  with  $\tau = \epsilon = 0.5$  being manually set; (ii) S2E [49], where  $R(t)$  is estimated with a bi-level optimisation; (iii) SSR [11], where  $R(t)$  is based on a relabelling pattern, (iv) CC [58] following the small-loss hypothesis [26] and cosine similarity for  $R(t)$ ; and (v) ours. (b) Accuracy of noisy-label learning methods on CIFAR100 [22] at 0.5 IDN [44], including DivideMix [26], FINE [21] and InstanceGM [15], without (left, blue) and (right, orange) integration of our proposed graphical model for estimating the noise rate  $\epsilon$  and sample selection rate based on  $\epsilon$ .
+
+seamlessly integrated with state-of-the-art (SOTA) noisy-label learning techniques, providing them with a precise noise rate estimate and subsequently refining the sample selection curriculum. In particular, our model's curriculum is not restrained by predefined  $R(t)$  functions [16, 49], but rather relies on a dynamically estimated noise rate sourced directly from the training set, as depicted in Fig. 2a. Our method dynamically estimates training set noise rates to mitigate overfitting and underfitting, seamlessly integrates with existing algorithms, and serves as a robust foundation for future noisy-label learning research. To summarise, our main contributions include:
+
+- An innovative noisy-label learning graphical model, shown in Fig. 1b, that not only estimates but also leverages the noise rate from the training dataset to produce a refined sample selection curriculum for SOTA LNL methods.  
+- A simple and synergistic integration strategy of our novel graphical model with several SOTA noisy-label learning algorithms, such as DivideMix [26] and SSR [11], to improve their sample selection effectiveness, leading to an increased test accuracy, as shown in Fig. 2b.
+
+Empirical evaluations show the role of our proposed sample selection methodology in improving the efficacy of leading noisy-label learning algorithms across various synthetic and real-world IDN benchmarks. Although our primary focus lies in addressing IDN problems, because of its more challenging and realistic nature, we have also applied our model to IIN problems, with detailed results in Tab. 6 and discussion in Appendix 3 of the supplementary material. With our innovative approach, we aim to improve the accuracy of SOTA LNL methods.
+
+# 2 Related Work
+
+It is well-known that DNNs suffer from overfitting when trained with noisy-labels [52], resulting in poor generalisation [28, 55]. To mitigate the problems related to noisy-label learning, several techniques have been developed, including noise-robust loss functions [30], noise-label sample selection [21, 26, 40, 58, 59], meta-learning [57], and re-labeling followed by sample selection [11]. These techniques can handle many types of label noise (e.g., symmetric and asymmetric), but the most challenging type, i.e., IDN [39], tends to be successfully addressed with methods that have a training stage based on sample selection techniques [21, 26, 40, 58, 59]. These sample selection techniques separate clean and noisy-label samples, where clean samples are treated as labelled, and noisy samples are discarded [8, 16, 18, 49] or treated as unlabeled samples [9, 15, 26, 35, 59] for semi-supervised learning [3]. Another solution consists of aligning clean and noisy samples with an information fusion method [19]. A major limitation of these approaches is the overly simplistic design of the curriculum to select clean and noisy-label samples during training. It is either predetermined [16, 18] or learned from a set of predetermined basis functions [49]. We argue that the design of a curriculum based on an estimated noise rate would benefit such methods, as motivated by Fig. 1a, but to the best of our knowledge, such estimation has not been explored by previous methods. The closest idea explored is based on the estimation of the type of noise instead of the noise rate [45]. It is possible to argue that the estimation of the label transition matrices [5, 7, 44, 60], composed of the learned noise rate that affects the transition between pairs of labels, is a way to estimate the label noise rate. However, they portray results of comparatively lower accuracy for large real-world datasets or for IDN problems [39, 44]. A possible reason for these poorer results is that label transition approaches suffer from identifiability issues [14], where any clean-label distribution assignment is acceptable as long as the distribution of observed labels can be reconstructed [13]. This makes the identification of the actual underlying clean-labels challenging. One solution is to consider the use of multiple annotations per sample to help analyse agreements and disagreements for improved identification of clean patterns [14, 31]. However, the annotation of datasets with a single label per training sample is already challenging; the complexity is significantly larger to acquire multiple labels per sample.
+
+An alternative technique to handle IDN problems is based on graphical models that represent the relationship between various observed and latent variables [15,45,50]. The approaches in [15,50] use graphical models that rely on a generative approach to produce noisy-labels from the respective image features and latent clean-labels. However, previous graphical models do not take into account the underlying noise rate parameter during modeling. Our work is the first graphical model approach to estimate the noise rate of the dataset. In addition, a close examination of existing literature reveals a trend: when traditional graphical models are integrated with SOTA noisy-label learning methods, the outcomes often fall short of expectations in terms of accuracy [2,15,50]. This observation underscores a strong point of our work. Our approach is uniquely tailored for
+
+easy integration with current SOTA noisy-label learning methods for sample selection, which, in turn, improves over the SOTA classification accuracy.
+
+# 3 Method
+
+In this section, we present our new graphical model that estimates the noise rate, which will be used in the sample selection process. Let  $\mathcal{D} = \{(x_i,\hat{y}_i)\}_{i = 1}^N$  be the noisy-label training set containing  $d$ -dimensional data vector  $x_{i}\in \mathcal{X}\subseteq \mathbb{R}^{d}$  and its respective  $C$ -dimensional one-hot encoded observed (potentially corrupted) label  $\hat{y}_i\in \hat{\mathcal{V}} = \{\hat{y}:\hat{y}\in \{0,1\} ^C\wedge \mathbf{1}_C^\top \hat{y} = 1\}$ , where  $\mathbf{1}_C$  is a vector of ones with  $C$  dimensions. The aim is to estimate the label noise rate  $\epsilon$ , used for the generation of noisy-label training data from the observed training dataset  $\mathcal{D}$  and integrate this label noise rate into the sample selection strategy.
+
+# 3.1 Graphical Model
+
+We portray the generation of noisy-label via the probabilistic graphical model shown in Fig. 1b. The observed random variables, denoted by shaded circles, are data  $X$  and the corresponding noisy-label  $\hat{Y}$ . We also have one latent variable, namely: the clean-label  $Y$ . Under our proposed modeling assumption, a noisy-label of a data instance can be generated as follows:
+
+- sample an instance from  $p(X)$ , i.e.:  $x \sim p(X)$  
+- sample a clean-label from the clean-label distribution:
+
+$$
+y \sim \operatorname {C a t e g o r i c a l} (Y; f _ {\theta_ {y}} (x))
+$$
+
+- sample a noisy-label from the noisy-label distribution:
+
+$$
+\hat {y} \sim \operatorname {C a t e g o r i c a l} (\hat {Y}; \epsilon \times f _ {\theta_ {\hat {y}}} (x, f _ {\theta_ {y}} (x)) + (1 - \epsilon) \times y),
+$$
+
+where  $\text{Categorical}()$  denotes a categorical distribution,  $f_{\theta_y}: \mathcal{X} \to \Delta_{C-1}$  and  $f_{\theta_{\hat{y}}}: \mathcal{X} \times \Delta_{C-1} \to \Delta_{C-1}$  denote two classifiers for the clean-label  $Y$  and noisy-label  $\hat{Y}$ , respectively, with  $\Delta_{C-1} = \{s : s \in [0,1]^C \wedge \mathbf{1}_C^\top s = 1\}$  being the  $(C-1)$ -dimensional probability simplex. According to the data generation process shown in Fig. 1b,  $\epsilon$  corresponds to  $\mathbb{E}_{(x,\hat{y}) \sim p(X,\hat{Y})}[P(\hat{y} \neq y|x)]$ , which is the label noise rate of the training dataset of interest. Our aim is to infer the parameters  $\theta_y, \theta_{\hat{y}}$  and  $\epsilon$  from a noisy-label dataset  $\mathcal{D}$  by maximising the following log-likelihood:
+
+$$
+\max  _ {\theta_ {y}, \theta_ {\hat {y}}, \epsilon} \mathbb {E} _ {(x _ {i}, \hat {y} _ {i}) \sim \mathcal {D}} [ \ln p (\hat {y} _ {i} | x _ {i}; \theta_ {y}, \theta_ {\hat {y}}, \epsilon) ] = \max  _ {\theta_ {y}, \theta_ {\hat {y}}, \epsilon} \mathbb {E} _ {(x _ {i}, \hat {y} _ {i}) \sim \mathcal {D}} [ \ln \sum_ {y _ {i}} p (\hat {y} _ {i}, y _ {i} | x _ {i}; \theta_ {y}, \theta_ {\hat {y}}, \epsilon) ]. \tag {1}
+$$
+
+Due to the presence of the clean-label  $y_{i}$ , it is difficult to directly evaluate the log-likelihood in Eq. (1). Therefore, we employ the expectation-maximisation (EM) algorithm [10] to maximise the log-likelihood. The main idea of the EM algorithm is to (i) construct a tight lower bound of the likelihood in Eq. (1) by estimating the posterior of the latent variable  $Y$  (known as expectation step) and (ii) maximise that lower bound (known as maximisation step). Formally, let
+
+$q(y_{i}|x,\hat{y};\rho)$  be an arbitrary distribution over a clean-label  $y_{i}$ . The evidence lower bound (ELBO) of the log-likelihood in Eq. (1) can be obtained through Jensen's inequality and is presented as follows:
+
+$$
+\begin{array}{l} Q \left(\theta_ {y}, \theta_ {\hat {y}}, \epsilon , \rho\right) = \mathbb {E} _ {\left(x _ {i}, \hat {y} _ {i}\right) \sim \mathcal {D}} \left[ \mathbb {E} _ {q \left(y _ {i} \mid x _ {i}; \hat {y} _ {i}; \rho\right)} \left[ \ln p \left(\hat {y} _ {i} \mid x _ {i}, y _ {i}; \theta_ {y}, \theta_ {\hat {y}}, \epsilon\right) \right] \right. \\ - \operatorname {K L} \left[ q \left(y _ {i} \mid x _ {i}, \hat {y} _ {i}; \rho\right) \| p \left(y _ {i} \mid x _ {i}; \theta_ {y}, \theta_ {\hat {y}}, \epsilon\right) \right] \\ = \mathbb {E} _ {\left(x _ {i}, \hat {y} _ {i}\right) \sim \mathcal {D}} \left[ \mathbb {E} _ {q \left(y _ {i} \mid x _ {i}; \hat {y} _ {i}; \rho\right)} \left[ \ln p \left(\hat {y} _ {i} \mid x _ {i}, y _ {i}; \theta_ {\hat {y}}, \epsilon\right) \right. \right. \\ \left. + \ln p \left(y _ {i} \mid x _ {i}; \theta_ {y}\right) \right] + \mathbb {H} \left[ q \left(y _ {i} \mid x _ {i}, \hat {y} _ {i}; \rho\right) \right], \tag {2} \\ \end{array}
+$$
+
+where  $\mathrm{KL}[q\| p]$  is the Kullback - Leibler divergence between distributions  $q$  and  $p$  and  $\mathbb{H}(q)$  is the entropy of the distribution  $q$ . The EM algorithm is then carried out iteratively by alternating the following two steps:
+
+E step: we maximise the ELBO in (2) w.r.t.  $q(y_{i}|x_{i},\hat{y}_{i};\rho)$ . Theoretically, such an optimisation results in KL  $[q(y_{i}|x_{i},\hat{y}_{i};\rho)\| p(y_{i}|x_{i},\hat{y}_{i})] = 0$  or  $q(y_{i}|x_{i},\hat{y}_{i};\rho) = p(y_{i}|x_{i},\hat{y}_{i})$ . This is equivalent to estimating the posterior of the clean-label  $y_{i}$  given noisy-label data  $(x_{i},\hat{y}_{i})$ . Obtaining the posterior  $p(y_{i}|x_{i},\hat{y}_{i})$  is, however, intractable for most deep-learning models. To mitigate such an issue, we follow the variational EM approach [33] by employing an approximate posterior  $q(y_{i}|x_{i},\hat{y}_{i};\rho^{(t)})$  that is the closest to the true posterior  $p(y_{i}|x_{i},\hat{y}_{i})$ , where:
+
+$$
+\rho^ {(t)} = \arg \max _ {\rho} Q \left(\theta_ {y} ^ {(t)}, \theta_ {\hat {y}} ^ {(t)}, \epsilon^ {(t)}, \rho\right), \tag {3}
+$$
+
+with the superscript  ${}^{(t)}$  denoting the parameters at the  $t$ -th iteration. Although this results in a non-tight lower bound of the log-likelihood in Eq. (1), it does increase the variational bound  $Q$ .
+
+M step: we maximise the ELBO in Eq. (2) w.r.t.  $\theta_y, \theta_{\hat{y}}$  and  $\epsilon$  given  $\rho^{(t)}$  obtained in the E step:
+
+$$
+\theta_ {y} ^ {(t + 1)}, \theta_ {\hat {y}} ^ {(t + 1)}, \epsilon^ {(t + 1)} = \arg \max  _ {\theta_ {y}, \theta_ {\hat {y}}, \epsilon} Q (\theta_ {y}, \theta_ {\hat {y}}, \epsilon , \rho^ {(t)}). \tag {4}
+$$
+
+The estimated noise rate  $\epsilon$  can then be integrated into certain noisy-label algorithms to train the models of interest as mentioned in Sec. 1. In addition, the inference of noise rate  $\epsilon$  might be associated with the identifiability issue when estimating the clean-label  $Y$  [29], i.e., there exists multiple sets of  $\rho$  and  $\theta_y$ , where each set can explain the observed noisy-label data equally well. Such issues are addressed in the following subsection.
+
+# 3.2 Sample Selection
+
+The identifiability issue when inferring the clean-label  $Y$  from noisy-label data  $(X, \hat{Y})$  can be mitigated either by acquiring multiple noisy-labels [29] or introducing additional constraints, such as small loss hypothesis [16] or FINE [21]. Since requesting additional noisy-labels per training sample is not always possible, we
+
+Algorithm 1 Proposed noisy-label learning that relies on the estimation of noise rate  $\epsilon$  to build a sample selection curriculum.  
+1: procedure NOISE RATE ESTIMATION AND INTEGRATION(D,T,λ)  
+2:  $\triangleright$ $\mathcal{D} = \{(x_i,\hat{y}_i)\}_{i = 1}^N$  training set with noisy-label data  
+3:  $\triangleright$  T: number of epochs  
+4:  $\triangleright$  λ: a hyper-parameter  
+5:  $\triangleright$  Notation:  $\Theta^{(t)} = (\theta_y^{(t)},\theta_{\hat{y}}^{(t)},\epsilon^{(t)})$   
+6: Initialise  $\theta_y^{(1)},\theta_{\hat{y}}^{(1)},\epsilon^{(1)}$  and  $\rho^{(0)}$   
+7:  $\theta_y^{(1)}\gets \mathrm{WARM~UP}(\mathcal{D},\theta_y^{(1)})$   
+8:  $t\gets 0$   
+9: for  $n_{\mathrm{epoch}} = 1:T$  do  
+10: for each mini-batch  $\mathcal{S}$  in SHUFFLE(D) do  
+11:  $t\gets t + 1$   
+12:  $\mathcal{S}_{\mathrm{clean}},\mathcal{S}_{\mathrm{noisy}}\gets \mathrm{SAMPLE~SELECTION}(\mathcal{S},\theta_y^{(t)},\epsilon^{(t)})$   
+13:  $\triangleright$  Variational E-step as in Eq. (3)  
+14:  $\rho^{(t)}\gets \mathrm{E~STEP}(\mathcal{S},\theta_y^{(t)},\theta_{\hat{y}}^{(t)},\epsilon^{(t)},\rho^{(t - 1)})$   
+15:  $\triangleright$  M-step as in Eq. (8)  
+16:  $\theta_y^{(t + 1)},\theta_{\hat{y}}^{(t + 1)},\epsilon^{(t + 1)}\gets \mathrm{M~STEP}(\mathcal{S}_{\mathrm{clean}},\mathcal{S}_{\mathrm{noisy}},\theta_y^{(t)},\theta_{\hat{y}}^{(t)},\epsilon^{(t)},\rho^{(t)},\lambda)$   
+17: return  $\theta_y$   
+1 parameter of the clean-label classifier
+
+follow the latter approach by imposing a constraint (scoring term), denoted as  $L(\theta_y, \epsilon^{(t)})$ , over  $\theta_y$  in the M step via a sample selection approach based on the estimated noise rate  $\epsilon^{(t)}$ . Formally, we propose a new curriculum when selecting samples as follows:
+
+$$
+R (t) = 1 - \epsilon^ {(t)}. \tag {5}
+$$
+
+In the simplest case, such as Co-teaching [16] or FINE [21], the constraint for  $\theta_y$  can be written as:
+
+$$
+L \left(\theta_ {y}, \epsilon^ {(t)}\right) = \sum_ {\left(x _ {i}, \hat {y} _ {i}\right) \in \mathcal {S} _ {\text {c l e a n}}} \operatorname {K L} \left[ \operatorname {C a t e g o r i c a l} (Y; \hat {y}) \| \operatorname {C a t e g o r i c a l} \left(Y; f _ {\theta_ {y}} \left(x _ {i}\right)\right) \right], \tag {6}
+$$
+
+where:
+
+$$
+\mathcal {S} _ {\text {c l e a n}} = \left\{\left(x _ {i}, \hat {y} _ {i}\right): \left(x _ {i}, \hat {y} _ {i}\right) \in \mathcal {D} \wedge z \left(x _ {i}, y _ {i}\right) \leq m \right\},
+$$
+
+$$
+m \in \{m: \Pr (z \left(x _ {i}, y _ {i}\right) \leq m) \geq R (t) \wedge \Pr (z \left(x _ {i}, y _ {i}\right) \geq m) \geq 1 - R (t) \},
+$$
+
+$$
+\mathcal {S} _ {\text {n o i s y}} = \mathcal {D} \backslash \mathcal {S} _ {\text {c l e a n}}. \tag {7}
+$$
+
+with  $R(t)$  defined in (5), and  $z(x,y)$  representing the score of a criterion (e.g., loss [26, 58, 59], distance to the largest eigenvectors [21], or KNN scores [11]). Intuitively, the loss in Eq. (6) is simply the cross-entropy loss on the  $\lfloor R(t)\times N\rfloor$  samples that have smallest scores (with  $\lfloor .\rfloor$  being the floor function). One can also extend to other SOTA models by replacing the loss  $L$  accordingly. For example,
+
+![](images/08c3a57bb884bedf5284bacc78cd61a6a3ead553af3eb4a53130280ac377ba00.jpg)  
+Fig. 3: Our training algorithm uses an existing noisy-label classifier (e.g., DivideMix [26]) parameterised by  $\theta_y$  as the clean-label model  $p(Y|X;\theta_y)$ . The generation of noisy-label (given  $X$  and  $Y$ ) is carried out by a model parameterised by noise rate  $\epsilon$  and  $\theta_{\tilde{y}}$ . The noisy-label classifier is based on a sample-selection mechanism that uses a curriculum  $R(t) = 1 - \epsilon^{(t)}$ .
+
+if DivideMix [26] is used as a base model to constrain  $\theta_y$ ,  $L$  will include two additional terms: loss on un-labeled data and regularisation using mixup [54].
+
+# 3.3 Training and Testing
+
+Given the sample selection approach in Sec. 3.2, the M step in Eq. (4) is slightly modified by integrating the constraint in Eq. (6), which can be written as
+
+$$
+\theta_ {y} ^ {(t + 1)}, \theta_ {\hat {y}} ^ {(t + 1)}, \epsilon^ {(t + 1)} = \arg \max  _ {\theta_ {y}, \theta_ {\hat {y}}, \epsilon} Q (\theta_ {y}, \theta_ {\hat {y}}, \epsilon , \rho^ {(t)}) - \lambda L (\theta_ {y}, \epsilon^ {(t)}), \tag {8}
+$$
+
+where  $\lambda$  is a hyper-parameter and  $L$  is defined in Eq. (6). The training procedure is summarised in Algorithm 1 and visualised in Fig. 3. In the implementation, we integrate the proposed method into existing models, such as DivideMix [26] or FINE [21]. Note that the clean-label classifier  $f_{\theta_y}(.)$  is also the clean classifier of the base model.
+
+# 4 Experiments
+
+We show extensive experiments in several noisy-label synthetic benchmarks with CIFAR100 [22], and real-world benchmarks, including CNWL's red mini-ImageNet [17], Clothing1M [45] and mini-WebVision [27]. Sec. 4.2 describes implementation details. We evaluate our approach by plugging SOTA models into  $p(y|x;\theta_y)$ , defined in Sec. 3, with results being shown in Sec. 4.3, and ablation studies in Sec. 4.4.
+
+# 4.1 Dataset Descriptions
+
+We follow the existing literature to generate the IDN labels [44] for CIFAR100 [22]. The dataset contains 50,000 training images and 10,000 testing images of shape  $32 \times 32 \times 3$ . The dataset is class-balanced with 100 different categories and the IDN rates considered are 0.2, 0.3, 0.4 and 0.5 [44]. Another important IDN benchmark dataset is the red mini-ImageNet, a real-world dataset from CNWL [17]. In this dataset, there are 100 distinct classes, with each class containing 600 images. The images and their corresponding noisy-labels have been crawled from the internet at various controllable label noise rates. For a fair comparison with the existing literature [9, 15, 46], we have resized the images to  $32 \times 32$  pixels from the  $84 \times 84$  original pixel settings. We show results with  $40\%$ ,  $60\%$  and  $60\%$  noise rates on this dataset. Clothing1M [45] is a real-world clothing classification dataset that contains 1 million images with an estimated noise rate of  $38.5\%$ . The dataset contains 14 different categories, and the labels are generated from surrounding texts. Images in this dataset are of different sizes, and we follow the resize structure suggested in [21, 26]. This dataset also contains  $50k$  manually validated clean training images,  $14k$  images for the validation set, and  $10k$  testing images. We have not used the clean training, validation set, or any extra training images while training. Only the testing set is used for evaluation. Mini-WebVision [26] contains 65,944 images with their respective labels from the 50 different initial categories from the WebVision [27], with image size of  $256 \times 256$  pixels. Following the evaluation process commonly used in this benchmark, 50 categories from the ILSVRC12 [23] dataset are also used for testing.
+
+# 4.2 Implementation
+
+All methods are implemented in Pytorch [36] and use one NVIDIA RTX 3090 card for training and testing. As mentioned in the original papers, hyperparameter settings are kept the same for the baselines used in the proposed algorithm. All classifier architectures are also kept the same as the baseline models. A random initialisation of noise rate parameter  $\epsilon$  with the sigmoid as its activation function is employed for all experiments to maintain the fairness of the comparisons with other approaches. The value of  $\lambda$  in Eq. (8) is set to 1 for all the cases. We integrate many SOTA approaches [11, 15, 21, 26, 58, 59] into our graphical model, as explained in Sec. 3.3. For CIFAR100 [22] with IDN [44], we integrate DivideMix [26], C2D [59], CC [58], and InstanceGM [15] into our model, given their superior performance across various noise rates. Additionally, we also use F-Dividemix from FINE [21], as shown in Fig. 2b. For red mini-ImageNet [17], we test our proposed approach with and without DINO self-supervision [4]. For the implementation without self-supervision, we use DivideMix [26] and InstanceGM [15], and for the self-supervised version, we only use InstanceGM [15]. The models for Clothing1M [45] and mini-WebVision [26] (validation on ImageNet [23]) are trained using DivideMix [26], SSR [11], C2D [59] and CC [58]. Additional implementation details, empirical analysis, and computational analysis are presented in the supplementary material in Appendices 1, 2 and 4, respectively.
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Noise Rates - IDN</td></tr><tr><td>0.2</td><td>0.3</td><td>0.4</td><td>0.5</td></tr><tr><td>CE [50]</td><td>30.42</td><td>24.15</td><td>21.45</td><td>14.42</td></tr><tr><td>PartT [44]</td><td>65.33</td><td>64.56</td><td>59.73</td><td>56.80</td></tr><tr><td>kMEIDTM [7]</td><td>69.16</td><td>66.76</td><td>63.46</td><td>59.18</td></tr><tr><td>DivideMix [26]</td><td>77.03</td><td>76.33</td><td>70.80</td><td>58.61</td></tr><tr><td>DivideMix-Ours</td><td>77.42</td><td>77.21</td><td>72.41</td><td>64.02</td></tr><tr><td></td><td>(+0.39)</td><td>(+0.88)</td><td>(+1.61)</td><td>(+5.41)</td></tr><tr><td>C2D [59]</td><td>78.61</td><td>78.18</td><td>72.89</td><td>63.19</td></tr><tr><td>C2D-Ours</td><td>79.07</td><td>78.59</td><td>73.31</td><td>65.28</td></tr><tr><td></td><td>(+0.46)</td><td>(+0.41)</td><td>(+0.42)</td><td>(+2.09)</td></tr><tr><td>CC [58]</td><td>79.61</td><td>77.56</td><td>76.58</td><td>63.19</td></tr><tr><td>CC-Ours</td><td>79.72</td><td>78.71</td><td>77.38</td><td>67.53</td></tr><tr><td></td><td>(+0.11)</td><td>(+1.15)</td><td>(+0.80)</td><td>(+4.34)</td></tr><tr><td>InstanceGM [15]</td><td>79.69</td><td>79.21</td><td>78.47</td><td>77.19</td></tr><tr><td>InstanceGM-Ours</td><td>79.61</td><td>79.40</td><td>79.52</td><td>78.21</td></tr><tr><td></td><td>(-0.08)</td><td>(+0.19)</td><td>(+1.05)</td><td>(+1.02)</td></tr></table>
+
+Table 1: Test accuracy % on (left) CIFAR100 [22] under different IDN [45], and (right) red mini-ImageNet [17]. Other models' results are from [7, 15, 46]. Here, we integrate DivideMix [26], C2D [59], CC [58] and InstanceGM [15] into our proposed model for CIFAR100 [22]. For red mini-ImageNet [17], we present the results with and without self-supervision [4]. We integrate DivideMix [26] and InstanceGM [15] into our model, with the latter tested with and without self-supervision.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Noise rate</td></tr><tr><td>0.4</td><td>0.6</td><td>0.8</td></tr><tr><td>CE [46]</td><td>42.70</td><td>37.30</td><td>29.76</td></tr><tr><td>MixUp [54]</td><td>46.40</td><td>40.58</td><td>33.58</td></tr><tr><td>MentorMix [17]</td><td>47.14</td><td>43.80</td><td>33.46</td></tr><tr><td>FaMUS [46]</td><td>51.42</td><td>45.10</td><td>35.50</td></tr><tr><td>DivideMix [26]</td><td>46.72</td><td>43.14</td><td>34.50</td></tr><tr><td>DivideMix-Ours</td><td>50.70</td><td>45.11</td><td>37.44</td></tr><tr><td></td><td>(+3.98)</td><td>(+1.97)</td><td>(+2.94)</td></tr><tr><td>InstanceGM [15]</td><td>52.24</td><td>47.96</td><td>39.62</td></tr><tr><td>InstanceGM-Ours</td><td>56.61</td><td>51.40</td><td>43.83</td></tr><tr><td></td><td>(+4.37)</td><td>(+3.44)</td><td>(+4.21)</td></tr><tr><td colspan="4">With self-supervised learning</td></tr><tr><td>PropMix [9]</td><td>56.22</td><td>52.84</td><td>43.42</td></tr><tr><td>InstanceGM-SS [15]</td><td>56.37</td><td>53.21</td><td>44.03</td></tr><tr><td>InstanceGM-SS-Ours</td><td>58.29</td><td>53.60</td><td>45.47</td></tr><tr><td></td><td>(+1.92)</td><td>(+0.39)</td><td>(+1.44)</td></tr></table>
+
+Table 2: Final estimated noise rate  $\epsilon$  for the Tab. 1, (left) CIFAR100 [22] under various IDN [44], and (right) red mini-ImageNet [17] with and without self-supervision.  
+
+<table><tr><td colspan="5">Estimated noise rates</td></tr><tr><td rowspan="2">Method</td><td colspan="4">Actual noise rate</td></tr><tr><td>0.2</td><td>0.3</td><td>0.4</td><td>0.5</td></tr><tr><td>DivideMix-Ours</td><td>0.18</td><td>0.34</td><td>0.47</td><td>0.53</td></tr><tr><td>C2D-Ours</td><td>0.19</td><td>0.33</td><td>0.38</td><td>0.52</td></tr><tr><td>CC-Ours</td><td>0.21</td><td>0.34</td><td>0.41</td><td>0.54</td></tr><tr><td>InstanceGM-Ours</td><td>0.23</td><td>0.37</td><td>0.42</td><td>0.47</td></tr></table>
+
+<table><tr><td colspan="3">Estimated noise rates</td></tr><tr><td rowspan="2">Method</td><td colspan="2">Actual noise rate</td></tr><tr><td>0.4</td><td>0.6</td></tr><tr><td>DivideMix-Ours</td><td>0.39</td><td>0.58</td></tr><tr><td>InstanceGM-Ours</td><td>0.38</td><td>0.55</td></tr><tr><td>InstanceGM-SS-Ours</td><td>0.48</td><td>0.53</td></tr><tr><td></td><td></td><td>0.73</td></tr></table>
+
+# 4.3 Comparison with SOTA
+
+This section compares our approach with SOTA methods on datasets with the IDN settings and noisy real-world settings. The bold text in tables indicate SOTA results, and our results are in the greyed rows.
+
+Synthetic Instance-Dependent Noise The comparison between various baselines and our proposed method on CIFAR100 [22] with IDN [44] is shown in Tab. 1 (left) with the noise rate ranging from 0.2 to 0.5. It is worth noting that using our proposed model with DivideMix [26], C2D [59], CC [58] and InstanceGM [15] improve their performance in almost all cases, particularly with large noise rates. Tab. 2 (left) also shows the final noise rate  $\epsilon$  estimated by our model which is reasonably close to the simulated noise rate displayed in the table's header.
+
+Table 3: Test accuracy (\%) of competing methods, and final estimated noise rate  $\epsilon$  on Clothing1M [45]. Also, we have not considered competing models that rely on a clean or validation set whilst training. We integrate DivideMix [26], C2D [59], SSR [11] and CC [58] into our model. DivideMix [26] and CC [58] shows the locally reproduced results. Mentioned noise rate by [45] is 0.385.  
+
+<table><tr><td>Method</td><td>Test accuracy (%)</td><td>Estimated noise rate</td></tr><tr><td>OT-Filter [12]</td><td>74.50</td><td></td></tr><tr><td>ELR+ with C2D [59]</td><td>74.58</td><td></td></tr><tr><td>AugDesc [35]</td><td>75.11</td><td></td></tr><tr><td>NCE [25]</td><td>75.30</td><td></td></tr><tr><td>DivideMix [26]</td><td>74.32</td><td></td></tr><tr><td>DivideMix-Ours</td><td>74.41 (+0.09)</td><td>0.41</td></tr><tr><td>C2D [59]</td><td>74.58</td><td></td></tr><tr><td>C2D-Ours</td><td>74.71 (+0.13)</td><td>0.41</td></tr><tr><td>SSR (class-imbalance) [11]</td><td>74.12</td><td></td></tr><tr><td>SSR-Ours</td><td>74.20 (+0.08)</td><td>0.42</td></tr><tr><td>CC [58]</td><td>75.24</td><td></td></tr><tr><td>CC-Ours</td><td>75.31 (+0.07)</td><td>0.41</td></tr></table>
+
+Real-World Noise We also evaluate our proposed method on various real-world noisy settings regarding test accuracy and estimated noise rates  $\epsilon$  in Tabs. 1 to 4. Similarly to the synthetic IDN in Tab. 1 (left), the results show that existing noisy-label robust methods can be easily integrated with our model to outperform current SOTA results for real-world noisy-label datasets. Tabs. 1 and 2 (right) shows the results on red mini-ImageNet using two configurations, including cases without self-supervision (top part of the table) and with self-supervision (bottom part of the table). The self-supervision DINO pre-training [4] relies only on images from red mini-ImageNet to enable a fair comparison with existing baselines [9, 15]. Results from Tab. 1 (right) demonstrate that our approach improves the performance of SOTA methods by a considerable margin in all cases. In fact, using estimated noise rate  $\epsilon$  (Tab. 2 (right)) while training InstanceGM [15] without self-supervision shows better performance than existing self-supervised baselines at 0.4 noise rate. Moreover, DivideMix [26], C2D [59], SSR [11], and CC [58] are used as a baselines for Clothing1M [45] as shown in Tab. 3, with results showing slight improvements with the use of our method. For mini-WebVision [26] (validation on ImageNet [23]), we use DivideMix [26], C2D [59], SSR [11], and CC [58] as baselines (Tab. 4). It is worth noting that our results are better than the SOTA for all settings in Tab. 4.
+
+# 4.4 Ablation
+
+We show an ablation study with testing accuracy (top) and training time (bottom) of our approach in Tab. 5 (left) on CIFAR100 [22] at 0.3 and 0.5 IDN [44] using DivideMix [26] as baseline. Detailed complexity analysis is shown in the supplementary material, Tab. 10. Initially, the accuracy result of baseline DivideMix [26] is  $76.33\%$ ,  $58.61\%$  for 0.3 and 0.5 IDN, respectively. In the second row, we fix the noise rate  $\epsilon$  at 0.3 and 0.5 for DivideMix's sample selection, as explained in Sec. 3.3 (without updating  $\epsilon$ ), then the results improved to  $78.14\%$  and  $64.44\%$ ,
+
+Table 4: Test accuracy (\%) and final estimated noise rate  $\epsilon$  on mini-WebVision [26] and validation on ImageNet [23]. We integrate DivideMix [26], Contrast-to-Divide (C2D) [59], SSR [11] and CC [58] into our model, whilst models suffixed with -Ours denotes our proposed approach. ImageNet [23] is only considered for validation.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="2">mini-WebVision</td><td colspan="2">ImageNet</td><td rowspan="2">Estimated noise rate</td></tr><tr><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td></tr><tr><td>BtR [38]</td><td>80.88</td><td>92.76</td><td>75.96</td><td>92.20</td><td></td></tr><tr><td>NCE [25]</td><td>79.50</td><td>93.80</td><td>76.30</td><td>94.10</td><td></td></tr><tr><td>DivideMix [26]</td><td>77.32</td><td>91.64</td><td>75.20</td><td>91.64</td><td></td></tr><tr><td>DivideMix-Ours</td><td>78.51</td><td>92.03</td><td>76.11</td><td>93.24</td><td>0.43</td></tr><tr><td></td><td>(+1.19)</td><td>(+0.39)</td><td>(+0.91)</td><td>(+1.60)</td><td></td></tr><tr><td>C2D [59]</td><td>79.42</td><td>92.32</td><td>78.57</td><td>93.04</td><td></td></tr><tr><td>C2D-Ours</td><td>80.20</td><td>92.82</td><td>79.16</td><td>93.12</td><td>0.43</td></tr><tr><td></td><td>(+0.78)</td><td>(+0.50)</td><td>(+0.59)</td><td>(+0.08)</td><td></td></tr><tr><td>SSR [11]</td><td>80.92</td><td>92.80</td><td>75.76</td><td>91.76</td><td></td></tr><tr><td>SSR-Ours</td><td>81.68</td><td>93.80</td><td>76.91</td><td>93.05</td><td>0.43</td></tr><tr><td></td><td>(+0.76)</td><td>(+1.00)</td><td>(+1.15)</td><td>(+1.29)</td><td></td></tr><tr><td>CC [58]</td><td>79.36</td><td>93.64</td><td>76.08</td><td>93.86</td><td>-</td></tr><tr><td>CC-Ours</td><td>80.01</td><td>93.79</td><td>77.11</td><td>94.21</td><td>0.44</td></tr><tr><td></td><td>(+0.65)</td><td>(+0.15)</td><td>(+1.03)</td><td>(+0.35)</td><td></td></tr></table>
+
+Table 5: (left) Ablation results on CIFAR100 at 0.3 and 0.5 IDN. We display accuracy results under different configurations and compare the training time of our approach against DivideMix [26]. The implementation settings and detailed computational analysis are described in Sec. 4.2 and Appendix 4 respectively. (right above) Ablation results for initialisation with different  $\epsilon$  values on CIFAR100 [22] at a synthetic noise rate of 0.5 IDN [44] with DivideMix-Ours. (right below) Ablation graph showing the learning pattern of the noise rate parameter estimation under different initialisation values, i.e.,  $\epsilon = 0.001$  (blue),  $\epsilon = 0.1$  (orange),  $\epsilon = 0.9$  (red), when trained on DivideMix-ours case at 0.5 IDN [44] on CIFAR100 [22].  
+
+<table><tr><td rowspan="2">Models</td><td colspan="2">Accuracy (%)</td></tr><tr><td>0.3</td><td>0.5</td></tr><tr><td>DivideMix [26]</td><td>76.33</td><td>58.61</td></tr><tr><td>DivideMix with fixed ε</td><td>78.14</td><td>64.44</td></tr><tr><td>Our method with pre-trained DivideMix</td><td>75.01</td><td>52.31</td></tr><tr><td>Our method with original DivideMix (no ε)</td><td>76.20</td><td>56.30</td></tr><tr><td>DivideMix-Ours</td><td>77.21</td><td>64.02</td></tr><tr><td colspan="3">Training Time (GPU-hours)</td></tr><tr><td>DivideMix [26]</td><td colspan="2">7.20</td></tr><tr><td>DivideMix-Ours</td><td colspan="2">8.50</td></tr><tr><td>DivideMix-Ours (Mixed Precision)</td><td colspan="2">6.10</td></tr></table>
+
+![](images/aa983ece11a754aafafd52ae1d8727f56159fc784823abeb033ac358abf72881.jpg)
+
+which is the ideal case (i.e., a perfect noise rate estimation) that motivated our work. In the third case, we use the proposed graphical model with pre-trained DivideMix [26] that shows accuracy of  $75.01\%$  and  $52.31\%$ . In the next case, the proposed graphical model is trained together with DivideMix [26] without considering the estimated noise rate  $\epsilon$  for sample selection, which results in accuracy of  $76.20\%$  and  $56.30\%$ . In the last row, we show the training of the proposed model with DivideMix [26], together with the estimation of noise rate  $\epsilon$ , and the
+
+selection of samples based on that, with  $\approx 1\%$  and  $\approx 8\%$  accuracy improvement to 0.3 and 0.5 IDN, which is quite close to our ideal case (second row). We also study the effect that the initialisation of the noise rate parameter  $\epsilon$  plays in our method. As described in Sec. 4.2, we randomly initialise  $\epsilon$  within the range  $(0,1)$ . To test the robustness of our method to this initialisation, we perform an ablation study by initialising  $\epsilon$  with three different values, namely: 0.001, 0.1, and 0.9 on CIFAR100 [24] at 0.5 IDN [44] using the DivideMix-ours approach. Our results, presented in Tab. 5 (right above and below), demonstrate that the initial value of  $\epsilon$  has a limited effect on the model's performance, highlighting the stability of our method across different initialisation of  $\epsilon$ . In the supplementary material, Tab. 7 (left) presents comparative analyses of our model against PartT [44] and SSR [11] on CIFAR100 [22] at 0.5 IDN [44], while Tab. 7 (right) showcases similar comparisons with baselines DivideMix [26] and InstanceGM [15] at a higher noise rate of 0.6 IDN [44]. Additionally, Tab. 8 provides further insights into the performance of DivideMix [26] on red mini-ImageNet [17] at lower noise rates of 0.1, 0.2 and 0.3. Tab. 9 illustrates noise rate estimation with standard deviation for our model integrated with DivideMix [26] and InstanceGM [15] on CIFAR100 [22] under IDN [44] settings at 0.2, 0.3, 0.4, and 0.5. Further statistical analysis is detailed in Appendix 5 with confidence interval presented in Tab. 12. Performance analysis with various architectures (Tab. 13) and lambda values (Tab. 14) are mentioned in Appendix 6. Threshold-based comparisons are in Appendix 7 and Tab. 15.
+
+# 5 Discussion and Conclusion
+
+In this work, we proposed an innovative graphical model for IDN noisy-label learning, focusing on the estimation of the label noise rate that is leveraged to introduce a robust sample selection curriculum. Given that SOTA IDN noisy-label learning approaches tend to rely on sample selection methods, our method can be seamlessly integrated to them to improve their performance in many synthetic and real-world benchmarks, including CIFAR100 [22], red mini-ImageNet [17], Clothing1M [45], mini-WebVision [26], and ImageNet [23].
+
+From a societal perspective, our methodology offers a positive impact by mitigating biases inherent in noisy data, thereby promoting more fair and accurate machine learning outcomes. It also opens the door to future research avenues, including exploring advanced noise rate estimation methodologies and investigating noise-robust loss functions such as GCE [56] and ELR [28] with it. Our choice of using the same network architecture for clean and noisy labels enables compatibility with co-teaching techniques [16,26]. However, investigating different network structures for clean and noisy labels remains a potential avenue for future research. Moreover, we aim to delve into its dynamics, uncovering substantial improvements for certain models while observing more marginal enhancements for others. For more detailed information, please refer to Appendix 8. Our approach also hints at potential breakthroughs in streamlining data annotation challenges.
+
+# References
+
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+        "type": "text",
+        "text": "Instant 3D Human Avatar Generation using Image Diffusion Models",
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+        "type": "text",
+        "text": "Nikos Kolotouros, Thiemo Alldieck, Enric Corona, Eduard Gabriel Bazavan, and Cristian Sminchisescu",
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+        "text": "Google Research\\* {kolotouros, alldieck, egbazavan, enriccorona, sminchisescu}@google.com",
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+        "img_path": "images/13947c3f92d8dc40fa114453e17f43421b851573c29a2de60d376a787ccfaa73.jpg",
+        "image_caption": [
+            "Fig. 1: We present AvatarPopUp, a new method for the automatic generation of 3D human assets. AvatarPopUp can generate rigged 3D models from text or from single images and has control over body pose and shape. In this example, we show 77 models generated from various text prompts in 12 minutes on a single GPU."
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+        "text": "Abstract. We present AvatarPopUp, a method for fast, high quality 3D human avatar generation from different input modalities, such as images and text prompts and with control over the generated pose and shape. The common theme is the use of diffusion-based image generation networks that are specialized for each particular task, followed by a 3D lifting network. We purposefully decouple the generation from the 3D modeling which allows us to leverage powerful image synthesis priors, trained on billions of text-image pairs. We fine-tune latent diffusion networks with additional image conditioning for image generation and back-view prediction, and to support qualitatively different multiple 3D hypotheses. Our partial fine-tuning approach allows to adapt the networks for each task without inducing catastrophic forgetting. In our experiments, we demonstrate that our method produces accurate, high-quality 3D avatars with diverse appearance that respect the multimodal text, image, and body control signals. Our approach can produce a 3D model in as few as 2 seconds, a four orders of magnitude speedup w.r.t. the vast majority of existing methods, most of which solve only a subset of our tasks, and with fewer controls. AvatarPopUp enables applications that require the controlled 3D generation of human avatars at scale. The project website can be found at https://www.nikoskolot.com/avatarpopulation/.",
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+        "type": "page_footnote",
+        "text": "* Now at Google DeepMind.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 Introduction",
+        "text_level": 1,
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+    },
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+        "type": "text",
+        "text": "We present AvatarPopUp, a method for instant generation of rigged full-body 3D human avatars, with multimodal controls in the form of text, images, and/or human pose and shape. The remarkable recent progress in image synthesis [15, 24, 54, 56, 58, 63] acted as a catalyst for a wide range of media generation applications. In just a few years, we have witnessed rapid developments in video generation [9, 23, 34, 68, 76], audio synthesis [49, 77] or text-to-3D object generation [40, 41, 51, 53, 65], among others. Pivotal to success of all these methods is their probabilistic nature, however this requires very large training sets. While inspiring efforts have been made [14], training set size is still a problem in many domains, and particularly for 3D. In an attempt to alleviate the need for massive 3D datasets, DreamFusion [51] leverages the rich priors of text-to-image diffusion models in an optimization framework. The influential DreamFusion ideas were also quickly adopted for 3D avatar creation [32, 37], a field previously dominated by image- or video-based reconstruction solutions [6, 8, 60, 61]. Text-to-avatar methods enabled novel creative processes, but came with a significant drawback. While image-based methods typically use pretrained feed-forward networks and create outputs in seconds, existing text-to-avatar solutions are optimization-based and take minutes to several hours to complete, per instance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we are closing this gap and present, for the first time, a methodology for instant, text-controlled, rigged, full-body 3D human avatar creation. Our AvatarPopUp is purely feed-forward, can be conditioned on images and textual descriptions, allows fine-grained control over the generated body pose and shape, can generate multiple hypotheses, and runs in 2-10 seconds per instance.",
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+        "text": "Key to success is our pragmatic decoupling of the two stages of probabilistic text-to-image generation and 3D lifting. Decoupling 2D generation and 3D lifting has two major advantages: (1) We can leverage the power of pretrained text-to-image generative networks, which have shown impressive results in modeling complex conditional distributions. Trained with large training sets of images, both generation quality and diversity are very high. (2) We alleviate the need for very large 3D datasets required to train state-of-the-art generative 3D models. Our method generates diverse plausible image configurations that contain rich enough information that can be lifted in 3D with minimal ambiguity. In other words, we distribute the workload between two expert systems: a pretrained probabilistic generation network fine-tuned for our task to produce front and back image views of the person, and a state-of-the-art unimodal, feed-forward image-to-3D model that can be trained using comparably small datasets.",
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+        "type": "text",
+        "text": "Our proposed decoupling strategy allows us to maximally exploit available data sources with different levels of supervision. We first fine-tune a pretrained Latent Diffusion network to generate images of people based on textual descriptions and with additional control over the desired pose and shape. This step does not require any ground truth 3D data for supervision and enables scaling our image generator to web scale data of images of people in various poses. Next, we leverage a small-scale dataset of scanned 3D human assets and fine-tune a second latent diffusion network to learn the distribution of back side views con",
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+        "text": "2",
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+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
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+    {
+        "type": "table",
+        "img_path": "images/7b3a3c98dd89b2fa8378124325d793e29af52efddfb4da07794600ca2bc71598.jpg",
+        "table_caption": [],
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+        "table_body": "<table><tr><td colspan=\"8\">Control from Text Control from Image Shape Control</td></tr><tr><td>Body</td><td>Shape</td><td>Generates</td><td>Geometry</td><td>Texture</td><td></td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓/X</td><td>Runtime</td><td></td></tr><tr><td>X</td><td>✓</td><td>X</td><td>✓</td><td>✓/X</td><td>X</td><td>several hours</td><td>Optimization-based text-to-3D [26,32,37]</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>seconds</td><td>Image-to-3D [4,8,60,61]</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>minutes</td><td>Hybrid [31]</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>seconds</td><td>3D GANs [16,25]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td>seconds</td><td>AvatarPopUp (Ours)</td></tr></table>",
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+        "type": "text",
+        "text": "Table 1: AvatarPopUp generates 3D assets with texture from text prompts or input images of a target subject and can be controlled with body pose and shape. In contrast to baselines that require up to hours per prompt, our model takes under five seconds and can de facto by used in interactive applications. In the experimental section we demonstrate the large diversity of the model, and applications in cloth editing.",
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+    {
+        "type": "text",
+        "text": "ditioned on a front view image of the person. We optionally also condition on a textual description that can naturally complement the evidence available in the front view image. Furthermore, we propose a novel fine-tuning strategy that prevents overfitting to the new datasets. Finally, we design and train a 3D reconstruction network that predicts a textured 3D shape in the form of an implicit signed distance field given the pair of front and back views and optionally 3D body signals. The resulting cascaded method, which we call AvatarPopUp supports a wide range of 3D generation and reconstruction tasks: First, it enables fast and interactive 3D generation of assets at scale, see Fig. 1. Second, we can repurpose parts of the cascade for image-based 3D reconstruction at state-of-the-art quality. Finally, we demonstrate how AvatarPopUp can be used for creative editing tasks exemplified in 3D virtual try-on with body shape preservation. To summarize, our main contributions are:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- A method for controllable 3D human avatar generation, based on multimodal text, pose, shape and image input signals, that outputs a detailed human mesh instance in 2-10 seconds.",
+            "- We propose a simple yet effective way to fine-tune pretrained diffusion models on small-scale datasets, without inducing catastrophic forgetting.",
+            "- While not our primary goal, our approach achieves state-of-the-art results in single-image 3D reconstruction and enables 3D creative editing applications."
+        ],
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+    {
+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Table 1 summarizes the characteristics of AvatarPopUp in comparison to previous work, along several important property axes.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Text-to-3D generation. The success of text-to-image models [55, 57, 59] was quickly followed by a significant amount of work on text-to-3D content generation [38, 45, 51, 66]. Due to limited training data, methods typically use optimization approaches, where a neural representation [47] is optimized per instance by minimizing a distillation loss [51] derived from large text-to-image models. This idea has been extended to generate human avatars [18, 27, 29, 32, 37, 69, 73, 78–80] or heads [19, 36, 39] enabling the text-based creation of 3D human assets that",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
+        "bbox": [
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+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "are diverse in terms of shape, appearance, clothing and various accessories. In these works, the optimization process is often regularized using a 3D body model [32,37,78], which also enables animation. However, such approaches generally take hours per instance, and rendering is slow. With the appearance of Gaussian Splatting [30], other works [2,42,82] reduced rendering time at the expense of accurate geometry. In any case, creating an avatar still takes a significant amount of time, making such methods unsuitable for interactive applications. In this work we propose an alternative direction, which also builds upon the success of text-to-image models and combines them with 3D reconstruction pipelines. Also related are 3D human generation methods. AG3D [16] and EVA3D [25] are GAN-based methods learned from 2D data, that allow to sample 3D humans anchored in a 3D body model. CHUPA [31] generates dual normal maps based on text and then fits a body model to obtain a full 3D representation. While generation is similar in spirit to our method, CHUPA requires optimization per instance and does not generate texture.",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Photorealistic 3D Human Reconstruction. Our framework generates 3D human assets and builds on top of state-of-the-art 3D reconstruction techniques. This has been widely explored in the past and can be roughly categorized by its use of explicit or implicit representations. An important line of work leverages 3D body models [43,50,72] and reconstructs their associated parameters, in some cases extended with vertex offsets to represent some clothing and hair detail [4-7, 48, 85]. Other efforts have considered voxels [67, 84], depth maps [17] and more recently implicit representations [8, 13, 21, 28, 60-62, 70, 71, 74, 75, 83]. Being topology free, the latter allows the representation of loose clothing more easily. They typically provide more detail and enable high-resolution reconstruction, often conditioned on local pixel-aligned features [60]. On the other hand, these methods yield reconstructions with no semantic labels that cannot be easily animated. To solve this problem, some work combined body models with implicit representations [13, 21, 27, 28, 70, 71], but this is prone to errors when the pose is noisy at inference time. In contrast, we drive the synthesis process with guidance from an input body model – sampled or estimated – so that the generated image is well aligned with the body prior. As we show in Sec. 4, this allows rigging the 3D avatar without post-processing and natively supports 3D animation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Given a single input image of a person, previous work aims to generate realistic reconstructions for the non-visible parts. However, this often leads to blurry textures and lack of geometric detail, e.g. no wrinkles. Some methods [60, 61, 70, 71] generate back normal maps to enhance details, or consider probabilistic reconstructions [3, 62]. However, all these methods cannot be prompted from text or other modalities and still yield limited diversity. In contrast, we guide the synthesis process by means of generated front and back images, yielding high-quality 3D reconstructions. Another challenge in previous work is limited training data. Most prior methods rely on a few hundred 3D scans, due to the pricey and laborious process of good quality human capture. We alleviate the need for large scale 3D training data by proposing a framework that can quickly generate humans with a given clothing, pose and shape.",
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+        "type": "page_number",
+        "text": "4",
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+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/162ab2d8066f91630fb298720f8e4fd1e5303b92e5df8162c95d919a99d4e1b2.jpg",
+        "image_caption": [
+            "Fig. 2: AvatarPopUp method. (Top) AvatarPopUp builds on the capacity of text-to-image models to generate highly detailed and diverse input images. First, a Latent Diffusion network takes a text prompt and a target body pose and shape  $\\mathcal{G}$ , and generates a highly detailed front image  $I_{f}$  of a person. Next, a second network generates a consistent back view  $I_{b}$  in the same pose and clothing. (Bottom) We perform pixel-aligned 3D reconstruction given the generated front/back views  $I_{f}, I_{b}$  and optionally the given 3D body pose and shape  $\\mathcal{G}$ . This decoupling enables the generation of 3D avatars from text, images or a combination of the two."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We learn a distribution  $p(X|c)$  of textured 3D shapes  $X$  conditioned on a collection of signals  $c$  that we factorize as follows",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (X | c) = \\int \\int p \\left(X \\mid I _ {f}, I _ {b}, c\\right) \\cdot p \\left(I _ {b} \\mid I _ {f}, c\\right) \\cdot p \\left(I _ {f} \\mid c\\right) d I _ {f} d I _ {b}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $p(X|I_f, I_b, c)$  is the probability of 3D shape  $X$  given  $c$  and front and back image observations  $I_f$  and  $I_b$  respectively,  $p(I_b|I_f, c)$  is the probability of the back view image given the front image  $I_f$  and conditioning signals  $c$ , and  $p(I_f|c)$  the conditional probability of front view images of the person given  $c$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Computing the integral in (1) is intractable, but our goal is to generate samples from the distribution rather than expectations. To do so, we employ ancestral sampling. We first sample a front view  $I_{f}$  given  $c$ , we then sample a back view  $I_{b}$  given  $I_{f}$  and  $c$ , and last we sample the 3D reconstruction based on the entire context. In practice,  $p(I_f|c)$  and  $p(I_b|I_f,c)$  are implemented using Latent Diffusion models, whereas  $p(X|I_f,I_b,c)$  is a unimodal, neural implicit field generator.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the case of single-image 3D reconstruction the conditioning signal  $c$  is  $I_{f}$ , and consequently we can omit the first step. For text-based generation,  $c$  is a text prompt describing the appearance of the person together with a signal encoding the body pose and shape. The conditioning information  $c$  may be extended with additional signals, as in the case of 3D editing, cf. Sec. 4.",
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
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+    {
+        "type": "text",
+        "text": "3.1 Controllable Text-to-Image Generator",
+        "text_level": 1,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Recent advances in diffusion-based text-to-image generation networks [56] have enabled synthesizing high-quality images given only a text prompt as input. However, for certain use cases, such as human generation, it is difficult to inject fine-grained, inherently continuous forms of control, like the 3D pose of people or their precise body shape proportions, when generating with text alone.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Inspired by ControlNet [81], we propose to add simultaneous control over body pose and shape by augmenting a pretrained Latent Diffusion network with an additional image input that jointly encodes both modalities. For control we use GHUM [72] but other models (e.g. [43]) can be used. Specifically given 3D pose and shape parameters  $\\pmb{\\theta}$  and  $\\pmb{\\beta}$  respectively, we render the corresponding mesh  $\\mathcal{M} = \\mathrm{GHUM}(\\pmb{\\theta},\\pmb{\\beta})$  using GHUM's template coordinates and posed vertex locations as 6D vertex colors, obtaining a dense, pixel-aligned pose- and shape-informed control signal  $\\mathcal{G}$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To fine-tune the network, we generate a dataset of images of people with corresponding GHUM 3D pose and shape parameters and text annotations. This dataset is comprised of a set of scanned assets [1] that are rendered from different viewpoints, as well as a set of real images scraped from the web. For the synthetic part of the dataset, the pose and shape parameters are obtained by fitting GHUM to 3D scans. We additionally use real images to which we fit GHUM using keypoint optimization in the style of [33]. For all images we obtained text annotations using an off-the shelf image captioning system [12] by prompting it to describe the clothing of the people in the image. Since we are interested in generating 3D human assets, we additionally mask out the background in all images, and train the network to output segmented images. This makes the downstream 3D reconstruction task easier, and improves the reconstruction quality because it encourages the network to focus on human appearance, rather than allocating capacity to model complex backgrounds.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We want to exploit the rich priors learned by text-to-image foundation models by fine-tuning a Latent Diffusion model [56] with the dense GHUM rendering as an additional input. For fine-tuning we propose a simpler and more lightweight method than a standard ControlNet. We pad the weights of the input convolutional layer with additional channels initialized with zeros, and we then fine-tune only the weights of the convolutional layers of the encoder network. All the decoder and attention layers are kept frozen. With this simple strategy, even though our model is trained on a relatively small set of images, it can generalize to unseen types of clothing. At the same time, our strategy is more practical than training a ControlNet, which involves keeping in separate copy of the original network weights in memory, and thus enables fine-tuning large models with moderate hardware utilization. We optimize the encoder of the diffusion model by minimizing the simple variant of the diffusion loss [24]",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} \\left(\\psi_ {\\text {e n c}}\\right) = \\mathbb {E} _ {\\mathcal {E} (x), \\epsilon , t, \\tau , \\mathcal {G}} \\left\\| \\epsilon - \\epsilon_ {\\psi} \\left(z _ {t}, t, \\tau , \\mathcal {E} (\\mathcal {G})\\right) \\right\\|, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $t \\in \\{1, \\dots, T\\}$  is the diffusion time step,  $\\epsilon \\sim \\mathcal{N}(0, I)$  the injected noise,  $z_{t} = \\alpha_{t} \\mathcal{E}(x) + \\nu_{t}$  is the noisy image latent,  $\\tau$  is the text encoding,  $\\mathcal{E}(\\mathcal{G})$  the",
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+    {
+        "type": "page_number",
+        "text": "6",
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+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "image",
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+    {
+        "type": "image",
+        "img_path": "images/01db6990a2368276c251bea01ea04cb4d3d3bdd0a1562e42583b377a7562c54b.jpg",
+        "image_caption": [],
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+    {
+        "type": "image",
+        "img_path": "images/69caf4714bb22336466c3167fea99aa8a152d2eb57025c327c4df4a0a4e78ad4.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/581460b48d12d79363f37c039c9742e8218ee53639a8e58fb60d61cc7cd679ab.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/cade929a17ec102891f1cc8fcf8972281ae09fad17a6875f4a71ac34d99e57bd.jpg",
+        "image_caption": [
+            "Fig. 3: Diverse back view hypotheses. Conditioned on the front view, our method is able to generate diverse plausible back views of the person, with different hairstyles, wrinkle patterns, or lighting. Our network can also be controlled with text (second row), to add fine-grained detail to our generated back-side views."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            279,
+            258,
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+            353
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/dc4a18690be7fdbe678f416b58d57f4d67372038af4ac46a7e6022b1cd0c7b98.jpg",
+        "image_caption": [
+            "No text conditioning"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            410,
+            258,
+            460,
+            352
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e2a400732757cac23a4a9922daf6f5839c31b9736fdd90dda848c9c8b4941f10.jpg",
+        "image_caption": [
+            "+“gray hair”"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            258,
+            589,
+            352
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/1daf589e7a6556f159cd04ac5d4f59caf3364c3b6768c12b31433d9c80a1db40.jpg",
+        "image_caption": [
+            "+“with a tattoo”"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            668,
+            258,
+            718,
+            352
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "latent encoding of the dense GHUM signal, and  $\\psi_{\\mathrm{enc}}$  the encoder subset of the denoising UNet parameters  $\\psi$ .",
+        "bbox": [
+            212,
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.2 Back View Generation",
+        "text_level": 1,
+        "bbox": [
+            214,
+            500,
+            449,
+            513
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "One could try to lift the generated front views from the previous stage to 3D directly by applying a single-image 3D reconstruction method like PHORHUM [8]. However, because of the inherent ambiguity of the problem this will result in significant loss of geometric detail and blurry textures for the non-visible body surfaces. To avoid this, we propose to fine-tune again a latent diffusion network with the same strategy as in the previous section. This time the additional image conditioning is a front view and optionally a text prompt, and we train the network to learn the distribution of back views conditioned on the front view. The additional text prompt can be used in cases where it is desired to additionally guide the generation by very specific properties. Fig. 3 shows different back sides sampled from the conditional distribution. We also show that the additional text inputs are useful in modulating certain parts of the generation that are not immediately deducible from the front image, such as hairstyles or specific patterns.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.3 3D Reconstruction Model",
+        "text_level": 1,
+        "bbox": [
+            214,
+            757,
+            477,
+            771
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our 3D reconstruction network is inspired by PHORHUM [8], and our design choices are informed by the limitations of typical single-image 3D reconstruction methods. Specifically, given a collection of input image signals  $\\mathcal{I} = \\{I_f, I_b, \\mathcal{G}\\}$ , we first concatenate them, and then use a convolutional encoder  $G$  to compute",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
+        "bbox": [
+            475,
+            114,
+            730,
+            127
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "a pixel-aligned feature map  $G(\\mathcal{I})$ . The 3D body control signal  $\\mathcal{G}$  is optional and may be omitted, e.g. for single-image reconstruction. Then, each point  $\\mathbf{x} \\in \\mathbb{R}^3$  in the scene gets projected on this feature map to get pixel-aligned features  $\\mathbf{z}_{\\mathbf{x}} = g(\\mathcal{I}, \\mathbf{x}; \\pi) = b(G(\\mathcal{I}), \\pi(\\mathbf{x}))$  using interpolation, where  $b(\\cdot)$  is the bilinear sampling operator and  $\\pi(\\mathbf{x})$  is the pixel location of the projection of  $\\mathbf{x}$  using the camera  $\\pi$ . These pixel aligned features are then concatenated with a positional encoding  $\\gamma(\\mathbf{x})$  of the 3D point and are fed to an MLP  $f$  that outputs the signed distance from the surface  $d$  as well as surface color  $c$ . Finally, the 3D shape  $S$  is represented as the zero-level-set of  $d$",
+        "bbox": [
+            212,
+            146,
+            787,
+            282
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} (\\mathcal {I}) = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} | f (g (I, \\mathbf {x}; \\pi), \\gamma (\\mathbf {x})) = (0, c) \\right\\}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            344,
+            292,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "$\\mathcal{S}$  can be transformed to a mesh directly, using Marching Cubes [44].",
+        "bbox": [
+            214,
+            319,
+            712,
+            335
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.4 Animation of Generated Avatars",
+        "text_level": 1,
+        "bbox": [
+            214,
+            356,
+            532,
+            371
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our method can generate diverse 3D avatars with various poses, shapes and appearances. Optionally, we may leverage the conditioning body model to rig the estimated 3D shape. As a result of our conditioning strategy, 3D avatars and the conditional body model instances are aligned in 3D. This allows us to anchor the reconstructed 3D shape on the body model surface [10] and re-pose or re-shape it accordingly. Alternatively, we may also transfer just the LBS skeleton and weights from the body model to the scan. This enables importing and animating the generated 3D assets in various rendering engines. See Fig. 8 and Sup. Mat. for examples and videos of animations of the generated 3D assets.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
+            215,
+            536,
+            375,
+            553
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Data. We use meshes from RenderPeople [1] for training as well as our own captured data, totaling in  $\\sim 10\\mathrm{K}$  scans with diverse poses, body shapes, and clothing styles. We render each scan with randomly sampled HDRI background, random cloth color augmentations, and lighting using Blender [11]. During this process, we render both front and back views used to train the different stages of our model. For the front image generation network we also use a set of  $10\\mathrm{K}$  real images on which we fitted the GHUM model using 2D keypoints. For testing we defined a split based on subject identity and held out  $\\sim 1\\mathrm{K}$  scans.",
+        "bbox": [
+            212,
+            566,
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+            686
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We provide results for 2 different versions of our model. The standard quality model is generated in 2 seconds by running 5 DDIM [64] steps during inference and Marching Cubes at  $256^{3}$  resolution. The high quality model is generated in 10 seconds using 50 DDIM steps and Marching Cubes at  $512^{3}$  resolution. The timings were recorded on a single 40 GB A100 GPU. Unless otherwise stated, all results we report are obtained using the high quality model.",
+        "bbox": [
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+            688,
+            787,
+            777
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Metrics and Baselines. We compare our method numerically for two different problems. First we consider the task of text-to-3D human generation, where we sample 100 different text prompts and compare against representative text-to-3D generation methods. For numerical comparisons we evaluate the text-image",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
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+        "img_path": "images/8c9a1eba9b64f3018c4f5159767cf74820e47964bd0031a4a402609ea2f6e9e0.jpg",
+        "image_caption": [
+            "Fig. 4: Diversity of our 3D generation. For the same text prompt and the same pose and shape conditioning, our model can generate a diverse set of 3D avatars that respect both the text and the 3D body controls."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "alignment using CLIP [52]. Specifically, we use the retrieval accuracy using CLIP, as proposed in [51]. We additionally show qualitative results.",
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+    {
+        "type": "text",
+        "text": "Second, we validate the performance of our 3D reconstruction component against state-of-the-art methods [8,27,60,61,70,71] considering both geometry and texture. Pixel-aligned image features dominate in recent work [8,60,61], but some methods proposed to combine them with body models [70,71], which offer advantages in being able to animate reconstructions. We also rely on pixel-aligned features, yet propose a method that inherently enables animation. We run AvatarPopUp by generating the back side of the subject and applying the reconstruction network. To evaluate 3D geometry, we report bi-directional Chamfer distance  $\\times 10^{-3}$ , Normal Consistency (NC ↑), and Volumetric Intersection over Union (IoU ↑) after ICP alignment. However, these metrics do not necessarily correlate with good visual quality, e.g. Chamfer distance is minimized by smooth, non-detailed geometry. To measure the quality of reconstructions, we additionally report FID scores [22] of the front/back views for both geometry and texture.",
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+        "type": "text",
+        "text": "4.1 Text-to-3D Generation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In Fig. 4 we generate different avatars given the same text prompt and driving poses. We can see that our model is able to create a very diverse set of assets, a property not observed in the previous text-to-3D generation methods [32].",
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+        "type": "text",
+        "text": "In Tab. 2 we use CLIP to evaluate our model against other text-to-3D generation methods. In general, CLIP-based metrics are not indicative of the generated image quality, because they only consider the alignment with the text, and often over-saturated images with extreme details tend to have high CLIP scores. To further demonstrate that our method generates higher quality avatars, we also include a qualitative comparison in Fig. 5.",
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+    },
+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
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+    },
+    {
+        "type": "page_number",
+        "text": "9",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Color</td><td colspan=\"2\">Color</td><td rowspan=\"2\">Runtime ↓</td><td></td></tr><tr><td>R-Prec. ↑</td><td>Top-3 ↑</td><td>R-Prec. ↑</td><td>Top-3 ↑</td><td></td></tr><tr><td>0.68</td><td>0.92</td><td>0.04</td><td>0.25</td><td>8h</td><td>DreamHuman [32]</td></tr><tr><td>0.56</td><td>0.82</td><td>0.03</td><td>0.15</td><td>3h</td><td>TADA [37]</td></tr><tr><td>-</td><td>-</td><td>0.03</td><td>0.08</td><td>3m</td><td>CHUPA [31]</td></tr><tr><td>0.58</td><td>0.73</td><td>0.08</td><td>0.17</td><td>~2s</td><td>Ours</td></tr><tr><td>0.62</td><td>0.77</td><td>0.11</td><td>0.17</td><td>~10s</td><td>Ours (high quality)</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Numerical comparisons with other text-to-3d human generation methods. We mark the best and second best results. Our method allows to trade-off speed and quality and we report results for two different settings.",
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+        "image_caption": [
+            "A person wearing a black off-shoulder top and a denim skirt",
+            "Fig. 5: Comparisons with text-to-3d human generation methods. Our method generates high quality results that respect the text prompt well, at a fraction of the others' runtime, cf. Tab. 3. TADA's results appear unnatural; DreamHuman failed for one subject and produces oversaturated colors; CHUPA failed to respect the prompt."
+        ],
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+    {
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+        "text": "4.2 Single-image 3D Reconstruction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "While not specifically designed for 3D reconstruction, our method achieves state-of-the-art performance also for this task. The evaluation setup is the following: given an input image  $I$ , we draw one random sample from the back view image generator network, and then feed the pair of front/back images to our 3D reconstruction network. For all methods we extract a textured 3D mesh using Marching Cubes and report numerical results in Tab. 3. Furthermore, we show qualitative results in Fig. 6. Notably, our method not only performs on par numerically and qualitatively on reconstructed front views, but also generates highly detailed back view texture and geometry. Finally, we also compare with the optimization-based method TeCH [27] in Fig. 7. TeCH produces detailed front and back geometry but also also exhibits problems at times, rooted in its 3D pose estimation method. Most importantly, TeCH runs for several hours per instance, while ours computes results in a single feed-forward pass, in only a few seconds.",
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+        "type": "header",
+        "text": "N. Kolotouros et al.",
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+    },
+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">3D Metrics</td><td colspan=\"4\">FID ↓</td><td></td></tr><tr><td>Ch. ↓</td><td>IoU ↑</td><td>NC ↑</td><td>Color. F</td><td>Color B.</td><td>Normal F.</td><td>Normal B.</td><td></td></tr><tr><td>7.1</td><td>0.50</td><td>0.72</td><td>-</td><td>-</td><td>29.6</td><td>57.2</td><td>PIFu [60]</td></tr><tr><td>6.2</td><td>0.52</td><td>0.74</td><td>-</td><td>-</td><td>26.9</td><td>52.5</td><td>PIFuHD [61]</td></tr><tr><td>7.0</td><td>0.48</td><td>0.72</td><td>-</td><td>-</td><td>36.1</td><td>49.0</td><td>ICON [71]</td></tr><tr><td>3.4</td><td>0.58</td><td>0.76</td><td>-</td><td>-</td><td>18.3</td><td>36.1</td><td>ECON [70]</td></tr><tr><td>0.84</td><td>0.71</td><td>0.87</td><td>11.0</td><td>40.8</td><td>11.2</td><td>38.8</td><td>PHORHUM* [8]</td></tr><tr><td>0.91</td><td>0.70</td><td>0.86</td><td>11.0</td><td>20.0</td><td>12.8</td><td>25.8</td><td>Ours</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3: Numerical comparisons with single-view 3D reconstructions methods and ablations of our method. We mark the best and second best results. All Chamfer metrics are  $\\times 10^{-3}$ . Not all methods generate colors. For fair comparisons, we retrained PHORHUM [8] using the same data as AvatarPopUp. We observe comparable results in terms of 3D metrics, however ours performs better on generating more realistic and diverse back views and back normals.",
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+    {
+        "type": "text",
+        "text": "4.3 3D Virtual Try On",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "An immediate application of our method is the option to perform 3D garment edits for a given identity. Given an input image, we first recover 3D pose and shape parameters of the person in the image. Using a text prompt and the identity preservation strategy introduced below, we can generate updated images of the same person wearing different garments or accessories. To preserve the identity of the person, we first locate the person's head in the source image and use then Repaint [46] to out-paint a novel body for the given head while still conditioning on the estimated pose and shape parameters. With this strategy we ensure that our method not only preserves the facial characteristics but also the overall body proportions. In Fig. 9 we illustrate such editing examples. The generated 3D edits present garment details like wrinkles on both front and back views, and preserve the subjects' facial appearance. Also, note that body shape and identity are well preserved for the subjects, even though only one image is given. While there has been a significant amount of 2D virtual try-on research [20,35,86], our methodology can generate consistent and highly detailed 3D meshes that can be animated and rendered from other viewpoints.",
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+        "text": "4.4 Animation",
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+    {
+        "type": "text",
+        "text": "AvatarPopUp enables animation of the generated assets by design, provided that its generation is conditioned on an underlying body model. In Fig. 8, we show an example of a generated avatar that is rigged automatically.",
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+    {
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+        "text": "4.5 Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Pose and shape encoding in the 3D reconstruction network. We compare the effectiveness of our additional pose and shape encoding inputs  $\\mathcal{G}$  to our reconstruction network. To do so, we use the same set of 100 text prompts as before and for each text prompt sample a random pose and shape configuration. For each  $(\\tau, \\theta, \\beta)$  triplet we run inferences and compute 2 meshes: one using",
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+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
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+    {
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+            "Fig. 6: Qualitative comparisons with state-of-the-art single image 3D reconstruction methods. Our method produces front color and normals on par with state-of-the-art and much more detailed back view hypotheses."
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+            ""
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+    {
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+        "img_path": "images/227939bc09641de63cfda27840ce207abcaf506027c3ad240eb91d9fee96c425.jpg",
+        "image_caption": [
+            "PIFuHD"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "only the front and back images, and another one additionally using the dense GHUM encodings. We then evaluate the Chamfer distance between each mesh and the corresponding GHUM mesh. The model using the additional GHUM signals has an average Chamfer distance of  $d_{\\mathrm{with}} = 1.4$  whereas the one without  $d_{\\mathrm{without}} = 8.6$ , thus validating our design choice. Not only is the control respected well, but this also allows for animation as discussed previously.",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Partial vs. Complete Network Finetuning. We finetune two Latent Diffusion networks, one in a standard way by optimizing all parameters, and another one using our proposed strategy where we only finetune the convolutional layers of the encoder. Empirically we observed that the network that was finetuned as a whole experienced catastrophic forgetting, and has poor performance when asked to generate types of garment not seen in the training set. Fig. 10 shows a comparison for text prompts not in the training set.",
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+    {
+        "type": "text",
+        "text": "5 Discussion & Conclusions",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Limitations. AvatarPopUp inherits limitations from other pixel-aligned methods, e.g. with regions parallel to camera rays being not as detailed in the reconstruction. Further, artifacts might be visible in poses or very loose clothing that are underrepresented during training.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ethical Considerations. We present a generative tool to create 3D human assets, thus reducing the risk of scanning and using real humans for training large scale 3D generative models. AvatarPopUp generates diverse results and can lead to a better coverage of subject distributions.",
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+        "text": "N. Kolotouros et al.",
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+        "img_path": "images/644893664bb6a0e81b86e5f6ed2631977fd60acfe99dfcc4712156cb815c5dff.jpg",
+        "image_caption": [
+            "Fig. 7: Additional comparisons with TeCH. TeCH is optimization-based and takes several hours to complete for a single reconstruction. Our results are obtained in seconds, yet are as detailed and even less noisy."
+        ],
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+        "img_path": "images/1e5512458355ed8fa858558aa05d8784f3f158ff317bff63f0750b309f745733.jpg",
+        "image_caption": [
+            "Ours"
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+        "img_path": "images/add9dc208474d3fb82997f320290655b0af98f036ed2a320767ba0541b6c766f.jpg",
+        "image_caption": [
+            "TeCH"
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+        "image_caption": [
+            "Fig. 8: Reposing example.. We first reconstruct an avatar \"wearing a gray suit\" in the A-pose and then we transfer it to different poses."
+        ],
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+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
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+        "page_idx": 12
+    },
+    {
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+        "text": "13",
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+    {
+        "type": "image",
+        "img_path": "images/ca6e8a5633e19c806361af05dbdef45340e11facaea29dab86c9e17767da3fa7.jpg",
+        "image_caption": [
+            "Fig. 9: Identity preserving 3D avatar editing. Our method allows for editing the clothing, while preserving the identity of the generated person. In each row we're using the image on the left as input, recover the person's pose and shape parameters and then run our method using the shown prompts. The generated avatars share the same identity and respect the target prompts."
+        ],
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+        "page_idx": 13
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+    {
+        "type": "image",
+        "img_path": "images/7fbc485cb9f842c8d7873adff5ae0bea9ddd8f3ed28deed93f6287a79c08f91e.jpg",
+        "image_caption": [
+            "Fig. 10: Partial vs. complete fine-tuning strategy. For each text prompt the first example is generated using our partial fine-tuning strategy whereas the second by fine-tuning the entire network. Empirically, partial fine-tuning is more resilient to catastrophic forgetting, generating more diverse and better text-aligned images."
+        ],
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+        "type": "text",
+        "text": "We have presented AvatarPopUp, a novel framework for generating 3D human avatars controlled by text or images and yielding rigged 3D models in 2-10 seconds. AvatarPopUp is purely feed-forward, allows for fine-grained control over the generated body pose and shape, and can produce multiple qualitatively different hypotheses. AvatarPopUp is composed of a cascade of expert systems, decoupling image generation and 3D lifting. Through this design choice, AvatarPopUp benefits from both web-scale image datasets, ensuring high generation diversity, and from smaller size accurate 3D datasets, resulting in reconstructions with increased detail and precisely controlled based on text and identity specifications. In the future, we would like to explore other 3D construction strategies besides pixel-aligned features. Longer term, we aim to support highly detailed and controllable 3D human model generation for entertainment, education, architecture and art, or medical applications.",
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+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+    },
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+        "page_idx": 17
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+    {
+        "type": "header",
+        "text": "N. Kolotouros et al.",
+        "bbox": [
+            271,
+            114,
+            403,
+            126
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
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+        "page_idx": 18
+    },
+    {
+        "type": "header",
+        "text": "Instant 3D Human Avatar Generation",
+        "bbox": [
+            475,
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+        ],
+        "page_idx": 18
+    },
+    {
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+    }
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2024/Instant 3D Human Avatar Generation using Image Diffusion Models/848a10c5-4ff1-45f7-8010-a0858cf611ea_origin.pdf

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2024/Instant 3D Human Avatar Generation using Image Diffusion Models/full.md

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+# Instant 3D Human Avatar Generation using Image Diffusion Models
+
+Nikos Kolotouros, Thiemo Alldieck, Enric Corona, Eduard Gabriel Bazavan, and Cristian Sminchisescu
+
+Google Research\* {kolotouros, alldieck, egbazavan, enriccorona, sminchisescu}@google.com
+
+![](images/13947c3f92d8dc40fa114453e17f43421b851573c29a2de60d376a787ccfaa73.jpg)  
+Fig. 1: We present AvatarPopUp, a new method for the automatic generation of 3D human assets. AvatarPopUp can generate rigged 3D models from text or from single images and has control over body pose and shape. In this example, we show 77 models generated from various text prompts in 12 minutes on a single GPU.
+
+Abstract. We present AvatarPopUp, a method for fast, high quality 3D human avatar generation from different input modalities, such as images and text prompts and with control over the generated pose and shape. The common theme is the use of diffusion-based image generation networks that are specialized for each particular task, followed by a 3D lifting network. We purposefully decouple the generation from the 3D modeling which allows us to leverage powerful image synthesis priors, trained on billions of text-image pairs. We fine-tune latent diffusion networks with additional image conditioning for image generation and back-view prediction, and to support qualitatively different multiple 3D hypotheses. Our partial fine-tuning approach allows to adapt the networks for each task without inducing catastrophic forgetting. In our experiments, we demonstrate that our method produces accurate, high-quality 3D avatars with diverse appearance that respect the multimodal text, image, and body control signals. Our approach can produce a 3D model in as few as 2 seconds, a four orders of magnitude speedup w.r.t. the vast majority of existing methods, most of which solve only a subset of our tasks, and with fewer controls. AvatarPopUp enables applications that require the controlled 3D generation of human avatars at scale. The project website can be found at https://www.nikoskolot.com/avatarpopulation/.
+
+# 1 Introduction
+
+We present AvatarPopUp, a method for instant generation of rigged full-body 3D human avatars, with multimodal controls in the form of text, images, and/or human pose and shape. The remarkable recent progress in image synthesis [15, 24, 54, 56, 58, 63] acted as a catalyst for a wide range of media generation applications. In just a few years, we have witnessed rapid developments in video generation [9, 23, 34, 68, 76], audio synthesis [49, 77] or text-to-3D object generation [40, 41, 51, 53, 65], among others. Pivotal to success of all these methods is their probabilistic nature, however this requires very large training sets. While inspiring efforts have been made [14], training set size is still a problem in many domains, and particularly for 3D. In an attempt to alleviate the need for massive 3D datasets, DreamFusion [51] leverages the rich priors of text-to-image diffusion models in an optimization framework. The influential DreamFusion ideas were also quickly adopted for 3D avatar creation [32, 37], a field previously dominated by image- or video-based reconstruction solutions [6, 8, 60, 61]. Text-to-avatar methods enabled novel creative processes, but came with a significant drawback. While image-based methods typically use pretrained feed-forward networks and create outputs in seconds, existing text-to-avatar solutions are optimization-based and take minutes to several hours to complete, per instance.
+
+In this paper, we are closing this gap and present, for the first time, a methodology for instant, text-controlled, rigged, full-body 3D human avatar creation. Our AvatarPopUp is purely feed-forward, can be conditioned on images and textual descriptions, allows fine-grained control over the generated body pose and shape, can generate multiple hypotheses, and runs in 2-10 seconds per instance.
+
+Key to success is our pragmatic decoupling of the two stages of probabilistic text-to-image generation and 3D lifting. Decoupling 2D generation and 3D lifting has two major advantages: (1) We can leverage the power of pretrained text-to-image generative networks, which have shown impressive results in modeling complex conditional distributions. Trained with large training sets of images, both generation quality and diversity are very high. (2) We alleviate the need for very large 3D datasets required to train state-of-the-art generative 3D models. Our method generates diverse plausible image configurations that contain rich enough information that can be lifted in 3D with minimal ambiguity. In other words, we distribute the workload between two expert systems: a pretrained probabilistic generation network fine-tuned for our task to produce front and back image views of the person, and a state-of-the-art unimodal, feed-forward image-to-3D model that can be trained using comparably small datasets.
+
+Our proposed decoupling strategy allows us to maximally exploit available data sources with different levels of supervision. We first fine-tune a pretrained Latent Diffusion network to generate images of people based on textual descriptions and with additional control over the desired pose and shape. This step does not require any ground truth 3D data for supervision and enables scaling our image generator to web scale data of images of people in various poses. Next, we leverage a small-scale dataset of scanned 3D human assets and fine-tune a second latent diffusion network to learn the distribution of back side views con
+
+<table><tr><td colspan="8">Control from Text Control from Image Shape Control</td></tr><tr><td>Body</td><td>Shape</td><td>Generates</td><td>Geometry</td><td>Texture</td><td></td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓/X</td><td>Runtime</td><td></td></tr><tr><td>X</td><td>✓</td><td>X</td><td>✓</td><td>✓/X</td><td>X</td><td>several hours</td><td>Optimization-based text-to-3D [26,32,37]</td></tr><tr><td>✓</td><td>X</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>seconds</td><td>Image-to-3D [4,8,60,61]</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>✓</td><td>✓</td><td>X</td><td>minutes</td><td>Hybrid [31]</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>seconds</td><td>3D GANs [16,25]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td>seconds</td><td>AvatarPopUp (Ours)</td></tr></table>
+
+Table 1: AvatarPopUp generates 3D assets with texture from text prompts or input images of a target subject and can be controlled with body pose and shape. In contrast to baselines that require up to hours per prompt, our model takes under five seconds and can de facto by used in interactive applications. In the experimental section we demonstrate the large diversity of the model, and applications in cloth editing.
+
+ditioned on a front view image of the person. We optionally also condition on a textual description that can naturally complement the evidence available in the front view image. Furthermore, we propose a novel fine-tuning strategy that prevents overfitting to the new datasets. Finally, we design and train a 3D reconstruction network that predicts a textured 3D shape in the form of an implicit signed distance field given the pair of front and back views and optionally 3D body signals. The resulting cascaded method, which we call AvatarPopUp supports a wide range of 3D generation and reconstruction tasks: First, it enables fast and interactive 3D generation of assets at scale, see Fig. 1. Second, we can repurpose parts of the cascade for image-based 3D reconstruction at state-of-the-art quality. Finally, we demonstrate how AvatarPopUp can be used for creative editing tasks exemplified in 3D virtual try-on with body shape preservation. To summarize, our main contributions are:
+
+- A method for controllable 3D human avatar generation, based on multimodal text, pose, shape and image input signals, that outputs a detailed human mesh instance in 2-10 seconds.  
+- We propose a simple yet effective way to fine-tune pretrained diffusion models on small-scale datasets, without inducing catastrophic forgetting.  
+- While not our primary goal, our approach achieves state-of-the-art results in single-image 3D reconstruction and enables 3D creative editing applications.
+
+# 2 Related Work
+
+Table 1 summarizes the characteristics of AvatarPopUp in comparison to previous work, along several important property axes.
+
+Text-to-3D generation. The success of text-to-image models [55, 57, 59] was quickly followed by a significant amount of work on text-to-3D content generation [38, 45, 51, 66]. Due to limited training data, methods typically use optimization approaches, where a neural representation [47] is optimized per instance by minimizing a distillation loss [51] derived from large text-to-image models. This idea has been extended to generate human avatars [18, 27, 29, 32, 37, 69, 73, 78–80] or heads [19, 36, 39] enabling the text-based creation of 3D human assets that
+
+are diverse in terms of shape, appearance, clothing and various accessories. In these works, the optimization process is often regularized using a 3D body model [32,37,78], which also enables animation. However, such approaches generally take hours per instance, and rendering is slow. With the appearance of Gaussian Splatting [30], other works [2,42,82] reduced rendering time at the expense of accurate geometry. In any case, creating an avatar still takes a significant amount of time, making such methods unsuitable for interactive applications. In this work we propose an alternative direction, which also builds upon the success of text-to-image models and combines them with 3D reconstruction pipelines. Also related are 3D human generation methods. AG3D [16] and EVA3D [25] are GAN-based methods learned from 2D data, that allow to sample 3D humans anchored in a 3D body model. CHUPA [31] generates dual normal maps based on text and then fits a body model to obtain a full 3D representation. While generation is similar in spirit to our method, CHUPA requires optimization per instance and does not generate texture.
+
+Photorealistic 3D Human Reconstruction. Our framework generates 3D human assets and builds on top of state-of-the-art 3D reconstruction techniques. This has been widely explored in the past and can be roughly categorized by its use of explicit or implicit representations. An important line of work leverages 3D body models [43,50,72] and reconstructs their associated parameters, in some cases extended with vertex offsets to represent some clothing and hair detail [4-7, 48, 85]. Other efforts have considered voxels [67, 84], depth maps [17] and more recently implicit representations [8, 13, 21, 28, 60-62, 70, 71, 74, 75, 83]. Being topology free, the latter allows the representation of loose clothing more easily. They typically provide more detail and enable high-resolution reconstruction, often conditioned on local pixel-aligned features [60]. On the other hand, these methods yield reconstructions with no semantic labels that cannot be easily animated. To solve this problem, some work combined body models with implicit representations [13, 21, 27, 28, 70, 71], but this is prone to errors when the pose is noisy at inference time. In contrast, we drive the synthesis process with guidance from an input body model – sampled or estimated – so that the generated image is well aligned with the body prior. As we show in Sec. 4, this allows rigging the 3D avatar without post-processing and natively supports 3D animation.
+
+Given a single input image of a person, previous work aims to generate realistic reconstructions for the non-visible parts. However, this often leads to blurry textures and lack of geometric detail, e.g. no wrinkles. Some methods [60, 61, 70, 71] generate back normal maps to enhance details, or consider probabilistic reconstructions [3, 62]. However, all these methods cannot be prompted from text or other modalities and still yield limited diversity. In contrast, we guide the synthesis process by means of generated front and back images, yielding high-quality 3D reconstructions. Another challenge in previous work is limited training data. Most prior methods rely on a few hundred 3D scans, due to the pricey and laborious process of good quality human capture. We alleviate the need for large scale 3D training data by proposing a framework that can quickly generate humans with a given clothing, pose and shape.
+
+![](images/162ab2d8066f91630fb298720f8e4fd1e5303b92e5df8162c95d919a99d4e1b2.jpg)  
+Fig. 2: AvatarPopUp method. (Top) AvatarPopUp builds on the capacity of text-to-image models to generate highly detailed and diverse input images. First, a Latent Diffusion network takes a text prompt and a target body pose and shape  $\mathcal{G}$ , and generates a highly detailed front image  $I_{f}$  of a person. Next, a second network generates a consistent back view  $I_{b}$  in the same pose and clothing. (Bottom) We perform pixel-aligned 3D reconstruction given the generated front/back views  $I_{f}, I_{b}$  and optionally the given 3D body pose and shape  $\mathcal{G}$ . This decoupling enables the generation of 3D avatars from text, images or a combination of the two.
+
+# 3 Method
+
+We learn a distribution  $p(X|c)$  of textured 3D shapes  $X$  conditioned on a collection of signals  $c$  that we factorize as follows
+
+$$
+p (X | c) = \int \int p \left(X \mid I _ {f}, I _ {b}, c\right) \cdot p \left(I _ {b} \mid I _ {f}, c\right) \cdot p \left(I _ {f} \mid c\right) d I _ {f} d I _ {b}, \tag {1}
+$$
+
+where  $p(X|I_f, I_b, c)$  is the probability of 3D shape  $X$  given  $c$  and front and back image observations  $I_f$  and  $I_b$  respectively,  $p(I_b|I_f, c)$  is the probability of the back view image given the front image  $I_f$  and conditioning signals  $c$ , and  $p(I_f|c)$  the conditional probability of front view images of the person given  $c$ .
+
+Computing the integral in (1) is intractable, but our goal is to generate samples from the distribution rather than expectations. To do so, we employ ancestral sampling. We first sample a front view  $I_{f}$  given  $c$ , we then sample a back view  $I_{b}$  given  $I_{f}$  and  $c$ , and last we sample the 3D reconstruction based on the entire context. In practice,  $p(I_f|c)$  and  $p(I_b|I_f,c)$  are implemented using Latent Diffusion models, whereas  $p(X|I_f,I_b,c)$  is a unimodal, neural implicit field generator.
+
+In the case of single-image 3D reconstruction the conditioning signal  $c$  is  $I_{f}$ , and consequently we can omit the first step. For text-based generation,  $c$  is a text prompt describing the appearance of the person together with a signal encoding the body pose and shape. The conditioning information  $c$  may be extended with additional signals, as in the case of 3D editing, cf. Sec. 4.
+
+# 3.1 Controllable Text-to-Image Generator
+
+Recent advances in diffusion-based text-to-image generation networks [56] have enabled synthesizing high-quality images given only a text prompt as input. However, for certain use cases, such as human generation, it is difficult to inject fine-grained, inherently continuous forms of control, like the 3D pose of people or their precise body shape proportions, when generating with text alone.
+
+Inspired by ControlNet [81], we propose to add simultaneous control over body pose and shape by augmenting a pretrained Latent Diffusion network with an additional image input that jointly encodes both modalities. For control we use GHUM [72] but other models (e.g. [43]) can be used. Specifically given 3D pose and shape parameters  $\pmb{\theta}$  and  $\pmb{\beta}$  respectively, we render the corresponding mesh  $\mathcal{M} = \mathrm{GHUM}(\pmb{\theta},\pmb{\beta})$  using GHUM's template coordinates and posed vertex locations as 6D vertex colors, obtaining a dense, pixel-aligned pose- and shape-informed control signal  $\mathcal{G}$ .
+
+To fine-tune the network, we generate a dataset of images of people with corresponding GHUM 3D pose and shape parameters and text annotations. This dataset is comprised of a set of scanned assets [1] that are rendered from different viewpoints, as well as a set of real images scraped from the web. For the synthetic part of the dataset, the pose and shape parameters are obtained by fitting GHUM to 3D scans. We additionally use real images to which we fit GHUM using keypoint optimization in the style of [33]. For all images we obtained text annotations using an off-the shelf image captioning system [12] by prompting it to describe the clothing of the people in the image. Since we are interested in generating 3D human assets, we additionally mask out the background in all images, and train the network to output segmented images. This makes the downstream 3D reconstruction task easier, and improves the reconstruction quality because it encourages the network to focus on human appearance, rather than allocating capacity to model complex backgrounds.
+
+We want to exploit the rich priors learned by text-to-image foundation models by fine-tuning a Latent Diffusion model [56] with the dense GHUM rendering as an additional input. For fine-tuning we propose a simpler and more lightweight method than a standard ControlNet. We pad the weights of the input convolutional layer with additional channels initialized with zeros, and we then fine-tune only the weights of the convolutional layers of the encoder network. All the decoder and attention layers are kept frozen. With this simple strategy, even though our model is trained on a relatively small set of images, it can generalize to unseen types of clothing. At the same time, our strategy is more practical than training a ControlNet, which involves keeping in separate copy of the original network weights in memory, and thus enables fine-tuning large models with moderate hardware utilization. We optimize the encoder of the diffusion model by minimizing the simple variant of the diffusion loss [24]
+
+$$
+\mathcal {L} \left(\psi_ {\text {e n c}}\right) = \mathbb {E} _ {\mathcal {E} (x), \epsilon , t, \tau , \mathcal {G}} \left\| \epsilon - \epsilon_ {\psi} \left(z _ {t}, t, \tau , \mathcal {E} (\mathcal {G})\right) \right\|, \tag {2}
+$$
+
+where  $t \in \{1, \dots, T\}$  is the diffusion time step,  $\epsilon \sim \mathcal{N}(0, I)$  the injected noise,  $z_{t} = \alpha_{t} \mathcal{E}(x) + \nu_{t}$  is the noisy image latent,  $\tau$  is the text encoding,  $\mathcal{E}(\mathcal{G})$  the
+
+![](images/1db3f8e20ecd95376e3f40ffa57af103cd1f5e34035f9d69a43d3c1d082b2377.jpg)
+
+![](images/01db6990a2368276c251bea01ea04cb4d3d3bdd0a1562e42583b377a7562c54b.jpg)
+
+![](images/69caf4714bb22336466c3167fea99aa8a152d2eb57025c327c4df4a0a4e78ad4.jpg)
+
+![](images/581460b48d12d79363f37c039c9742e8218ee53639a8e58fb60d61cc7cd679ab.jpg)
+
+![](images/cade929a17ec102891f1cc8fcf8972281ae09fad17a6875f4a71ac34d99e57bd.jpg)  
+Fig. 3: Diverse back view hypotheses. Conditioned on the front view, our method is able to generate diverse plausible back views of the person, with different hairstyles, wrinkle patterns, or lighting. Our network can also be controlled with text (second row), to add fine-grained detail to our generated back-side views.
+
+![](images/dc4a18690be7fdbe678f416b58d57f4d67372038af4ac46a7e6022b1cd0c7b98.jpg)  
+No text conditioning
+
+![](images/e2a400732757cac23a4a9922daf6f5839c31b9736fdd90dda848c9c8b4941f10.jpg)  
++“gray hair”
+
+![](images/1daf589e7a6556f159cd04ac5d4f59caf3364c3b6768c12b31433d9c80a1db40.jpg)  
++“with a tattoo”
+
+latent encoding of the dense GHUM signal, and  $\psi_{\mathrm{enc}}$  the encoder subset of the denoising UNet parameters  $\psi$ .
+
+# 3.2 Back View Generation
+
+One could try to lift the generated front views from the previous stage to 3D directly by applying a single-image 3D reconstruction method like PHORHUM [8]. However, because of the inherent ambiguity of the problem this will result in significant loss of geometric detail and blurry textures for the non-visible body surfaces. To avoid this, we propose to fine-tune again a latent diffusion network with the same strategy as in the previous section. This time the additional image conditioning is a front view and optionally a text prompt, and we train the network to learn the distribution of back views conditioned on the front view. The additional text prompt can be used in cases where it is desired to additionally guide the generation by very specific properties. Fig. 3 shows different back sides sampled from the conditional distribution. We also show that the additional text inputs are useful in modulating certain parts of the generation that are not immediately deducible from the front image, such as hairstyles or specific patterns.
+
+# 3.3 3D Reconstruction Model
+
+Our 3D reconstruction network is inspired by PHORHUM [8], and our design choices are informed by the limitations of typical single-image 3D reconstruction methods. Specifically, given a collection of input image signals  $\mathcal{I} = \{I_f, I_b, \mathcal{G}\}$ , we first concatenate them, and then use a convolutional encoder  $G$  to compute
+
+a pixel-aligned feature map  $G(\mathcal{I})$ . The 3D body control signal  $\mathcal{G}$  is optional and may be omitted, e.g. for single-image reconstruction. Then, each point  $\mathbf{x} \in \mathbb{R}^3$  in the scene gets projected on this feature map to get pixel-aligned features  $\mathbf{z}_{\mathbf{x}} = g(\mathcal{I}, \mathbf{x}; \pi) = b(G(\mathcal{I}), \pi(\mathbf{x}))$  using interpolation, where  $b(\cdot)$  is the bilinear sampling operator and  $\pi(\mathbf{x})$  is the pixel location of the projection of  $\mathbf{x}$  using the camera  $\pi$ . These pixel aligned features are then concatenated with a positional encoding  $\gamma(\mathbf{x})$  of the 3D point and are fed to an MLP  $f$  that outputs the signed distance from the surface  $d$  as well as surface color  $c$ . Finally, the 3D shape  $S$  is represented as the zero-level-set of  $d$
+
+$$
+\mathcal {S} (\mathcal {I}) = \left\{\mathbf {x} \in \mathbb {R} ^ {3} | f (g (I, \mathbf {x}; \pi), \gamma (\mathbf {x})) = (0, c) \right\}. \tag {3}
+$$
+
+$\mathcal{S}$  can be transformed to a mesh directly, using Marching Cubes [44].
+
+# 3.4 Animation of Generated Avatars
+
+Our method can generate diverse 3D avatars with various poses, shapes and appearances. Optionally, we may leverage the conditioning body model to rig the estimated 3D shape. As a result of our conditioning strategy, 3D avatars and the conditional body model instances are aligned in 3D. This allows us to anchor the reconstructed 3D shape on the body model surface [10] and re-pose or re-shape it accordingly. Alternatively, we may also transfer just the LBS skeleton and weights from the body model to the scan. This enables importing and animating the generated 3D assets in various rendering engines. See Fig. 8 and Sup. Mat. for examples and videos of animations of the generated 3D assets.
+
+# 4 Experiments
+
+Data. We use meshes from RenderPeople [1] for training as well as our own captured data, totaling in  $\sim 10\mathrm{K}$  scans with diverse poses, body shapes, and clothing styles. We render each scan with randomly sampled HDRI background, random cloth color augmentations, and lighting using Blender [11]. During this process, we render both front and back views used to train the different stages of our model. For the front image generation network we also use a set of  $10\mathrm{K}$  real images on which we fitted the GHUM model using 2D keypoints. For testing we defined a split based on subject identity and held out  $\sim 1\mathrm{K}$  scans.
+
+We provide results for 2 different versions of our model. The standard quality model is generated in 2 seconds by running 5 DDIM [64] steps during inference and Marching Cubes at  $256^{3}$  resolution. The high quality model is generated in 10 seconds using 50 DDIM steps and Marching Cubes at  $512^{3}$  resolution. The timings were recorded on a single 40 GB A100 GPU. Unless otherwise stated, all results we report are obtained using the high quality model.
+
+Metrics and Baselines. We compare our method numerically for two different problems. First we consider the task of text-to-3D human generation, where we sample 100 different text prompts and compare against representative text-to-3D generation methods. For numerical comparisons we evaluate the text-image
+
+![](images/8c9a1eba9b64f3018c4f5159767cf74820e47964bd0031a4a402609ea2f6e9e0.jpg)  
+Fig. 4: Diversity of our 3D generation. For the same text prompt and the same pose and shape conditioning, our model can generate a diverse set of 3D avatars that respect both the text and the 3D body controls.
+
+alignment using CLIP [52]. Specifically, we use the retrieval accuracy using CLIP, as proposed in [51]. We additionally show qualitative results.
+
+Second, we validate the performance of our 3D reconstruction component against state-of-the-art methods [8,27,60,61,70,71] considering both geometry and texture. Pixel-aligned image features dominate in recent work [8,60,61], but some methods proposed to combine them with body models [70,71], which offer advantages in being able to animate reconstructions. We also rely on pixel-aligned features, yet propose a method that inherently enables animation. We run AvatarPopUp by generating the back side of the subject and applying the reconstruction network. To evaluate 3D geometry, we report bi-directional Chamfer distance  $\times 10^{-3}$ , Normal Consistency (NC ↑), and Volumetric Intersection over Union (IoU ↑) after ICP alignment. However, these metrics do not necessarily correlate with good visual quality, e.g. Chamfer distance is minimized by smooth, non-detailed geometry. To measure the quality of reconstructions, we additionally report FID scores [22] of the front/back views for both geometry and texture.
+
+# 4.1 Text-to-3D Generation
+
+In Fig. 4 we generate different avatars given the same text prompt and driving poses. We can see that our model is able to create a very diverse set of assets, a property not observed in the previous text-to-3D generation methods [32].
+
+In Tab. 2 we use CLIP to evaluate our model against other text-to-3D generation methods. In general, CLIP-based metrics are not indicative of the generated image quality, because they only consider the alignment with the text, and often over-saturated images with extreme details tend to have high CLIP scores. To further demonstrate that our method generates higher quality avatars, we also include a qualitative comparison in Fig. 5.
+
+<table><tr><td colspan="2">Color</td><td colspan="2">Color</td><td rowspan="2">Runtime ↓</td><td></td></tr><tr><td>R-Prec. ↑</td><td>Top-3 ↑</td><td>R-Prec. ↑</td><td>Top-3 ↑</td><td></td></tr><tr><td>0.68</td><td>0.92</td><td>0.04</td><td>0.25</td><td>8h</td><td>DreamHuman [32]</td></tr><tr><td>0.56</td><td>0.82</td><td>0.03</td><td>0.15</td><td>3h</td><td>TADA [37]</td></tr><tr><td>-</td><td>-</td><td>0.03</td><td>0.08</td><td>3m</td><td>CHUPA [31]</td></tr><tr><td>0.58</td><td>0.73</td><td>0.08</td><td>0.17</td><td>~2s</td><td>Ours</td></tr><tr><td>0.62</td><td>0.77</td><td>0.11</td><td>0.17</td><td>~10s</td><td>Ours (high quality)</td></tr></table>
+
+Table 2: Numerical comparisons with other text-to-3d human generation methods. We mark the best and second best results. Our method allows to trade-off speed and quality and we report results for two different settings.
+
+![](images/dca817aad1b5c4cf1303324e456c60a0543ca2f879737932aa8e2ffeef5c575e.jpg)  
+A person wearing a black off-shoulder top and a denim skirt  
+Fig. 5: Comparisons with text-to-3d human generation methods. Our method generates high quality results that respect the text prompt well, at a fraction of the others' runtime, cf. Tab. 3. TADA's results appear unnatural; DreamHuman failed for one subject and produces oversaturated colors; CHUPA failed to respect the prompt.
+
+# 4.2 Single-image 3D Reconstruction
+
+While not specifically designed for 3D reconstruction, our method achieves state-of-the-art performance also for this task. The evaluation setup is the following: given an input image  $I$ , we draw one random sample from the back view image generator network, and then feed the pair of front/back images to our 3D reconstruction network. For all methods we extract a textured 3D mesh using Marching Cubes and report numerical results in Tab. 3. Furthermore, we show qualitative results in Fig. 6. Notably, our method not only performs on par numerically and qualitatively on reconstructed front views, but also generates highly detailed back view texture and geometry. Finally, we also compare with the optimization-based method TeCH [27] in Fig. 7. TeCH produces detailed front and back geometry but also also exhibits problems at times, rooted in its 3D pose estimation method. Most importantly, TeCH runs for several hours per instance, while ours computes results in a single feed-forward pass, in only a few seconds.
+
+<table><tr><td colspan="3">3D Metrics</td><td colspan="4">FID ↓</td><td></td></tr><tr><td>Ch. ↓</td><td>IoU ↑</td><td>NC ↑</td><td>Color. F</td><td>Color B.</td><td>Normal F.</td><td>Normal B.</td><td></td></tr><tr><td>7.1</td><td>0.50</td><td>0.72</td><td>-</td><td>-</td><td>29.6</td><td>57.2</td><td>PIFu [60]</td></tr><tr><td>6.2</td><td>0.52</td><td>0.74</td><td>-</td><td>-</td><td>26.9</td><td>52.5</td><td>PIFuHD [61]</td></tr><tr><td>7.0</td><td>0.48</td><td>0.72</td><td>-</td><td>-</td><td>36.1</td><td>49.0</td><td>ICON [71]</td></tr><tr><td>3.4</td><td>0.58</td><td>0.76</td><td>-</td><td>-</td><td>18.3</td><td>36.1</td><td>ECON [70]</td></tr><tr><td>0.84</td><td>0.71</td><td>0.87</td><td>11.0</td><td>40.8</td><td>11.2</td><td>38.8</td><td>PHORHUM* [8]</td></tr><tr><td>0.91</td><td>0.70</td><td>0.86</td><td>11.0</td><td>20.0</td><td>12.8</td><td>25.8</td><td>Ours</td></tr></table>
+
+Table 3: Numerical comparisons with single-view 3D reconstructions methods and ablations of our method. We mark the best and second best results. All Chamfer metrics are  $\times 10^{-3}$ . Not all methods generate colors. For fair comparisons, we retrained PHORHUM [8] using the same data as AvatarPopUp. We observe comparable results in terms of 3D metrics, however ours performs better on generating more realistic and diverse back views and back normals.
+
+# 4.3 3D Virtual Try On
+
+An immediate application of our method is the option to perform 3D garment edits for a given identity. Given an input image, we first recover 3D pose and shape parameters of the person in the image. Using a text prompt and the identity preservation strategy introduced below, we can generate updated images of the same person wearing different garments or accessories. To preserve the identity of the person, we first locate the person's head in the source image and use then Repaint [46] to out-paint a novel body for the given head while still conditioning on the estimated pose and shape parameters. With this strategy we ensure that our method not only preserves the facial characteristics but also the overall body proportions. In Fig. 9 we illustrate such editing examples. The generated 3D edits present garment details like wrinkles on both front and back views, and preserve the subjects' facial appearance. Also, note that body shape and identity are well preserved for the subjects, even though only one image is given. While there has been a significant amount of 2D virtual try-on research [20,35,86], our methodology can generate consistent and highly detailed 3D meshes that can be animated and rendered from other viewpoints.
+
+# 4.4 Animation
+
+AvatarPopUp enables animation of the generated assets by design, provided that its generation is conditioned on an underlying body model. In Fig. 8, we show an example of a generated avatar that is rigged automatically.
+
+# 4.5 Ablation Study
+
+Pose and shape encoding in the 3D reconstruction network. We compare the effectiveness of our additional pose and shape encoding inputs  $\mathcal{G}$  to our reconstruction network. To do so, we use the same set of 100 text prompts as before and for each text prompt sample a random pose and shape configuration. For each  $(\tau, \theta, \beta)$  triplet we run inferences and compute 2 meshes: one using
+
+![](images/33f7851c4d76bff20fb1c6fd45e6c8df67519d153221809c899f5db5aef1c0c4.jpg)
+
+![](images/8e76543a34a53fe154685c8f8fdab35449968cff6ecd28b41931c8a9e6862184.jpg)
+
+![](images/1a277a21efc4e57daeed803f8b0c412f8ffdb6a95d5267679749727b5d40ff08.jpg)  
+Fig. 6: Qualitative comparisons with state-of-the-art single image 3D reconstruction methods. Our method produces front color and normals on par with state-of-the-art and much more detailed back view hypotheses.
+
+![](images/e79dc5f2dedb4b3ffdf3bf42737cd570d004c8ecaa1c8c7ac072c867c4af560b.jpg)
+
+![](images/8ac23b6f8be52bac373b46279c603a437dc6cf667e7ff312e21282fce33fae41.jpg)
+
+![](images/c005d6f61016cf555a1f4332c9f7c4c534e90b5f546040205e819479751e93b7.jpg)
+
+![](images/577b67f56e47e08f57816e503d5e515d093325fc5537f9cf62057260038e20df.jpg)
+
+![](images/f446eb4225152364a096a181f1464f51327cc608605628e28236310c96cdbe4a.jpg)  
+Ours
+
+![](images/cd0de6d86362a5fa18e9385ccd15422ac54614390d4ab7ec8682c73ee8863a87.jpg)
+
+![](images/f2ac061c35fa60b0f87b0fb223d1065cf808553e8c4e96565f8bb564ea206bfa.jpg)
+
+![](images/1ae583bb3a87dcbd16e91e626ca5c29c9236a0d206d8a46b537de1b18d5eb1d4.jpg)
+
+![](images/964b0c392b24ab8509e4eaeeb90c3449626aa9910e7945c0e6981bc61f1c079d.jpg)
+
+![](images/1e00fcc6ec50608af2f4641d9ee6804db03edbd9f36657dea13c35cb78157725.jpg)  
+PHORHUM
+
+![](images/8c5920f736078ba8bc63186005d4bedecea707dd22e2bc532eb429d6c33ffd8e.jpg)
+
+![](images/cc7e1d9099b9174a99c2ac3d57a8518d4fd370fcd087890a32876bc2d53b6234.jpg)
+
+![](images/39bb2b5585ebbd15757b5ecbd220da8505d42aa5141e57c8a4c0a52d23f86a0b.jpg)
+
+![](images/208dab8bc67d85f3a927ccaa1a57637c436ee52f0d30e42e31b6b96ad1e42a62.jpg)
+
+![](images/7d0ed829c20412a073bdd09e851b60956f11e3e14aa9fb83ef930a400ff22c74.jpg)
+
+![](images/a95d4bd010c91addafda3846475302ee32d4172e6e61044918dd164d4b4da8b8.jpg)
+
+![](images/227939bc09641de63cfda27840ce207abcaf506027c3ad240eb91d9fee96c425.jpg)  
+PIFuHD
+
+only the front and back images, and another one additionally using the dense GHUM encodings. We then evaluate the Chamfer distance between each mesh and the corresponding GHUM mesh. The model using the additional GHUM signals has an average Chamfer distance of  $d_{\mathrm{with}} = 1.4$  whereas the one without  $d_{\mathrm{without}} = 8.6$ , thus validating our design choice. Not only is the control respected well, but this also allows for animation as discussed previously.
+
+Partial vs. Complete Network Finetuning. We finetune two Latent Diffusion networks, one in a standard way by optimizing all parameters, and another one using our proposed strategy where we only finetune the convolutional layers of the encoder. Empirically we observed that the network that was finetuned as a whole experienced catastrophic forgetting, and has poor performance when asked to generate types of garment not seen in the training set. Fig. 10 shows a comparison for text prompts not in the training set.
+
+# 5 Discussion & Conclusions
+
+Limitations. AvatarPopUp inherits limitations from other pixel-aligned methods, e.g. with regions parallel to camera rays being not as detailed in the reconstruction. Further, artifacts might be visible in poses or very loose clothing that are underrepresented during training.
+
+Ethical Considerations. We present a generative tool to create 3D human assets, thus reducing the risk of scanning and using real humans for training large scale 3D generative models. AvatarPopUp generates diverse results and can lead to a better coverage of subject distributions.
+
+![](images/644893664bb6a0e81b86e5f6ed2631977fd60acfe99dfcc4712156cb815c5dff.jpg)  
+Fig. 7: Additional comparisons with TeCH. TeCH is optimization-based and takes several hours to complete for a single reconstruction. Our results are obtained in seconds, yet are as detailed and even less noisy.
+
+![](images/1e5512458355ed8fa858558aa05d8784f3f158ff317bff63f0750b309f745733.jpg)  
+Ours
+
+![](images/add9dc208474d3fb82997f320290655b0af98f036ed2a320767ba0541b6c766f.jpg)  
+TeCH
+
+![](images/798f16ce9656d504b756b7a0d45247a153e8448229982b1f4b3b01101a7f5eeb.jpg)  
+Fig. 8: Reposing example.. We first reconstruct an avatar "wearing a gray suit" in the A-pose and then we transfer it to different poses.
+
+![](images/ca6e8a5633e19c806361af05dbdef45340e11facaea29dab86c9e17767da3fa7.jpg)  
+Fig. 9: Identity preserving 3D avatar editing. Our method allows for editing the clothing, while preserving the identity of the generated person. In each row we're using the image on the left as input, recover the person's pose and shape parameters and then run our method using the shown prompts. The generated avatars share the same identity and respect the target prompts.
+
+![](images/7fbc485cb9f842c8d7873adff5ae0bea9ddd8f3ed28deed93f6287a79c08f91e.jpg)  
+Fig. 10: Partial vs. complete fine-tuning strategy. For each text prompt the first example is generated using our partial fine-tuning strategy whereas the second by fine-tuning the entire network. Empirically, partial fine-tuning is more resilient to catastrophic forgetting, generating more diverse and better text-aligned images.
+
+We have presented AvatarPopUp, a novel framework for generating 3D human avatars controlled by text or images and yielding rigged 3D models in 2-10 seconds. AvatarPopUp is purely feed-forward, allows for fine-grained control over the generated body pose and shape, and can produce multiple qualitatively different hypotheses. AvatarPopUp is composed of a cascade of expert systems, decoupling image generation and 3D lifting. Through this design choice, AvatarPopUp benefits from both web-scale image datasets, ensuring high generation diversity, and from smaller size accurate 3D datasets, resulting in reconstructions with increased detail and precisely controlled based on text and identity specifications. In the future, we would like to explore other 3D construction strategies besides pixel-aligned features. Longer term, we aim to support highly detailed and controllable 3D human model generation for entertainment, education, architecture and art, or medical applications.
+
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+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
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+        "text": "Niki Amini-Naieni<sup>1</sup>, Tomas Jakab<sup>1</sup>, Andrea Vedaldi<sup>1</sup>, and Ronald Clark<sup>1</sup>",
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+        "text": "Abstract. Neural Radiance Fields (NeRFs) have markedly improved novel view synthesis, but accurate uncertainty quantification in their image predictions remains an open problem. The prevailing methods for estimating uncertainty, including the state-of-the-art Density-aware NeRF Ensembles (DANE) [29], quantify uncertainty without calibration. This frequently leads to over- or under-confidence in image predictions, which can undermine their real-world applications. In this paper, we propose a method which, for the first time, achieves calibrated uncertainties for NeRFs. To accomplish this, we overcome a significant challenge in adapting existing calibration techniques to NeRFs: a need to hold out ground truth images from the target scene, reducing the number of images left to train the NeRF. This issue is particularly problematic in sparse-view settings, where we can operate with as few as three images. To address this, we introduce the concept of a meta-calibrator that performs uncertainty calibration for NeRFs with a single forward pass without the need for holding out any images from the target scene. Our meta-calibrator is a neural network that takes as input the NeRF images and uncalibrated uncertainty maps and outputs a scene-specific calibration curve that corrects the NeRF's uncalibrated uncertainties. We show that the meta-calibrator can generalize on unseen scenes and achieves well-calibrated and state-of-the-art uncertainty for NeRFs, significantly beating DANE and other approaches. This opens opportunities to improve applications that rely on accurate NeRF uncertainty estimates such as next-best view planning and potentially more trustworthy image reconstruction for medical diagnosis.",
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+        "text": "Keywords: NeRFs  $\\cdot$  Uncertainty calibration  $\\cdot$  Few-shot learning",
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+        "text": "1 Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Recent advancements in scene representations have led to promising new approaches for novel view synthesis and scene reconstruction. Among these, Neural Radiance Fields (NeRFs) [16] have emerged as a particularly powerful tool, offering unprecedented levels of realism and detail in rendered images. The core idea behind NeRFs is to represent a scene as a continuous vector-valued function, parameterized by a neural network, that maps spatial coordinates and view directions to color and density values. This approach enables the creation",
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+        "img_path": "images/931aa5f9312feb8cc27913728d089273215c2cacdf110ac6aad8da7b08aa1d22.jpg",
+        "image_caption": [
+            "Fig. 1: We propose a method for efficiently calibrating the uncertainties from NeRF models. Our approach is based on a meta-calibrator that takes as input features from the rendered NeRF images and uncalibrated uncertainty maps and predicts the calibration function,  $R_{\\theta}(\\cdot)$ , for the NeRF model. Our meta-calibrator generalizes across scenes, so it only needs to be trained once, and can predict the calibration function in a single forward pass without any ground truth data from the target scene."
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+        "type": "text",
+        "text": "of detailed 3D representations from sets of 2D images, revolutionizing 3D reconstruction.",
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+        "text": "However, despite their impressive capabilities, traditional NeRF models lack an essential component: an accurate measure of uncertainty in their predictions. Accurate uncertainties are crucial for applying NeRFs to safety-critical problems such as MRI image reconstruction from sparse data [7], where unreliable confidence estimates could lead to misdiagnosis. More accurate uncertainties could also enhance practical methods such as uncertainty-guided next-best view planning techniques [9]. Prior approaches have attempted to estimate NeRF uncertainties [5, 14, 26, 27, 29], but they all overlook the problem of calibration. Thus, the uncertainties they output are not as accurate as they could be.",
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+        "type": "text",
+        "text": "In particular, the state-of-the-art uncertainty estimation method for NeRFs, Density-aware NeRF Ensembles (DANE) [29], produces uncalibrated uncertainties. As a result, the confidence intervals and variances do not match the true confidence, meaning it has limited applicability to real-world problems. This constraint is significant as it restricts the use of NeRFs in safety-critical and sparse-data settings, where knowing the confidence in predictions is crucial.",
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+    {
+        "type": "text",
+        "text": "The best NeRF methods for the sparse-view setting overlook the problem of calibration as well. FlipNeRF [24], the state-of-the-art technique for sparse-view reconstruction, uses uncertainties from an uncalibrated mixture of Laplacians to enhance its training process. Therefore, the uncertainties it outputs at inference as an artifact of training are not accurate.",
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+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In this paper, we present a novel approach for obtaining calibrated uncertainties for NeRF models in the sparse-view setting. Our strategy integrates the Laplacian mixture from FlipNeRF [24] with the calibration techniques by Kuleshov et al [12]. However, naively applying the calibration method by Kuleshov et al to FlipNeRF does not work due to a significant challenge of the sparse-view setting: there is a lack of held-out data from the target scene for fitting the calibrator. Specifically, holding out just one image for calibration could decrease the size of the training set by over  $30\\%$  , resulting in significant performance degradation of the NeRF. To overcome this, we make use of a unique observation: while calibration curves exhibit significant variation across scenes, they also demonstrate a significant regularity in their structure. Utilizing this insight, we propose the concept of a meta-calibrator that learns a low-dimensional representation of the NeRF calibration curves and infers them from scene features. We motivate and show why this meta-calibrator is necessary and demonstrate that it achieves more accurate uncertainties than DANE [29] without holding out any images from the target scene.",
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+    {
+        "type": "text",
+        "text": "Specifically, our contributions are: (1) the first investigation into obtaining calibrated uncertainties from NeRFs, (2) a novel meta-calibrator for fitting the calibration model without using held-out data, and (3) experiments on the real-world Local Light Field Fusion (LLFF) [15] and DTU [8] datasets showing that our meta-calibrator achieves state-of-the-art and well-calibrated uncertainties for real scenes. We also demonstrate that our uncertainties can be leveraged for effective next-best view planning.",
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+        "type": "text",
+        "text": "2 Related Work",
+        "text_level": 1,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Neural Radiance Fields (NeRFs). NeRFs [16] are a popular method for novel view synthesis. From a set of 2D images, NeRFs learn a neural network representation of a single scene. A trained NeRF model outputs estimates of the volume density and emitted radiance at any 3D location and viewing direction. Novel views can be generated by applying volume rendering [10] to the density and radiance values predicted by the NeRF model for points along rays cast into the scene. Due to their simplicity and impressive performance, NeRFs have become a popular technique for solving a variety of rendering problems.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Over the last few years, several extensions of NeRFs have been explored [11, 18, 21, 28, 31]. These include speeding up training and inference [13, 23, 30], modeling dynamic scenes [3], learning from a sparse set of training views [1, 6, 19, 24, 25], and estimating the uncertainty in NeRF predictions [5, 14, 22, 26, 27, 29]. Sparse NeRF methods aim to accurately render novel views when only a few training views are available from the target scene. NeRF uncertainty estimation techniques strive to accurately predict the confidence in the views rendered. Although uncertainty estimation is particularly important in the sparse-view",
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+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "3",
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+    {
+        "type": "text",
+        "text": "setting, where NeRF renderings are especially unreliable, the main aim of sparse NeRF methods is not to output accurate uncertainties.",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Sparse-view NeRF Methods. Despite this, recent sparse NeRF methods do produce uncertainties as an artifact of their training process. Both MixNeRF [25] and FlipNeRF [24], the state-of-the-art approach, model the RGB color channels given a ray as independent random variables that follow a mixture model. FlipNeRF further uses the uncertainties of the pixel colors to regularize the training process, producing more accurate image reconstructions at inference. However, neither MixNeRF nor FlipNeRF outputs calibrated uncertainties.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our method significantly extends sparse NeRF methods to obtain more accurate and well-calibrated uncertainties at inference. To benefit from the superior performance of FlipNeRF [24] at sparse novel view synthesis, we apply the proposed meta-calibrator to the learned distribution from FlipNeRF, producing more accurate uncertainties without sacrificing state-of-the-art image quality. However, our approach can be applied to any NeRF method that outputs uncertainties, so it is distinct from FlipNeRF and MixNeRF. In essence, the proposed meta-calibrator augments sparse NeRF methods to achieve state-of-the-art uncertainty, beating both FlipNeRF and techniques designed explicitly for NeRF uncertainty estimation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Uncertainty in NeRFs. The growing line of methods specifically designed for accurately estimating NeRF uncertainties [5,14,22,26,27,29] do not address the problem of calibration. The current state-of-the-art uncertainty estimation technique for NeRFs is Density-aware NeRF Ensembles (DANE) [29]. DANE adds an epistemic uncertainty term to a naive ensembles approach with five ensemble members. Thus, DANE is very costly as it requires training five NeRFs to obtain uncertainty estimates. Another NeRF uncertainty estimation approach is Stochastic Neural Radiance Fields (S-NeRF) [27], which learns a probability distribution over all possible radiance fields by modeling the volume density and radiance as random variables that follow a joint distribution. S-NeRF employs variational inference to sample from an approximation to this distribution and uses the variances of the sampled pixel colors as the estimated uncertainties. Conditional-flow NeRF (CF-NeRF) [26] builds on S-NeRF by combining latent variable modeling and conditional normalizing flows to relax the strong constraints S-NeRF imposes over the radiance distribution. Despite the growing number of techniques in this area of study, all prior work does not consider calibration, outputting unreliable uncertainties as a result. Our work achieves more accurate uncertainties than these prior methods by filling the gap of uncertainty calibration for NeRFs and drawing on well-established techniques in calibrated regression [12].",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Uncertainty Calibration in Deep Learning. While uncertainty calibration has been studied for Bayesian deep learning methods [4, 12], it has not been adapted for or applied successfully to NeRF uncertainty estimates. This may be",
+        "bbox": [
+            215,
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
+            217,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
+            271,
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+            127
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "because NeRFs introduce additional complexity in the uncertainty estimation process as the neural network model needs to be trained per-scene.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This makes uncertainty calibration challenging as methods for calibrated regression [12] require either using the training set or held-out data to achieve calibrated uncertainties. Using the training set to fit the calibrator results in severe overfitting (see Sec. 2 of the Supplementary). Holding out data from the target scene for calibration means there is less data to train the NeRF, making it more inaccurate at novel view synthesis (see Sec. 3 of the Supplementary). Thus, a trivial application of [12] to NeRFs would not be satisfactory. In this work, we propose the concept of a meta-calibrator that, in contrast to [12], does not require held-out data and achieves calibrated uncertainty estimates for NeRFs.",
+        "bbox": [
+            212,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3 Method",
+        "text_level": 1,
+        "bbox": [
+            215,
+            351,
+            330,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present a method that calibrates NeRF uncertainties. To this end, we propose a novel meta-calibrator that accepts uncalibrated NeRF uncertainties and predicted images as inputs and outputs a scene-specific calibration curve, correcting the uncalibrated confidence levels. An overview of our method can be seen in Fig. 1. Crucially, our approach does not require holding out any images from the target scene. Thus, it can be applied to sparse-view settings, where holding out a single image could significantly harm the NeRF's performance. In Sec. 3.1, we explain the necessary background concepts, in Sec. 3.2, we describe how we obtain the corrected uncertainty values, and in Sec. 3.3 we detail our meta-calibrator.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1 Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Neural Radiance Fields (NeRFs). Neural Radiance Fields (NeRFs) [16] represent a scene as a continuous vector-valued function with inputs a Cartesian point  $\\mathbf{x} = (x,y,z)$  and unit viewing direction vector  $\\mathbf{d} = (u,v,w)$  and outputs an emitted radiance  $\\pmb {c} = (\\nu ,\\varrho ,\\theta)$  and volume density  $\\sigma$  . By optimizing the weights  $\\Theta$  of a neural network approximation  $\\mathbf{F}_{\\Theta}$  to this representation, NeRFs can render the color of any pixel in a synthetic image of the scene. To achieve this, principles from classical volume rendering [10] are applied to the radiance and density values estimated by  $\\mathbf{F}_{\\Theta}$  for points along a ray cast from the origin  $\\mathbf{x_0}$  of the virtual camera, through the pixel, and into the scene. More specifically, the expected color  $\\mathbf{c}(\\mathbf{r})$  of a camera ray  $\\mathbf{r}(t) = \\mathbf{x_0} + t\\mathbf{d}$  with near and far bounds  $t_n$  and  $t_f$  is:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {c} (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (\\mathbf {r} (t)) \\boldsymbol {c} (\\mathbf {r} (t), \\mathbf {d}) d t, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            375,
+            750,
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+            785
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $T(t) = e^{-\\int_{t_n}^t \\sigma(\\mathbf{r}(s)) ds}$ . The integral in Eq. (1) is estimated with numerical quadrature to obtain the colors of the pixels in the synthetic image from the NeRF model outputs. NeRF optimizes  $\\Theta$  according to Eq. (1) with gradient",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
+        "bbox": [
+            285,
+            114,
+            730,
+            128
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "descent, since the numerical quadrature is differentiable. Conventional NeRFs do not provide an uncertainty associated with their predictions, so extensions like DANE [29] have been developed.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Base NeRF Uncertainties. To obtain the initial uncertainties, we have two options for our base model: (1) DANE [29], the state-of-the-art method for NeRF uncertainty estimation or (2) FlipNeRF [24], the state-of-the-art method for sparse novel view synthesis. DANE requires training five NeRFs per scene and provides poor image quality in the sparse-view setting, so we choose FlipNeRF. We show in the experiments that applying our meta-calibrator to FlipNeRF results in more accurate and well-calibrated uncertainties than those output by DANE. Our base FlipNeRF uncertainties are inferred from a mixture of Laplacians with location and scale parameters learned during training.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "FlipNeRF [24] models the joint distribution of the color  $\\mathbf{C} = (R,G,B)$  given a ray  $\\mathbf{r}$  with a mixture of Laplacians:",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (\\mathbf {C} = \\mathbf {c} | \\mathbf {r}) = \\sum_ {j = 1} ^ {M} \\pi_ {j} \\mathcal {F} (\\mathbf {C} = \\mathbf {c}; \\boldsymbol {\\mu} _ {j}, \\boldsymbol {\\beta} _ {j}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            366,
+            396,
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+            436
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $M$  is the number of sampled points along the ray  $r$ .  $\\mathcal{F}(\\mathbf{C} = \\mathbf{c};\\pmb{\\mu}_j,\\pmb{\\beta}_j)$  is the 3D Laplacian probability density with location parameter  $\\pmb{\\mu}_{j} = (\\mu_{j}^{R},\\mu_{j}^{G},\\mu_{j}^{B})$  and scale parameter  $\\beta_{i} = (\\beta_{j}^{R},\\beta_{j}^{G},\\beta_{j}^{B})$  evaluated at the color  $\\mathbf{c}$ . More specifically, the mixing coefficients  $\\{\\pi_j\\}_{j = 1}^M$  are the normalized coefficients of the radiance values along a ray in Eq. (2), the location parameters  $\\{\\pmb{\\mu}_{j}\\}_{j = 1}^{M}$  are the estimated RGB radiance values, and the scale parameters  $\\{\\pmb{\\beta}_{j}\\}_{j = 1}^{M}$  are an additional output of the model. These parameters are optimized by FlipNeRF during training.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We now go into detail about how the location and scale parameters are obtained. FlipNeRF [24] learns these parameters by minimizing the negative log-likelihood of the training set  $\\mathcal{D} = \\{(\\mathbf{r_i},\\mathbf{c_i})\\}_{i = 1}^N$  containing the rays  $\\mathbf{r_i}$  and colors  $\\mathbf{c_i}$  from the pixels in the ground truth images of the scene assuming the distribution in Eq. (2). FlipNeRF additionally minimizes the average scale parameters through an auxiliary uncertainty-aware emptiness loss for reducing floating artifacts. The negative log-likelihood loss and the uncertainty-aware emptiness loss are added to FlipNeRF's total training loss, which incorporates other terms such as the mean squared error. As a result of this training process, the location and scale parameters can be inferred by FlipNeRF at new poses. We obtain the uncalibrated confidence levels of predicted ray colors from these location and scale parameters.",
+        "bbox": [
+            212,
+            568,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Using the distribution in Eq. (2), we can easily compute the confidence level for a given ray  $\\mathbf{r_t}$ , which we denote as  $F_{t}$ . The CDF for the Laplacian mixture has a closed form expression parameterized by the location and scales output by the pretrained FlipNeRF [24]. Thus, we can use this CDF to predict the confidence level of the ground truth color  $\\mathbf{c_t}$  of any ray by evaluating it at the given",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
+            217,
+            114,
+            228,
+            126
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
+            271,
+            114,
+            421,
+            127
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "color value,  $p_t = F_t(\\mathbf{c_t})$ . However, these initial confidence levels are uncalibrated and, hence, inaccurate.",
+        "bbox": [
+            212,
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+            782,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Calibrated regression. In [12], Kuleshov et al extend calibration methods for classification to regression. They define a forecaster  $H: \\mathcal{X} \\to (\\mathcal{Y} \\to [0,1])$  as a function that outputs for each  $x_{t} \\in \\mathcal{X}$ , a CDF  $F_{t}$ . Given a pretrained forecaster  $H$ , they suggest training an auxiliary model  $R: [0,1] \\to [0,1]$  by fitting  $R$  to a recalibration dataset  $D = \\left\\{\\left([H(x_{t})](y_{t}), \\hat{P}([H(x_{t})](y_{t}))\\right)\\right\\}_{t=1}^{T}$ , where",
+        "bbox": [
+            212,
+            203,
+            784,
+            292
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {P} (p) = \\left| \\left\\{y _ {t}: [ H \\left(x _ {t}\\right) ] \\left(y _ {t}\\right) \\leq p \\text {f o r} t = 1, \\dots , T \\right\\} \\right| / T\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            326,
+            301,
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+            318
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "is the empirical confidence level corresponding to the predicted confidence level  $p$ . The fitted  $R$  forms the calibration curve that corrects the expected confidence levels. We can now obtain predictive posterior values that closely match the true confidences using  $\\hat{F}_t \\equiv R \\circ F_t$  for the test data.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "However, as mentioned before, there are numerous challenges associated with applying this recalibration procedure. Firstly, note that it requires ground-truth values  $(y_{t})$  for the predictions we are recalibrating. This means that in order to prevent overfitting we need to reserve part of the training dataset specifically for fitting the calibrator (which leaves less data for training the NeRF — a significant issue if we only have a few input views). Secondly, it does not actually prescribe how to compute a suitable uncertainty value from the predicted distribution. In Sec. 3.3, we address the former issue, and in Sec. 3.2, we address the latter.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.2 Calculating uncertainty",
+        "text_level": 1,
+        "bbox": [
+            214,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The predictive posterior in Eq. (2) provides a distribution over likely ray colors for a NeRF model, but it does not inherently offer a straightforward metric for quantifying uncertainty at a specific point in the reconstruction. Intuitively, as the variance of this distribution increases, so does the uncertainty of the model's output at that point. Therefore, the variance or standard deviation is a popular choice for quantifying the uncertainty [24,26,27,29]. However, in the case of the corrected mixture distribution obtained from raymarching, this can be slow to compute especially if it has to be done for each pixel. Therefore, we turn to a metric that can be calculated directly from the calibrated CDF  $\\hat{F}^t$ .",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We propose to use the interquartile range of each calibrated distribution:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\kappa^ {C} \\left(\\mathbf {r} _ {\\mathbf {t}}\\right) = \\left[ \\hat {F} _ {t} ^ {C} \\right] ^ {- 1} \\left(\\frac {3}{4}\\right) - \\left[ \\hat {F} _ {t} ^ {C} \\right] ^ {- 1} \\left(\\frac {1}{4}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            768,
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+            801
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $\\kappa^C (\\mathbf{r_t})$  represents the uncertainty at a ray  $\\mathbf{r_t}$  in the color channel  $C$ . This difference provides a measure of the statistical dispersion and thus serves",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
+        "bbox": [
+            285,
+            114,
+            730,
+            127
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d4266a2b88d6ec9833101b28ab0e4ae1b897b32bf656aaae7ef21df07d7cbd39.jpg",
+        "image_caption": [
+            "(a) Creating a parametric model of the calibration curves."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            233,
+            145,
+            491,
+            258
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/fc20e2f750952699e6d84c4ea763729a17e3d80e0cab4ff95679774442b6f859.jpg",
+        "image_caption": [
+            "(b) Predicting the curve parameters.",
+            "Fig. 2: Meta-calibrator design. In stage (a) we fit a low-dimensional parametric model of the calibration curves. The meta-calibrator then predicts these curve parameters from rendered images of the scene and their associated uncalibrated uncertainty maps (b)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "as a robust measure of the spread of the output channel. By averaging the interquartile range over the color channels, we obtain a single scalar value that effectively quantifies the uncertainty of the NeRF model for the given ray. As shown in our experiments, this method is very computational efficient, and it provides an accurate estimate of uncertainty.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.3 Meta-calibrator",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To overcome the challenge that, especially in the sparse-view setting, there is no held-out data available for fitting the calibrator, we propose a novel metacalibrator that infers the calibration curves from uncalibrated NeRF predictions. To do this, we leverage the insight that the calibration curves demonstrate significant regularity. We posit a low-dimensional model of the calibration curves can be learned and predicted using the images and uncalibrated uncertainty maps inferred by the NeRF, enabling us to estimate the calibration function without evaluating the empirical confidence levels using held-out data from the target scene. We now describe this meta-calibrator (illustrated in Fig. 2) in detail.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "A Parametric Model for Calibration Curves. We first fit a low-dimensional representation of the calibration curves using Principal Component Analysis (PCA). To create the training set for learning this representation, we sample held-out images from  $K$  scenes and apply the calibration procedure by Kuleshov et al. [12] to form  $K$  ground truth calibration curves. To construct the training vector  $\\mathbf{v_k} \\in \\mathbb{R}^{1 \\times M}$  for scene  $k \\leq K$ , we sample  $M$  evenly spaced points along its ground truth calibration curve. We find that fitting the PCA model using only a few scenes (21 in our case) provides a good enough approximation to capture the variation in the test curves (see Sec. 4). Here,  $\\mathbf{V} = [\\mathbf{v}_k] \\in \\mathbb{R}^{K \\times M}$  contains the ground truth calibration curves for the training scenes, with  $K$  representing the number of curves and  $M$  the sample count along each curve. PCA is then used to determine the basis vectors  $\\mathbf{U} = (\\mathbf{u_1}, \\mathbf{u_2}, \\dots, \\mathbf{u_n})$  and coefficients  $\\theta = (\\alpha_1, \\alpha_2, \\dots, \\alpha_n)$ , so that each calibration curve can be represented as:",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
+            217,
+            114,
+            227,
+            126
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
+            271,
+            114,
+            421,
+            127
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "$\\mathbf{v}_k = \\sum_{i=1}^n \\alpha_i \\mathbf{u}_i$ . The parameters  $\\theta$  fully describe the calibration functions.",
+        "bbox": [
+            212,
+            145,
+            753,
+            162
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To find the optimal number of components, we compute the explained variance, and find that in our case most of the variance is explained using only  $n = 3$  components (see experiments). To ensure the calibrator is monotonically increasing, we derive the final calibration function  $R_{\\theta}(\\cdot)$  using isotonic regression applied to the curve approximated by  $\\pmb{\\theta} \\cdot \\mathbf{U}$ . The idea is that the low-dimensional representation of the calibration curves encoded in  $\\mathbf{U}$  will generalise to new target scenes without any additional scene-specific data.",
+        "bbox": [
+            212,
+            176,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Predicting Calibration Parameters. What remains is to estimate the calibration parameters,  $\\theta$ , for a new scene. As we do not want to use additional held-out data from the target scene, we propose predicting these parameters using scene-specific features computed from the pretrained NeRF outputs. This approach is motivated by the human ability to visually identify inaccuracies in the renderings such as floaters and unnatural artifacts. Specifically, we use a Multi-Layer Perceptron (MLP) with three layers of output size: [128, 128, 3] and Leaky ReLU activations throughout except the last layer as the meta-calibrator to estimate  $\\theta$  given features extracted by the DINOv2 model [20] from rendered images  $(\\mathbf{f}_I)$  and uncalibrated uncertainty maps  $(\\mathbf{f}_{\\kappa})$ . The goal here is to have DINOv2 extract features that describe the rendering imperfections, correlating with the calibration curve. We find that training the MLP model on only a few scenes (30 in our case) allows it to generalize well to new test scenes. Once trained, the meta-calibrator can predict the calibration curve of a new target scene as:  $\\theta = MLP([\\mathbf{f}_I,\\mathbf{f}_{\\kappa}])$ , without using any additional ground truth data.",
+        "bbox": [
+            212,
+            297,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In summary, the meta-calibrator can correct the confidence levels of the model without requiring ground truth data at any stage, suggesting potential enhancements to applications that rely on uncertainty such as next-best view selection (see Sec. 4.3).",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments",
+        "text_level": 1,
+        "bbox": [
+            214,
+            625,
+            375,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The objective of the experiments is to: 1) validate that our approach achieves more accurate uncertainties (lower negative log-likelihood and calibration error) than state-of-the-art approaches for NeRF uncertainty estimation (Sec. 4.1); 2) demonstrate the meta-calibrator improves the accuracy of the uncalibrated uncertainties (decreases both the negative log-likelihood and calibration error) without requiring any held-out data from the target scene (Sec. 4.2); 3) explain the motivation for certain meta-calibrator design decisions; and 4) show that our uncertainties can be leveraged for applications such as next-best view planning (Sec. 4.3).",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "For additional results showing: 1) why the PCA representation of the calibration curves is necessary; 2) that using the training set results in severe overfitting; 3) that holding out data results in poor performance at image reconstruction; 4)",
+        "bbox": [
+            212,
+            794,
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+            842
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
+        "bbox": [
+            285,
+            114,
+            730,
+            128
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            774,
+            114,
+            784,
+            126
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "the influence of the number of samples along the ray on the uncertainty quality; and 5) the efficiency of our uncertainty metric (Eq. (3)) over other approaches, please refer to Sections 1, 2, 3, 4, and 6 of the Supplementary respectively.",
+        "bbox": [
+            212,
+            146,
+            782,
+            191
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Metrics and calibration curves. We use a variant of the calibration error from [12] to evaluate the effectiveness of the meta-calibrator. Specifically, given a test set  $\\mathcal{D} = \\{(\\mathbf{r_t},\\mathbf{c_t})\\}_{t = 1}^T = \\{(\\mathbf{r_t},(r_t,g_t,b_t))\\}_{t = 1}^T$ , we report:",
+        "bbox": [
+            212,
+            203,
+            784,
+            250
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nE R R = \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\left(p _ {t} - \\hat {P} \\left(p _ {t}\\right)\\right) ^ {2}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            398,
+            260,
+            784,
+            299
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "where  $p_t$  is the expected confidence level for data point  $(\\mathbf{r_t}, c_t)$ , and  $\\hat{P}(p_t)$  is the empirical frequency of data points within that confidence level. More specifically, for each  $t \\in \\{1, \\dots, T\\}$ , we set  $p_t = M_t^C(c_t)$  and,",
+        "bbox": [
+            212,
+            306,
+            782,
+            354
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {P} (p) = \\left| \\left\\{c _ {t}: M _ {t} ^ {C} \\left(c _ {t}\\right) \\leq p \\text {f o r} t = 1, \\dots , T \\right\\} \\right| / T, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            357,
+            784,
+            377
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "where  $M \\equiv F$  for uncalibrated errors and  $M \\equiv \\hat{F}$  for calibrated errors, and  $C \\in \\{R, G, B\\}$ . Note that this formulation of the calibration error is equivalent to the one in [12] with a confidence level for every unique  $p_t$  and weights that more significantly penalize errors from frequently predicted confidence levels.",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Following [12], we plot  $\\{(p_t, \\hat{P}(p_t))\\}_{t=1}^T$  before and after calibration for each color channel to generate calibration curves. A perfectly calibrated forecaster would produce the straight line  $p_t = \\hat{P}(p_t)$  as each expected confidence level would equal the empirical one. Intuitively, our version of the calibration error is the mean squared vertical distance of points on the calibration curve from a perfectly straight line. If an expected confidence level occurs  $N$  times in the test data, its distance is counted  $N$  times in the mean. Following [29], we additionally report the negative log-likelihood (NLL) of the test data averaged across all scenes. Following [24], we include PSNR and LPIPS [32] to evaluate image quality.",
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+    {
+        "type": "text",
+        "text": "Datasets. We use 30 scenes from 3 datasets: Realistic Synthetic  $360^{\\circ}$  [16], the subset of scenes in DTU [8] used in [24], and LLFF [15] for training the metacalibrator and test it on a hold-out scene from either LLFF or DTU to show it generalizes to new target scenes.",
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+    {
+        "type": "text",
+        "text": "Baselines We compare our approach against the state-of-the-art method for NeRF uncertainty estimation DANE [29] as well as other methods in Sec. 4.1. In Tab. 1, following [29], we implement the naive ensembles approach and DANE using a public implementation of Instant-NGP [2,17] and 5 ensemble members. In Sec. 4.2, we compare the uncalibrated uncertainties to the uncertainties calibrated by our meta-calibrator.",
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+    {
+        "type": "text",
+        "text": "Meta-calibrator Design The results guiding our decisions to use 3 Principal Component Analysis (PCA) components to represent the calibration curves, fit the PCA components using 21 training scenes, and train the meta-calibrator on 30 scenes to predict the PCA coefficients are shown in Fig. 3.",
+        "bbox": [
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+        "type": "page_number",
+        "text": "10",
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+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
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+    },
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+        "image_caption": [
+            "(a) Explained variance plot showing most of the variance of the calibration curves is explained using only 3 PCA components."
+        ],
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+        "image_caption": [
+            "(b) Graph showing calibration error on new scenes is sufficiently low when using 21 scenes to fit 3-coefficient PCA model (i.e. it's an order of magnitude lower than we can expect from the final calibration, meaning good generalization to unseen scenes)."
+        ],
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+        "image_caption": [
+            "(c) Graph showing increasing number of training scenes for meta-calibrator decreases calibration error for the test scene  $T$ -Rex from LLFF [15], with 30 scenes resulting in good generalization to the held-out scene and well-calibrated uncertainties.",
+            "Fig. 3: Meta-calibrator design decisions. Results showing using 3 components for Principal Component Analysis (PCA) model of calibration curves, 21 scenes to fit PCA model, and 30 scenes to train meta-calibrator achieves good generalization to new test scenes."
+        ],
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+        "img_path": "images/052d8564e43b4738dc859bb16c4b5211d53dd8da70521e6538e95c5ad13b0592.jpg",
+        "table_caption": [
+            "Table 1: Quantitative results on standard sparse NeRF benchmark. Our proposed approach results in significantly better uncertainties and image quality than the state-of-the-art NeRF uncertainty estimation method DANE [29] does on the challenging 3-view LLFF [15] dataset. Specifically, our meta-calibrator reduces the calibration error to  $6\\%$  of DANE's calibration error and the negative log-likelihood to be over 100  $\\%$  lower than DANE's. Note: lower calibration error (Cal. Err.) and negative log-likelihood (NLL) values indicate more accurate uncertainties. Results are averaged over all 8 scenes in LLFF."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">Uncert ainty</td><td>Image</td><td>Quality</td></tr><tr><td>Cal. Err. (↓)</td><td>NLL (↓)</td><td>PSNR (↑)</td><td>LPIPS (↓)</td></tr><tr><td>Naïve Ens.</td><td>0.0505</td><td>4.39</td><td>15.19</td><td>0.646</td></tr><tr><td>DANE [29]</td><td>0.0441</td><td>3.75</td><td>15.19</td><td>0.646</td></tr><tr><td>Ours</td><td>0.0026</td><td>-0.68</td><td>19.34</td><td>0.235</td></tr></table>",
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+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
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+    {
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+        "text": "11",
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+    {
+        "type": "text",
+        "text": "4.1 Comparison to State-of-the-art",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we compare our approach to prior methods for NeRF uncertainty estimation. We achieve more accurate uncertainties (94% reduction in calibration error and over 100% reduction in negative log-likelihood) than those estimated by DANE [29], the state-of-the-art method. These results are shown in Tab. 1 for the challenging 3-view LLFF [15] dataset from prior work on sparse novel view synthesis [19,24,25] and Tab. 2 for the less challenging version of LLFF from prior work on NeRF uncertainty estimation [14,26,27,29]. In Fig. 5a, we compare the calibration curves from our approach to DANE's, illustrating that the meta-calibrator predicts expected confidences that match the true ones while DANE does not.",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/4d7c7acee6cd8b344d416a7a078bafb068672e896c6b653369c89db8153bef5a.jpg",
+        "image_caption": [
+            "Fig. 4: Quantitative comparison of uncalibrated and calibrated uncertainties. In (a), we show calibration curves on test data from four scenes in LLFF [15]. The color of each curve indicates the color channel it corresponds to. The calibrated curves are much closer to the ideal calibration (dashed lines), demonstrating that the meta-calibrator works very well. In (b), the average calibration error and negative log-likelihood before and after calibration are reported for LLFF, clearly showing the meta-calibrator improves the accuracy of the uncertainties (lowering calibration error and negative log-likelihood). To test generalization, the meta-calibrator was also applied to held-out scenes in DTU [8], achieving a  $70\\%$  reduction in calibration error on average."
+        ],
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+    {
+        "type": "text",
+        "text": "4.2 Comparison to Uncalibrated Uncertainties",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we compare our uncalibrated base NeRF uncertainties to our calibrated uncertainties obtained from applying the proposed meta-calibrator. In Fig. 6 we show that the calibrated uncertainties better highlight floaters and other errors in the NeRF renderings. In Fig. 4, we show that the meta-calibrator predicts expected confidence that closely match the true ones, lowering both the calibration error and the negative log-likelihood of the uncalibrated uncertainties.",
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+    {
+        "type": "page_number",
+        "text": "12",
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+    },
+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/98b0e41a417b73ed8991fc2a21a635878910fca5ab3c73964ffc0bec10abf746.jpg",
+        "table_caption": [
+            "Table 2: Quantitative results on standard NeRF uncertainty estimation benchmark. Here, we present results on the LLFF [15] dataset used in prior work [14, 26, 27, 29] on uncertainty estimation for NeRFs. This dataset is less challenging than the one in Tab. 1 since 4-12 views are used for training instead of 3. Our proposed approach results in significantly better uncertainties than prior methods for NeRF uncertainty estimation on all 8 scenes in LLFF. Note: lower negative log-likelihood values indicate more accurate uncertainties.  $M$  indicates the number of ensemble members, and MC-DO refers to Monte Carlo Dropout sampling with  $M$  sample configurations. This table is Tab. 1 from [29] with our results added as an additional column. Please refer to [29] for further details."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Scene</td><td rowspan=\"2\"># of Train. Views</td><td colspan=\"8\">Negative Log-likelihood (↓)</td></tr><tr><td>MC-DO M=5</td><td>Naïve Ens. M=5</td><td>NeRF-W [14]</td><td>S-NeRF [27]</td><td>CF-NeRF [26]</td><td>DANE [29] M=5</td><td>DANE [29] M=10</td><td>Ours</td></tr><tr><td>Fern</td><td>4</td><td>4.90</td><td>2.47</td><td>2.16</td><td>2.01</td><td>—</td><td>-0.98</td><td>-1.00</td><td>-1.41</td></tr><tr><td>Orchids</td><td>5</td><td>5.74</td><td>2.23</td><td>2.24</td><td>1.95</td><td>—</td><td>-0.28</td><td>-0.31</td><td>-0.84</td></tr><tr><td>Leaves</td><td>5</td><td>2.72</td><td>2.66</td><td>0.79</td><td>0.68</td><td>—</td><td>0.97</td><td>0.73</td><td>-1.19</td></tr><tr><td>Flower</td><td>7</td><td>4.63</td><td>1.63</td><td>1.71</td><td>1.27</td><td>—</td><td>1.00</td><td>0.85</td><td>-2.05</td></tr><tr><td>Fortress</td><td>8</td><td>5.19</td><td>2.29</td><td>1.04</td><td>-0.03</td><td>—</td><td>-1.30</td><td>-1.30</td><td>-1.99</td></tr><tr><td>Room</td><td>8</td><td>5.06</td><td>2.13</td><td>4.93</td><td>2.35</td><td>—</td><td>-1.35</td><td>-1.35</td><td>-2.17</td></tr><tr><td>T-Rex</td><td>11</td><td>4.10</td><td>2.28</td><td>1.91</td><td>1.37</td><td>—</td><td>-0.31</td><td>-0.69</td><td>-1.49</td></tr><tr><td>Horns</td><td>12</td><td>4.18</td><td>2.17</td><td>0.78</td><td>0.60</td><td>—</td><td>-0.55</td><td>-0.66</td><td>-2.18</td></tr><tr><td colspan=\"2\">Avg.</td><td>4.57</td><td>2.23</td><td>1.95</td><td>1.27</td><td>0.57</td><td>-0.35</td><td>-0.47</td><td>-1.67</td></tr></table>",
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+    {
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+        "img_path": "images/2d07211d4bd062480b310d0bdf06858042dc99302597f89c54a366456d60b3c2.jpg",
+        "image_caption": [
+            "(a) Calibration curves for the Fern scene from 3-view LLFF [15]."
+        ],
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+    {
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+        "img_path": "images/e3e883abb1668e94b629fb55e7d1037e931ef4f52c6da77c20f6d51dbe06af47.jpg",
+        "image_caption": [
+            "(b) Next-best View Planning on Horns from LLFF [15].",
+            "Fig. 5: Comparison to DANE [29]. Results comparing our uncertainties to those from the state-of-the-art method DANE. In (a) we show DANE's RGB calibration curves are not closely aligned with the perfectly calibrated lines, meaning it is miscalibrated. It is significantly over-confident for expected confidence levels close to 1 and under-confident for confidence levels close to 0. In comparison, the curves for our approach are extremely close to the ideal calibration (dashed lines), demonstrating that the meta-calibrator works very well, predicting expected confidences that match the true ones. This is also verified by how our calibration error is over two orders of magnitude smaller than DANE's. In (b) we show that our approach results in more efficient performance gains over DANE for next-best view planning."
+        ],
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+    {
+        "type": "header",
+        "text": "Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator",
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+        "text": "13",
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+        "page_idx": 12
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+    {
+        "type": "image",
+        "img_path": "images/772e986f14d98b9828f9bfaedd02765dd81cdf962ac1fb0f1f0b7934a7d90052.jpg",
+        "image_caption": [
+            "(a) Ground Truth",
+            "Fig. 6: Qualitative comparison of uncalibrated and calibrated uncertainties from the Flower scene in LLFF [15]. The calibrated uncertainties (d) clearly detect incorrect regions (indicated by the red boxes) better than the uncalibrated uncertainties (c) do. This is apparent by noting that (d) and (e) look more similar than (c) and (e)."
+        ],
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+    },
+    {
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+        "img_path": "images/0396d509886d8986cbbb310048ba4947368c50a9cd34d677c2dc8b942ce16e40.jpg",
+        "image_caption": [
+            "(b) NeRF Image"
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+    {
+        "type": "image",
+        "img_path": "images/81cdbc67aa61107e29a81b8c38c286f8543e19698907e8ecf1aec0fba758f609.jpg",
+        "image_caption": [
+            "(c) Uncalibrated Uncertainty"
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ca22ab0ca68246f8540977f906d1c3eb9e1c771bafb219b95e24638c50cc8fae.jpg",
+        "image_caption": [
+            "(d) Calibrated Uncertainty"
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+    },
+    {
+        "type": "image",
+        "img_path": "images/0c476a28b0a02923fae760d9da2b1a27895cd36bf62cc1fb6f6d757335777f28.jpg",
+        "image_caption": [
+            "(e) Actual Error"
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+    {
+        "type": "text",
+        "text": "4.3 Application: Next-best View Planning",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we show that our uncertainties can be leveraged for next-best view planning. Specifically, we start by training the NeRF model for 2000 iterations on a training set of three images. The next-best view is selected by evaluating the average calibrated pixel uncertainty (obtained using the meta-calibrator) for each of the candidate views, and the view with the highest uncertainty is added to the training set. The average PSNR of the test images is reported after each training iteration. In Fig. 5b we show that using our approach results in greater performance gains (higher PSNRs) than DANE [29] does. In the Fig. 1 of the Supplementary, we also compare the information gain from rays selected according to the highest calibrated uncertainties to the information gain from rays selected according to the highest uncalibrated uncertainties and show our meta-calibrator produces higher average PSNRs on the test set for scenes in DTU [8] than the uncalibrated uncertainties do. Thus, calibration specifically re-orders the pixel uncertainties so that rays more likely to raise the PSNR are picked earlier in next-best view planning. In Sec. 5 of the Supplementary, we include a detailed theoretical example showing that such re-ordering is possible.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 Conclusion",
+        "text_level": 1,
+        "bbox": [
+            214,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In this paper we addressed the open problem of obtaining calibrated uncertainties from NeRF models. We introduce the concept of a meta-calibrator that infers the calibration curves from scene features, and using this approach achieve state-of-the-art uncertainty without holding out any ground truth data from the target scene. By enabling efficient and accurate calibration of NeRF models without relying on additional data, our method represents a significant step forward in the practical application of NeRF to real-world scenarios and opens up new avenues for the use of NeRF in situations where data is limited and uncertainty is critical.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "14",
+        "bbox": [
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+        "page_idx": 13
+    },
+    {
+        "type": "header",
+        "text": "N. Amini-Naieni et al.",
+        "bbox": [
+            271,
+            114,
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+            127
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. The authors would like to thank Seunghyeon Seo for his support on FlipNeRF, and Oishi Deb for her insightful feedback on uncertainty estimation. Niki Amini-Naieni is funded by an AWS Studentship, the Reuben Foundation, and the AIMS CDT program at the University of Oxford. Tomas Jakab is sponsored by EPSRC VisualAI EP/T028572/1 and Andrea Vedaldi by ERC-CoG UNION 101001212.",
+        "bbox": [
+            212,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            215,
+            261,
+            321,
+            277
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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