Add Batch 106b4e8e-0db4-47d6-9274-55b7374c9313 data

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@@ -7335,3 +7335,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_content_list.json

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+        "text": "Sheng Xu $^{1\\dagger}$ , Yanjing Li $^{1\\dagger}$ , Mingbao Lin $^{3}$ , Peng Gao $^{4}$ , Guodong Guo $^{5}$ , Jinhu Lu $^{1,2}$ , Baochang Zhang $^{1,2*}$ $^{1}$  Beihang University  \n $^{2}$  Zhongguancun Laboratory  \n $^{3}$  Tencent  \n $^{4}$  Shanghai AI Laboratory  \n $^{5}$  UNIUBI Research, Universal Ubiquitous Co.",
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+        "text": "The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by  $6.6\\times$  and achieve  $39.4\\%$  AP, with only  $2.6\\%$  performance gaps than its real-valued counterpart on the COCO dataset<sup>1</sup>.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem.",
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+        "img_path": "images/8156cf2f15f19b131f79b7183987c36c7b62f255802f7021454e16e457f5de81.jpg",
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+        "type": "image",
+        "img_path": "images/3adddb20ddfb6562d837c9002e09030289bca8f8a4171abca63cc56fc35c6e37.jpg",
+        "image_caption": [
+            "(b) 4-bit DETR-R50"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/43ddb4a0e46f89a0a644c9d7bacbd5db54540eea7587e8f33923960758423819.jpg",
+        "image_caption": [
+            "Figure 1. The histogram of query values  $\\mathbf{q}$  (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9]."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset",
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "$\\dagger$  Equal contribution.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "* Corresponding author: bczhang@buaa.edu.cn",
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{1}$ Code: https://github.com/SteveTsui/Q-DETR",
+        "bbox": [
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+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "3842",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/212d2dd96265f5ff199cdad769f4646e2b479ae54c58646fc765cdb77f0c6adb.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/7ea89e0832bcf3d9a3ff705e69ca60c51428f4d85b5ada2bcfce4e4ddef14d22.jpg",
+        "image_caption": [
+            "(a) Real-valued DETR-R50",
+            "(b) 4-bit DETR-R50",
+            "Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves  $76.9\\%$ $\\mathrm{AP}_{50}$ , leaving a  $6.4\\%$  performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a  $2 \\sim 4$ -bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "3843",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/e14e6d7bf16502bdbbfef0806f218e3f421ce352046ef7f791139d22bbb35d7a.jpg",
+        "image_caption": [
+            "Architecture of quantized decoder"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            99,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/7401aae9e52ea80a8fb67f38f65d8a5a1a3a60a044a3d502a6bba7bb018998ab.jpg",
+        "image_caption": [
+            "Learning Q-DETR with DRD",
+            "Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. The Challenge of Quantizing DETR",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Quantized DETR baseline",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow  $\\mathrm{LSQ + [2]}$  to introduce a general framework of asymmetric activation quantization and symmetric weight quantization:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\boldsymbol {x} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\left(\\boldsymbol {x} - z\\right)}{\\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \\right\\} \\right\\lceil , \\mathbf {w} _ {q} = \\left\\lfloor \\operatorname {c l i p} \\left\\{\\frac {\\mathbf {w}}{\\alpha_ {\\mathbf {w}}}, Q _ {n} ^ {\\mathbf {w}}, Q _ {p} ^ {\\mathbf {w}} \\right\\} \\right\\rceil , \\\\ Q _ {a} (x) = \\alpha_ {x} \\circ \\mathbf {x} _ {q} + z, \\quad Q _ {w} (x) = \\alpha_ {\\mathbf {w}} \\circ \\mathbf {w} _ {q}, \\tag {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\operatorname{clip}\\{y, r_1, r_2\\}$  clips the input  $y$  with value bounds  $r_1$  and  $r_2$ ; the  $[y]$  rounds  $y$  to its nearest integer; the  $\\circ$  denotes the channel-wise multiplication. And  $Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1$ ,  $Q_n^{\\mathbf{w}} = -2^{b-1}$ ,  $Q_p^{\\mathbf{w}} = 2^{b-1} - 1$  are the discrete bounds for  $a$ -bit activations and  $b$ -bit weights.  $x$  generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {Q} - \\operatorname {F C} (\\boldsymbol {x}) = Q _ {a} (\\boldsymbol {x}) \\cdot Q _ {w} (\\mathbf {w}) = \\alpha_ {x} \\alpha_ {\\mathbf {w}} \\circ \\left(\\boldsymbol {x} _ {q} \\odot \\mathbf {w} _ {q} + z / \\alpha_ {x} \\circ \\mathbf {w} _ {q}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\cdot$  denotes the matrix multiplication and  $\\odot$  denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output  $\\mathbf{E}$ , DETR performs co-attention between object queries  $\\mathbf{O}$  and the vi",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3844",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a5c972047c20bda899b5fbf274b37c7127f9b4a5c59762ec87268a7689ec6b8c.jpg",
+        "image_caption": [
+            "Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            99,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "sual features  $\\mathbf{E}$ , which are formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {q} = \\mathrm {Q - F C} (\\mathbf {O}), \\mathbf {k}, \\mathbf {v} = \\mathrm {Q - F C} (\\mathbf {E})\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {A} _ {i} = \\operatorname {s o f t m a x} \\left(Q _ {a} (\\mathbf {q}) _ {i} \\cdot Q _ {a} (\\mathbf {k}) _ {i} ^ {\\top} / \\sqrt {d}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {D} _ {i} = Q _ {a} (\\mathbf {A}) _ {i} \\cdot Q _ {a} (\\mathbf {v}) _ {i},\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{D}$  is the multi-head co-attention module, i.e., the coattended feature for the object query. The  $d$  denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Challenge Analysis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e.,  $(1) + (2) + (3)$ , brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to  $2.1\\%$  in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "graded information representation is the main obstacle to a better quantized DETR.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. The Proposed Q-DETR",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Information Bottleneck of Q-DETR",
+        "text_level": 1,
+        "bbox": [
+            500,
+            170,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts  $\\mathcal{T}$  and  $\\mathcal{S}$ , respectively.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta^ {S}} I (X; \\mathbf {E} ^ {S}) - \\beta I (\\mathbf {E} ^ {S}, \\mathbf {q} ^ {S}; \\boldsymbol {y} ^ {G T}) - \\gamma I (\\mathbf {q} ^ {S}; \\mathbf {q} ^ {\\mathcal {T}}), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            454,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{q}^T$  and  $\\mathbf{q}^S$  represent the queries in the teacher and student DETR methods as predefined in Eq. (3);  $\\beta$  and  $\\gamma$  are the Lagrange multipliers [35];  $\\theta^S$  is the parameters of the student; and  $I(\\cdot)$  returns the mutual information of two input variables. The first item  $I(X; \\mathbf{E}^S)$  minimizes information between input and visual features  $\\mathbf{E}^S$  to extract task-oriented hints [40]. The second item  $I(\\mathbf{E}^S, \\mathbf{q}^S; \\boldsymbol{y}^{GT})$  maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The core issue of this paper is to solve the third item  $I(\\mathbf{q}^S;\\mathbf{q}^T)$ , which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nI (\\mathbf {q} ^ {\\mathcal {S}}; \\mathbf {q} ^ {\\mathcal {T}}) = H (\\mathbf {q} ^ {\\mathcal {S}}) - H (\\mathbf {q} ^ {\\mathcal {S}} | \\mathbf {q} ^ {\\mathcal {T}}), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $H(\\mathbf{q}^S)$  returns the self information entropy expected to be maximized while  $H(\\mathbf{q}^S|\\mathbf{q}^T)$  is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "(1) Quantizing backbone (2) Quantizing encoder (3) Quantizing MHA of decoder (4) Quantizing MLPs",
+        "bbox": [
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+            114,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "3845",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the two items, which is explicitly defined as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\min  _ {\\theta} H (\\mathbf {q} ^ {S ^ {*}} | \\mathbf {q} ^ {\\mathcal {T}}), \\\\ s. t. \\quad \\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\underset {\\mathbf {q} ^ {\\mathcal {S}}} {\\arg \\max } H (\\mathbf {q} ^ {\\mathcal {S}}). \\tag {6} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query  $\\mathbf{q}^{S^*}$  and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Distribution Rectification Distillation",
+        "text_level": 1,
+        "bbox": [
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+            277,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy,  $H(\\mathbf{q}^S)$  can be implicitly expanded as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nH \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) = - \\int_ {\\mathbf {q} _ {i} ^ {\\mathcal {S}} \\in \\mathbf {q} ^ {\\mathcal {S}}} p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right) \\log p \\left(\\mathbf {q} _ {i} ^ {\\mathcal {S}}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            369,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However, an explicit form of  $H(\\mathbf{q}^S)$  can only be parameterized with a regular distribution  $p(\\mathbf{q}_i^S)$ . Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean  $\\mu (\\mathbf{q}^S)$  and variance  $\\sigma (\\mathbf{q}^S)$  of query  $\\mathbf{q}^S$  whose distribution is then modeled as  $\\mathbf{q}^S\\sim \\mathcal{N}(\\mu (\\mathbf{q}^S),\\sigma (\\mathbf{q}^S))$ . Then, the self-information entropy of the student query can be proceeded as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} H (\\mathbf {q} ^ {\\mathcal {S}}) = - \\mathbb {E} [ \\log \\mathcal {N} (\\mu (\\mathbf {q} ^ {\\mathcal {S}}), \\sigma (\\mathbf {q} ^ {\\mathcal {S}})) ] \\\\ = - \\mathbb {E} [ \\log [ (2 \\pi \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}) ^ {\\frac {1}{2}} \\exp (- \\frac {(\\mathbf {q} _ {i} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})) ^ {2}}{2 \\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2}})) ] \\\\ = \\frac {1}{2} \\log 2 \\pi \\sigma \\left(\\mathbf {q} ^ {\\mathcal {S}}\\right) ^ {2}. \\tag {8} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The above objective reaches its maximum of  $H(\\mathbf{q}^{S^*}) = (1/2) \\log 2\\pi e[\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}]$  when  $\\mathbf{q}^{S^*} = [\\mathbf{q}^S - \\mu(\\mathbf{q}^S)] / [\\sqrt{\\sigma(\\mathbf{q}^S)^2 + \\epsilon_{\\mathbf{q}^S}}]$  where  $\\epsilon_{\\mathbf{q}^S} = 1e^{-5}$  is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter  $\\beta_{\\mathbf{q}^S}$  is added to move the mean value. A learnable scaling parameter  $\\gamma_{\\mathbf{q}^S}$  is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows:",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {q} ^ {\\mathcal {S} ^ {*}} = \\frac {\\mathbf {q} ^ {\\mathcal {S}} - \\mu (\\mathbf {q} ^ {\\mathcal {S}})}{\\sqrt {\\sigma (\\mathbf {q} ^ {\\mathcal {S}}) ^ {2} + \\epsilon_ {\\mathbf {q} ^ {\\mathcal {S}}}}} \\gamma_ {\\mathbf {q} ^ {\\mathcal {S}}} + \\beta_ {\\mathbf {q} ^ {\\mathcal {S}}}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            142,
+            859,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "in which case the maximum self-information entropy of student query becomes  $H(\\mathbf{q}^{\\mathcal{S}^*}) = (1/2) \\log 2\\pi e[(\\sigma_{\\mathbf{q}^{\\mathcal{S}}}^2 + \\epsilon_{\\mathbf{q}^{\\mathcal{S}}}) / \\gamma_{\\mathbf{q}^{\\mathcal{S}}}^2]$ . Therefore, in the forward propagation, we can obtain the current optimal query  $\\mathbf{q}^{\\mathcal{S}^*}$  via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by  $\\pmb{y}^{GT} = \\{c_i^{GT}, b_i^{GT}\\}_{i=1}^{N_{gt}}$  as a set of ground-truth objects where  $N_{gt}$  is the number of foregrounds,  $c_i^{GT}$  and  $b_i^{GT}$  respectively represent the class and coordinate (bound- ing box) for the  $i$ -th object. In DETR, each query is associated with an object. Therefore, we can obtain  $N$  objects for teacher and student as well, denoted as  $\\pmb{y}^S = \\{c_j^S, b_j^S\\}_{j=1}^N$  and  $\\pmb{y}^T = \\{c_j^T, b_j^T\\}_{j=1}^N$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify \"well-matched\" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nG _ {i} = \\max  _ {1 \\leq j \\leq N} \\operatorname {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {S}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            472,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{GIOU}(\\cdot)$  is the generalized intersection over union function [32]. Each  $G_{i}$  reflects the \"closeness\" of student proposals to the  $i$ -th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nb _ {j} ^ {\\mathcal {S}} = \\left\\{ \\begin{array}{l l} b _ {j} ^ {\\mathcal {S}}, & \\text {G I o U} \\left(b _ {i} ^ {G T}, b _ {j} ^ {\\mathcal {S}}\\right) > \\tau G _ {i}, \\forall i \\\\ \\varnothing , & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            555,
+            589,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  is a threshold controlling the proportion of distilled queries. After removing object-empty  $(\\varnothing)$  queries in  $\\tilde{\\pmb{q}}^S$ , we form a distillation-desired query set of students denoted as  $\\tilde{\\pmb{q}}^S$  associated with its object set  $\\tilde{\\pmb{y}}^S = \\{\\tilde{c}_j^S, \\tilde{b}_j^S\\}_{j=1}^N$ . Correspondingly, we can obtain a teacher query set  $\\tilde{\\pmb{y}}^T = \\{\\tilde{c}_j^T, \\tilde{b}_j^T\\}_{j=1}^N$ . For the  $j$ -th student query, its corresponding teacher query is matched as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {c} _ {j} ^ {\\mathcal {T}}, \\tilde {b} _ {j} ^ {\\mathcal {T}} = \\underset {\\tilde {c} _ {k} ^ {\\mathcal {T}}, \\tilde {b} _ {k} ^ {\\mathcal {T}}} {\\arg \\max } \\sum_ {k = 1} ^ {N} \\mu_ {1} \\operatorname {G I o U} \\left(\\tilde {b} _ {j} ^ {\\mathcal {S}}, b _ {k} ^ {\\mathcal {T}}\\right) - \\mu_ {2} \\| \\tilde {b} _ {j} ^ {\\mathcal {S}} - b _ {k} ^ {\\mathcal {T}} \\| _ {1}, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            753,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mu_{1} = 2$  and  $\\mu_{2} = 5$  control the matching function, values of which is to follow [4].",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, the upper-level optimization after rectification in Eq. (6) becomes:",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta} H \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}} \\mid \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right). \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            635,
+            878,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "3846",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between  $\\tilde{\\mathbf{q}}^{S^*}$  and  $\\tilde{\\mathbf{q}}^T$ , optima of which, i.e.,  $\\tilde{\\mathbf{q}}^{S^*} = \\tilde{\\mathbf{q}}^T$ , is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes:",
+        "bbox": [
+            76,
+            90,
+            468,
+            165
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {D R D} \\left(\\tilde {\\mathbf {q}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\mathbf {q}} ^ {\\mathcal {T}}\\right) = \\mathbb {E} \\left[ \\left\\| \\tilde {\\mathbf {D}} ^ {\\mathcal {S} ^ {*}} - \\tilde {\\mathbf {D}} ^ {\\mathcal {T}} \\right\\| _ {2} \\right], \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            140,
+            176,
+            468,
+            194
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where we use the Euclidean distance of co-attented feature  $\\tilde{\\mathbf{D}}$  (see Eq. 3) containing the information query  $\\tilde{\\mathbf{q}}$  for optimization.",
+        "bbox": [
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+            205,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are:",
+        "bbox": [
+            76,
+            251,
+            468,
+            311
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {G T} \\left(\\boldsymbol {y} ^ {G T}, \\boldsymbol {y} ^ {\\mathcal {S}}\\right) + \\lambda \\mathcal {L} _ {D R D} \\left(\\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {S} ^ {*}}, \\tilde {\\boldsymbol {\\mathbf {q}}} ^ {\\mathcal {T}}\\right), \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            319,
+            468,
+            337
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{GT}$  is the common detection loss for missions such as proposal classification and coordinate regression [4], and  $\\lambda$  is a tradeoff hyper-parameter.",
+        "bbox": [
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+            345,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            404,
+            207,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Datasets and Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
+            530,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP,  $\\mathrm{AP}_{50}$  (default VOC metric), and  $\\mathrm{AP}_{75}$ . We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list  $\\mathrm{AP}_{50}$ ,  $\\mathrm{AP}_{75}$ ,  $\\mathrm{AP}_s$ ,  $\\mathrm{AP}_m$ , and  $\\mathrm{AP}_l$ .",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f81fb84b5bb6aab549b17b32fa5da6cc62eb498e5c10813514540515dba9c182.jpg",
+        "image_caption": [
+            "(a) Effect of  $\\tau$  and  $\\lambda$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/47952eabf7f40ca87b81667b8ca2c1c9243c9c288b2ab9cb3103439d10a90646.jpg",
+        "image_caption": [
+            "(b) Mutual information curves.",
+            "Figure 5. (a) We select  $\\tau$  and  $\\lambda$  using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of  $I(X; \\mathbf{E})$  and  $I(\\boldsymbol{y}^{GT}; \\mathbf{E}, \\mathbf{q})$  (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of  $1e^{-4}$ . We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP<sub>50</sub> on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP<sub>50</sub> on VOC and 44.4% AP on COCO) as teacher network.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
+            604,
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+            619
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Hyper-parameter selection. As mentioned above, we select hyper-parameters  $\\tau$  and  $\\lambda$  in this part using the 4-bit Q-DETR model. We show the model performance  $(\\mathrm{AP}_{50})$  with different setups of hyper-parameters  $\\{\\tau ,\\lambda \\}$  in Fig.5 (a), where we conduct ablative experiments on the baseline  $+\\mathrm{DA}(\\mathrm{AP}_{50} = 78.8\\%)$ . As can be seen, the performances increase first and then decrease with the increase of  $\\tau$  from left to right. Since  $\\tau$  controls the proportion of selected distillation-desired queries, we show that the full-imitation  $(\\tau = 0)$  performs worse than the vanilla baseline with no distillation  $(\\tau = 1)$ , showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of  $\\tau$  from left to right. The Q-DETR obtains better performances with  $\\tau$  set as 0.5 and 0.6. With the varying value of  $\\lambda$ , we find  $\\{\\lambda ,\\tau \\} = \\{2.5,0.6\\}$  boost the performance of Q-DETR most, achieving  $82.7\\%$  AP on VOC test2007. Based on the ablative study above, we set hyper-parameters  $\\tau$  and  $\\lambda$  as 0.6 and 2.5",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "3847",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/714db789979e193ffa0cab743198c4ee6537499428e88f61c41805171caa2c36.jpg",
+        "table_caption": [
+            "Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>#Bits</td><td>\\(AP_{50}\\)</td><td>#Bits</td><td>\\(AP_{50}\\)</td><td>#Bits</td><td>\\(AP_{50}\\)</td></tr><tr><td>Real-valued</td><td>32-32-32</td><td>83.3</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>78.0</td><td>3-3-8</td><td>76.8</td><td>2-2-8</td><td>69.7</td></tr><tr><td>+DA</td><td>4-4-8</td><td>78.8</td><td>3-3-8</td><td>78.0</td><td>2-2-8</td><td>71.6</td></tr><tr><td>+FQM</td><td>4-4-8</td><td>81.5</td><td>3-3-8</td><td>80.9</td><td>2-2-8</td><td>74.9</td></tr><tr><td>+DA+FQM(Q-DETR)</td><td>4-4-8</td><td>82.7</td><td>3-3-8</td><td>82.1</td><td>2-2-8</td><td>76.4</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "for the experiments in this paper.",
+        "bbox": [
+            76,
+            308,
+            294,
+            321
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on  $\\mathrm{AP}_{50}$  (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%.",
+        "bbox": [
+            75,
+            321,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test  $\\mathrm{AP}_{50}$  to quantify  $I(\\boldsymbol{y}^{GT};\\mathbf{E},\\mathbf{q})$ . We employ a reconstruction decoder to decode the encoded feature  $\\mathbf{E}$  to reconstruct the input and quantify  $I(X;\\mathbf{E})$  using the  $\\ell_1$  loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Results on PASCAL VOC",
+        "text_level": 1,
+        "bbox": [
+            76,
+            664,
+            310,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e.  $1333 \\times 800$ . We mainly discuss the  $\\mathrm{AP}_{50}$  (default VOC metric) in the following.",
+        "bbox": [
+            75,
+            688,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture",
+        "bbox": [
+            75,
+            795,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/82eed12095fb7a4f5a22f0bdd3105b3808bf5341e615bf02f5f30004c2ceeb53.jpg",
+        "table_caption": [
+            "Table 2. We report AP,  $\\mathrm{AP}_{50}$ , and  $\\mathrm{AP}_{75}$  (\\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Method</td><td>#Bits</td><td>AP</td><td>\\( AP_{50} \\)</td><td>\\( AP_{75} \\)</td></tr><tr><td rowspan=\"12\">DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>59.5</td><td>83.3</td><td>64.7</td></tr><tr><td>Percentile</td><td rowspan=\"2\">8-8-8</td><td>54.7</td><td>79.2</td><td>60.1</td></tr><tr><td>VT-PTQ</td><td>57.6</td><td>82.3</td><td>63.1</td></tr><tr><td>LSQ</td><td></td><td>49.7</td><td>76.9</td><td>53.0</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>51.3</td><td>78.0</td><td>54.1</td></tr><tr><td>Q-DETR</td><td></td><td>57.1</td><td>82.7</td><td>61.5</td></tr><tr><td>LSQ</td><td></td><td>47.0</td><td>75.3</td><td>49.1</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>49.2</td><td>76.8</td><td>51.8</td></tr><tr><td>Q-DETR</td><td></td><td>56.8</td><td>82.1</td><td>61.2</td></tr><tr><td>LSQ</td><td></td><td>42.6</td><td>68.2</td><td>44.8</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>44.0</td><td>69.7</td><td>45.8</td></tr><tr><td>Q-DETR</td><td></td><td>50.7</td><td>76.4</td><td>54.1</td></tr><tr><td rowspan=\"12\">SMCA-DETR -R50</td><td>Real-valued</td><td>32-32-32</td><td>56.7</td><td>83.7</td><td>62.0</td></tr><tr><td>Percentile</td><td rowspan=\"2\">8-8-8</td><td>54.7</td><td>79.2</td><td>60.1</td></tr><tr><td>VT-PTQ</td><td>55.9</td><td>83.0</td><td>61.3</td></tr><tr><td>LSQ</td><td></td><td>49.6</td><td>78.6</td><td>53.4</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>50.7</td><td>79.5</td><td>55.4</td></tr><tr><td>Q-DETR</td><td></td><td>56.2</td><td>83.3</td><td>61.6</td></tr><tr><td>LSQ</td><td></td><td>47.7</td><td>76.5</td><td>51.7</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>49.9</td><td>77.5</td><td>53.6</td></tr><tr><td>Q-DETR</td><td></td><td>54.3</td><td>82.6</td><td>59.5</td></tr><tr><td>LSQ</td><td></td><td>42.3</td><td>69.7</td><td>44.8</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>43.9</td><td>70.4</td><td>46.1</td></tr><tr><td>Q-DETR</td><td></td><td>50.2</td><td>76.7</td><td>52.6</td></tr></table>",
+        "bbox": [
+            501,
+            155,
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+            537
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "and bit-width, which significantly validates the effectiveness of our method.",
+        "bbox": [
+            498,
+            564,
+            888,
+            593
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by  $6.3\\%$ ,  $5.1\\%$  and  $3.8\\%$  on  $\\mathrm{AP}_{50}$ , a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance.",
+        "bbox": [
+            498,
+            595,
+            890,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Results on COCO",
+        "text_level": 1,
+        "bbox": [
+            500,
+            710,
+            671,
+            724
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various",
+        "bbox": [
+            498,
+            839,
+            890,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "3848",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/75a9dded57022f71844b11e49ff060da2adeb508c57fa60eb2467e4cd037cde3.jpg",
+        "table_caption": [
+            "Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Method</td><td>#Bits</td><td>Size(MB)</td><td>OPs(G)</td><td>AP</td><td>AP50</td><td>AP75</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td rowspan=\"12\">DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>159.32</td><td>85.51</td><td>42.0</td><td>62.4</td><td>44.2</td><td>20.5</td><td>45.8</td><td>61.1</td></tr><tr><td>Percentile</td><td>8-8-8</td><td>39.83</td><td>23.01</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VT-PTQ</td><td></td><td></td><td></td><td>41.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>33.3</td><td>53.7</td><td>33.9</td><td>12.8</td><td>37.0</td><td>51.6</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>19.92</td><td>13.02</td><td>34.1</td><td>55.3</td><td>35.4</td><td>14.3</td><td>38.0</td><td>53.8</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>39.4</td><td>60.2</td><td>41.4</td><td>17.7</td><td>43.4</td><td>59.9</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>31.0</td><td>52.3</td><td>32.1</td><td>11.3</td><td>33.9</td><td>48.5</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>15.03</td><td>7.61</td><td>32.3</td><td>52.2</td><td>32.9</td><td>12.3</td><td>35.4</td><td>50.3</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>36.1</td><td>55.9</td><td>37.5</td><td>14.6</td><td>39.4</td><td>55.2</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>24.7</td><td>44.6</td><td>26.5</td><td>6.3</td><td>25.3</td><td>42.7</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>10.03</td><td>5.32</td><td>26.6</td><td>46.6</td><td>26.5</td><td>8.4</td><td>28.2</td><td>44.4</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>31.4</td><td>51.3</td><td>31.6</td><td>11.6</td><td>34.3</td><td>49.6</td></tr><tr><td rowspan=\"12\">SMCA-DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>164.75</td><td>86.65</td><td>41.0</td><td>62.2</td><td>43.6</td><td>21.9</td><td>44.3</td><td>59.1</td></tr><tr><td>Percentile</td><td>8-8-8</td><td>41.19</td><td>23.66</td><td>37.5</td><td>58.5</td><td>40.1</td><td>17.6</td><td>39.1</td><td>55.9</td></tr><tr><td>VT-PTQ</td><td></td><td></td><td></td><td>40.2</td><td>61.0</td><td>42.6</td><td>20.3</td><td>42.9</td><td>57.7</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>33.9</td><td>55.0</td><td>35.0</td><td>13.2</td><td>37.2</td><td>51.4</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>20.59</td><td>13.48</td><td>35.0</td><td>56.4</td><td>36.4</td><td>15.6</td><td>38.3</td><td>52.5</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>38.3</td><td>59.7</td><td>39.8</td><td>17.7</td><td>41.7</td><td>56.8</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>30.1</td><td>52.6</td><td>31.4</td><td>11.9</td><td>33.4</td><td>46.6</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>15.68</td><td>8.05</td><td>31.8</td><td>53.7</td><td>32.6</td><td>12.6</td><td>35.2</td><td>49.8</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>35.0</td><td>56.3</td><td>36.9</td><td>15.0</td><td>39.0</td><td>53.1</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>23.9</td><td>42.2</td><td>24.2</td><td>9.4</td><td>26.2</td><td>37.5</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>10.84</td><td>4.54</td><td>25.4</td><td>44.3</td><td>25.2</td><td>8.4</td><td>27.2</td><td>40.3</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>30.5</td><td>51.8</td><td>31.8</td><td>12.0</td><td>33.2</td><td>48.0</td></tr></table>",
+        "bbox": [
+            91,
+            127,
+            875,
+            510
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "detectors. We follow [40] to calculate memory usage, by adding  $32 \\times$  the number of real-valued weights and  $a \\times$  the number of quantized weights in the  $a$ -bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds  $\\left\\{\\frac{1}{32}, \\frac{1}{16}, \\frac{1}{8}\\right\\}$  of the number of  $\\{2,3,4\\}$ -bit multiplications equals the OPs following [24].",
+        "bbox": [
+            75,
+            535,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of  $2/3/4$ -bit baseline by  $4.8\\%$ ,  $3.8\\%$  and  $5.1\\%$  AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed  $2/3/4$ -bit Q-DETR achieves computation acceleration and storage savings by  $16.07 \\times / 11.23 \\times / 6.57 \\times$  and  $15.88 \\times / 10.60 \\times / 7.99 \\times$ . The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection.",
+        "bbox": [
+            75,
+            657,
+            468,
+            883
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the SMCA-DETR-R50 model, we observe similar",
+        "bbox": [
+            96,
+            883,
+            468,
+            898
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates  $6.42 \\times$  with only a  $2.7\\%$  performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods.",
+        "bbox": [
+            496,
+            535,
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+            612
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. We effectively employ a distribution alignment module to solve inner-level and a foreground-aware query matching scheme to solve upper level. As a result, Q-DETR significantly boosts performance of low-bit DETR. Extensive experiments show that Q-DETR surpasses state-of-the-arts in DETR quantization.",
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+        "text": "7. Acknowledgements",
+        "text_level": 1,
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+        "text": "This work was supported by National Natural Science Foundation of China under Grant 62141604, 62076016, Beijing Natural Science Foundation L223024.",
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+        "text": "3849",
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+    },
+    {
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2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/758f64fe-cfe8-4994-bd86-745fec52e6d7_origin.pdf

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2023/Q-DETR_ An Efficient Low-Bit Quantized Detection Transformer/full.md

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+# Q-DETR: An Efficient Low-Bit Quantized Detection Transformer
+
+Sheng Xu $^{1\dagger}$ , Yanjing Li $^{1\dagger}$ , Mingbao Lin $^{3}$ , Peng Gao $^{4}$ , Guodong Guo $^{5}$ , Jinhu Lu $^{1,2}$ , Baochang Zhang $^{1,2*}$ $^{1}$  Beihang University  
+ $^{2}$  Zhongguancun Laboratory  
+ $^{3}$  Tencent  
+ $^{4}$  Shanghai AI Laboratory  
+ $^{5}$  UNIUBI Research, Universal Ubiquitous Co.
+
+# Abstract
+
+The recent detection transformer (DETR) has advanced object detection, but its application on resource-constrained devices requires massive computation and memory resources. Quantization stands out as a solution by representing the network in low-bit parameters and operations. However, there is a significant performance drop when performing low-bit quantized DETR (Q-DETR) with existing quantization methods. We find that the bottlenecks of Q-DETR come from the query information distortion through our empirical analyses. This paper addresses this problem based on a distribution rectification distillation (DRD). We formulate our DRD as a bi-level optimization problem, which can be derived by generalizing the information bottleneck (IB) principle to the learning of Q-DETR. At the inner level, we conduct a distribution alignment for the queries to maximize the self-information entropy. At the upper level, we introduce a new foreground-aware query matching scheme to effectively transfer the teacher information to distillation-desired features to minimize the conditional information entropy. Extensive experimental results show that our method performs much better than prior arts. For example, the 4-bit Q-DETR can theoretically accelerate DETR with ResNet-50 backbone by  $6.6\times$  and achieve  $39.4\%$  AP, with only  $2.6\%$  performance gaps than its real-valued counterpart on the COCO dataset<sup>1</sup>.
+
+# 1. Introduction
+
+Inspired by the success of natural language processing (NLP), object detection with transformers (DETR) has been introduced to train an end-to-end detector via a transformer encoder-decoder [4]. Unlike early works [22, 31] that often employ convolutional neural networks (CNNs) and require post-processing procedures, e.g., non-maximum suppression (NMS), and hand-designed sample selection, DETR treats object detection as a direct set prediction problem.
+
+![](images/b47e025e70e302f5e79025c7b330255d3d8a381daa5d068aee71250b90faccb5.jpg)
+
+![](images/58e77532541a7f2ba0fc9047e639c676fc6a1902b28eff415a9f5bd61e81e899.jpg)
+
+![](images/18b15d8ecd08b2a6746d8a20492c258c57b9109c76d5d9a7c04afb4562f715f8.jpg)
+
+![](images/8156cf2f15f19b131f79b7183987c36c7b62f255802f7021454e16e457f5de81.jpg)
+
+![](images/3adddb20ddfb6562d837c9002e09030289bca8f8a4171abca63cc56fc35c6e37.jpg)  
+(b) 4-bit DETR-R50
+
+![](images/43ddb4a0e46f89a0a644c9d7bacbd5db54540eea7587e8f33923960758423819.jpg)  
+Figure 1. The histogram of query values  $\mathbf{q}$  (blue shadow) and corresponding PDF curves (red curve) of Gaussian distribution [17], w.r.t the cross attention of different decoder layers in (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50 (baseline). Gaussian distribution is generated from the statistical mean and variance of the query values. The query in quantized DETR-R50 bears information distortion compared with the real-valued one. Experiments are performed on the VOC dataset [9].
+
+Despite this attractiveness, DETR usually has a tremendous number of parameters and float-pointing operations (FLOPs). For instance, there are 39.8M parameters taking up 159MB memory usage and 86G FLOPs in the DETR model with ResNet-50 backbone [12] (DETR-R50). This leads to an unacceptable memory and computation consumption during inference, and challenges deployments on devices with limited supplies of resources.
+
+Therefore, substantial efforts on network compression have been made towards efficient online inference [7, 33, 43, 44]. Quantization is particularly popular for deploying on AI chips by representing a network in low-bit formats. Yet prior post-training quantization (PTQ) for DETR [26] derives quantized parameters from pre-trained real-valued models, which often restricts the model performance in a sub-optimized state due to the lack of fine-tuning on the training data. In particular, the performance drastically drops when quantized to ultra-low bits (4-bits or less). Alternatively, quantization-aware training (QAT) [25, 42] performs quantization and fine-tuning on the training dataset
+
+![](images/212d2dd96265f5ff199cdad769f4646e2b479ae54c58646fc765cdb77f0c6adb.jpg)
+
+![](images/7ea89e0832bcf3d9a3ff705e69ca60c51428f4d85b5ada2bcfce4e4ddef14d22.jpg)  
+(a) Real-valued DETR-R50  
+(b) 4-bit DETR-R50  
+Figure 2. Spatial attention weight maps in the last decoder of (a) real-valued DETR-R50, and (b) 4-bit quantized DETR-R50. The green rectangle denotes the ground-truth bounding box. Following [29], the highlighted area denotes the large attention weights in the selected four heads in compliance with bound prediction. Compared to its real-valued counterpart that focuses on the ground-truth bounds, quantized DETR-R50 deviates significantly.
+
+simultaneously, leading to trivial performance degradation even with significantly lower bits. Though QAT methods have been proven to be very effective in compressing CNNs [8, 27] for computer vision tasks, an exploration of low-bit DETR remains untouched.
+
+In this paper, we first build a low-bit DETR baseline, a straightforward solution based on common QAT techniques [2]. Through an empirical study of this baseline, we observe significant performance drops on the VOC [9] dataset. For example, a 4-bit quantized DETR-R50 using LSQ [8] only achieves  $76.9\%$ $\mathrm{AP}_{50}$ , leaving a  $6.4\%$  performance gaps compared with the real-valued DETR-R50. We find that the incompatibility of existing QAT methods mainly stems from the unique attention mechanism in DETR, where the spatial dependencies are first constructed between the object queries and encoded features. Then the co-attended object queries are fed into box coordinates and class labels by a feed-forward network. A simple application of existing QAT methods on DETR leads to query information distortion, and therefore the performance severely degrades. Fig. 1 exhibits an example of information distortion in query features of 4-bit DETR-R50, where we can see significant distribution variation of the query modules in quantized DETR and real-valued version. The query information distortion causes the inaccurate focus of spatial attention, which can be verified by following [29] to visualize the spatial attention weight maps in 4-bit and real-valued DETR-R50 in Fig. 2. We can see that the quantized DETR-R50 bear's inaccurate object localization. Therefore, a more generic method for DETR quantization is necessary.
+
+To tackle the issue above, we propose an efficient low-bit quantized DETR (Q-DETR) by rectifying the query information of the quantized DETR as that of the real-valued counterpart. Fig. 3 provides an overview of our Q-DETR, which is mainly accomplished by a distribution rectifica
+
+tion knowledge distillation method (DRD). We find ineffective knowledge transferring from the real-valued teacher to the quantized student primarily because of the information gap and distortion. Therefore, we formulate our DRD as a bi-level optimization framework established on the information bottleneck principle (IB). Generally, it includes an inner-level optimization to maximize the self-information entropy of student queries and an upper-level optimization to minimize the conditional information entropy between student and teacher queries. At the inner level, we conduct a distribution alignment for the query guided by its Gaussian-like distribution, as shown in Fig. 1, leading to an explicit state in compliance with its maximum information entropy in the forward propagation. At the upper level, we introduce a new foreground-aware query matching that filters out low-qualified student queries for exact one-to-one query matching between student and teacher, providing valuable knowledge gradients to push minimum conditional information entropy in the backward propagation.
+
+This paper attempts to introduce a generic method for DETR quantization. The significant contributions in this paper are outlined as follows: (1) We develop the first QAT quantization framework for DETR, dubbed Q-DETR. (2) We use a bi-level optimization distillation framework, abbreviated as DRD. (3) We observe a significant performance increase compared to existing quantized baselines.
+
+# 2. Related Work
+
+Quantization. Quantized neural networks often possess low-bit (1~4-bit) weights and activations to accelerate the model inference and save memory. For example, DoReFa-Net [45] exploits convolution kernels with low bit-width parameters and gradients to accelerate training and inference. TTQ [46] uses two real-valued scaling coefficients to quantize the weights to ternary values. Zhuang et al. [48] present a  $2 \sim 4$ -bit quantization scheme using a two-stage approach to alternately quantize the weights and activations, providing an optimal tradeoff among memory, efficiency, and performance. In [14], the quantization intervals are parameterized, and optimal values are obtained by directly minimizing the task loss of the network. ZeroQ [3] supports uniform and mixed-precision quantization by optimizing for a distilled dataset which is engineered to match the statistics of the batch normalization across different network layers. Xie et al. [41] introduced transfer learning into network quantization to obtain an accurate low-precision model by utilizing Kullback-Leibler (KL) divergence. Fang et al. [10] enabled accurate approximation for tensor values that have bell-shaped distributions with long tails and found the entire range by minimizing the quantization error. Li et al. [17] proposed an information rectification module and distribution-guided distillation to push the bit-width in a quantized vision transformer. At
+
+![](images/e14e6d7bf16502bdbbfef0806f218e3f421ce352046ef7f791139d22bbb35d7a.jpg)  
+Architecture of quantized decoder
+
+![](images/7401aae9e52ea80a8fb67f38f65d8a5a1a3a60a044a3d502a6bba7bb018998ab.jpg)  
+Learning Q-DETR with DRD  
+Figure 3. Overview of the proposed Q-DETR framework. We introduce the distribution rectification distillation method (DRD) to refine the performance of Q-DETR. From left to right, we respectively show the detailed decoder architecture of Q-DETR and the learning framework of Q-DETR. The Q-Backbone, Q-Encoder, and Q-Decoder denote quantized architectures, respectively.
+
+the same time, we address the quantization in DETR from the IB principle. The architectural design has also drawn increasing attention using extra shortcut [27], and parallel parameter-free shortcuts [25] for example.
+
+Detection Transformer. Driven by the success of transformers [37], several researchers have also explored transformer frameworks for vision tasks. The first DETR [4] work introduces the Transformer structure based on the attention mechanism for object detection. But the main drawback of DETR lies in the highly inefficient training process. The approach of another work modifies the multi-head attention mechanism (MHA). Deformable-DETR [47] constructs a sparse and point-to-point MHA mechanism using a static point-wise query sampling method around the reference points. SMCA-DETR [11] introduces a Gaussian-distributed spatial function before formulating a spatially modulated co-attention. DAB-DETR [21] re-defines the query of DETR as dynamic anchor boxes and performs soft ROI pooling layer-by-layer in a cascade manner. DN-DETR [16] introduces query denoising into query generation, reducing the bipartite graph matching difficulty and leading to faster convergence. Another set of arts improves DETR methods using additional learning constraints. For example, UP-DETR [6] proposes a novel self-supervised loss to enhance the convergence speed and the performance of DETR.
+
+However, prior arts mainly focus on the training efficiency of DETR, few of which have discussed the quantization of DETR. To this end, we first build a quantized DETR baseline and then address the query information distortion problem based on the IB principle. Finally, a new KD method based on a foreground-aware query matching scheme is achieved to solve Q-DETR effectively.
+
+# 3. The Challenge of Quantizing DETR
+
+# 3.1. Quantized DETR baseline
+
+We first construct a baseline to study the low-bit DETR since no relevant work has been previously proposed. To this end, we follow  $\mathrm{LSQ + [2]}$  to introduce a general framework of asymmetric activation quantization and symmetric weight quantization:
+
+$$
+\begin{array}{l} \boldsymbol {x} _ {q} = \left\lfloor \operatorname {c l i p} \left\{\frac {\left(\boldsymbol {x} - z\right)}{\alpha_ {x}}, Q _ {n} ^ {x}, Q _ {p} ^ {x} \right\} \right\lceil , \mathbf {w} _ {q} = \left\lfloor \operatorname {c l i p} \left\{\frac {\mathbf {w}}{\alpha_ {\mathbf {w}}}, Q _ {n} ^ {\mathbf {w}}, Q _ {p} ^ {\mathbf {w}} \right\} \right\rceil , \\ Q _ {a} (x) = \alpha_ {x} \circ \mathbf {x} _ {q} + z, \quad Q _ {w} (x) = \alpha_ {\mathbf {w}} \circ \mathbf {w} _ {q}, \tag {1} \\ \end{array}
+$$
+
+where  $\operatorname{clip}\{y, r_1, r_2\}$  clips the input  $y$  with value bounds  $r_1$  and  $r_2$ ; the  $[y]$  rounds  $y$  to its nearest integer; the  $\circ$  denotes the channel-wise multiplication. And  $Q_n^x = -2^{a-1}, Q_p^x = 2^{a-1} - 1$ ,  $Q_n^{\mathbf{w}} = -2^{b-1}$ ,  $Q_p^{\mathbf{w}} = 2^{b-1} - 1$  are the discrete bounds for  $a$ -bit activations and  $b$ -bit weights.  $x$  generally denotes the activation in this paper, including the input feature map of convolution and fully-connected layers and input of multi-head attention modules. Based on this, we first give the quantized fully-connected layer as:
+
+$$
+\operatorname {Q} - \operatorname {F C} (\boldsymbol {x}) = Q _ {a} (\boldsymbol {x}) \cdot Q _ {w} (\mathbf {w}) = \alpha_ {x} \alpha_ {\mathbf {w}} \circ \left(\boldsymbol {x} _ {q} \odot \mathbf {w} _ {q} + z / \alpha_ {x} \circ \mathbf {w} _ {q}\right), \tag {2}
+$$
+
+where  $\cdot$  denotes the matrix multiplication and  $\odot$  denotes the matrix multiplication with efficient bit-wise operations. The straight-through estimator (STE) [1] is used to retain the derivation of the gradient in backward propagation.
+
+In DETR [4], the visual features generated by the backbone are augmented with position embedding and fed into the transformer encoder. Given an encoder output  $\mathbf{E}$ , DETR performs co-attention between object queries  $\mathbf{O}$  and the vi
+
+![](images/a5c972047c20bda899b5fbf274b37c7127f9b4a5c59762ec87268a7689ec6b8c.jpg)  
+Figure 4. Performance of 3/4-bit quantized DETR-R50 on VOC with different quantized modules.
+
+sual features  $\mathbf{E}$ , which are formulated as:
+
+$$
+\mathbf {q} = \mathrm {Q - F C} (\mathbf {O}), \mathbf {k}, \mathbf {v} = \mathrm {Q - F C} (\mathbf {E})
+$$
+
+$$
+\mathbf {A} _ {i} = \operatorname {s o f t m a x} \left(Q _ {a} (\mathbf {q}) _ {i} \cdot Q _ {a} (\mathbf {k}) _ {i} ^ {\top} / \sqrt {d}\right), \tag {3}
+$$
+
+$$
+\mathbf {D} _ {i} = Q _ {a} (\mathbf {A}) _ {i} \cdot Q _ {a} (\mathbf {v}) _ {i},
+$$
+
+where  $\mathbf{D}$  is the multi-head co-attention module, i.e., the coattended feature for the object query. The  $d$  denotes the feature dimension in each head. More FC layers transform the decoder's output features of each object query for the final output. Given box and class predictions, the Hungarian algorithm [4] is applied between predictions and ground-truth box annotations to identify the learning targets of each object query.
+
+# 3.2. Challenge Analysis
+
+Intuitively, the performance of the quantized DETR baseline largely depends on the information representation capability mainly reflected by the information in the multi-head attention module. Unfortunately, such information is severely degraded by the quantized weights and inputs in the forward pass. Also, the rounded and discrete quantization significantly affect the optimization during backpropagation.
+
+We conduct the quantitively ablative experiments by progressively replacing each module of the real-valued DETR baseline with a quantized one and compare the average precision (AP) drop on the VOC dataset [9] as shown in Fig. 4. We find that quantizing the MHA decoder module to low bits, i.e.,  $(1) + (2) + (3)$ , brings the most significant accuracy drops of accuracy among all parts of the DETR methods, up to  $2.1\%$  in the 3-bit DETR-R50. At the same time, other parts of DETR show comparative robustness to the quantization function. Consequently, the critical problem of improving the quantized DETR methods is restoring the information in MHA modules after quantization. Other qualitative results in Fig. 1 and Fig. 2 also indicate that the de
+
+graded information representation is the main obstacle to a better quantized DETR.
+
+# 4. The Proposed Q-DETR
+
+# 4.1. Information Bottleneck of Q-DETR
+
+To address the information distortion of the quantized DETR, we aim to improve the representation capacity of the quantized networks in a knowledge distillation framework. Generally, we utilize a real-valued DETR as a teacher and a quantized DETR as a student, which are distinguished with superscripts  $\mathcal{T}$  and  $\mathcal{S}$ , respectively.
+
+Our Q-DETR pursues the best tradeoff between performance and compression, which is precisely the goal of the information bottleneck (IB) method through quantifying the mutual information that the intermediate layer contains about the input (less is better) and the desired output (more is better) [35, 36]. In our case, the intermediate layer comes from the student, while the desired output includes the ground-truth labels as well as the queries of the teacher for distillation. Thus, the objective target of our Q-DETR is:
+
+$$
+\min  _ {\theta^ {S}} I (X; \mathbf {E} ^ {S}) - \beta I (\mathbf {E} ^ {S}, \mathbf {q} ^ {S}; \boldsymbol {y} ^ {G T}) - \gamma I (\mathbf {q} ^ {S}; \mathbf {q} ^ {\mathcal {T}}), \tag {4}
+$$
+
+where  $\mathbf{q}^T$  and  $\mathbf{q}^S$  represent the queries in the teacher and student DETR methods as predefined in Eq. (3);  $\beta$  and  $\gamma$  are the Lagrange multipliers [35];  $\theta^S$  is the parameters of the student; and  $I(\cdot)$  returns the mutual information of two input variables. The first item  $I(X; \mathbf{E}^S)$  minimizes information between input and visual features  $\mathbf{E}^S$  to extract task-oriented hints [40]. The second item  $I(\mathbf{E}^S, \mathbf{q}^S; \boldsymbol{y}^{GT})$  maximizes information between extracted visual features and ground-truth labels for better object detection. These two items can be easily accomplished by common network training and detection loss constraints, such as proposal classification and coordinate regression.
+
+The core issue of this paper is to solve the third item  $I(\mathbf{q}^S;\mathbf{q}^T)$ , which attempts to address the information distortion in student query via introducing teacher query as a priori knowledge. To accomplish our goal, we first expand the third item and reformulate it as:
+
+$$
+I (\mathbf {q} ^ {\mathcal {S}}; \mathbf {q} ^ {\mathcal {T}}) = H (\mathbf {q} ^ {\mathcal {S}}) - H (\mathbf {q} ^ {\mathcal {S}} | \mathbf {q} ^ {\mathcal {T}}), \tag {5}
+$$
+
+where  $H(\mathbf{q}^S)$  returns the self information entropy expected to be maximized while  $H(\mathbf{q}^S|\mathbf{q}^T)$  is the conditional entropy expected to be minimized. It is challenging to optimize the above maximum & minimum items simultaneously. Instead, we make a compromise to reformulate Eq. (5) as a bi-level issue [5, 20] that alternately optimizes
+
+the two items, which is explicitly defined as:
+
+$$
+\begin{array}{l} \min  _ {\theta} H (\mathbf {q} ^ {S ^ {*}} | \mathbf {q} ^ {\mathcal {T}}), \\ s. t. \quad \mathbf {q} ^ {\mathcal {S} ^ {*}} = \underset {\mathbf {q} ^ {\mathcal {S}}} {\arg \max } H (\mathbf {q} ^ {\mathcal {S}}). \tag {6} \\ \end{array}
+$$
+
+Such an objective involves two sub-problems, including an inner-level optimization to derive the current optimal query  $\mathbf{q}^{S^*}$  and an upper-level optimization to conduct knowledge transfer from the teacher to the student. Below, we show that the two sub-problems can be solved in the forward & backward network propagation's.
+
+# 4.2. Distribution Rectification Distillation
+
+Inner-level optimization. We first detail the maximization of self-information entropy. According to the definition of self information entropy,  $H(\mathbf{q}^S)$  can be implicitly expanded as:
+
+$$
+H \left(\mathbf {q} ^ {\mathcal {S}}\right) = - \int_ {\mathbf {q} _ {i} ^ {\mathcal {S}} \in \mathbf {q} ^ {\mathcal {S}}} p \left(\mathbf {q} _ {i} ^ {\mathcal {S}}\right) \log p \left(\mathbf {q} _ {i} ^ {\mathcal {S}}\right). \tag {7}
+$$
+
+However, an explicit form of  $H(\mathbf{q}^S)$  can only be parameterized with a regular distribution  $p(\mathbf{q}_i^S)$ . Luckily, the statistical results in Fig. 1 show that the query distribution tends to follow a Gaussian distribution, which is also observed in [17]. This enables us to solve the inner-level optimization in a distribution alignment fashion. To this end, we first calculate the mean  $\mu (\mathbf{q}^S)$  and variance  $\sigma (\mathbf{q}^S)$  of query  $\mathbf{q}^S$  whose distribution is then modeled as  $\mathbf{q}^S\sim \mathcal{N}(\mu (\mathbf{q}^S),\sigma (\mathbf{q}^S))$ . Then, the self-information entropy of the student query can be proceeded as:
+
+$$
+\begin{array}{l} H (\mathbf {q} ^ {\mathcal {S}}) = - \mathbb {E} [ \log \mathcal {N} (\mu (\mathbf {q} ^ {\mathcal {S}}), \sigma (\mathbf {q} ^ {\mathcal {S}})) ] \\ = - \mathbb {E} [ \log [ (2 \pi \sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2}) ^ {\frac {1}{2}} \exp (- \frac {(\mathbf {q} _ {i} ^ {\mathcal {S}} - \mu (\mathbf {q} ^ {\mathcal {S}})) ^ {2}}{2 \sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2}})) ] \\ = \frac {1}{2} \log 2 \pi \sigma \left(\mathbf {q} ^ {\mathcal {S}}\right) ^ {2}. \tag {8} \\ \end{array}
+$$
+
+The above objective reaches its maximum of  $H(\mathbf{q}^{S^*}) = (1/2) \log 2\pi e[\sigma(\mathbf{q}^S)^2 + \epsilon_{\mathbf{q}^S}]$  when  $\mathbf{q}^{S^*} = [\mathbf{q}^S - \mu(\mathbf{q}^S)] / [\sqrt{\sigma(\mathbf{q}^S)^2 + \epsilon_{\mathbf{q}^S}}]$  where  $\epsilon_{\mathbf{q}^S} = 1e^{-5}$  is a small constant added to prevent a zero denominator. In practice, the mean and variance might be inaccurate due to query data bias. To solve this we use the concepts in batch normalization (BN) [13,34] where a learnable shifting parameter  $\beta_{\mathbf{q}^S}$  is added to move the mean value. A learnable scaling parameter  $\gamma_{\mathbf{q}^S}$  is multiplied to move the query to the adaptive position. In this situation, we rectify the information entropy of the query in the student as follows:
+
+$$
+\mathbf {q} ^ {\mathcal {S} ^ {*}} = \frac {\mathbf {q} ^ {\mathcal {S}} - \mu (\mathbf {q} ^ {\mathcal {S}})}{\sqrt {\sigma (\mathbf {q} ^ {\mathcal {S}}) ^ {2} + \epsilon_ {\mathbf {q} ^ {\mathcal {S}}}}} \gamma_ {\mathbf {q} ^ {\mathcal {S}}} + \beta_ {\mathbf {q} ^ {\mathcal {S}}}, \tag {9}
+$$
+
+in which case the maximum self-information entropy of student query becomes  $H(\mathbf{q}^{\mathcal{S}^*}) = (1/2) \log 2\pi e[(\sigma_{\mathbf{q}^{\mathcal{S}}}^2 + \epsilon_{\mathbf{q}^{\mathcal{S}}}) / \gamma_{\mathbf{q}^{\mathcal{S}}}^2]$ . Therefore, in the forward propagation, we can obtain the current optimal query  $\mathbf{q}^{\mathcal{S}^*}$  via Eq. (9), after which, the upper-level optimization is further executed as detailed in the following contents.
+
+Upper-level optimization. We continue minimizing the conditional information entropy between the student and the teacher. Following DETR [4], we denote the ground-truth labels by  $\pmb{y}^{GT} = \{c_i^{GT}, b_i^{GT}\}_{i=1}^{N_{gt}}$  as a set of ground-truth objects where  $N_{gt}$  is the number of foregrounds,  $c_i^{GT}$  and  $b_i^{GT}$  respectively represent the class and coordinate (bound- ing box) for the  $i$ -th object. In DETR, each query is associated with an object. Therefore, we can obtain  $N$  objects for teacher and student as well, denoted as  $\pmb{y}^S = \{c_j^S, b_j^S\}_{j=1}^N$  and  $\pmb{y}^T = \{c_j^T, b_j^T\}_{j=1}^N$ .
+
+The minimization of the conditional information entropy requires the student and teacher objects to be in a one-to-one matching. However, it is problematic for DETR due primarily to the sparsity of prediction results and the instability of the query's predictions [16]. We propose a foreground-aware query matching to rectify "well-matched" queries to solve this. Concretely, we match the ground-truth bounding boxes with this student to find the maximum coincidence as:
+
+$$
+G _ {i} = \max  _ {1 \leq j \leq N} \operatorname {G I o U} \left(b _ {i} ^ {G T}, b _ {j} ^ {S}\right), \tag {10}
+$$
+
+where  $\mathrm{GIOU}(\cdot)$  is the generalized intersection over union function [32]. Each  $G_{i}$  reflects the "closeness" of student proposals to the  $i$ -th ground-truth object. Then, we retain highly qualified student proposals around at least one ground truth to benefit object recognition [38] as:
+
+$$
+b _ {j} ^ {\mathcal {S}} = \left\{ \begin{array}{l l} b _ {j} ^ {\mathcal {S}}, & \text {G I o U} \left(b _ {i} ^ {G T}, b _ {j} ^ {\mathcal {S}}\right) > \tau G _ {i}, \forall i \\ \varnothing , & \text {o t h e r w i s e}, \end{array} \right. \tag {11}
+$$
+
+where  $\tau$  is a threshold controlling the proportion of distilled queries. After removing object-empty  $(\varnothing)$  queries in  $\tilde{\pmb{q}}^S$ , we form a distillation-desired query set of students denoted as  $\tilde{\pmb{q}}^S$  associated with its object set  $\tilde{\pmb{y}}^S = \{\tilde{c}_j^S, \tilde{b}_j^S\}_{j=1}^N$ . Correspondingly, we can obtain a teacher query set  $\tilde{\pmb{y}}^T = \{\tilde{c}_j^T, \tilde{b}_j^T\}_{j=1}^N$ . For the  $j$ -th student query, its corresponding teacher query is matched as:
+
+$$
+\tilde {c} _ {j} ^ {\mathcal {T}}, \tilde {b} _ {j} ^ {\mathcal {T}} = \underset {\tilde {c} _ {k} ^ {\mathcal {T}}, \tilde {b} _ {k} ^ {\mathcal {T}}} {\arg \max } \sum_ {k = 1} ^ {N} \mu_ {1} \operatorname {G I o U} \left(\tilde {b} _ {j} ^ {\mathcal {S}}, b _ {k} ^ {\mathcal {T}}\right) - \mu_ {2} \| \tilde {b} _ {j} ^ {\mathcal {S}} - b _ {k} ^ {\mathcal {T}} \| _ {1}, \tag {12}
+$$
+
+where  $\mu_{1} = 2$  and  $\mu_{2} = 5$  control the matching function, values of which is to follow [4].
+
+Finally, the upper-level optimization after rectification in Eq. (6) becomes:
+
+$$
+\min  _ {\theta} H \left(\tilde {\mathbf {q}} ^ {\mathcal {S} ^ {*}} \mid \tilde {\mathbf {q}} ^ {\mathcal {T}}\right). \tag {13}
+$$
+
+Optimizing Eq.(13) is challenging. Alternatively, we minimize the norm distance between  $\tilde{\mathbf{q}}^{S^*}$  and  $\tilde{\mathbf{q}}^T$ , optima of which, i.e.,  $\tilde{\mathbf{q}}^{S^*} = \tilde{\mathbf{q}}^T$ , is exactly the same with that in Eq. (13). Thus, the final loss for our distribution rectification distillation loss becomes:
+
+$$
+\mathcal {L} _ {D R D} \left(\tilde {\mathbf {q}} ^ {\mathcal {S} ^ {*}}, \tilde {\mathbf {q}} ^ {\mathcal {T}}\right) = \mathbb {E} \left[ \left\| \tilde {\mathbf {D}} ^ {\mathcal {S} ^ {*}} - \tilde {\mathbf {D}} ^ {\mathcal {T}} \right\| _ {2} \right], \tag {14}
+$$
+
+where we use the Euclidean distance of co-attented feature  $\tilde{\mathbf{D}}$  (see Eq. 3) containing the information query  $\tilde{\mathbf{q}}$  for optimization.
+
+In backward propagation, the gradient updating drives the student queries toward their teacher hints. Therefore we accomplish our distillation. The overall training losses for our Q-DETR model are:
+
+$$
+\mathcal {L} = \mathcal {L} _ {G T} \left(\boldsymbol {y} ^ {G T}, \boldsymbol {y} ^ {\mathcal {S}}\right) + \lambda \mathcal {L} _ {D R D} \left(\tilde {\boldsymbol {\mathbf {q}}} ^ {\mathcal {S} ^ {*}}, \tilde {\boldsymbol {\mathbf {q}}} ^ {\mathcal {T}}\right), \tag {15}
+$$
+
+where  $L_{GT}$  is the common detection loss for missions such as proposal classification and coordinate regression [4], and  $\lambda$  is a tradeoff hyper-parameter.
+
+# 5. Experiments
+
+In this section, we evaluate the performance of the proposed Q-DETR mode using popular DETR [4] and SMCA-DETR [11] models. To the best of our knowledge, there is no publicly available source code on quantization-aware training of DETR methods at this point, so we implement the baseline and LSQ [8] methods ourselves.
+
+# 5.1. Datasets and Implementation Details
+
+Datasets. We first conduct the ablative study and hyper-parameter selection on the PASCAL VOC dataset [9], which contains natural images from 20 different classes. We use the VOC trainval2012, and VOC trainval2007 sets to train our model, which contains approximately 16k images, and the VOC test2007 set to evaluate our Q-DETR, which contains 4952 images. We report COCO-style metrics for the VOC dataset: AP,  $\mathrm{AP}_{50}$  (default VOC metric), and  $\mathrm{AP}_{75}$ . We further conduct the experiments on the COCO 2017 [18] object detection tracking. Specifically, we train the models on COCO train2017 and evaluate the models on COCO val2017. We list the average precision (AP) for IoUs∈[0.5:0.05:0.95], designated as AP, using COCO's standard evaluation metric. For further analyzing our method, we also list  $\mathrm{AP}_{50}$ ,  $\mathrm{AP}_{75}$ ,  $\mathrm{AP}_s$ ,  $\mathrm{AP}_m$ , and  $\mathrm{AP}_l$ .
+
+Implementation Details. Our Q-DETR is trained with the DETR [4] and SMCA-DETR [11] framework. We select the ResNet-50 [12] and modify it with Pre-Activation structures and RPRELU [25] function following [23]. PyTorch [30] is used for implementing Q-DETR. We run the experiments on 8 NVIDIA Tesla A100 GPUs with 80 GB memory. We use ImageNet ILSVRC12 [15] to pre-train
+
+![](images/f81fb84b5bb6aab549b17b32fa5da6cc62eb498e5c10813514540515dba9c182.jpg)  
+(a) Effect of  $\tau$  and  $\lambda$ .
+
+![](images/47952eabf7f40ca87b81667b8ca2c1c9243c9c288b2ab9cb3103439d10a90646.jpg)  
+(b) Mutual information curves.  
+Figure 5. (a) We select  $\tau$  and  $\lambda$  using 4-bit Q-DETR-R50 on VOC. (b) The mutual information curves of  $I(X; \mathbf{E})$  and  $I(\boldsymbol{y}^{GT}; \mathbf{E}, \mathbf{q})$  (Eq. 4) on the information plane. The red curves represent the teacher model (DETR-R101). The orange, green, red, and purple lines represent the 4-bit baseline, 4-bit baseline + DA, 4-bit baseline + FQM, and 4-bit baseline + DA + FQM (4-bit Q-DETR).
+
+the backbone of a quantized student. The training protocol is the same as the employed frameworks [4, 11]. Specifically, we use a batch size of 16. AdamW [28] is used to optimize the Q-DETR, with the initial learning rate of  $1e^{-4}$ . We train for 300/500 epochs for the Q-DETR on VOC/COCO dataset, and the learning rate is multiplied by 0.1 at the 200/400-th epoch, respectively. Following the SMCA-DETR, we train the Q-SMCA-DETR for 50 epochs, and the learning rate is multiplied by 0.1 at the 40-th epoch on both the VOC and COCO datasets. We utilize a multistillation strategy, where we save the encoder and decoder network as real-valued at the first stage. Then we train the fully quantized DETR at the second stage, where we load the weight from the checkpoint of first stage. We select real-valued DETR-R101 (84.5% AP<sub>50</sub> on VOC and 43.5% AP on COCO) and SMCA-DETR-R101 (85.3% AP<sub>50</sub> on VOC and 44.4% AP on COCO) as teacher network.
+
+# 5.2. Ablation Study
+
+Hyper-parameter selection. As mentioned above, we select hyper-parameters  $\tau$  and  $\lambda$  in this part using the 4-bit Q-DETR model. We show the model performance  $(\mathrm{AP}_{50})$  with different setups of hyper-parameters  $\{\tau ,\lambda \}$  in Fig.5 (a), where we conduct ablative experiments on the baseline  $+\mathrm{DA}(\mathrm{AP}_{50} = 78.8\%)$ . As can be seen, the performances increase first and then decrease with the increase of  $\tau$  from left to right. Since  $\tau$  controls the proportion of selected distillation-desired queries, we show that the full-imitation  $(\tau = 0)$  performs worse than the vanilla baseline with no distillation  $(\tau = 1)$ , showing query selection is necessary. The figure also shows that the performances increase first and then decrease with the increase of  $\tau$  from left to right. The Q-DETR obtains better performances with  $\tau$  set as 0.5 and 0.6. With the varying value of  $\lambda$ , we find  $\{\lambda ,\tau \} = \{2.5,0.6\}$  boost the performance of Q-DETR most, achieving  $82.7\%$  AP on VOC test2007. Based on the ablative study above, we set hyper-parameters  $\tau$  and  $\lambda$  as 0.6 and 2.5
+
+Table 1. Evaluating the components of Q-DETR-R50 on the VOC dataset. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations. DA denotes the distribution alignment module. FQM denotes foreground-aware query matching.  
+
+<table><tr><td>Method</td><td>#Bits</td><td>\(AP_{50}\)</td><td>#Bits</td><td>\(AP_{50}\)</td><td>#Bits</td><td>\(AP_{50}\)</td></tr><tr><td>Real-valued</td><td>32-32-32</td><td>83.3</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>78.0</td><td>3-3-8</td><td>76.8</td><td>2-2-8</td><td>69.7</td></tr><tr><td>+DA</td><td>4-4-8</td><td>78.8</td><td>3-3-8</td><td>78.0</td><td>2-2-8</td><td>71.6</td></tr><tr><td>+FQM</td><td>4-4-8</td><td>81.5</td><td>3-3-8</td><td>80.9</td><td>2-2-8</td><td>74.9</td></tr><tr><td>+DA+FQM(Q-DETR)</td><td>4-4-8</td><td>82.7</td><td>3-3-8</td><td>82.1</td><td>2-2-8</td><td>76.4</td></tr></table>
+
+for the experiments in this paper.
+
+Effectiveness of components. We show quantitative improvements of components in Q-DETR in Tab. 1. As shown in Tab. 1, the quantized DETR baseline suffers a severe performance drop on  $\mathrm{AP}_{50}$  (13.6%, 6.5%, and 5.3% with 2/3/4-bit, respectively). DA and FQM improve the performance when used alone, and the two techniques further boost the performance considerably when combined. For example, the DA improves the 2-bit baseline by 1.9%, and the FQM achieves a 5.2% performance improvement. While combining the DA and FQM, the performance improvement achieves 6.7%.
+
+Information analysis. We further show the information plane following [39] in Fig. 5(b). We adopt the test  $\mathrm{AP}_{50}$  to quantify  $I(\boldsymbol{y}^{GT};\mathbf{E},\mathbf{q})$ . We employ a reconstruction decoder to decode the encoded feature  $\mathbf{E}$  to reconstruct the input and quantify  $I(X;\mathbf{E})$  using the  $\ell_1$  loss. As shown in Fig. 5(b), the curve of the larger teacher DETR-R101 is usually on the right of the curve of small student models, which indicates a greater ability of information representation. Likewise, the purple line (Q-DETR-R50) is usually on the right of the three left curves, showing the information representation improvements with the proposed methods.
+
+# 5.3. Results on PASCAL VOC
+
+We first compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks for object detection task with the VOC dataset. We also report the detection performance of the 8-bit post-training quantization networks, such as percentile [19], VT-PTQ [26]. We use the input resolution following [4], i.e.  $1333 \times 800$ . We mainly discuss the  $\mathrm{AP}_{50}$  (default VOC metric) in the following.
+
+We evaluate the proposed Q-DETR on DETR-R50 models in Tab.2. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger compression ratio than 8-bit VT-PTQ, but with a bit of performance improvement (82.7% vs. 82.3%). Also, the proposed method boosts the performance of 2/3/4-bit baseline by 6.7%, 5.3%, and 4.7% with the same architecture
+
+Table 2. We report AP,  $\mathrm{AP}_{50}$ , and  $\mathrm{AP}_{75}$  (\%) with state-of-the-art quantization methods on DETR and SMCA-DETR using VOC test2007. #Bits (W-A-Attention) denotes the bit-width of weights, activations, and attention activations.  
+
+<table><tr><td>Model</td><td>Method</td><td>#Bits</td><td>AP</td><td>\( AP_{50} \)</td><td>\( AP_{75} \)</td></tr><tr><td rowspan="12">DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>59.5</td><td>83.3</td><td>64.7</td></tr><tr><td>Percentile</td><td rowspan="2">8-8-8</td><td>54.7</td><td>79.2</td><td>60.1</td></tr><tr><td>VT-PTQ</td><td>57.6</td><td>82.3</td><td>63.1</td></tr><tr><td>LSQ</td><td></td><td>49.7</td><td>76.9</td><td>53.0</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>51.3</td><td>78.0</td><td>54.1</td></tr><tr><td>Q-DETR</td><td></td><td>57.1</td><td>82.7</td><td>61.5</td></tr><tr><td>LSQ</td><td></td><td>47.0</td><td>75.3</td><td>49.1</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>49.2</td><td>76.8</td><td>51.8</td></tr><tr><td>Q-DETR</td><td></td><td>56.8</td><td>82.1</td><td>61.2</td></tr><tr><td>LSQ</td><td></td><td>42.6</td><td>68.2</td><td>44.8</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>44.0</td><td>69.7</td><td>45.8</td></tr><tr><td>Q-DETR</td><td></td><td>50.7</td><td>76.4</td><td>54.1</td></tr><tr><td rowspan="12">SMCA-DETR -R50</td><td>Real-valued</td><td>32-32-32</td><td>56.7</td><td>83.7</td><td>62.0</td></tr><tr><td>Percentile</td><td rowspan="2">8-8-8</td><td>54.7</td><td>79.2</td><td>60.1</td></tr><tr><td>VT-PTQ</td><td>55.9</td><td>83.0</td><td>61.3</td></tr><tr><td>LSQ</td><td></td><td>49.6</td><td>78.6</td><td>53.4</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>50.7</td><td>79.5</td><td>55.4</td></tr><tr><td>Q-DETR</td><td></td><td>56.2</td><td>83.3</td><td>61.6</td></tr><tr><td>LSQ</td><td></td><td>47.7</td><td>76.5</td><td>51.7</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>49.9</td><td>77.5</td><td>53.6</td></tr><tr><td>Q-DETR</td><td></td><td>54.3</td><td>82.6</td><td>59.5</td></tr><tr><td>LSQ</td><td></td><td>42.3</td><td>69.7</td><td>44.8</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>43.9</td><td>70.4</td><td>46.1</td></tr><tr><td>Q-DETR</td><td></td><td>50.2</td><td>76.7</td><td>52.6</td></tr></table>
+
+and bit-width, which significantly validates the effectiveness of our method.
+
+Besides, our method generates convincing results on SMCA-DETR. As shown in Tab. 2, the performance of the proposed Q-DETR with SMCA-DETR-R50 outperforms the 2/3/4-bit Baseline method by  $6.3\%$ ,  $5.1\%$  and  $3.8\%$  on  $\mathrm{AP}_{50}$ , a large margin. Compared with 8-bit post-training quantization methods, our method achieves a significantly higher compression rate and comparable performance.
+
+# 5.4. Results on COCO
+
+We further show comparison on the large-scale COCO [18] dataset. We compare our method with the 2/3/4-bit baseline and LSQ [8] based on the same frameworks. We also report the detection performance of the 8-bit posttraining quantization networks, such as percentile [19], VT-PTQ [26]. The AP with different IoU thresholds, and AP of objects with varying scales are all reported in Tab. 3.
+
+Tab. 3 lists the comparison of several quantization approaches and detection frameworks in computing complexity, storage cost. Our Q-DETR significantly accelerates computation and reduces storage requirements for various
+
+Table 3. Comparison with state-of-the-art quantization methods using DETR and SMCA-DETR on COCO val2017. #Bits (W-A-Attention) denotes bit-width of weights, activations, and attention activations.  
+
+<table><tr><td>Model</td><td>Method</td><td>#Bits</td><td>Size(MB)</td><td>OPs(G)</td><td>AP</td><td>AP50</td><td>AP75</td><td>APs</td><td>APm</td><td>APl</td></tr><tr><td rowspan="12">DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>159.32</td><td>85.51</td><td>42.0</td><td>62.4</td><td>44.2</td><td>20.5</td><td>45.8</td><td>61.1</td></tr><tr><td>Percentile</td><td>8-8-8</td><td>39.83</td><td>23.01</td><td>38.6</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VT-PTQ</td><td></td><td></td><td></td><td>41.2</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>33.3</td><td>53.7</td><td>33.9</td><td>12.8</td><td>37.0</td><td>51.6</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>19.92</td><td>13.02</td><td>34.1</td><td>55.3</td><td>35.4</td><td>14.3</td><td>38.0</td><td>53.8</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>39.4</td><td>60.2</td><td>41.4</td><td>17.7</td><td>43.4</td><td>59.9</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>31.0</td><td>52.3</td><td>32.1</td><td>11.3</td><td>33.9</td><td>48.5</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>15.03</td><td>7.61</td><td>32.3</td><td>52.2</td><td>32.9</td><td>12.3</td><td>35.4</td><td>50.3</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>36.1</td><td>55.9</td><td>37.5</td><td>14.6</td><td>39.4</td><td>55.2</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>24.7</td><td>44.6</td><td>26.5</td><td>6.3</td><td>25.3</td><td>42.7</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>10.03</td><td>5.32</td><td>26.6</td><td>46.6</td><td>26.5</td><td>8.4</td><td>28.2</td><td>44.4</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>31.4</td><td>51.3</td><td>31.6</td><td>11.6</td><td>34.3</td><td>49.6</td></tr><tr><td rowspan="12">SMCA-DETR-R50</td><td>Real-valued</td><td>32-32-32</td><td>164.75</td><td>86.65</td><td>41.0</td><td>62.2</td><td>43.6</td><td>21.9</td><td>44.3</td><td>59.1</td></tr><tr><td>Percentile</td><td>8-8-8</td><td>41.19</td><td>23.66</td><td>37.5</td><td>58.5</td><td>40.1</td><td>17.6</td><td>39.1</td><td>55.9</td></tr><tr><td>VT-PTQ</td><td></td><td></td><td></td><td>40.2</td><td>61.0</td><td>42.6</td><td>20.3</td><td>42.9</td><td>57.7</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>33.9</td><td>55.0</td><td>35.0</td><td>13.2</td><td>37.2</td><td>51.4</td></tr><tr><td>Baseline</td><td>4-4-8</td><td>20.59</td><td>13.48</td><td>35.0</td><td>56.4</td><td>36.4</td><td>15.6</td><td>38.3</td><td>52.5</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>38.3</td><td>59.7</td><td>39.8</td><td>17.7</td><td>41.7</td><td>56.8</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>30.1</td><td>52.6</td><td>31.4</td><td>11.9</td><td>33.4</td><td>46.6</td></tr><tr><td>Baseline</td><td>3-3-8</td><td>15.68</td><td>8.05</td><td>31.8</td><td>53.7</td><td>32.6</td><td>12.6</td><td>35.2</td><td>49.8</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>35.0</td><td>56.3</td><td>36.9</td><td>15.0</td><td>39.0</td><td>53.1</td></tr><tr><td>LSQ</td><td></td><td></td><td></td><td>23.9</td><td>42.2</td><td>24.2</td><td>9.4</td><td>26.2</td><td>37.5</td></tr><tr><td>Baseline</td><td>2-2-8</td><td>10.84</td><td>4.54</td><td>25.4</td><td>44.3</td><td>25.2</td><td>8.4</td><td>27.2</td><td>40.3</td></tr><tr><td>Q-DETR</td><td></td><td></td><td></td><td>30.5</td><td>51.8</td><td>31.8</td><td>12.0</td><td>33.2</td><td>48.0</td></tr></table>
+
+detectors. We follow [40] to calculate memory usage, by adding  $32 \times$  the number of real-valued weights and  $a \times$  the number of quantized weights in the  $a$ -bit networks. The number of operations (OPs) is calculated in the same way as [40]. Current CPUs can handle both bit-wise XNOR and bit-count operations in parallel. The respective number of FLOPs adds  $\left\{\frac{1}{32}, \frac{1}{16}, \frac{1}{8}\right\}$  of the number of  $\{2,3,4\}$ -bit multiplications equals the OPs following [24].
+
+We summarize the experimental results on COCO val2017 of Q-DETR-R50 from lines 2 to 17 in Tab.3. For the DETR-R50 model, compared with the 8-bit PTQ method, our 4-bit Q-DETR achieves a much larger acceleration than the 8-bit VT-PTQ but with an acceptable performance gap. Also, the proposed method boosts the performance of  $2/3/4$ -bit baseline by  $4.8\%$ ,  $3.8\%$  and  $5.1\%$  AP with the same architecture and bit-width, which is significant on the large-scale COCO dataset. Compared with the real-valued counterparts, the proposed  $2/3/4$ -bit Q-DETR achieves computation acceleration and storage savings by  $16.07 \times / 11.23 \times / 6.57 \times$  and  $15.88 \times / 10.60 \times / 7.99 \times$ . The above results are of great significance in the real-time inference of object detection. All of the improvements have impacts on object detection.
+
+For the SMCA-DETR-R50 model, we observe similar
+
+performance improvements and compression ratios. For example, the 4-bit Q-SMCA-DETR-R50 theoretically accelerates  $6.42 \times$  with only a  $2.7\%$  performance gap compared with the real-valued counterpart, which is significant for real-time DETR methods.
+
+# 6. Conclusion
+
+This paper introduces a novel method for training quantized DETR (Q-DETR) with knowledge distillation to rectify the query distribution. Q-DETR generalizes the information bottleneck (IB) principle and leads a bi-level distribution rectification distillation. We effectively employ a distribution alignment module to solve inner-level and a foreground-aware query matching scheme to solve upper level. As a result, Q-DETR significantly boosts performance of low-bit DETR. Extensive experiments show that Q-DETR surpasses state-of-the-arts in DETR quantization.
+
+# 7. Acknowledgements
+
+This work was supported by National Natural Science Foundation of China under Grant 62141604, 62076016, Beijing Natural Science Foundation L223024.
+
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen",
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+        "img_path": "images/e35abe3c93774187015fffd290bc71c99c77f4a716874f885f457d34433d322c.jpg",
+        "image_caption": [
+            "Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2]."
+        ],
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+        "img_path": "images/ebbf56ed8b02233525afdee7b734883d1b9987eb94f993c2944da32b50605a90.jpg",
+        "image_caption": [],
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+    {
+        "type": "text",
+        "text": "erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures.",
+        "bbox": [
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+        "text": "Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models.",
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+        "text": "Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_number",
+        "text": "2321",
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+    {
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+        "img_path": "images/c8d6095f716cf4912c526deb9e6e83fd023966593a8d27477e9378310725d4c9.jpg",
+        "image_caption": [
+            "Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates."
+        ],
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+    {
+        "type": "text",
+        "text": "challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text.",
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+    {
+        "type": "text",
+        "text": "The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon.",
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+    {
+        "type": "text",
+        "text": "The main contributions of our work are:",
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+    {
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+        "text": "- We present a novel quantization-based motion matching framework for speech-driven gesture generation.",
+        "bbox": [
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+        "type": "list",
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+        "list_items": [
+            "- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization.",
+            "- We design a phase guidance strategy to select optimal audio and text candidates for motion matching.",
+            "- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2322",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/588f51f05d2070063f33b8c5f910136474356f75b8e40df2f83722a9aea7b1da.jpg",
+        "image_caption": [
+            "Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "based motion matching with phase guidance.",
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+    {
+        "type": "text",
+        "text": "3. Our Approach",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step.",
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+    {
+        "type": "text",
+        "text": "3.1. Learning a discrete latent space representation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence  $\\mathbf{G} \\in \\mathbb{R}^{T \\times D_g}$ , where  $T$  denotes the number of gestures and  $D_g$  pose dimension. We first adopt a 1D temporal convolution network  $E_g$  to encode the joint sequence  $\\mathbf{G}$  to context-aware features  $\\mathbf{g} \\in \\mathbb{R}^{T' \\times C}$ , where  $T' = T / d$ ,  $d$  is the temporal down-sampling rate, and  $C$  is the channel dimension of features. This process could be written as  $\\mathbf{g} = E_g(\\mathbf{G})$ . Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook  $\\mathcal{Z}_g$  elements  $\\mathbf{g_q} \\in \\mathbb{R}^{T' \\times C}$ , where  $\\mathbf{g_q} \\in \\mathcal{Z}_g^T$ ,  $\\mathcal{Z}_g$  is a set of  $C_b$  codes of dimension  $n_z$ , we quantize  $\\mathbf{g}$  by mapping each temporal feature  $\\mathbf{g}_i$  to its closest codebook element  $z_j$  as  $\\mathbf{q}(.)$ :",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {g} _ {\\mathbf {q}, i} = \\mathbf {q} (\\mathbf {g}) = \\arg \\min  _ {\\mathbf {z} _ {j} \\in \\mathcal {Z} _ {g}} \\| \\mathbf {g} _ {i} - \\mathbf {z} _ {j} \\| \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "A following de-convolutional decoder  $D_g$  projects  $\\mathbf{g_q}$  back to the motion space as a pose sequence  $\\hat{\\mathbf{G}}_1$ , which can be formulated as",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {G}} _ {1} = D _ {g} \\left(\\mathbf {g} _ {q}\\right) = D _ {g} \\left(\\mathbf {q} \\left(E _ {g} (\\mathbf {G})\\right)\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Thus the encoder, decoder and codebook can be trained by optimizing:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {g e s t u r e} \\left(E _ {g}, D _ {g}, \\mathcal {Z} _ {g}\\right)} = \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G}\\right) + \\left\\| \\operatorname {s g} [ \\mathbf {g} ] - \\mathbf {g} _ {\\mathbf {q}} \\right\\| \\tag {3} \\\\ + \\beta \\| \\mathbf {g} - \\mathrm {s g} [ \\mathbf {g _ {q}} ] \\| \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{rec}$  is the reconstruction loss that constrains the predicted joint sequence to ground truth,  $\\mathrm{sg}[\\cdot ]$  denotes the stop-gradient operation, and the term  $\\| \\mathbf{g} - \\mathrm{sg}\\left[\\mathbf{g_q}\\right]\\|$  is the \"commitment loss\" with weighting factor  $\\beta$  [42].",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {r e c}} \\left(\\hat {\\mathbf {G}} _ {1}, \\mathbf {G} _ {1}\\right) = \\left\\| \\hat {\\mathbf {G}} _ {1} - \\mathbf {G} _ {1} \\right\\| _ {1} + \\alpha_ {1} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime} - \\mathbf {G} _ {1} ^ {\\prime} \\right\\| _ {1} \\tag {4} \\\\ + \\alpha_ {2} \\left\\| \\hat {\\mathbf {G}} _ {1} ^ {\\prime \\prime} - \\mathbf {G} _ {1} ^ {\\prime \\prime} \\right\\| _ {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "2323",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input  $\\mathbf{G}$  i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation  $\\mathbf{z}$ , for each time step  $i$ , the quantization module replaces the original representation  $\\mathbf{z}$  by  $\\hat{\\mathbf{z}} = \\mathbf{a}_{\\mathbf{q},i}$  from  $\\mathcal{Z}_a$ , which contains a set of  $C_b'$  codes of dimension  $n_z'$ .",
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+    {
+        "type": "text",
+        "text": "3.2. Motion Matching based on Audio and Text",
+        "text_level": 1,
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Our motion matching algorithm takes a discrete text sequence  $\\mathbf{t} = [\\mathbf{t}_0, \\mathbf{t}_1, \\dots, \\mathbf{t}_{T' - 1}]$ , a discrete audio sequence  $\\mathbf{a_q} = [\\mathbf{a_{q,0}}, \\mathbf{a_{q,1}}, \\dots, \\mathbf{a_{q,T'}} - 1]$ , and one initial previous pose code  $\\mathbf{g}_{-1}$ , and optionally a sequence of control masks  $\\mathbf{M} = [\\mathbf{m}_0, \\mathbf{m}_1, \\dots, \\mathbf{m}_{T' - 1}]$ . The outputs are audio-based candidate  $\\mathbf{C}_a = [\\mathbf{c}_{0,a}, \\mathbf{c}_{1,a}, \\dots, \\mathbf{c}_{T' - 1,a}]$  and text-based candidate  $\\mathbf{C}_t = [\\mathbf{c}_{0,t}, \\mathbf{c}_{1,t}, \\dots, \\mathbf{c}_{T' - 1,t}]$ .  $T'$  denotes the number of speech segments during inference.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To find the appropriate output gesture sequence  $\\mathbf{C}_a$  and  $\\mathbf{C}_t$  from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code  $\\mathbf{g}_{-1}$  for every  $T$  frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code  $\\mathbf{g}_{-1}$  and the joints corresponding to each code  $\\mathbf{g_q}$  in the codebook to get the pose-based pre-candidate  $\\hat{\\mathbf{C}}_g = \\left\\{\\hat{\\mathbf{C}}_g^0,\\hat{\\mathbf{C}}_g^1,\\dots ,\\hat{\\mathbf{C}}_g^{C_b}\\right\\}$ . In the first iteration, the previous pose code  $\\mathbf{g}_{-1}$  is initialized by either randomly sampling a code from codebook  $\\mathcal{Z}_g$  or set to be the code with the most frequent occurrences in the codebook (the code of mean pose).",
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+    },
+    {
+        "type": "text",
+        "text": "Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence  $\\mathbf{F}_a = [\\mathbf{F}_{a,0},\\mathbf{F}_{a,1},\\dots ,\\mathbf{F}_{a,T^{\\prime} - 1}]$ . To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database,",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/561973762b93813c2f17ca25b1a35de12b0254e7490a0b52ef0bc487c6fce9ae.jpg",
+        "image_caption": [
+            "Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            514,
+            94,
+            880,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "we calculate the audio feature similarity of the corresponding code per  $d$  frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate  $\\hat{\\mathbf{C}}_a = \\left\\{\\hat{\\mathbf{C}}_a^0,\\hat{\\mathbf{C}}_a^1,\\dots ,\\hat{\\mathbf{C}}_a^{C_b}\\right\\}$ . Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence  $\\mathbf{F}_t$ . For every clip in the database, we calculate the text features cosine similarity of the corresponding code per  $d$  frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is  $\\hat{\\mathbf{C}}_t = \\left\\{\\hat{\\mathbf{C}}_t^0,\\hat{\\mathbf{C}}_t^1,\\dots ,\\hat{\\mathbf{C}}_t^{C_b}\\right\\}$",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate  $\\mathbf{C}_a$  based on  $\\hat{\\mathbf{C}}_g$  and  $\\hat{\\mathbf{C}}_a$ , and text candidate  $\\mathbf{C}_t$  based on  $\\hat{\\mathbf{C}}_g$  and  $\\hat{\\mathbf{C}}_t$ . Then we select the final gesture from  $\\mathbf{C}_a$  and  $\\mathbf{C}_t$  according to the phase guide.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3. Phase-Guided Gesture Generation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network  $E_{p}$  to a latent space of the motion  $\\mathbf{G}$ , which can be formulated as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {L} = E _ {p} (\\mathbf {G}) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "2324",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{L} \\in \\mathbb{R}^{T \\times M}$ ,  $M$  is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of  $\\mathbf{L}$  and create the zero-indexed matrix of Fourier coefficients  $\\mathbf{c} \\in \\mathbb{C}^{M \\times K + 1}$ ,  $K = \\left\\lfloor \\frac{T}{2} \\right\\rfloor$ , written as  $\\mathbf{c} = FFT(\\mathbf{L})$ . Power spectrum  $\\mathbf{p} \\in \\mathbb{R}^{M \\times K + 1}$  for each channel is  $\\mathbf{p}_{i,j} = \\frac{2}{T} |\\mathbf{c}_{i,j}|^2$ , where  $i$  is the channel index and  $j$  is the index for the frequency bands. Assumed that there are  $T$  points in a time window of  $N$  seconds. The periodic parameters are computed by:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {A} _ {i} = \\sqrt {\\frac {2}{T} \\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {F} _ {i} = \\frac {\\sum_ {j = 1} ^ {K} \\left(\\mathbf {f} _ {j} \\cdot \\mathbf {p} _ {i , j}\\right)}{\\sum_ {j = 1} ^ {K} \\mathbf {p} _ {i , j}}, \\quad \\mathbf {B} _ {i} = \\frac {\\mathbf {c} _ {i , 0}}{T}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{f} = (0,1 / N,2 / N,\\dots ,K / N)$  is frequencies vector.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Phase shift  $\\mathbf{S} \\in \\mathbb{R}^{M}$  for each latent curve  $\\mathbf{S}_i$  can be predicted by a fully connected layer  $FC$ , which can be formulated as:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left(s _ {x}, s _ {y}\\right) = F C \\left(\\mathbf {L} _ {i}\\right), \\quad \\mathbf {S} _ {i} = \\operatorname {a t a n 2} \\left(s _ {y}, s _ {x}\\right) \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For each temporal motion  $\\mathbf{G}$ , within a centered time window  $\\mathcal{T} = \\left[-\\frac{t_1 - t_0}{2}, -\\frac{t_1 - t_0}{2} + \\frac{t_1 - t_0}{N - 1}, \\dots, \\frac{t_1 - t_0}{2}\\right]$ , where  $t_0 \\leq t \\leq t_1$ , the decoder  $D_p$  takes all periodic parameters as its input, and maps back to the original motion curves:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {L}} = f (\\mathcal {T}; \\mathbf {A}, \\mathbf {F}, \\mathbf {B}, \\mathbf {S}) = \\mathbf {A} \\cdot \\sin (2 \\pi \\cdot (\\mathbf {F} \\cdot \\mathcal {T} - \\mathrm {S})) + \\mathbf {B} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {G}} _ {2} = h (\\hat {\\mathbf {L}}) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding  $\\mathbf{L}$ .",
+        "bbox": [
+            76,
+            647,
+            468,
+            693
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {p h a s e}} = \\mathcal {L} _ {\\text {p h a s e - r e c o n}} (\\mathbf {G}, \\hat {\\mathbf {G}} _ {\\mathbf {2}}) \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            702,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After training, phase manifold  $\\mathcal{P}$  of a sample motion which captures a lot of \"information\" about the current state of the original time series data is",
+        "bbox": [
+            76,
+            731,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {P} _ {2 i - 1} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\sin \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right), \\quad \\mathcal {P} _ {2 i} ^ {(t)} = \\mathrm {A} _ {i} ^ {(t)} \\cdot \\cos \\left(2 \\pi \\cdot \\mathrm {S} _ {i} ^ {(t)}\\right) \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            76,
+            786,
+            478,
+            824
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{P}\\in \\mathbb{R}^{2M}$",
+        "bbox": [
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+            824,
+            194,
+            838
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto",
+        "bbox": [
+            75,
+            839,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/cd14b049e39e037f1f7483572bf9e42dc51f401e83431c1b48b65f82f73d9a31.jpg",
+        "image_caption": [
+            "(a) Rotational velocity space."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            640,
+            90,
+            753,
+            143
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a85253e41749a017c6eb2d233aa80676278ef9c6d5884fc5322a6b1d88fc5e6.jpg",
+        "image_caption": [
+            "(b) Latent space learned by convolutional and fully connected."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            601,
+            166,
+            792,
+            251
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/87d56a2a641907bb6ccf00d30892b695b58b7d39df493cc4926c5267511b14f6.jpg",
+        "image_caption": [
+            "(c) Phase space.",
+            "Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            601,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames  $N_{strid}$  of the manifold phase  $\\mathcal{P}_{-1}$  corresponding to the frame of the initial code and the first frames of the manifold phase  $\\mathcal{P}_{a/t}$  corresponding to the audio/text candidate  $\\mathbf{C}_a$  and  $\\mathbf{C}_t$  within  $N_{phase}$  frames, which can be written as  $\\text{concat}[\\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \\mathcal{P}_{a/t}^{[N_{strid}]}$  and  $\\text{concat}[\\mathcal{P}_{-1}^{[-N_{strid}]}, \\mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}]$ . Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            630,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "2325",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0470df749c2bb5a1b8fc216dd32923a97d3fcabb6e82c2b4178c8d4c41ca6196.jpg",
+        "image_caption": [
+            "(a) The phase manifold of the seed code to be matched.",
+            "Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate  $\\mathbf{C}_a$  and text candidate  $\\mathbf{C}_t$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            112,
+            90,
+            243,
+            231
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/57417fdb192726bd1146df1f316eeadc16acca6950440f41e27169beadb2f486.jpg",
+        "image_caption": [
+            "(b) The phase manifold of the candidate to be matched."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            307,
+            90,
+            441,
+            231
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers \"wayne\" (male speaker) and \"kieks\" (female speaker), and constructed separate databases for our experiments.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers.  $3 \\times 3$  rotation matrix features are computed as gesture sequences, with pose dimension  $D_{g}$  is 9. Down-sampling rate  $d$  is 8. The size  $C_b$  of codebook  $\\mathcal{Z}_g$  is set to 512 with dimension  $n_z$  is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of  $T = 240$  (4 seconds), using the ADAM [22] optimizer (learning rate is e-4,  $\\beta_{1} = 0.5$ ,  $\\beta_{2} = 0.98$ ) with a batch size of 128 for 200 epochs. We set  $\\beta = 0.1$  for Equation (3) and  $\\alpha_{1} = 1$ ,  $\\alpha_{2} = 1$  for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with  $d = 32$ . As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of  $10^{-4}$  and a batch size of 128. The number of phase channels  $M$  is set to 8. To calculate the phase similarity, the number of frames is set to  $N_{phase} = 8$  and  $N_{stride} = 3$ . The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook  $\\mathcal{Z}_q$ .",
+        "bbox": [
+            76,
+            489,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis",
+        "bbox": [
+            75,
+            839,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tance [25],  $H\\left(\\boldsymbol{h}^{(1)}, \\boldsymbol{h}^{(2)}\\right) = \\sqrt{1 - \\sum_{i} \\sqrt{h_{i}^{(1)} \\cdot h_{i}^{(2)}}}$  between the histograms  $\\boldsymbol{h}^{(1)}$  and  $\\boldsymbol{h}^{(2)}$ . The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Comparison to Existing Methods",
+        "text_level": 1,
+        "bbox": [
+            498,
+            285,
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+            301
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921  $(44\\%)$  and 3837.068  $(39\\%)$  than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space.",
+        "bbox": [
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+            309,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants \"How human-like does the gesture motion appear?\" In terms of appropriateness evaluation, each evaluation page asked participants \"How appropriate are the gestures for the speech?\" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) \"Excellent\", \"Good\", \"Fair\", \"Poor\", and \"Bad\". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1.",
+        "bbox": [
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+            551,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human",
+        "bbox": [
+            498,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "2326",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/757f145197ca1987b82db9a9ec0d786620bbdc560532551ea6ee9746940e829c.jpg",
+        "table_caption": [
+            "Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with  $95\\%$  confidence intervals."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Name</td><td colspan=\"3\">Objective evaluation</td><td colspan=\"2\">Subjective evaluation</td></tr><tr><td>Hellinger distance average↓</td><td>FGD on feature space↓</td><td>FGD on raw data space↓</td><td>Human-likeness</td><td>Appropriateness</td></tr><tr><td>Ground Truth (GT)</td><td>0.0</td><td>0.0</td><td>0.0</td><td>3.79 ± 0.19</td><td>3.62 ± 0.21</td></tr><tr><td>End2End [47]</td><td>0.146</td><td>64.990</td><td>16739.978</td><td>3.64 ± 0.11</td><td>3.23 ± 0.14</td></tr><tr><td>Trimodal [46]</td><td>0.155</td><td>48.322</td><td>12869.98</td><td>3.31 ± 0.17</td><td>3.20 ± 0.19</td></tr><tr><td>StyleGestures [5]</td><td>0.136</td><td>35.842</td><td>9846.927</td><td>3.66 ± 0.08</td><td>3.30 ± 0.11</td></tr><tr><td>KNN [17]</td><td>0.364</td><td>43.030</td><td>12470.061</td><td>2.38 ± 0.10</td><td>2.35 ± 0.13</td></tr><tr><td>CaMN [31]</td><td>0.149</td><td>52.496</td><td>10549.455</td><td>3.65 ± 0.16</td><td>3.29 ± 0.15</td></tr><tr><td>Ours</td><td>0.136</td><td>19.921</td><td>5742.281</td><td>4.00 ± 0.14</td><td>3.66 ± 0.23</td></tr></table>",
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+        "table_caption": [
+            "Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Name</td><td colspan=\"3\">Objective evaluation</td><td colspan=\"2\">Subjective evaluation</td></tr><tr><td>Hellinger distance average↓</td><td>FGD on feature space↓</td><td>FGD on raw data space↓</td><td>Human-likeness</td><td>Appropriateness</td></tr><tr><td>w/o wavvq + WavLM</td><td>0.151</td><td>19.943</td><td>6009.859</td><td>3.87 ± 0.21</td><td>3.64 ± 0.21</td></tr><tr><td>w/o audio</td><td>0.134</td><td>20.401</td><td>5871.044</td><td>3.87 ± 0.21</td><td>3.63 ± 0.20</td></tr><tr><td>w/o text</td><td>0.118</td><td>23.929</td><td>6389.866</td><td>3.57 ± 0.29</td><td>3.41 ± 0.23</td></tr><tr><td>w/o phase</td><td>0.138</td><td>19.195</td><td>5759.167</td><td>3.90 ± 0.11</td><td>3.65 ± 0.17</td></tr><tr><td>w/o motion matching (GRU + codebook)</td><td>0.140</td><td>30.404</td><td>11642.641</td><td>3.78 ± 0.14</td><td>3.43 ± 0.16</td></tr><tr><td>Ours</td><td>0.136</td><td>19.921</td><td>5742.281</td><td>4.07 ± 0.15</td><td>3.77 ± 0.21</td></tr></table>",
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+        "text": "likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more \"related to the semantics\" with \"more natural\", while our method \"lacking power and exaggerated gestures\" compared to GT. More details regarding the user study are shown in the supplementary material.",
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+        "text": "4.2. Ablation Studies",
+        "text_level": 1,
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+        "text": "Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video.",
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+        "type": "text",
+        "text": "We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively.",
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+        "type": "text",
+        "text": "Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant.",
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+        "img_path": "images/d19feb63e29ec809be67e210cb72e7bb433171fcebf1e2d8fedd0a4df462551a.jpg",
+        "image_caption": [
+            "Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase",
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+    {
+        "type": "page_number",
+        "text": "2327",
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+    {
+        "type": "text",
+        "text": "guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by  $10.483(53\\%)$  and 6460.202  $(107\\%)$ , respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space.",
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+    {
+        "type": "text",
+        "text": "User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed.",
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+    {
+        "type": "text",
+        "text": "4.3. Controllability",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold  $\\mathbf{r}$ , the search can be restricted to consider only codes corresponding to wrists above  $\\mathbf{r}$ . Here is an example. The most frequent gesture in the database of \"wayne\" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that \"wayne\" is a habitual right-handed",
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+    {
+        "type": "image",
+        "img_path": "images/749f1ef66e344cf56d62a37d3348d75b94bad3f0d20cfb26f296570fea7e7d5d.jpg",
+        "image_caption": [
+            "Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons.",
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+    {
+        "type": "text",
+        "text": "5. Discussion and Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures.",
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+    {
+        "type": "text",
+        "text": "Acknowledgments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030).",
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+        "type": "page_number",
+        "text": "2328",
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+    {
+        "type": "text",
+        "text": "References",
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+            "[48] Youngwoo Yoon, Pieter Wolfert, Taras Kucherenko, Carla Viegas, Teodor Nikolov, Mihail Tsakov, and Gustav Eje Henter. The GENEA challenge 2022: A large evaluation of data-driven co-speech gesture generation. In International Conference on Multimodal Interaction, ICMI, pages 736-747, 2022. 1",
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+            "[50] Chi Zhou, Tengyue Bian, and Kang Chen. Gesturemaster: Graph-based speech-driven gesture generation. In International Conference on Multimodal Interaction, ICMI, pages 764-770, 2022. 1, 2, 3, 4",
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2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/dedf7a8a-5cf9-4beb-aa1f-59750898d75f_origin.pdf

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2023/QPGesture_ Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation/full.md

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+# QPGesture: Quantization-Based and Phase-Guided Motion Matching for Natural Speech-Driven Gesture Generation
+
+Sicheng Yang $^{1}$  Zhiyong Wu $^{2,1,4}$  Minglei Li $^{2}$  Zhensong Zhang $^{3}$
+
+Lei Hao<sup>3</sup> Weihong Bao<sup>1</sup> Haolin Zhuang<sup>1</sup>
+
+$^{1}$  Tsinghua University  $^{2}$  Huawei Cloud Computing Technologies Co., Ltd
+
+<sup>3</sup> Huawei Noah's Ark Lab <sup>4</sup> The Chinese University of Hong Kong
+
+{yangsc21, bwh21, zhuanghl21}@mails.tsinghua.edu.cn zywu@sz.tsinghua.edu.cn
+
+{liminglei29, zhangzhensong, haolei5}@huawei.com
+
+# Abstract
+
+Speech-driven gesture generation is highly challenging due to the random jitters of human motion. In addition, there is an inherent asynchronous relationship between human speech and gestures. To tackle these challenges, we introduce a novel quantization-based and phase-guided motion matching framework. Specifically, we first present a gesture VQ-VAE module to learn a codebook to summarize meaningful gesture units. With each code representing a unique gesture, random jittering problems are alleviated effectively. We then use Levenshtein distance to align diverse gestures with different speech. Levenshtein distance based on audio quantization as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, we introduce phase to guide the optimal gesture matching based on the semantics of context or rhythm of audio. Phase guides when text-based or speech-based gestures should be performed to make the generated gestures more natural. Extensive experiments show that our method outperforms recent approaches on speech-driven gesture generation. Our code, database, pre-trained models and demos are available at https://github.com/YoungSeng/QPGesture.
+
+# 1. Introduction
+
+Nonverbal behavior plays a key role in conveying messages in human communication [26], including facial expressions, hand gestures and body gestures. Co-speech gesture helps better self-expression [45]. However, producing human-like and speech-appropriate gestures is still very difficult due to two main challenges: 1) Random jittering: People make many small jitters and movements when they speak, which can lead to a decrease in the quality of the gen
+
+![](images/e35abe3c93774187015fffd290bc71c99c77f4a716874f885f457d34433d322c.jpg)  
+Figure 1. Gesture examples generated by our proposed method on various types of speech. The character is from Mixamo [2].
+
+![](images/ebbf56ed8b02233525afdee7b734883d1b9987eb94f993c2944da32b50605a90.jpg)
+
+erated gestures. 2) Inherent asynchronicity with speech: Unlike speech with face or lips, there is an inherent asynchronous relationship between human speech and gestures.
+
+Most existing gesture generation studies intend to solve the two challenges in a single ingeniously designed neural network that directly maps speech to 3D joint sequence in high-dimensional continuous space [18, 24, 27, 31] using a sliding window with a fixed step size [17, 46, 47]. However, such methods are limited by the representation power of proposed neural networks, like the GENEA gesture-generation challenge results. No system in GENEA challenge 2020 [26] rated above a bottom line that paired the input speech audio with mismatched excerpts of training data motion. In GENEA challenge 2022 [48], a motion matching based method [50] ranked first in the human-likeness evaluation and upper-body appropriateness evaluation, and outperformed all other neural network-based models. These results indicate that motion matching based models, if designed properly, are more effective than neural network based models.
+
+Inspired by this observation, in this work, we propose a novel quantization-based motion matching framework for audio-driven gesture generation. Our framework includes two main components aiming at solving the two above challenges, respectively. First, to address the random jittering
+
+![](images/c8d6095f716cf4912c526deb9e6e83fd023966593a8d27477e9378310725d4c9.jpg)  
+Figure 2. Gesture generation pipeline of our proposed framework. 'Quan.' is short for 'quantization' and 'Cand.' is short for 'candidate'. Given a piece of audio, text and seed pose, the audio and gesture are quantized. The candidate for the speech is calculated based on the Levenshtein distance, and the candidate for the text is calculated based on the cosine similarity. The optimal gesture is selected based on phase-guidance corresponding to the seed code and the phase corresponding to the two candidates.
+
+challenge, we compress human gestures into a space that is lower dimensional and discrete, to reduce input redundancy. Instead of manually indicating the gesture units [23], we use a vector quantized variational autoencoder (VQ-VAE) [42] to encode and quantize joint sequences to a codebook in an unsupervised manner, using a quantization bottleneck. Each learned code is shown to represent a unique gesture pose. By reconstructing the discrete gestures, some random jittering problems such as grabbing hands and pushing glasses will be solved. Second, to address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used based on audio quantization. Levenshtein distance helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well. Moreover, unlike the recent gesture matching models [17, 50], we also consider the semantic information of the context. Third, since the body motion is composed of multiple periodic motions spatially, meanwhile the phase values are able to describe the nonlinear periodicity of the high-dimensional motion curves well [39], we use phase to guide how the gestures should be matched to speech and text.
+
+The inference procedure of our framework is shown in Figure 2. Given a piece of audio, text and seed pose, the audio and gesture are first quantized. The best candidate for the speech is calculated based on the Levenshtein distance, and the best candidate for the text is calculated based on the cosine similarity. Then the most optimal gesture is selected based on the phase corresponding to the seed code and the phase corresponding to the two candidates. Our code, database, pre-trained models and demos will be publicly available soon.
+
+The main contributions of our work are:
+
+- We present a novel quantization-based motion matching framework for speech-driven gesture generation.
+
+- We propose to align diverse gestures with different speech using Levenshtein distance, based on audio quantization.  
+- We design a phase guidance strategy to select optimal audio and text candidates for motion matching.  
+- Extensive experiments show that jittering and asynchronicity issues can be effectively alleviated by our framework.
+
+# 2. Related Work
+
+End-to-end Co-speech Gesture Generation. Gesture generation is a complex problem that requires understanding speech, gestures, and their relationships. Data-driven approaches attempt to learn gesticulation skills from human demonstrations. The present studies mainly consider four modalities: text [6,43,47], audio [15,18,24,29,36], gesture motion, and speaker identity [4, 5, 9, 31, 32, 44, 46]. Habibie et al. [18] propose the first approach to jointly synthesize both the synchronous 3D conversational body and hand gestures, as well as 3D face and head animations. Ginosar et al. [15] propose a cross-modal translation method based on the speech-driven gesture gestures of a single speaker. Liu et al. [32] propose a hierarchical audio learner extracts audio representations across semantic granularities and a hierarchical pose inferior renders the entire human pose. Kucherenko et al. [24] propose Aud2Repr2Pose architecture to evaluate the impact of different gesture and speech representations on gesture generation. Qian et al. [36] use conditional learning to resolve the ambiguity of co-speech gesture synthesis by learning the template vector to improve gesture quality.
+
+As for learning individual styles, Yoon et al. [46] propose the first end-to-end method for generating co-speech gestures using the tri-modality of text, audio and speaker
+
+![](images/588f51f05d2070063f33b8c5f910136474356f75b8e40df2f83722a9aea7b1da.jpg)  
+Figure 3. Structure of gesture VQ-VAE. After learning the discrete latent representation of human gesture, the gesture VQ-VAE encode and summarize meaningful gesture units, and reconstruct the target gesture sequence from quantized latent features.
+
+identity. Ahuja et al. [4] train a single model for multiple speakers while learning style embeddings for gestures of each speaker. Alexanderson et al. [5] adapt MoGlow to speech-driven gesture synthesis and added a framework for high-level control the gesturing style. Liang et al. [30] propose a semantic energized generation method for semantic-aware gesture generation. Li et al. [29] propose a conditional variational autoencoder that models one-to-many audio-to-motion mapping by splitting the cross-modal latent code into shared code and motion-specific code.
+
+Michael et al. [10] propose motion matching, which is a k-Nearest Neighbor (KNN) search method for searching a large database of animations. Zhou et al. [51] utilize a graph-based framework to synthesize body motions for conversations. Ferstl et al. [14] predict expressive gestures based on database matching. Habibie et al. [17] predicted motion using a KNN algorithm and use a conditional generative adversarial network to refine the result. Zhou et al. [50] calculate rhythm signature and style signature using StyleGestures [5], and synthesized graph-based matching gesture. Recently, a large-scale 3D gestures dataset BEAT [31] is built from multi-camera videos based on six modalities of data, which we used in this task.
+
+Quantization-based Pose representation. Kipp has represented gestures as predefined unit gestures [23]. Van et al. [42] propose Vector VQ-VAE to generate discrete representations. Guo et al. [16] use motion tokens to generate human full-body motions from texts, and their reciprocal task. Lucas et al. [34] propose to train a GPT-like model for next-index prediction in that space. Hong et al. [21] use a pose codebook created by clustering to generate diverse poses. Li et al. [38] propose to pose VQ-VAE to encode and summarize dancing units. Existing studies have shown that quantification helps to reduce motion freezing during motion generation and retains the details of motion well [7].
+
+In our work, we encode and quantize meaningful gesture constituents and generate human-like gestures by speech
+
+based motion matching with phase guidance.
+
+# 3. Our Approach
+
+Our approach takes a piece of audio, corresponding text, seed pose and optionally a sequence of control signals as inputs, and outputs a sequence of gesture motion. We first prepossess these inputs as well as the motion database into their quantized discrete forms automatically. We then find the best candidate for the speech and the best candidate for the text, respectively. Finally, we select the optimal gestures based on the phase corresponding to the seed code and the phase corresponding to the two candidates. The rest of this section describes the details of each step.
+
+# 3.1. Learning a discrete latent space representation
+
+Gesture Quantization. We design a pose VQ-VAE as shown in Figure 3. Given the gesture sequence  $\mathbf{G} \in \mathbb{R}^{T \times D_g}$ , where  $T$  denotes the number of gestures and  $D_g$  pose dimension. We first adopt a 1D temporal convolution network  $E_g$  to encode the joint sequence  $\mathbf{G}$  to context-aware features  $\mathbf{g} \in \mathbb{R}^{T' \times C}$ , where  $T' = T / d$ ,  $d$  is the temporal down-sampling rate, and  $C$  is the channel dimension of features. This process could be written as  $\mathbf{g} = E_g(\mathbf{G})$ . Codebook could index an embedding table with samples drawn from the distributions [42]. To learn the corresponding codebook  $\mathcal{Z}_g$  elements  $\mathbf{g_q} \in \mathbb{R}^{T' \times C}$ , where  $\mathbf{g_q} \in \mathcal{Z}_g^T$ ,  $\mathcal{Z}_g$  is a set of  $C_b$  codes of dimension  $n_z$ , we quantize  $\mathbf{g}$  by mapping each temporal feature  $\mathbf{g}_i$  to its closest codebook element  $z_j$  as  $\mathbf{q}(.)$ :
+
+$$
+\mathbf {g} _ {\mathbf {q}, i} = \mathbf {q} (\mathbf {g}) = \arg \min  _ {\mathbf {z} _ {j} \in \mathcal {Z} _ {g}} \| \mathbf {g} _ {i} - \mathbf {z} _ {j} \| \tag {1}
+$$
+
+A following de-convolutional decoder  $D_g$  projects  $\mathbf{g_q}$  back to the motion space as a pose sequence  $\hat{\mathbf{G}}_1$ , which can be formulated as
+
+$$
+\hat {\mathbf {G}} _ {1} = D _ {g} \left(\mathbf {g} _ {q}\right) = D _ {g} \left(\mathbf {q} \left(E _ {g} (\mathbf {G})\right)\right) \tag {2}
+$$
+
+Thus the encoder, decoder and codebook can be trained by optimizing:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {g e s t u r e} \left(E _ {g}, D _ {g}, \mathcal {Z} _ {g}\right)} = \mathcal {L} _ {\text {r e c}} \left(\hat {\mathbf {G}} _ {1}, \mathbf {G}\right) + \left\| \operatorname {s g} [ \mathbf {g} ] - \mathbf {g} _ {\mathbf {q}} \right\| \tag {3} \\ + \beta \| \mathbf {g} - \mathrm {s g} [ \mathbf {g _ {q}} ] \| \\ \end{array}
+$$
+
+where  $\mathcal{L}_{rec}$  is the reconstruction loss that constrains the predicted joint sequence to ground truth,  $\mathrm{sg}[\cdot ]$  denotes the stop-gradient operation, and the term  $\| \mathbf{g} - \mathrm{sg}\left[\mathbf{g_q}\right]\|$  is the "commitment loss" with weighting factor  $\beta$  [42].
+
+Inspired by Bailando [38], a music-driven dance model, we add velocity loss and acceleration loss to the reconstruction loss to prevent jitters in generated gesture:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {r e c}} \left(\hat {\mathbf {G}} _ {1}, \mathbf {G} _ {1}\right) = \left\| \hat {\mathbf {G}} _ {1} - \mathbf {G} _ {1} \right\| _ {1} + \alpha_ {1} \left\| \hat {\mathbf {G}} _ {1} ^ {\prime} - \mathbf {G} _ {1} ^ {\prime} \right\| _ {1} \tag {4} \\ + \alpha_ {2} \left\| \hat {\mathbf {G}} _ {1} ^ {\prime \prime} - \mathbf {G} _ {1} ^ {\prime \prime} \right\| _ {1} \\ \end{array}
+$$
+
+And to avoid encoding confusion caused by the global shift of joints, we normalize the absolute locations of input  $\mathbf{G}$  i.e., set the root joints (hips) to 0, and make objects face the same direction. Standard normalization (zero mean and unit variant) is applied to all joints.
+
+Audio Quantization. We use vq-wav2vec Gumbel-Softmax model [8] pre-trained on a clean 100h subset of Librispeech [35] which is discretized to 102.4K tokens. We multiply the values of the two groups together as the token of the segment of audio. The convolutional encoder produces a representation  $\mathbf{z}$ , for each time step  $i$ , the quantization module replaces the original representation  $\mathbf{z}$  by  $\hat{\mathbf{z}} = \mathbf{a}_{\mathbf{q},i}$  from  $\mathcal{Z}_a$ , which contains a set of  $C_b'$  codes of dimension  $n_z'$ .
+
+# 3.2. Motion Matching based on Audio and Text
+
+Our motion matching algorithm takes a discrete text sequence  $\mathbf{t} = [\mathbf{t}_0, \mathbf{t}_1, \dots, \mathbf{t}_{T' - 1}]$ , a discrete audio sequence  $\mathbf{a_q} = [\mathbf{a_{q,0}}, \mathbf{a_{q,1}}, \dots, \mathbf{a_{q,T'}} - 1]$ , and one initial previous pose code  $\mathbf{g}_{-1}$ , and optionally a sequence of control masks  $\mathbf{M} = [\mathbf{m}_0, \mathbf{m}_1, \dots, \mathbf{m}_{T' - 1}]$ . The outputs are audio-based candidate  $\mathbf{C}_a = [\mathbf{c}_{0,a}, \mathbf{c}_{1,a}, \dots, \mathbf{c}_{T' - 1,a}]$  and text-based candidate  $\mathbf{C}_t = [\mathbf{c}_{0,t}, \mathbf{c}_{1,t}, \dots, \mathbf{c}_{T' - 1,t}]$ .  $T'$  denotes the number of speech segments during inference.
+
+Considering too long gesture clips time decreases the diversity of gestures and too short gesture clips time results in poor human likeness [50], we split each gesture motion in the dataset into clip-level gesture clips automatically by time interval of words larger than 0.5 seconds in text transcriptions. These clip-level data form the speech-gesture database in Figure 1.
+
+To find the appropriate output gesture sequence  $\mathbf{C}_a$  and  $\mathbf{C}_t$  from the database, we consider both the similarity with respect to the current test speech as well as the previously searched pose code  $\mathbf{g}_{-1}$  for every  $T$  frame interval for better continuity between consecutive syntheses, as in [46]. During each iteration, we first compare the Euclidean distance between the joints corresponding to initial code  $\mathbf{g}_{-1}$  and the joints corresponding to each code  $\mathbf{g_q}$  in the codebook to get the pose-based pre-candidate  $\hat{\mathbf{C}}_g = \left\{\hat{\mathbf{C}}_g^0,\hat{\mathbf{C}}_g^1,\dots ,\hat{\mathbf{C}}_g^{C_b}\right\}$ . In the first iteration, the previous pose code  $\mathbf{g}_{-1}$  is initialized by either randomly sampling a code from codebook  $\mathcal{Z}_g$  or set to be the code with the most frequent occurrences in the codebook (the code of mean pose).
+
+Audio-based Search. To encode information about the relevant past and future codes, we use a search-centered window (0.5 seconds long) as a feature for the current time, then we get audio features sequence  $\mathbf{F}_a = [\mathbf{F}_{a,0},\mathbf{F}_{a,1},\dots ,\mathbf{F}_{a,T^{\prime} - 1}]$ . To address the inherent asynchronicity of speech and gestures, Levenshtein distance [28] is used to measure the similarity of the test audio by comparing the current test audio feature with the audio feature of clips from the database. For every clip in the database,
+
+![](images/561973762b93813c2f17ca25b1a35de12b0254e7490a0b52ef0bc487c6fce9ae.jpg)  
+Figure 4. Architecture of the Periodic Autoencoder Network. The convolutional network encoder learns a lower dimensional embedding of the gesture. Then differentiable real Fast Fourier Transform (FFT) and fully connected network is applied to get periodic parameters: amplitude (A), frequency (F), offset (B) and phase shift (S). The deconvolutional network decoder map all periodic parameters back to the original motion curves to force the periodic parameters to reconstruct the original latent embedding.
+
+we calculate the audio feature similarity of the corresponding code per  $d$  frame and take the minimum value as the audio candidate distance for each code. Then we get audiobased pre-candidate  $\hat{\mathbf{C}}_a = \left\{\hat{\mathbf{C}}_a^0,\hat{\mathbf{C}}_a^1,\dots ,\hat{\mathbf{C}}_a^{C_b}\right\}$ . Levenshtein distance as a similarity metric of corresponding speech of gestures helps match more appropriate gestures with speech, and solves the alignment problem of speech and gestures well (see Section 4.2).
+
+Text-based Search. Similarly, we use the text before and after 0.5 seconds as the sentence of the current code. To obtain the semantic information of the context, we use Sentence-BERT [37] to compute sentence embeddings, as text features sequence  $\mathbf{F}_t$ . For every clip in the database, we calculate the text features cosine similarity of the corresponding code per  $d$  frame and take the minimum value as the text candidate distance for each code. Then text-based pre-candidate is  $\hat{\mathbf{C}}_t = \left\{\hat{\mathbf{C}}_t^0,\hat{\mathbf{C}}_t^1,\dots ,\hat{\mathbf{C}}_t^{C_b}\right\}$
+
+Instead of weighting the similarity score of audio/text and pose terms, we add pose similarity ranks and audio/text similarity ranks for every pre-candidate to select the lowest rank [17] result as the audio/text candidate. The generated gesture will be discontinuous if only speech (audio and text) matching is considered, so as shown in the figure 2, we first compute the pre-candidates of pose, audio, and text, then compute audio candidate  $\mathbf{C}_a$  based on  $\hat{\mathbf{C}}_g$  and  $\hat{\mathbf{C}}_a$ , and text candidate  $\mathbf{C}_t$  based on  $\hat{\mathbf{C}}_g$  and  $\hat{\mathbf{C}}_t$ . Then we select the final gesture from  $\mathbf{C}_a$  and  $\mathbf{C}_t$  according to the phase guide.
+
+# 3.3. Phase-Guided Gesture Generation
+
+To transform the motion space into a learned phase manifold, we utilize a temporal periodic autoencoder architecture structure similar to DeepPhase [39]. The architecture is shown in figure 4. First, we adopt a 1D temporal convolution network  $E_{p}$  to a latent space of the motion  $\mathbf{G}$ , which can be formulated as
+
+$$
+\mathbf {L} = E _ {p} (\mathbf {G}) \tag {5}
+$$
+
+where  $\mathbf{L} \in \mathbb{R}^{T \times M}$ ,  $M$  is the number of latent channels, that is, the number of desired phase channels to be extracted from the motion. For each channel, our goal is to extract a good phase offset to capture its current point as part of a larger cycle.
+
+It is complicated to calculate the phase of a cluttered curve directly, so we calculate periodic parameters amplitude (A), frequency (F), offset (B) and phase shift (S) first. We apply differentiable real Fast Fourier Transform (FFT) to each channel of  $\mathbf{L}$  and create the zero-indexed matrix of Fourier coefficients  $\mathbf{c} \in \mathbb{C}^{M \times K + 1}$ ,  $K = \left\lfloor \frac{T}{2} \right\rfloor$ , written as  $\mathbf{c} = FFT(\mathbf{L})$ . Power spectrum  $\mathbf{p} \in \mathbb{R}^{M \times K + 1}$  for each channel is  $\mathbf{p}_{i,j} = \frac{2}{T} |\mathbf{c}_{i,j}|^2$ , where  $i$  is the channel index and  $j$  is the index for the frequency bands. Assumed that there are  $T$  points in a time window of  $N$  seconds. The periodic parameters are computed by:
+
+$$
+\mathbf {A} _ {i} = \sqrt {\frac {2}{T} \sum_ {j = 1} ^ {K} \mathbf {p} _ {i , j}}, \quad \mathbf {F} _ {i} = \frac {\sum_ {j = 1} ^ {K} \left(\mathbf {f} _ {j} \cdot \mathbf {p} _ {i , j}\right)}{\sum_ {j = 1} ^ {K} \mathbf {p} _ {i , j}}, \quad \mathbf {B} _ {i} = \frac {\mathbf {c} _ {i , 0}}{T}, \tag {6}
+$$
+
+where  $\mathbf{f} = (0,1 / N,2 / N,\dots ,K / N)$  is frequencies vector.
+
+Phase shift  $\mathbf{S} \in \mathbb{R}^{M}$  for each latent curve  $\mathbf{S}_i$  can be predicted by a fully connected layer  $FC$ , which can be formulated as:
+
+$$
+\left(s _ {x}, s _ {y}\right) = F C \left(\mathbf {L} _ {i}\right), \quad \mathbf {S} _ {i} = \operatorname {a t a n 2} \left(s _ {y}, s _ {x}\right) \tag {7}
+$$
+
+For each temporal motion  $\mathbf{G}$ , within a centered time window  $\mathcal{T} = \left[-\frac{t_1 - t_0}{2}, -\frac{t_1 - t_0}{2} + \frac{t_1 - t_0}{N - 1}, \dots, \frac{t_1 - t_0}{2}\right]$ , where  $t_0 \leq t \leq t_1$ , the decoder  $D_p$  takes all periodic parameters as its input, and maps back to the original motion curves:
+
+$$
+\hat {\mathbf {L}} = f (\mathcal {T}; \mathbf {A}, \mathbf {F}, \mathbf {B}, \mathbf {S}) = \mathbf {A} \cdot \sin (2 \pi \cdot (\mathbf {F} \cdot \mathcal {T} - \mathrm {S})) + \mathbf {B} \tag {8}
+$$
+
+$$
+\hat {\mathbf {G}} _ {2} = h (\hat {\mathbf {L}}) \tag {9}
+$$
+
+The network is learned with the periodic parameters via the following loss function, which forces the periodic parameters to reconstruct the original latent embedding  $\mathbf{L}$ .
+
+$$
+\mathcal {L} _ {\text {p h a s e}} = \mathcal {L} _ {\text {p h a s e - r e c o n}} (\mathbf {G}, \hat {\mathbf {G}} _ {\mathbf {2}}) \tag {10}
+$$
+
+After training, phase manifold  $\mathcal{P}$  of a sample motion which captures a lot of "information" about the current state of the original time series data is
+
+$$
+\mathcal {P} _ {2 i - 1} ^ {(t)} = \mathrm {A} _ {i} ^ {(t)} \cdot \sin \left(2 \pi \cdot \mathrm {S} _ {i} ^ {(t)}\right), \quad \mathcal {P} _ {2 i} ^ {(t)} = \mathrm {A} _ {i} ^ {(t)} \cdot \cos \left(2 \pi \cdot \mathrm {S} _ {i} ^ {(t)}\right) \tag {11}
+$$
+
+where  $\mathcal{P}\in \mathbb{R}^{2M}$
+
+We visualize the phase features and the velocity features in Figure 5. The Principle Components (PCs) of the original joint rotational velocities, replacing the phase layers with fully connected layers and phase features are projected onto
+
+![](images/cd14b049e39e037f1f7483572bf9e42dc51f401e83431c1b48b65f82f73d9a31.jpg)  
+(a) Rotational velocity space.
+
+![](images/9a85253e41749a017c6eb2d233aa80676278ef9c6d5884fc5322a6b1d88fc5e6.jpg)  
+(b) Latent space learned by convolutional and fully connected.
+
+![](images/87d56a2a641907bb6ccf00d30892b695b58b7d39df493cc4926c5267511b14f6.jpg)  
+(c) Phase space.  
+Figure 5. 2D PCA embedding of feature distributions for different motion domains. Each color represents gestures from a single motion clip that are temporally connected, which means that neighboring frames in the motion data should be closely connected in the embedding
+
+a 2D plane. It can be observed that the phase manifold has a consistent structure similar to polar coordinates. The cycles represent the primary period of the individual motions, where the timing is represented by the angle around the center, and the amplitude is the velocity of the motion. Samples smoothly transition between cycles of different amplitude or frequency, which indicate the transition between movements.
+
+The phase manifold of the motion curve is shown in Figure 6. Instead of using phase to set network weights as in [20, 40, 49] to generate motion, we use phase guidance to select motion. To find the appropriate motion alignments, we calculate the cosine similarity of the latter frames  $N_{strid}$  of the manifold phase  $\mathcal{P}_{-1}$  corresponding to the frame of the initial code and the first frames of the manifold phase  $\mathcal{P}_{a/t}$  corresponding to the audio/text candidate  $\mathbf{C}_a$  and  $\mathbf{C}_t$  within  $N_{phase}$  frames, which can be written as  $\text{concat}[\mathcal{P}_{-1}^{[(N_{strid} - N_{phase})]}}, \mathcal{P}_{a/t}^{[N_{strid}]}$  and  $\text{concat}[\mathcal{P}_{-1}^{[-N_{strid}]}, \mathcal{P}_{a/t}^{[N_{phase} - N_{strid}]}]$ . Candidates with more similar phase manifolds will also have more natural motion as the final matching gestures. Please refer to the supplements for the pseudo-code of our algorithm.
+
+# 4. Experiments
+
+Dataset. We perform the training and evaluation on the BEAT dataset proposed in [31], which to our best knowl
+
+![](images/0470df749c2bb5a1b8fc216dd32923a97d3fcabb6e82c2b4178c8d4c41ca6196.jpg)  
+(a) The phase manifold of the seed code to be matched.  
+Figure 6. Sinusoidal diagram of learned phase manifold within a sliding window. The blue lines in (a) and (b) indicate the ground truth results, and the orange and green lines indicate the candidates to be matched, i.e., audio candidate  $\mathbf{C}_a$  and text candidate  $\mathbf{C}_t$ .
+
+![](images/57417fdb192726bd1146df1f316eeadc16acca6950440f41e27169beadb2f486.jpg)  
+(b) The phase manifold of the candidate to be matched.
+
+edge is the largest publicly available motion capture dataset for human gesture generation. We divided the data into 8:1:1 by training, validation, and testing, and trained codebooks and baselines using data from all speakers. Because motion matching is more time-consuming, we selected 4 hours of data from two speakers "wayne" (male speaker) and "kieks" (female speaker), and constructed separate databases for our experiments.
+
+Implementation Details. In this work, we use 15 joints corresponding to the upper body without hands or fingers.  $3 \times 3$  rotation matrix features are computed as gesture sequences, with pose dimension  $D_{g}$  is 9. Down-sampling rate  $d$  is 8. The size  $C_b$  of codebook  $\mathcal{Z}_g$  is set to 512 with dimension  $n_z$  is 512. While training the gesture VQ-VAE, gesture data are cropped to a length of  $T = 240$  (4 seconds), using the ADAM [22] optimizer (learning rate is e-4,  $\beta_{1} = 0.5$ ,  $\beta_{2} = 0.98$ ) with a batch size of 128 for 200 epochs. We set  $\beta = 0.1$  for Equation (3) and  $\alpha_{1} = 1$ ,  $\alpha_{2} = 1$  for Equation (4). In terms of motion matching, the window lengths for audio and text are 4 pose codes corresponding to each of the past and future speech information, with  $d = 32$ . As for phase guidance, we use the rotational velocity as input to the network. We train the network using the AdamW [33] optimizer for 100 epochs, using a learning rate and weight decay both of  $10^{-4}$  and a batch size of 128. The number of phase channels  $M$  is set to 8. To calculate the phase similarity, the number of frames is set to  $N_{phase} = 8$  and  $N_{stride} = 3$ . The whole framework is learned in less than one day on one NVIDIA A100 GPU. The initial pose code is generated by randomly sampling a code from the codebook  $\mathcal{Z}_q$ .
+
+Evaluation Metrics. The distance between speed histograms is used to evaluate gesture quality. We calculate speed-distribution histograms and compare to the speed distribution of natural motion by computing the Hellinger dis
+
+tance [25],  $H\left(\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}\right) = \sqrt{1 - \sum_{i} \sqrt{h_{i}^{(1)} \cdot h_{i}^{(2)}}}$  between the histograms  $\boldsymbol{h}^{(1)}$  and  $\boldsymbol{h}^{(2)}$ . The Fréchet gesture distance (FGD) [46] on feature space is proposed as a metric to quantify the quality of the generated gestures. This metric is based on the FID [19] metric used in image generation studies. Similarly, we calculate FGD on raw data space used in [3]. To compute the FGD, we trained an autoencoder using the Trinity dataset [13]. Lower Hellinger distance and FGD are better. We also report average jerk, average acceleration, Canonical correlation analysis (CCA), Diversity, and Beat Align Score in the supplements.
+
+# 4.1. Comparison to Existing Methods
+
+We compare our proposed framework with End2End [47] (Text-based), Trimodal [46] (Text, audio and identity, flow-based), StyleGestures [5] (Audio-based), KNN [17] (Audio, motion matching-based) and CaMN [31] (Multimodal-based). The quantitative results are shown in Table 1. According to the comparison, our proposed model consistently performs favorably against all the other existing methods on all evaluations. Specifically, on the metric of Hellinger distance average, we achieve the same good results as StyleGestures. Since well-trained models should produce motion with similar properties to a specific speaker, our method has a similar motion-speed profile for any given joint. And our method improves 15.921  $(44\%)$  and 3837.068  $(39\%)$  than the best compared baseline model StyleGestures on FGD on feature space and FGD on raw data space.
+
+User Study. To further understand the real visual performance of our method, we conduct a user study among the gesture sequences generated by each compared method and the ground truth data. Following the evaluation in GE-NEA [5], for each method, from the 30-minute test set we selected 38 short segments of test speech and corresponding test motion to be used in the evaluations. Segments are around 8 to 15 seconds long, and ideally not shorter than 6 seconds. The experiment is conducted with 23 participants separately. The generated gesture data is visualized on an avatar via Blender [1] rendering. For human-likeness evaluation, each evaluation page asked participants "How human-like does the gesture motion appear?" In terms of appropriateness evaluation, each evaluation page asked participants "How appropriate are the gestures for the speech?" Each page presented six videos to be rated on a scale from 5 to 1 with 1-point intervals with labels (from best to worst) "Excellent", "Good", "Fair", "Poor", and "Bad". The mean opinion scores (MOS) on human-likeness and appropriateness are reported in the last two columns in Table 1.
+
+Our method significantly surpasses the compared state-of-the-art methods with both human-likeness and appropriateness, and even above the ground truth (GT) in human
+
+Table 1. Quantitative results on test set. Bold indicates the best metric. Among compared methods, End2End [47], Trimodal [46], StyleGestures [5], KNN [17] and CaMN [31] are reproduced using officially released code with some optimized settings. For more details please refer to the supplementary material. Objective evaluation is recomputed using the officially updated evaluation code [41]. Human-likeness and appropriateness are results of MOS with  $95\%$  confidence intervals.  
+
+<table><tr><td rowspan="2">Name</td><td colspan="3">Objective evaluation</td><td colspan="2">Subjective evaluation</td></tr><tr><td>Hellinger distance average↓</td><td>FGD on feature space↓</td><td>FGD on raw data space↓</td><td>Human-likeness</td><td>Appropriateness</td></tr><tr><td>Ground Truth (GT)</td><td>0.0</td><td>0.0</td><td>0.0</td><td>3.79 ± 0.19</td><td>3.62 ± 0.21</td></tr><tr><td>End2End [47]</td><td>0.146</td><td>64.990</td><td>16739.978</td><td>3.64 ± 0.11</td><td>3.23 ± 0.14</td></tr><tr><td>Trimodal [46]</td><td>0.155</td><td>48.322</td><td>12869.98</td><td>3.31 ± 0.17</td><td>3.20 ± 0.19</td></tr><tr><td>StyleGestures [5]</td><td>0.136</td><td>35.842</td><td>9846.927</td><td>3.66 ± 0.08</td><td>3.30 ± 0.11</td></tr><tr><td>KNN [17]</td><td>0.364</td><td>43.030</td><td>12470.061</td><td>2.38 ± 0.10</td><td>2.35 ± 0.13</td></tr><tr><td>CaMN [31]</td><td>0.149</td><td>52.496</td><td>10549.455</td><td>3.65 ± 0.16</td><td>3.29 ± 0.15</td></tr><tr><td>Ours</td><td>0.136</td><td>19.921</td><td>5742.281</td><td>4.00 ± 0.14</td><td>3.66 ± 0.23</td></tr></table>
+
+Table 2. Ablation studies results. 'w/o' is short for 'without'. Bold indicates the best metric.  
+
+<table><tr><td rowspan="2">Name</td><td colspan="3">Objective evaluation</td><td colspan="2">Subjective evaluation</td></tr><tr><td>Hellinger distance average↓</td><td>FGD on feature space↓</td><td>FGD on raw data space↓</td><td>Human-likeness</td><td>Appropriateness</td></tr><tr><td>w/o wavvq + WavLM</td><td>0.151</td><td>19.943</td><td>6009.859</td><td>3.87 ± 0.21</td><td>3.64 ± 0.21</td></tr><tr><td>w/o audio</td><td>0.134</td><td>20.401</td><td>5871.044</td><td>3.87 ± 0.21</td><td>3.63 ± 0.20</td></tr><tr><td>w/o text</td><td>0.118</td><td>23.929</td><td>6389.866</td><td>3.57 ± 0.29</td><td>3.41 ± 0.23</td></tr><tr><td>w/o phase</td><td>0.138</td><td>19.195</td><td>5759.167</td><td>3.90 ± 0.11</td><td>3.65 ± 0.17</td></tr><tr><td>w/o motion matching (GRU + codebook)</td><td>0.140</td><td>30.404</td><td>11642.641</td><td>3.78 ± 0.14</td><td>3.43 ± 0.16</td></tr><tr><td>Ours</td><td>0.136</td><td>19.921</td><td>5742.281</td><td>4.07 ± 0.15</td><td>3.77 ± 0.21</td></tr></table>
+
+likeness and appropriateness. However, there is no significant difference compared to the appropriateness of GT. According to the feedback from participants, our generated gesture is more "related to the semantics" with "more natural", while our method "lacking power and exaggerated gestures" compared to GT. More details regarding the user study are shown in the supplementary material.
+
+# 4.2. Ablation Studies
+
+Moreover, we conduct ablation studies to address the performance effects of different components in the framework. The results of our ablations studies are summarized in Table 2. The visual comparisons of this study can be also referred to the supplementary video.
+
+We explore the effectiveness of the following components: (1) Levenshtein distance, (2) audio modality, (3) text modality, (4) phase guidance, (5) motion matching. We performed the experiments on each of the five components, respectively.
+
+Supported by the results in Table 2, when we do not use vq-wav2vec or Levenshtein distance to measure the similarity of corresponding speech of gestures, but use WavLM [11] pre-trained on Librispeech and cosine similarity instead, the performances of all metrics have deteriorated. The change of FGD on feature space was not significant.
+
+![](images/d19feb63e29ec809be67e210cb72e7bb433171fcebf1e2d8fedd0a4df462551a.jpg)  
+Figure 7. Comparison of gestures blended with and without phase guidance. Black shading indicates no phase guidance.
+
+The Hellinger distance average and FGD on raw data space deteriorated by 0.015 (11%), and 267.578 (4.7%), respectively. When the model is trained without audio, we select two candidates for text-based motion matching instead of one, and then synthesize the gesture based on phase guidance. The FGD on feature space and FGD on raw data space deteriorated by 0.48 (2%) and 128.763 (2%), respectively. When the model is trained without text, similarly, two candidates for audio-based motion matching are selected instead of one. The FGD on feature space and FGD on raw data space deteriorated by 4.008 (20%) and 647.585 (11%), respectively. Notice that when one of the modalities of both text and speech is not used, the FGD metric increases while the Hellinger distance average metric decreases, which indicates that the quality of the gestures generated when only one modality is used decreases, but the distribution of the velocity becomes better. When the phase
+
+guidance is removed, we select one candidate every time between two candidates using the distance in the rotational velocity space (Not randomly select one candidate). The results showed a slight increase in Hellinger distance average and FGD on raw data space and a slight decrease in FGD on feature space, but none of the changes were significant. One possible explanation is that the phase space loses information from the original feature space to generate more natural actions, as shown in Figure 7. When the model is trained using deep gated recurrent unit (GRU) [12] to learn pose code instead of motion matching, The FGD on feature space and FGD on raw data space deteriorated by  $10.483(53\%)$  and 6460.202  $(107\%)$ , respectively. This demonstrates the advantage of the matching model over the generative model. Further, this model has a comparable performance with baselines, which also proves the efficiency of the codebook encoded gesture space.
+
+User Study. Similarly, we conduct a user study of ablation studies. We use the same approach as in Section 4.1, with the difference that we use another avatar character to test the robustness of the results. The MOS on human-likeness and appropriateness are shown in the last two columns in Table 2. The score of our proposed framework is similar to the previous one, which will be a bit higher, indicating that even if the generated results are the same, the rating may be related to the visual perception of different characters. However, there was no significant change. The results demonstrate that the final performance of the model decrease without any module. Notice that the score without text decreases more than the score without audio, indicating that the matched gestures are mostly semantically related. Not using phase space has the least effect on the results, which is consistent with expectations, since phase only provides guidance. Another significant result is that the results without audio and using audio without Levenshtein distance or audio quantization are close, which effectively indicates the effectiveness of Levenshtein distance. Furthermore, the results without model matching has a comparable performance in terms of naturalness with GT, the effectiveness of the codebook encoded gesture unit was also confirmed.
+
+# 4.3. Controllability
+
+Since we use motion matching to generate gestures, it is easy to control the gesture or take out the code for interpretation. For example, to generate a sequence of body gestures where the left wrist is always above a specified threshold  $\mathbf{r}$ , the search can be restricted to consider only codes corresponding to wrists above  $\mathbf{r}$ . Here is an example. The most frequent gesture in the database of "wayne" that we found, besides the average pose, is the gesture corresponding to the code '318', as shown in Figure 8. This can be explained by that "wayne" is a habitual right-handed
+
+![](images/749f1ef66e344cf56d62a37d3348d75b94bad3f0d20cfb26f296570fea7e7d5d.jpg)  
+Figure 8. Visualization of how a gesture changes when codes are changed. We replace twelve code '318' in a motion sequence (240 frames, 30 codes) with code '260' on a habitual right-handed speaker.
+
+speaker. We choose a preferred left-handed code '260' to replace it, and the result is shown in the figure. In practice, to produce natural gestures, it is sufficient to add the code frequency score and adjust the weights appropriately when matching. Please refer to the supplementary video for more comparisons.
+
+# 5. Discussion and Conclusion
+
+In this paper, we present a quantization-based and phase-guided motion matching framework for speech-driven gesture generation. Specifically, we address the random jittering issue by using discrete representation that encodes human gestures. Besides, we tackle the inherent asynchronicity of speech and gestures and flexibility of the current motion matching models by Levenshtein distance based on audio quantization. Then, phase-guided audio-based or text-based candidates are used as the final result. Experiments on the standard benchmark (i.e., BEAT dataset) along with user studies show that proposed framework achieves state-of-the-art performance both qualitatively and quantitatively. There is room for improvement in this research, besides text and audio, more modalities (e.g. emotions, facial expressions) could be taken into consideration to generate more appropriate gestures.
+
+# Acknowledgments
+
+This work is supported by National Natural Science Foundation of China (NSFC) (62076144), Shenzhen Key Laboratory of next generation interactive media innovative technology (ZDSYS20210623092001004) and Shenzhen Science and Technology Program (WDZC20220816140515001, JCYJ20220818101014030).
+
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+[49] He Zhang, Sebastian Starke, Taku Komura, and Jun Saito. Mode-adaptive neural networks for quadruped motion control. ACM Trans. Graph., 37(4):145, 2018. 5  
+[50] Chi Zhou, Tengyue Bian, and Kang Chen. Gesturemaster: Graph-based speech-driven gesture generation. In International Conference on Multimodal Interaction, ICMI, pages 764-770, 2022. 1, 2, 3, 4  
+[51] Yang Zhou, Jimei Yang, Dingzeyu Li, Jun Saito, Deepali Aneja, and Evangelos Kalogerakis. Audio-driven neural gesture reenactment with video motion graphs. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, pages 3408-3418, 2022. 3

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2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_content_list.json

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+    {
+        "type": "text",
+        "text": "Q: How to Specialize Large Vision-Language Models to Data-Scarce VQA Tasks? A: Self-Train on Unlabeled Images!",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
+        "bbox": [
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+            305
+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/03965e14b1009cd2745e52bb2345565fe94bb6775fa4da04f0c07e16fd5652aa.jpg",
+        "image_caption": [
+            "Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image  $I$  without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers  $(Q,A)$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content",
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "* work done while at NEC Labs America",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "15005",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3e4b943819c4228181fd9f28b9570fa942cc03b174fa245b394684d05216f4f0.jpg",
+        "image_caption": [
+            "Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
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+        "img_path": "images/1338f0d6729f7208a8733a9fd6cc12ec31588ca937e3217f748b7773fd568866.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "text",
+        "text": "than a short caption can describe).",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase \"this is a\". We convert each caption into a boolean question where the correct answer is \"yes\" by inserting the caption into the template is this a <caption>? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between \"yes\" and \"no\" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers \"no\" to at least  $5\\%$  of the questions, increasing to  $15\\%$  as the diversity of captions increases (adjusted by top- $p$  parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model  $\\mathrm{VQG}_{IC}$ . Next, we use  $\\mathrm{VQG}_{IC}$  as a teacher to",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "pseudolabel unlabeled images by sampling questions and answers from  $\\mathrm{VQG}_{IC}$  with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Benefits: SelTDA allows us generate synthetic training data by approximating the distribution  $P(Q, A|I)$  of the target VQA task, where  $Q, A, I$  represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs.",
+            "2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed.",
+            "3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "15006",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
+            89,
+            218,
+            106
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization.",
+        "bbox": [
+            75,
+            296,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model.",
+        "bbox": [
+            75,
+            492,
+            470,
+            840
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self",
+        "bbox": [
+            75,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our goal is to pseudolabel an unlabeled image  $I$  with a generated question-answer pair  $(Q, A)$  using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model  $\\mathrm{VQG_{IC}}$  to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating  $P(Q, A|I)$  that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image.",
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+    {
+        "type": "text",
+        "text": "3.1. The Teacher: Direct Image-Conditional VQG",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image  $I$ , a question  $Q$  and answer  $A$ , the VQA student must approximate  $P(Q \\mid Q, I)$ , while the teacher model must approximate  $P(Q, A \\mid I)$ . Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate  $P(Q \\mid I, A)$ , that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "15007",
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+    {
+        "type": "image",
+        "img_path": "images/1b844b835973f755de7d2b3a15912d25d1506e699186fd4ae59ac4648da7d292.jpg",
+        "image_caption": [
+            "Figure 3. Overview of the proposed framework. We first create the teacher  $\\mathrm{VQG}_{IC}$  (§3.1), use  $\\mathrm{VQG}_{IC}$  to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
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+        "type": "image",
+        "img_path": "images/07eb44d222a5f5a01e155ae42d95abd930b5fc2bd92482ff77ed3650a8b213c0.jpg",
+        "image_caption": [
+            "Question: what is the cat wearing?  \nAnswers: necktie, tie"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
+            277,
+            187,
+            347
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/7028f5f12d0e2415bc374ecca7788f763487cfe32d46aa2b05fde2e063073630.jpg",
+        "image_caption": [
+            "Question: how is the egg cooked? Answer: fried"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            93,
+            386,
+            218,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/cd87a2039c4183818b9a7151627b2c40bcf3c0a3ac083fd466f88d2721d854a1.jpg",
+        "image_caption": [
+            "Question: how many items of food are present here?  \nAnswers: 2"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            305,
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+            421,
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+    {
+        "type": "image",
+        "img_path": "images/f9013b0e122b47e981b019a685a592fdfae273ed025e4b6d73924bb935ca1efe.jpg",
+        "image_caption": [
+            "Question: what activity is the baby learning? Answer: feeding, eating, nutrition"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "image",
+        "img_path": "images/5a3885a05ec6c2ed434e18984c44ea16a9b1692d2cec15620b7b0584800ea3dd.jpg",
+        "image_caption": [
+            "Question: what color is the sky in the picture?  \nAnswers: clear, blue"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/8943e59bbb0aa9f14364f1d18c10b2466ffc22b68ab75b92f522a3b67c6b3f48.jpg",
+        "image_caption": [
+            "Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/42a7928b3661f35b2ac5d7a2a0b66f6aa08229493cfa4d92c5cce7d9373ad563.jpg",
+        "image_caption": [
+            "Question: what city is this?  \nAnswers: london, uk"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/5188f6d8d4c231fd410025f49ec9f6ebb416f7a22adce852c9cdc6f462bf5d53.jpg",
+        "image_caption": [
+            "Question: what is the name of this party? Answer: baby shower",
+            "Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "approaches, we develop an image-conditional approach  $(\\mathrm{VQG}_{IC})$  that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions  $P(Y|I)$ , where  $Y$  is often a distribution over a (finite) label space.",
+        "bbox": [
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+        "type": "text",
+        "text": "To create the  $\\mathrm{VQG}_{IC}$  teacher that approximates  $P(Q,A|I)$ , we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate  $P(T|I)$ , where  $T = (Q,A)$ . Let  $\\mathcal{D}_{QA}$  be a question-answer dataset we wish to create a teacher from. For a sample  $(Q,A,I)\\in \\mathcal{D}_{QA}$ , we transform it into a target sequence of tokens  $y_{1:N} = (y_1,y_2,\\dots y_n)$  by entering  $(Q,A)$  into a structured template of the form \"Question: <question>? Answer: <answer>.\" where <question> and <answer> are replaced by the content of  $Q$  and  $A$  respectively. Once  $y_{1:N} = (y_1,y_2,\\dots y_n)$  is",
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+    {
+        "type": "text",
+        "text": "obtained, we train the model by optimizing",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V Q G}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {<   n}, x\\right) \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "over all question-image-answer pairs in  $\\mathcal{D}_{QA}$ , where  $x$  is the latent encoded features in the standard encoder-decoder architecture and  $\\theta$  represents the VLM parameters. The  $\\mathrm{VQG_{IC}}$  thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that  $\\mathrm{VQG_{IC}}$  is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of  $P(T|I)$ , having been exposed to a diverse number of images and paired text. The  $\\mathrm{VQG_{IC}}$  teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair  $(Q', A')$  is generated jointly as a text  $T'$ , allowing us to sample from  $P(T|I)$ .",
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Training the Student with Unlabeled Data",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Once the VQG<sub>IC</sub> teacher model has been obtained, self-training with unlabeled data can proceed. To produce a",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "15008",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "pseudolabel  $(Q', A')$  for an unlabeled image  $I_u$ , we first obtain  $\\mathbf{L}_{1:N} = \\mathrm{VQG_{IC}}(I_u)$ , where  $\\mathbf{L}_{1:N}$  are the logits of the decoder. The logits  $\\mathbf{L}_{1:N}$  define a distribution  $P(L_N \\mid L_{1:N-1})$  over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text  $T'$  from  $P(L_N \\mid L_{1:N-1})$ . The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair  $(Q', A')$  from the decoded text  $T'$ . This pair  $(Q', A') = T'$  is a sample from  $P(T|I)$ , and reflects textual knowledge about the content of an image known to the VLM.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form  $(Q', A', I_u)$ , representing self-generated training data  $\\mathcal{D}_{QA}'$  in the style of a target dataset  $\\mathcal{D}_{QA}$ . We then augment the real dataset  $\\mathcal{D}_{QA}$  with the self-generated question-answer pairs on unlabeled images  $\\mathcal{D}_{QA}'$  to create a self-augmented training dataset  $\\mathcal{D}_{\\mathrm{Aug}QA} = \\mathcal{D}_{QA}' \\cup \\mathcal{D}_{QA}$ . The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {V Q A}} = - \\sum_ {n = 1} ^ {N} \\log P _ {\\theta} \\left(y _ {n} \\mid y _ {<   n}, x _ {n}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $x_{n}$  is the  $n$ -th element of the multimodal sequence embeddings  $\\mathbf{X}_{1:N}$  produced by  $\\mathrm{VLM}(Q, I; \\theta)$ ,  $Q, I$  are the question and image,  $y_{1:N}$  is the sequence of answer tokens, and  $\\theta$  represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels  $(Q', A')$  be generated even when  $\\mathcal{D}_{QA}$  is small, and few pairs are available for adapting the teacher  $\\mathrm{VQG}_{IC}$ ? Knowledge about the content of the image in a textual form  $P(T|I)$  is already well-learned by the VLM from which we initialize  $\\mathrm{VQG}_{IC}$ . Thus,  $\\mathcal{D}_{QA}$  only needs sufficient pairs to teach  $\\mathrm{VQG}_{IC}$  how to construct annotations matching the style of  $\\mathcal{D}_{QA}$ .",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/4b2ac891bc4bcf4b33b4e44e2b6b93430ddbd5054e0149181ab6abe4221cb0af.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Model</td><td colspan=\"2\">A-OKVQA</td></tr><tr><td>Validation</td><td>Test</td></tr><tr><td>(a)</td><td>ViLBERT [34]</td><td>49.1</td><td>41.5</td></tr><tr><td>(b)</td><td>LXMERT [46]</td><td>51.4</td><td>41.6</td></tr><tr><td>(c)</td><td>KRISP [36]</td><td>51.9</td><td>42.2</td></tr><tr><td>(d)</td><td>GPV-2 [18]</td><td>60.3</td><td>53.7</td></tr><tr><td>(e)</td><td>BLIP [26]</td><td>57.1</td><td></td></tr><tr><td>(f)</td><td>\\( BLIP_{\\text{VQAv2}} \\) [26]</td><td>67.8</td><td>59.5</td></tr><tr><td>(g)</td><td>BLIP + SelTDA</td><td>62.1</td><td>54.5</td></tr><tr><td colspan=\"2\">% gain w.r.t baseline</td><td>+5.0</td><td></td></tr><tr><td colspan=\"2\">% gain w.r.t best prior work</td><td>+1.8</td><td>+0.8</td></tr><tr><td>(h)</td><td>\\( BLIP_{\\text{VQAv2}} + SelTDA \\)</td><td>68.9</td><td>59.5</td></tr><tr><td colspan=\"2\">% gain w.r.t baseline</td><td>+1.1</td><td>+0.0</td></tr><tr><td colspan=\"2\">% gain w.r.t best prior work</td><td>+8.6</td><td>+5.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/d60f2b11b45af6a8eb85ab73e614439db12331d8b98f1de32b18fdc7e5670f73.jpg",
+        "table_caption": [
+            "Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td rowspan=\"2\">Model</td><td colspan=\"2\">ArtVQA Accuracy</td></tr><tr><td></td><td>Overall</td><td>Grounded</td></tr><tr><td>(a)</td><td>BAN [22]</td><td>22.4</td><td>-</td></tr><tr><td>(b)</td><td>BLIP [26]</td><td>21.36</td><td>81.71</td></tr><tr><td>(c)</td><td>VIKING [12]</td><td>55.5</td><td>78.74</td></tr><tr><td>(d)</td><td>VIKINGVLM</td><td>55.9</td><td>81.9</td></tr><tr><td>(e)</td><td>BLIP + SelTDA</td><td>21.68</td><td>83.86</td></tr><tr><td></td><td>% gain w.r.t baseline</td><td>+0.32</td><td>+2.15</td></tr><tr><td>(f)</td><td>VIKINGVLM + SelTDA</td><td>56.86</td><td>83.86</td></tr><tr><td></td><td>% gain w.r.t baseline</td><td>+0.92</td><td>+1.96</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions.",
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+    },
+    {
+        "type": "text",
+        "text": "size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of  $480 \\times 480$  and an image size of  $384 \\times 384$  for VQG. For all datasets, we use the official training, validation, and test splits.",
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+    },
+    {
+        "type": "text",
+        "text": "Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top- $p$  of 0.92. Additional experiments and visualizations can be found in the supplemental material.",
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Self-Training: A-OKVQA & ArtVQA",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi",
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+    {
+        "type": "page_number",
+        "text": "15009",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e8cd2dcac3f0ee0c15a91b64e997d82ef1b409d9c6fa25891da37d31eee41fc4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Question Type</td><td>Well-Posed Question</td><td>Answers Correct</td><td>Answerable</td><td>% of Total (95% CI)</td></tr><tr><td>External Knowledge</td><td>73%</td><td>62%</td><td>70%</td><td>29.6% - 50.00%</td></tr><tr><td>Visual Identification</td><td>94%</td><td>88%</td><td>94%</td><td>11.18% - 27.65 %</td></tr><tr><td>Visual Reasoning</td><td>83%</td><td>70%</td><td>80%</td><td>32.54% - 53.17%</td></tr><tr><td>Overall (95% CI)</td><td>71.16% - 87.96%</td><td>59.77% - 78.98%</td><td>68.83% - 86.22%</td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the  $95\\%$  confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about  $79.5\\%$  on the validation set.",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b5a2ef978d058822c9a3043cdda23a29dda1114974be441603f10370c689fc7.jpg",
+        "image_caption": [
+            "Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/d2b0cf5b89d1ad3dd5343369cccf1d07ca9f3e4b27cfec84a32030d19e925ed5.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/4ca10f4794329ee94ff924f1bfc11d327de68edfaaa390acc945da36e4f3a8e8.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            640,
+            246,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/983aa70c3c59d8d9f24f1fe9ed408ee2eef44725a6b8cbaf944c32bf50704548.jpg",
+        "image_caption": [
+            "Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when  $447k$  real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablations & Analysis of Pseudolabels",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. \"what is this object?\"). Next, we show using t-SNE [47] that the teacher model learns to copy the \"style\" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "15010",
+        "bbox": [
+            480,
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3693bf927c7c923c6428dbc133ac1a877e66dd1f0cb304068b8a69c2d123068f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\">Images</td><td colspan=\"3\">Questions</td><td rowspan=\"2\">Multiplier</td><td rowspan=\"2\">Accuracy</td><td rowspan=\"2\">% Gain</td><td rowspan=\"2\">Questions/Image</td></tr><tr><td>Labeled</td><td>Unlabeled</td><td>Real</td><td>Synthetic</td><td>Total</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>0</td><td>17,000</td><td>1x (baseline)</td><td>57.11</td><td></td><td>N/A</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>17,000</td><td>34,000</td><td>2x</td><td>57.85</td><td>+0.74</td><td>1 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>34,000</td><td>51,000</td><td>3x</td><td>60.01</td><td>+2.90</td><td>2 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>51,000</td><td>68,000</td><td>4x</td><td>59.73</td><td>+2.62</td><td>3 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>0</td><td>17k</td><td>1x (baseline)</td><td>57.11</td><td></td><td>N/A</td></tr><tr><td>17,000</td><td>8,500</td><td>17,000</td><td>17,000</td><td>34,000</td><td>2x</td><td>60.69</td><td>+3.57</td><td>2 / 1</td></tr><tr><td>17,000</td><td>17,000</td><td>17,000</td><td>34,000</td><td>51,000</td><td>3x</td><td>62.09</td><td>+4.98</td><td>2 / 1</td></tr><tr><td>17,000</td><td>25,500</td><td>17,000</td><td>51,000</td><td>68,000</td><td>4x</td><td>61.31</td><td>+4.20</td><td>2 / 1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3731eaa068471b7de94b7fc946dae82b588deb480588b73e0e64f2ea40fec558.jpg",
+        "table_caption": [
+            "Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"3\"># of Real + Synthetic QA Pairs</td><td colspan=\"3\">Robustness Test Sets</td><td rowspan=\"2\">Avg. % Increase</td><td rowspan=\"2\">Robustness Total</td></tr><tr><td>Real</td><td>Synthetic</td><td>Multiplier</td><td>AdVQA</td><td>VQA-CE</td><td>VQA-Rephrasings</td></tr><tr><td>(a)</td><td>17,000</td><td>0</td><td>×1</td><td>31.06</td><td>51.43</td><td>65.88</td><td>0</td><td>148.37</td></tr><tr><td>(b)</td><td>17,000</td><td>2,000</td><td>×1.1</td><td>37.09</td><td>52.96</td><td>67.94</td><td>+3.21</td><td>157.99</td></tr><tr><td>(c)</td><td>17,000</td><td>4,500</td><td>×1.3</td><td>36.99</td><td>53.15</td><td>67.98</td><td>+3.25</td><td>158.12</td></tr><tr><td>(d)</td><td>17,000</td><td>8,000</td><td>×1.5</td><td>37.34</td><td>53.33</td><td>67.57</td><td>+3.29</td><td>158.24</td></tr><tr><td>(e)</td><td>17,000</td><td>12,000</td><td>×1.7</td><td>37.43</td><td>52.62</td><td>67.35</td><td>+3.01</td><td>157.4</td></tr><tr><td>(f)</td><td>17,000</td><td>17,000</td><td>×2</td><td>36.95</td><td>52.05</td><td>66.95</td><td>+2.53</td><td>155.95</td></tr><tr><td>(g)</td><td>17,000</td><td>34,000</td><td>×3</td><td>36.89</td><td>51.00</td><td>65.64</td><td>+1.72</td><td>153.53</td></tr><tr><td>(h)</td><td>17,000</td><td>51,000</td><td>×4</td><td>36.06</td><td>50.25</td><td>64.78</td><td>+0.91</td><td>151.09</td></tr><tr><td></td><td colspan=\"3\">Max % increase on each dataset</td><td>+6.03</td><td>+1.9</td><td>+2.1</td><td></td><td>+9.87</td></tr></table>",
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+        "type": "text",
+        "text": "Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA.",
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+        "type": "text",
+        "text": "We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4).",
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+        "type": "text",
+        "text": "Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is  $50\\%$  the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling.",
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+        "type": "text",
+        "text": "4.3. Robustness",
+        "text_level": 1,
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+        "text": "We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three",
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+        "type": "text",
+        "text": "known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA",
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+        "type": "page_number",
+        "text": "15011",
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+        "type": "text",
+        "text": "models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a  $2.1\\%$  performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA.",
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+    {
+        "type": "text",
+        "text": "4.4. Domain Generalization",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers.",
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+    {
+        "type": "text",
+        "text": "4.5. Numerical Reasoning",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Numerical reasoning is required to answer questions such as \"how many sheep are looking at the camera\". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of  $29.81\\%$  and  $24.71\\%$  on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of  $3.63\\%$  and  $10.57\\%$ . These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly,",
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+    {
+        "type": "table",
+        "img_path": "images/b5c17177a6ca2b91968a9b008bd5cf438fe644bb3d2a37d4f0fb3b0c598b3be4.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">Target (0-shot)</td></tr><tr><td>ArtVQA</td><td>PathVQA</td><td>RSVQA</td></tr><tr><td>Baseline (BLIP)</td><td>31.65</td><td>25.09</td><td>37.78</td></tr><tr><td>BLIP + SelTDA</td><td>38.03</td><td>26.76</td><td>38.99</td></tr><tr><td>% gain w.r.t baseline</td><td>+6.38</td><td>+1.67</td><td>+1.1</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/9feb7d8d7bd8b618442127438956b19aaa391b5e6b915ffc5c7c90f14127caa4.jpg",
+        "table_caption": [
+            "Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Initialization</td><td colspan=\"2\"># Training Pairs</td><td colspan=\"2\">Numerical Reasoning</td></tr><tr><td>Real</td><td>Synth</td><td>VQAv2</td><td>VQA-Rephrasings</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>0</td><td>13.49</td><td>13.06</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>2000</td><td>38.73</td><td>33.74</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>4500</td><td>40.4</td><td>35.91</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>8000</td><td>42.9</td><td>36.5</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>12000</td><td>43.3</td><td>37.77</td></tr><tr><td colspan=\"3\">max % gain w.r.t baseline</td><td>+29.81</td><td>+24.71</td></tr><tr><td>BLIP</td><td>17000</td><td>0</td><td>1.42</td><td>1.29</td></tr><tr><td>BLIP</td><td>17000</td><td>17000</td><td>4.53</td><td>11.44</td></tr><tr><td>BLIP</td><td>17000</td><td>34000</td><td>5.05</td><td>11.77</td></tr><tr><td>BLIP</td><td>17000</td><td>51000</td><td>4.26</td><td>11.86</td></tr><tr><td colspan=\"3\">max % gain w.r.t baseline</td><td>+3.63</td><td>+10.57</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA).  $\\mathrm{BLIP}_{\\mathit{VQAv2}}$  indicates transfer learning from VQAv2, and BLIP indicates direct finetuning.",
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+    {
+        "type": "text",
+        "text": "even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word \"how\" is a high-probability word to start a question with, and is naturally followed by \"many\" (Fig 6) resulting in numerical questions being generated.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion & Future Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. Finally, self-training is yet to be explored with recently developed billion-parameter VLMs [9, 25].",
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+        "type": "page_number",
+        "text": "15012",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            173,
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+        ],
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+    },
+    {
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+        "sub_type": "ref_text",
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2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/cca6ed83-7faa-4a3c-a2de-be98beed4aed_origin.pdf

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2023/Q_ How To Specialize Large Vision-Language Models to Data-Scarce VQA Tasks_ A_ Self-Train on Unlabeled Images!/full.md

@@ -0,0 +1,274 @@
+# Q: How to Specialize Large Vision-Language Models to Data-Scarce VQA Tasks? A: Self-Train on Unlabeled Images!
+
+Zaid Khan†* Vijay Kumar BG Samuel Schulter* Xiang Yu* Yun Fu† Manmohan Chandraker* Northeastern University, NEC Labs America, Amazon, UC San Diego
+
+# Abstract
+
+Finetuning a large vision language model (VLM) on a target dataset after large scale pretraining is a dominant paradigm in visual question answering (VQA). Datasets for specialized tasks such as knowledge-based VQA or VQA in non natural-image domains are orders of magnitude smaller than those for general-purpose VQA. While collecting additional labels for specialized tasks or domains can be challenging, unlabeled images are often available. We introduce SelTDA (Self-Taught Data Augmentation), a strategy for finetuning large VLMs on small-scale VQA datasets. SelTDA uses the VLM and target dataset to build a teacher model that can generate question-answer pseudolabels directly conditioned on an image alone, allowing us to pseudolabel unlabeled images. SelTDA then finetunes the initial VLM on the original dataset augmented with freshly pseudolabeled images. We describe a series of experiments showing that our self-taught data augmentation increases robustness to adversarially searched questions, counterfactual examples and rephrasings, improves domain generalization, and results in greater retention of numerical reasoning skills. The proposed strategy requires no additional annotations or architectural modifications, and is compatible with any modern encoder-decoder multimodal transformer. Code available at https://github.com/codezakh/SelTDA.
+
+# 1. Introduction
+
+Large, pretrained vision language foundation models [3, 20, 25, 26, 35, 49] are approaching human-level performance on visual question answering (VQA) [26, 50–52, 54, 62], as measured by the standard VQAv2 [13] benchmark. Yet on more complex VQA tasks [37, 43] there is a larger gap between humans and machines. One difficulty is the small scale of datasets for complex VQA tasks or those in domains beyond natural images. The first solution to deal with the
+
+![](images/03965e14b1009cd2745e52bb2345565fe94bb6775fa4da04f0c07e16fd5652aa.jpg)  
+Figure 1. SelTDA expands the self-training paradigm to VQA. By self-generating supervision (orange line) for an image  $I$  without needing extra annotations, we can augment a target dataset with new images and their pseudo-questions and answers  $(Q,A)$ .
+
+data scarcity is to employ transfer learning from a larger VQA dataset (e.g. VQAv2) to the smaller, specialized VQA dataset. However weaknesses of VQA models such as lack of consistency [44], weakness to adversarially searched questions [27] and tendency to cheat by learning shortcuts [8] can be exacerbated when fine-tuning on small datasets.
+
+Collecting annotations to expand a dataset for knowledge-intensive tasks or specialized domains is often prohibitively expensive. However, unlabeled images are cheap and often available. How can we exploit unlabeled images for specific visual question answering tasks? One possibility is to generate new question+answer pairs for the unlabeled images, and use them during training. However, existing methods for visual question generation require images with annotations — either ground truth captions [2,4], or bounding boxes [21,48]. Even if these annotations were to be acquired, they induce a limited set of possible questions; they are limited to objects and concepts included in the acquired annotation, which are in turn limited by the finite label space of pretrained object detectors and the information disparity between a caption and an image (an image usually contains much more content
+
+![](images/3e4b943819c4228181fd9f28b9570fa942cc03b174fa245b394684d05216f4f0.jpg)  
+Figure 2. Motivating experiment. We sample increasingly diverse captions from BLIP [26], convert them to questions, and pose the questions to BLIP after finetuning on VQAv2. As caption diversity increases, self-agreement decreases (right panel). Despite the diversity, many captions remain correct (middle panel), suggesting that the VLM has knowledge that is not exhausted by task-specific finetuning.
+
+![](images/1338f0d6729f7208a8733a9fd6cc12ec31588ca937e3217f748b7773fd568866.jpg)
+
+than a short caption can describe).
+
+Motivating Experiment: In Fig 2, we show that a large vision-language model (VLM) pretrained on web-scale data contains knowledge that can be drawn out with image-conditional text generation, but which the model cannot verify when posed as a visual question-answering task. We prompt the BLIP [26] VLM (pretrained on 129M image-text pairs) to caption 1000 images from the CC3M [45] dataset starting with the phrase "this is a". We convert each caption into a boolean question where the correct answer is "yes" by inserting the caption into the template is this a <caption>? Next, we ask a BLIP VLM finetuned on the VQAv2 dataset [13] to choose between "yes" and "no" for each caption turned into a question. Surprisingly, the VQA-finetuned BLIP answers "no" to at least  $5\%$  of the questions, increasing to  $15\%$  as the diversity of captions increases (adjusted by top- $p$  parameter in nucleus sampling). This suggests the possibility that the VLM has knowledge it cannot exploit when answering questions, but is accessible when directly generating text conditioned on an image.
+
+Approach: To exploit unlabeled images for VQA, we propose SelTDA, a three-stage framework for Self-Taught Data Augmentation (Fig 1 bottom panel). We adapt the paradigm of self-training used in object detection [29, 65] and image classification [41, 60] for VQA. In classification / detection, the task of labeling an image is identical to prediction, and the teacher and student optimize identically structured objectives. In VQA self-training, the student and teacher tasks are different. A teacher must pose and answer a question given an image, while the student provides an answers given a question and image. To handle this, we first cast the task of the teacher as a direct image-to-text generation task, and introduce a teacher model by updating the weights of the VLM to learn an image-conditional visual question generation model  $\mathrm{VQG}_{IC}$ . Next, we use  $\mathrm{VQG}_{IC}$  as a teacher to
+
+pseudolabel unlabeled images by sampling questions and answers from  $\mathrm{VQG}_{IC}$  with stochastic decoding. Finally, we augment the original VQA dataset with the newly labeled image-question-answer pairs, and finetune the VLM for visual question answering on the augmented VQA dataset.
+
+Benefits: SelTDA allows us generate synthetic training data by approximating the distribution  $P(Q, A|I)$  of the target VQA task, where  $Q, A, I$  represents a question, answer, and image respectively. One benefit is that the synthetic data increases the number of training pairs available for finetuning, which effects an increase in raw performance. A second benefit is an increase in the diversity of questions and answers due to the introduction of new images and the stochastic nature of the text decoding, which results in increased robustness and domain generalization. A third benefit is the distillation of knowledge from pretraining and transfer learning into the synthetic training data, which can teach new skills (e.g. domain generalization) or prevent the forgetting of specific skills (e.g. numerical reasoning). Finally SelTDA is architecture-agnostic given a vision-language model capable of image-conditional text-generation. Our contributions can be summarized as follows:
+
+1. We introduce SelTDA, a variant of the self-training paradigm that is designed for VQA and large generative pretrained VLMs.  
+2. We propose treating visual question generation as a direct image-to-text task by leveraging the autoregressive decoder of a large, pretrained VLM, enabling us to generate questions and answers from an unlabeled image with no auxiliary annotations needed.  
+3. We show that a large VLM trained with the proposed SelTDA gains increased robustness, domain generalization, numerical reasoning, and performance when finetuning on small-scale VQA datasets.
+
+# 2. Related Work
+
+Augmentation for VQA The method of [53] augments images by using an MLP to classify possible answers in the image and using an LSTM to generate questions matching the answer. While this works with unlabeled images, it is not used for self-training, has a limited label space, and does not leverage large VLMs. KDDAug [6] augments existing question answer pairs by generating pseudoanswers and achieves increases in robustness. ConCat [19] similarly trains more robust models by augmenting the existing QA pairs in a dataset. In contrast to this line of work, we seek to exploit unlabeled images by generating new questions and answers, and using a large VLM to generate augmentation.
+
+Few/Zero-shot Generalization Large VLMs have shown impressive generalization to unseen tasks after large-scale pretraining [1], echoing similar achievements in natural language processing [7, 55]. We explore zero-shot generalization to similar tasks in new domains. Domain adaptation in VQA has been explored, first by [5, 58] and most recently by [63]. These fall into the general line of feature adaptation methods for domain adaptation, as they align domain features. Our method is more similar to pseudolabeling based methods for domain adaptation [24, 31] with the difference being that our pseudolabels are natural language rather than distributions. Moreover, we do not focus on adaptation, but zero-shot generalization.
+
+Visual Question Generation is a well-explored topic with a long history of prior work [23, 28, 38, 64]. In contrast to prior work, our VQG teacher model does not rely on or need paired ground truth annotations for an unlabeled image to generate questions. SimpleAug [21] and GuidedVQG [48] relies on annotations such as bounding boxes to generate new questions, and requires pretrained object detectors, which have a limited label space. WeaQ [2] requires captions to already be present, as does [4], which additionally uses a large language model (T5-XXL with 11B parameters) to generate questions. One similarity of our approach to [4] is that we both seek to use knowledge in a large model to generate questions, with the main differences being that we do not require ground-truth captions for unlabeled images, and we use a large vision-language model than a large language model. VQAPG [61] is similar to our approach in not requiring any ground-truth annotations, but focuses on creating a joint question-generation and question answering model that is consistent, rather than self-training a model with unlabeled data. The authors of [17] propose a VQG method that does not rely on ground-truth annotations, but their method is LSTM-based, rather than based on self-training with a large vision-language model.
+
+Self-Training uses labeled data to train a teacher model. The teacher model provides labels for auxiliary unlabeled data. Finally, a student model is trained on the labeled data augmented with newly-labeled data. Previous work in self
+
+training for computer vision focuses on image-classification [57, 59] or object detection [29, 41, 60, 65]. A significant difference between classical self-training and our setting is that in the more traditional settings, the teacher and student have the same task. In our setting, the task of the teacher (ask a question) is different than the task of the student (answer a question). More similar to us, [42] uses self-training for question-answering. However, the teacher model of [42] has a fundamentally different task, since it is a reading comprehension task, where the ground-truth answer is mentioned within the passage itself. In our task, the teacher model must generate the ground-truth answer from its own internal knowledge and by inspecting an image.
+
+# 3. Method
+
+Our goal is to pseudolabel an unlabeled image  $I$  with a generated question-answer pair  $(Q, A)$  using a teacher (initialized from the VLM), and then train a student model (the initial VLM) on the real VQA pairs augmented with the generated VQA pairs. To generate the pseudolabels, we first learn a visual question generation model on the real question-answer pairs and images as the teacher. We denote this model  $\mathrm{VQG_{IC}}$  to highlight the image-conditional nature of the model, because the model generates both a question and answer conditional on an image alone. This approach is end-to-end, requires no ground truth annotations, bounding boxes, or handcrafted guidance, and provides a generative model approximating  $P(Q, A|I)$  that we can sample from. We then feed the teacher model unlabeled images and stochastically decode from the teacher model to generate pseudolabels, which we parse into question answer pairs. After the real samples in the dataset have been augmented with the self-generated samples, VQA training can proceed as normal. Our approach is compatible with any modern encoder-decoder multimodal architecture. This is because our approach relies entirely on direct image-to-text generation, which is possible in modern large vision language models since their autoregressive decoders are designed to produce text conditioned on an image.
+
+# 3.1. The Teacher: Direct Image-Conditional VQG
+
+Self-training requires a teacher model to produce pseudolabels that the student model then learns to mimic. In order to use unlabeled data for VQA, the teacher model must be able to pose a question and provide an answer given an unlabeled image, which is a different task from VQA. Given an image  $I$ , a question  $Q$  and answer  $A$ , the VQA student must approximate  $P(Q \mid Q, I)$ , while the teacher model must approximate  $P(Q, A \mid I)$ . Previous approaches to visual question generation (VQG) cannot work with unlabeled data because they approximate  $P(Q \mid I, A)$ , that is, they generate a question conditional on the image and a potential answer. In contrast to these previous, answer-conditional VQG
+
+![](images/1b844b835973f755de7d2b3a15912d25d1506e699186fd4ae59ac4648da7d292.jpg)  
+Figure 3. Overview of the proposed framework. We first create the teacher  $\mathrm{VQG}_{IC}$  (§3.1), use  $\mathrm{VQG}_{IC}$  to pseudolabel unlabeled images (§3.2), and finetune student on the original training pairs augmented with the pseudolabeled images. The pseudolabels are natural language.
+
+![](images/07eb44d222a5f5a01e155ae42d95abd930b5fc2bd92482ff77ed3650a8b213c0.jpg)  
+Question: what is the cat wearing?  
+Answers: necktie, tie
+
+![](images/7028f5f12d0e2415bc374ecca7788f763487cfe32d46aa2b05fde2e063073630.jpg)  
+Question: how is the egg cooked? Answer: fried
+
+![](images/cd87a2039c4183818b9a7151627b2c40bcf3c0a3ac083fd466f88d2721d854a1.jpg)  
+Question: how many items of food are present here?  
+Answers: 2
+
+![](images/f9013b0e122b47e981b019a685a592fdfae273ed025e4b6d73924bb935ca1efe.jpg)  
+Question: what activity is the baby learning? Answer: feeding, eating, nutrition
+
+![](images/5a3885a05ec6c2ed434e18984c44ea16a9b1692d2cec15620b7b0584800ea3dd.jpg)  
+Question: what color is the sky in the picture?  
+Answers: clear, blue
+
+![](images/8943e59bbb0aa9f14364f1d18c10b2466ffc22b68ab75b92f522a3b67c6b3f48.jpg)  
+Question: why is the elephant painted? Answer: to be rode, for entertainment, decoration
+
+![](images/42a7928b3661f35b2ac5d7a2a0b66f6aa08229493cfa4d92c5cce7d9373ad563.jpg)  
+Question: what city is this?  
+Answers: london, uk
+
+![](images/5188f6d8d4c231fd410025f49ec9f6ebb416f7a22adce852c9cdc6f462bf5d53.jpg)  
+Question: what is the name of this party? Answer: baby shower  
+Figure 4. Example questions and answers generated by the teacher on unlabeled images. The questions include unusual pairings (cat wearing necktie) or require broad knowledge (identifying a baby shower or London landmarks) and inferences about scenes (the baby is learning).
+
+approaches, we develop an image-conditional approach  $(\mathrm{VQG}_{IC})$  that we use as a teacher model. Our approach also contrasts with self-training in image classification or object detection, which benefit from having the teacher and student both approximating and predicting identically structured distributions  $P(Y|I)$ , where  $Y$  is often a distribution over a (finite) label space.
+
+To create the  $\mathrm{VQG}_{IC}$  teacher that approximates  $P(Q,A|I)$ , we treat the problem of learning such a model as a text-generation problem, and wish to train the autoregressive decoder of the vision-language model to approximate  $P(T|I)$ , where  $T = (Q,A)$ . Let  $\mathcal{D}_{QA}$  be a question-answer dataset we wish to create a teacher from. For a sample  $(Q,A,I)\in \mathcal{D}_{QA}$ , we transform it into a target sequence of tokens  $y_{1:N} = (y_1,y_2,\dots y_n)$  by entering  $(Q,A)$  into a structured template of the form "Question: <question>? Answer: <answer>." where <question> and <answer> are replaced by the content of  $Q$  and  $A$  respectively. Once  $y_{1:N} = (y_1,y_2,\dots y_n)$  is
+
+obtained, we train the model by optimizing
+
+$$
+\mathcal {L} _ {\mathrm {V Q G}} = - \sum_ {n = 1} ^ {N} \log P _ {\theta} \left(y _ {n} \mid y _ {<   n}, x\right) \tag {1}
+$$
+
+over all question-image-answer pairs in  $\mathcal{D}_{QA}$ , where  $x$  is the latent encoded features in the standard encoder-decoder architecture and  $\theta$  represents the VLM parameters. The  $\mathrm{VQG_{IC}}$  thus learns to maximize the conditional likelihood of a question-answer pair represented as a unified string, given an image. Recall that  $\mathrm{VQG_{IC}}$  is initialized from the parameters of an autoregressive VLM. The VLM is a quality approximator of  $P(T|I)$ , having been exposed to a diverse number of images and paired text. The  $\mathrm{VQG_{IC}}$  teacher can tap into this reservoir of knowledge, because a pseudo question-answer pair  $(Q', A')$  is generated jointly as a text  $T'$ , allowing us to sample from  $P(T|I)$ .
+
+# 3.2. Training the Student with Unlabeled Data
+
+Once the VQG<sub>IC</sub> teacher model has been obtained, self-training with unlabeled data can proceed. To produce a
+
+pseudolabel  $(Q', A')$  for an unlabeled image  $I_u$ , we first obtain  $\mathbf{L}_{1:N} = \mathrm{VQG_{IC}}(I_u)$ , where  $\mathbf{L}_{1:N}$  are the logits of the decoder. The logits  $\mathbf{L}_{1:N}$  define a distribution  $P(L_N \mid L_{1:N-1})$  over the tokens of the model's natural language vocabulary. We then apply nucleus sampling [15] to stochastically decode a text  $T'$  from  $P(L_N \mid L_{1:N-1})$ . The structured format of the generation template can then be easily parsed by a regular expression to recover a pseudo-question-answer pair  $(Q', A')$  from the decoded text  $T'$ . This pair  $(Q', A') = T'$  is a sample from  $P(T|I)$ , and reflects textual knowledge about the content of an image known to the VLM.
+
+We then proceed to pseudolabel the desired number of images and obtain any number of triplets of the form  $(Q', A', I_u)$ , representing self-generated training data  $\mathcal{D}_{QA}'$  in the style of a target dataset  $\mathcal{D}_{QA}$ . We then augment the real dataset  $\mathcal{D}_{QA}$  with the self-generated question-answer pairs on unlabeled images  $\mathcal{D}_{QA}'$  to create a self-augmented training dataset  $\mathcal{D}_{\mathrm{Aug}QA} = \mathcal{D}_{QA}' \cup \mathcal{D}_{QA}$ . The teacher model is no longer needed, and the student can be initialized from the checkpoint obtained after large-scale pretraining that the teacher model was initialized from. At this point, VQA training can proceed as normal. In our setting, we use the training procedure of BLIP [26] in which VQA is treated as an open-ended generation task, and the VQA objective can be expressed as the standard language modeling loss
+
+$$
+\mathcal {L} _ {\mathrm {V Q A}} = - \sum_ {n = 1} ^ {N} \log P _ {\theta} \left(y _ {n} \mid y _ {<   n}, x _ {n}\right) \tag {2}
+$$
+
+where  $x_{n}$  is the  $n$ -th element of the multimodal sequence embeddings  $\mathbf{X}_{1:N}$  produced by  $\mathrm{VLM}(Q, I; \theta)$ ,  $Q, I$  are the question and image,  $y_{1:N}$  is the sequence of answer tokens, and  $\theta$  represents the VLM parameters, which we initialize from the pretrained weights rather than the teacher. Why can high quality pseudolabels  $(Q', A')$  be generated even when  $\mathcal{D}_{QA}$  is small, and few pairs are available for adapting the teacher  $\mathrm{VQG}_{IC}$ ? Knowledge about the content of the image in a textual form  $P(T|I)$  is already well-learned by the VLM from which we initialize  $\mathrm{VQG}_{IC}$ . Thus,  $\mathcal{D}_{QA}$  only needs sufficient pairs to teach  $\mathrm{VQG}_{IC}$  how to construct annotations matching the style of  $\mathcal{D}_{QA}$ .
+
+# 4. Experiments
+
+Experimental Setup We implement our framework in PyTorch [39] and use the same hyperparameter settings for all experiments. Our settings are taken from [26]. We train each VQA model for 10 epochs, using the AdamW [33] optimizer with a weight decay of 0.05 and a linear LR decay to 0 from an initial LR 2e-5. Each VQG model is trained for 10 epochs with the same weight decay and an initial LR of 2e-5. For VQA, we use a global batch size of 64 on 4 GPUs, with a per device batch size of 16. For VQG, we use a global batch
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Model</td><td colspan="2">A-OKVQA</td></tr><tr><td>Validation</td><td>Test</td></tr><tr><td>(a)</td><td>ViLBERT [34]</td><td>49.1</td><td>41.5</td></tr><tr><td>(b)</td><td>LXMERT [46]</td><td>51.4</td><td>41.6</td></tr><tr><td>(c)</td><td>KRISP [36]</td><td>51.9</td><td>42.2</td></tr><tr><td>(d)</td><td>GPV-2 [18]</td><td>60.3</td><td>53.7</td></tr><tr><td>(e)</td><td>BLIP [26]</td><td>57.1</td><td></td></tr><tr><td>(f)</td><td>\( BLIP_{\text{VQAv2}} \) [26]</td><td>67.8</td><td>59.5</td></tr><tr><td>(g)</td><td>BLIP + SelTDA</td><td>62.1</td><td>54.5</td></tr><tr><td colspan="2">% gain w.r.t baseline</td><td>+5.0</td><td></td></tr><tr><td colspan="2">% gain w.r.t best prior work</td><td>+1.8</td><td>+0.8</td></tr><tr><td>(h)</td><td>\( BLIP_{\text{VQAv2}} + SelTDA \)</td><td>68.9</td><td>59.5</td></tr><tr><td colspan="2">% gain w.r.t baseline</td><td>+1.1</td><td>+0.0</td></tr><tr><td colspan="2">% gain w.r.t best prior work</td><td>+8.6</td><td>+5.8</td></tr></table>
+
+Table 1. SelTDA improves performance on knowledge-based VQA, even on a strong baseline pretrained on 129M pairs.  
+
+<table><tr><td></td><td rowspan="2">Model</td><td colspan="2">ArtVQA Accuracy</td></tr><tr><td></td><td>Overall</td><td>Grounded</td></tr><tr><td>(a)</td><td>BAN [22]</td><td>22.4</td><td>-</td></tr><tr><td>(b)</td><td>BLIP [26]</td><td>21.36</td><td>81.71</td></tr><tr><td>(c)</td><td>VIKING [12]</td><td>55.5</td><td>78.74</td></tr><tr><td>(d)</td><td>VIKINGVLM</td><td>55.9</td><td>81.9</td></tr><tr><td>(e)</td><td>BLIP + SelTDA</td><td>21.68</td><td>83.86</td></tr><tr><td></td><td>% gain w.r.t baseline</td><td>+0.32</td><td>+2.15</td></tr><tr><td>(f)</td><td>VIKINGVLM + SelTDA</td><td>56.86</td><td>83.86</td></tr><tr><td></td><td>% gain w.r.t baseline</td><td>+0.92</td><td>+1.96</td></tr></table>
+
+Table 2. SelTDA improves VQA on fine art images [12] for VIKING and BLIP models. Grounded denotes visually grounded questions.
+
+size of 128, with a per device batch size of 32. All models are initialized from pretrained BLIP [26] checkpoints. For VQA, we use an image size of  $480 \times 480$  and an image size of  $384 \times 384$  for VQG. For all datasets, we use the official training, validation, and test splits.
+
+Baseline As a strong baseline model, we use the ViT-B/16 version of the BLIP [26] model pretrained on 129M image-text pairs. BLIP [26] has an autoregressive decoder and is trained for text-generation, making it easy to adapt to text-generation tasks. When decoding, we use nucleus sampling with a top- $p$  of 0.92. Additional experiments and visualizations can be found in the supplemental material.
+
+# 4.1. Self-Training: A-OKVQA & ArtVQA
+
+We evaluate SelTDA in two domains: outside knowledge VQA on natural images with A-OKVQA [43] and outside knowledge VQA on fine-art images with AQUA [12]. We use the COCO 2017 unlabeled set [30] as a source of addi
+
+<table><tr><td>Question Type</td><td>Well-Posed Question</td><td>Answers Correct</td><td>Answerable</td><td>% of Total (95% CI)</td></tr><tr><td>External Knowledge</td><td>73%</td><td>62%</td><td>70%</td><td>29.6% - 50.00%</td></tr><tr><td>Visual Identification</td><td>94%</td><td>88%</td><td>94%</td><td>11.18% - 27.65 %</td></tr><tr><td>Visual Reasoning</td><td>83%</td><td>70%</td><td>80%</td><td>32.54% - 53.17%</td></tr><tr><td>Overall (95% CI)</td><td>71.16% - 87.96%</td><td>59.77% - 78.98%</td><td>68.83% - 86.22%</td><td></td></tr></table>
+
+Table 3. We manually inspect 100 questions and answers generated by the teacher model finetuned on A-OKVQA. We show the  $95\%$  confidence interval obtained by a proportion test. Annotator agreement on A-OKVQA is about  $79.5\%$  on the validation set.
+
+![](images/9b5a2ef978d058822c9a3043cdda23a29dda1114974be441603f10370c689fc7.jpg)  
+Figure 5. A T-SNE embedding shows that questions generated by a teacher finetuned on ArtVQA (orange) differ from real VQAv2 questions (blue) and are more similar to the real ArtVQA questions (green), yet more diverse, covering a larger area. We use SimCSE [10] to obtain a dense vector representation of each sentence. All the sets of questions are embedded together with T-SNE.
+
+![](images/d2b0cf5b89d1ad3dd5343369cccf1d07ca9f3e4b27cfec84a32030d19e925ed5.jpg)
+
+![](images/4ca10f4794329ee94ff924f1bfc11d327de68edfaaa390acc945da36e4f3a8e8.jpg)
+
+![](images/983aa70c3c59d8d9f24f1fe9ed408ee2eef44725a6b8cbaf944c32bf50704548.jpg)  
+Figure 6. Sunburst chart of questions generated by a teacher model finetuned on A-OKVQA.
+
+tional images for A-OKVQA, and SemArt [11] as a source of fine art images for ArtVQA. On A-OKVQA, we perform model selection over students trained with varying amounts of SelTDA with the training set, and on ArtVQA, we use the validation set. On A-OKVQA (Table 1), we show that
+
+self-taught data augmentation improves overall performance, especially in the setting where no extra data (VQAv2) is available. BLIP with SelTDA achieves SOTA performance on A-OKVQA without transfer learning (row g in Table 1), even relative to competitors using transfer learning. This performance improvement holds even when  $447k$  real pairs from VQAv2 are used for transfer learning, suggesting that self-taught data augmentation offers real improvements over manual annotations. On fine art VQA (Table 2), we show that self-taught data augmentation achieves state-of-the-art and improves overall performance, with a large increase for visually grounded questions.
+
+# 4.2. Ablations & Analysis of Pseudolabels
+
+We manually evaluate 100 randomly sampled questions generated by the teacher model on A-OKVQA (Table 3). The generated questions and answers are noisier than the real questions and answers, but the levels of noise are not substantially below the human agreement on A-OKVQA. Questions which require visual reasoning or external knowledge are harder to generate correctly compared to those that require simpler visual identification (e.g. "what is this object?"). Next, we show using t-SNE [47] that the teacher model learns to copy the "style" of questions in a particular dataset (Fig 5). Synthetic questions generated by a teacher finetuned for a specific dataset (ArtVQA) are more similar to the style of the questions found in the target dataset compared to real questions from a different dataset (VQAv2), while being more diverse.
+
+<table><tr><td colspan="2">Images</td><td colspan="3">Questions</td><td rowspan="2">Multiplier</td><td rowspan="2">Accuracy</td><td rowspan="2">% Gain</td><td rowspan="2">Questions/Image</td></tr><tr><td>Labeled</td><td>Unlabeled</td><td>Real</td><td>Synthetic</td><td>Total</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>0</td><td>17,000</td><td>1x (baseline)</td><td>57.11</td><td></td><td>N/A</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>17,000</td><td>34,000</td><td>2x</td><td>57.85</td><td>+0.74</td><td>1 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>34,000</td><td>51,000</td><td>3x</td><td>60.01</td><td>+2.90</td><td>2 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>51,000</td><td>68,000</td><td>4x</td><td>59.73</td><td>+2.62</td><td>3 / 1</td></tr><tr><td>17,000</td><td>0</td><td>17,000</td><td>0</td><td>17k</td><td>1x (baseline)</td><td>57.11</td><td></td><td>N/A</td></tr><tr><td>17,000</td><td>8,500</td><td>17,000</td><td>17,000</td><td>34,000</td><td>2x</td><td>60.69</td><td>+3.57</td><td>2 / 1</td></tr><tr><td>17,000</td><td>17,000</td><td>17,000</td><td>34,000</td><td>51,000</td><td>3x</td><td>62.09</td><td>+4.98</td><td>2 / 1</td></tr><tr><td>17,000</td><td>25,500</td><td>17,000</td><td>51,000</td><td>68,000</td><td>4x</td><td>61.31</td><td>+4.20</td><td>2 / 1</td></tr></table>
+
+Table 4. SelTDA can improve performance even without additional unlabeled images, by generating more QA pairs for already labeled images. However, using previously unlabeled and unseen images results in further improvements. A-OKVQA is used.  
+
+<table><tr><td rowspan="2"></td><td colspan="3"># of Real + Synthetic QA Pairs</td><td colspan="3">Robustness Test Sets</td><td rowspan="2">Avg. % Increase</td><td rowspan="2">Robustness Total</td></tr><tr><td>Real</td><td>Synthetic</td><td>Multiplier</td><td>AdVQA</td><td>VQA-CE</td><td>VQA-Rephrasings</td></tr><tr><td>(a)</td><td>17,000</td><td>0</td><td>×1</td><td>31.06</td><td>51.43</td><td>65.88</td><td>0</td><td>148.37</td></tr><tr><td>(b)</td><td>17,000</td><td>2,000</td><td>×1.1</td><td>37.09</td><td>52.96</td><td>67.94</td><td>+3.21</td><td>157.99</td></tr><tr><td>(c)</td><td>17,000</td><td>4,500</td><td>×1.3</td><td>36.99</td><td>53.15</td><td>67.98</td><td>+3.25</td><td>158.12</td></tr><tr><td>(d)</td><td>17,000</td><td>8,000</td><td>×1.5</td><td>37.34</td><td>53.33</td><td>67.57</td><td>+3.29</td><td>158.24</td></tr><tr><td>(e)</td><td>17,000</td><td>12,000</td><td>×1.7</td><td>37.43</td><td>52.62</td><td>67.35</td><td>+3.01</td><td>157.4</td></tr><tr><td>(f)</td><td>17,000</td><td>17,000</td><td>×2</td><td>36.95</td><td>52.05</td><td>66.95</td><td>+2.53</td><td>155.95</td></tr><tr><td>(g)</td><td>17,000</td><td>34,000</td><td>×3</td><td>36.89</td><td>51.00</td><td>65.64</td><td>+1.72</td><td>153.53</td></tr><tr><td>(h)</td><td>17,000</td><td>51,000</td><td>×4</td><td>36.06</td><td>50.25</td><td>64.78</td><td>+0.91</td><td>151.09</td></tr><tr><td></td><td colspan="3">Max % increase on each dataset</td><td>+6.03</td><td>+1.9</td><td>+2.1</td><td></td><td>+9.87</td></tr></table>
+
+Table 5. SelTDA improves robustness of VQA models on AdVQA (adversarily searched questions), VQA-CE (multimodal shortcut learning) and VQA-Rephrasings test sets. The baseline (a) is trained on VQAv2 after pretraining, then finetuned on A-OKVQA.
+
+We show that the performance gains of SelTDA are due to novel-question answer pairs (first half of Tab 4) that add information not present in the ground-truth QA pairs, not only due to the additional images. However, the student model benefits from both the novel-question answer pairs and unlabeled images (second half of Table 4).
+
+Optimal Amount of Augmentation We explore how the amount of augmentation affects performance. The highest performance on the A-OKVQA validation and test sets is reached when the number of synthetic is double that of the real pairs (Table 4). When transfer learning from VQAv2, the ratio is different, and peak performance is reached when the number of synthetic pairs is  $50\%$  the number of real pairs (Table 5,4). Performance and robustness improvements (Table 5) saturate as increasing amounts of synthetic pairs are added, which may be the result of task-irrelevant information seeping into the dataset due to stochastic sampling.
+
+# 4.3. Robustness
+
+We investigate whether the self-taught data augmentation improves robustness of VQA models. We consider three
+
+known weaknesses. The first is adversarially searched questions, collected in the AdVQA [27] dataset through human-in-the-loop attacks against state-of-the-art VQA models. In Table 5, we show that models trained with self-taught data augmentation perform significantly better (20% relative improvement and 6% absolute improvement) on AdVQA. The second form of robustness we consider is resistance to multimodal shortcut learning, which the VQA-CE (Counterexamples) [8] test set measures. The test set is constructed so that models which have learned to answer questions using shortcuts based on correlations in the VQAv2 training set (ex: tennis racket detected + question about sport → always answer tennis) will display reduced performance on the VQA-CE test set. We construct our A-OKVQA models by transfer learning from the VQAv2 training set, so VQA-CE can be used to test multimodal shortcut learning in our models. In Table 5, we show that models trained with self-taught data augmentation are more resistant to shortcut learning (1.9% absolute improvement on VQA-CE) compared to the baseline model trained without self-taught data augmentation. Finally, we consider robustness to rephrasings. VQA
+
+models have been shown to be inconsistent when evaluated on rephrasings [44]. The VQA-Rephrasings test set consists of 3 human-provided rephrasings of the questions in the VQAv2 test set, intended to test the robustness of the model to rephrasings. On VQA-Rephrasings, self-taught data augmentation induces a  $2.1\%$  performance improvement relative to the baseline model, though both the baseline model and augmented models were initialized from the same weights learned on the VQAv2 training set prior to finetuning on A-OKVQA.
+
+# 4.4. Domain Generalization
+
+We hypothesize that self-taught data augmentation may improve domain generalization, because the student model has been exposed to a greater diversity of questions and answers. To test this, we compare the generalization of the baseline model and models trained with self-taught data augmentation on unseen test sets from three different domains. Concretely, we treat the natural-image based A-OKVQA task as the source task, and evaluate on VQA datasets from three target domains: medical, fine art, and remote sensing. For medical VQA, we use the PathVQA [14] dataset containing question and answers on pathology images. For fine art, we used the previously described AQUA [12] dataset for visual question answering on art images. For remote sensing, we use the RSVQA dataset [32], containing question and answers on satellite images. We display the results in Table 6. Across all three domains, self-taught data augmentation improves domain generalization over the baseline model. The improvement is greatest on fine art images, as the fine art domain is closest to the natural image domain with respect to the images, questions, and answers.
+
+# 4.5. Numerical Reasoning
+
+Numerical reasoning is required to answer questions such as "how many sheep are looking at the camera". Naive transfer learning from VQAv2 to A-OKVQA results in catastrophic forgetting of numerical reasoning, and naive finetuning on A-OKVQA results in models with poor numerical reasoning. In Table 7, we show that SelTDA significantly aids numerical reasoning when finetuning on a small-scale VQA dataset such as A-OKVQA. We measure numerical reasoning using questions labeled as requiring numerical answers on VQAv2 and the VQA-Rephrasings datasets. When transfer learning from VQAv2 (first half of Table 7), self-taught data augmentation results in an absolute increase of  $29.81\%$  and  $24.71\%$  on numerical questions on VQAv2 and VQA-Rephrasings. When finetuning directly on A-OKVQA (2nd half of Table 7), self-taught data augmentation results in an absolute increase of  $3.63\%$  and  $10.57\%$ . These results suggest that self-taught data augmentation can prevent catastrophic forgetting of numerical reasoning when transfer learning, and improve numerical reasoning significantly,
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">Target (0-shot)</td></tr><tr><td>ArtVQA</td><td>PathVQA</td><td>RSVQA</td></tr><tr><td>Baseline (BLIP)</td><td>31.65</td><td>25.09</td><td>37.78</td></tr><tr><td>BLIP + SelTDA</td><td>38.03</td><td>26.76</td><td>38.99</td></tr><tr><td>% gain w.r.t baseline</td><td>+6.38</td><td>+1.67</td><td>+1.1</td></tr></table>
+
+Table 6. SelTDAimproves domain generalization from natural images (A-OKVQA) to art QA, medical QA, and remote sensing QA.  
+
+<table><tr><td rowspan="2">Initialization</td><td colspan="2"># Training Pairs</td><td colspan="2">Numerical Reasoning</td></tr><tr><td>Real</td><td>Synth</td><td>VQAv2</td><td>VQA-Rephrasings</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>0</td><td>13.49</td><td>13.06</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>2000</td><td>38.73</td><td>33.74</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>4500</td><td>40.4</td><td>35.91</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>8000</td><td>42.9</td><td>36.5</td></tr><tr><td>BLIPVQAv2</td><td>17000</td><td>12000</td><td>43.3</td><td>37.77</td></tr><tr><td colspan="3">max % gain w.r.t baseline</td><td>+29.81</td><td>+24.71</td></tr><tr><td>BLIP</td><td>17000</td><td>0</td><td>1.42</td><td>1.29</td></tr><tr><td>BLIP</td><td>17000</td><td>17000</td><td>4.53</td><td>11.44</td></tr><tr><td>BLIP</td><td>17000</td><td>34000</td><td>5.05</td><td>11.77</td></tr><tr><td>BLIP</td><td>17000</td><td>51000</td><td>4.26</td><td>11.86</td></tr><tr><td colspan="3">max % gain w.r.t baseline</td><td>+3.63</td><td>+10.57</td></tr></table>
+
+Table 7. SelTDA improves numerical reasoning when finetuning on a small-scale dataset (A-OKVQA).  $\mathrm{BLIP}_{\mathit{VQAv2}}$  indicates transfer learning from VQAv2, and BLIP indicates direct finetuning.
+
+even when the dataset used to train the teacher model has few numerical reasoning questions. One reason for this is that the word "how" is a high-probability word to start a question with, and is naturally followed by "many" (Fig 6) resulting in numerical questions being generated.
+
+# 5. Conclusion & Future Work
+
+We present SelTDA, a framework for self-improving large VLMs on small-scale visual question answering tasks with unlabeled data. The limitations of SelTDA suggest several opportunities for further work. First, the pseudo-QA pairs can be noisy. Combining SelTDA with methods for fact-checking based on external knowledge [40], logically consistent self-reasoning [16], or chain-of-thought prompting [56] to rationalize answers may result in higher quality pairs for self-training. Second, learning the teacher model may fail for specialized domains (e.g. medical), because the vocabulary is too specialized. Third, biases in the VLM or pretraining data may be amplified by self-training, and addressing these biases may reduce multimodal shortcut learning. Finally, self-training is yet to be explored with recently developed billion-parameter VLMs [9, 25].
+
+# References
+
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+[2] Pratyay Banerjee, Tejas Gokhale, Yezhou Yang, and Chitta Baral. Weaqa: Weak supervision via captions for visual question answering. In FINDINGS, 2021. 1, 3  
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+        "text": "Quality-aware Pre-trained Models for Blind Image Quality Assessment",
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+        "text": "Kai Zhao†, Kun Yuan†, Ming Sun, Mading Li and Xing Wen Kuaishou Technology",
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+        "text": "{zhaokai05,yuankun03,sunming03,limading,wenxing}@kuaishou.com",
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+        "text": "Blind image quality assessment (BIQA) aims to automatically evaluate the perceived quality of a single image, whose performance has been improved by deep learning-based methods in recent years. However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly  $2 \\times 10^{7}$ . After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets.",
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+        "text": "1. Introduction",
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+        "text": "With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33].",
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+            "Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged."
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+        "text": "Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively.",
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+        "text": "Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers",
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "$\\dagger$  Equal contribution.",
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+    {
+        "type": "text",
+        "text": "propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62].",
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+    {
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+        "text": "Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44].",
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+    {
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+        "text": "In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows:",
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+            "- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of  $10^{7}$ , our method can generate more than  $2 \\times 10^{14}$  possible pairs for contrastive learning.",
+            "- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images."
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Blind Image Quality Assessment",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Self-supervised Learning",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose",
+        "bbox": [
+            500,
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+            890,
+            900
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "22303",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27].",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Image Degradation Modelling",
+        "text_level": 1,
+        "bbox": [
+            76,
+            491,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            753,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To excavate the potential of the \"pre-training and finetuning\" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Reviewing the Framework of SSL",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {I n f o N C E}} = - \\log \\frac {\\exp (q \\cdot k _ {+} / \\tau)}{\\sum_ {i = 0} ^ {N} \\exp (q \\cdot k _ {i} / \\tau)}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $q$  is an encoded query,  $k_{i}$  is the  $i$ -th encoded key of a dictionary consisting of  $N$  samples, and  $k_{+}$  is a single key that matches  $q$ . And  $\\tau$  is a temperature hyper-parameter.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Degradation Space",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "22304",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/b1232fd1c076a3948f9f6d6900587cad67094a7c8f5aa47b7f22ea694026bc4b.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image  $\\mathbf{y}$ , the process can be formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} = \\mathcal {D} (\\mathbf {y}; w, p), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{D}$  denotes the function of degradation.  $w$  represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And  $p\\in \\{0,1\\}$  indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} = \\mathcal {D} ^ {o} (\\mathbf {y}) = \\mathcal {D} _ {o} \\left(\\dots \\mathcal {D} _ {1} (\\mathbf {y}; w _ {1}, p _ {1}) \\dots ; w _ {o}, p _ {o}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $o$  is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "degradation type, involving multiple repeated processes of  $\\mathcal{D}^o (\\mathbf{x})$ , where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is  $2 \\times \\sum_{i=1}^{9} \\mathbf{C}_{9}^{i} \\times \\mathbf{A}_{i}^{i} \\approx 2 \\times 10^{7}$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Quality-aware Pretext Task",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Suppose we have  $N$  images  $\\mathbf{y}^{(1)},\\dots ,\\mathbf{y}^{(N)}$ . As shown in Fig. 3, each image  $\\mathbf{y}^{(n)}$  will be differently augmented by  $K$  degradation compositions, obtaining different \"views\"  $\\mathbf{x}_1^{(n)},\\dots ,\\mathbf{x}_K^{(n)}$  that own consistent content but with different perceptual qualities. Then we extract a \"query\" (or \"anchor\") and a \"key\" patch that originates from the same view  $\\mathbf{x}_k^{(n)}$  but with different locations, denoted  $\\mathbf{x}_{k,i}^{(n)}$  and  $\\mathbf{x}_{k,j}^{(n)}$  respectively. The query and key are considered as a positive pair due to their consistent content and degrada",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22305",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/70f2387e572644c152be2fa6cbfc89b14cf7e9b18708f4e96acbd26651b06331.jpg",
+        "image_caption": [
+            "Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            89,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/022847d98af6aede2f8c880e0e7e2c15f7b5670f44ce8938da9dec248e8b3cf0.jpg",
+        "table_caption": [
+            "Table 1. Comparison of two types of pretext tasks, where  $\\tilde{k}$  represents a degradation/augmentation type different from  $k$ ,  $\\tilde{n}$  is an image different from  $n$ , and * denotes an arbitrary value."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Pretext task</td><td>Positive Pair</td><td>Negative Pair</td></tr><tr><td>semantic-aware</td><td>(x(nk,i), x(nk,j))</td><td>(x(n)*, x(n*))</td></tr><tr><td>quality-aware</td><td>(x(nk,i), x(nk,j))</td><td>(x(n)*, x(n*), x(nk,*))</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different \"views\" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around  $10\\%$ . Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1.",
+        "bbox": [
+            75,
+            532,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathcal{F}$  denote the transformation of the encoder network. Given an input patch  $\\mathbf{x}_{k,i}^{(n)}$ , the encoded feature can be noted as  $\\mathbf{f}_{k,i}^{(n)} = \\mathcal{F}(\\mathbf{x}_{k,i}^{(n)}) / ||\\mathcal{F}(\\mathbf{x}_{k,i}^{(n)})||$ , after a  $\\mathcal{L}_2$  normalization",
+        "bbox": [
+            75,
+            849,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows:",
+        "bbox": [
+            498,
+            395,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {Q C}} = - \\beta \\cdot \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau\\right)}{\\sum_ {\\tilde {k} \\neq k} ^ {K} \\exp \\left(\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {\\tilde {k} , j} ^ {(n)} / \\tau\\right)} \\tag {4} \\\\ - \\log \\sum_ {k = 1} ^ {K} \\frac {\\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k , j} ^ {(n)} / \\tau)}{\\sum_ {\\bar {n} \\neq n} ^ {N} \\sum_ {k ^ {\\prime} = 1} ^ {K} \\exp (\\mathbf {f} _ {k , i} ^ {(n)} \\cdot \\mathbf {f} _ {k ^ {\\prime} , j} ^ {(\\bar {n})} / \\tau)}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            534,
+            452,
+            890,
+            536
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs.  $\\beta$  is a coefficient for balancing.",
+        "bbox": [
+            496,
+            546,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating  $2 \\times 10^{14}$  possible pairs during the pre-training phase.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            744,
+            633,
+            762
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Evaluation Criteria",
+        "text_level": 1,
+        "bbox": [
+            500,
+            770,
+            790,
+            786
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073",
+        "bbox": [
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+            794,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22306",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/a937e77c4275ccc663ea29d1fd5de9fbe434f7824337aefd939afef9d9f8cab2.jpg",
+        "table_caption": [
+            "Table 2. Details of selected BIQA datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Size</td><td>Resolution</td><td>MOS Range</td></tr><tr><td>BID [12]</td><td>586</td><td>480P~2112P</td><td>0~5</td></tr><tr><td>CLIVE [20]</td><td>1,162</td><td>500P~640P</td><td>0~100</td></tr><tr><td>KonIQ10K [29]</td><td>10,073</td><td>768P</td><td>0~100</td></tr><tr><td>SPAQ [17]</td><td>11,125</td><td>1080P~4368P</td><td>0~100</td></tr><tr><td>FLIVE [79]</td><td>39,810</td><td>160P~700P</td><td>0~100</td></tr></table>",
+        "bbox": [
+            99,
+            114,
+            442,
+            204
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2.",
+        "bbox": [
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+            217,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a  $80\\%$  training set and a  $20\\%$  testing set randomly.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters,  $\\beta$  and  $\\tau$  in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size  $320 \\times 320$  pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparison with SOTA BIQA Methods",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to  $0.8875(+3.0\\%)$  of SRCC and  $0.9109(+4.6\\%)$  of PLCC in BID,  $0.8947(+4.0\\%)$  of SRCC and  $0.9141(+2.4\\%)$  of PLCC in CLIVE,  $0.9271(+1.1\\%)$  of SRCC and  $0.9413(+1.3\\%)$  of PLCC in KonIQ10K,  $0.9250(+0.8\\%)$  of SRCC and  $0.9279(+0.7\\%)$  of PLCC in SPAQ, and  $0.5746(+0.9\\%)$  of SRCC and  $0.6748(+1.4\\%)$  of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training).",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios.",
+        "bbox": [
+            496,
+            667,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{\\dagger}$ Results in FLIVE follow an aligned train/test split with CONTRIQUE. When using random  $80\\% / 20\\%$  splits, SRCC is 0.5746, PLCC is 0.6748.",
+        "bbox": [
+            500,
+            875,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "22307",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/50abb59ae2cdd7e251c02d74b35b3038f3ea3addb7075535188941e624a490d6.jpg",
+        "table_caption": [
+            "Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “ $\\star$ ” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td><td colspan=\"2\">KonIQ10K</td><td colspan=\"2\">SPAQ</td><td colspan=\"2\">FLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>NIQE [48]</td><td>0.4772</td><td>0.4713</td><td>0.4536</td><td>0.4676</td><td>0.5260</td><td>0.4745</td><td>0.6973</td><td>0.6850</td><td>0.1048</td><td>0.1409</td></tr><tr><td>ILNIQE [85]</td><td>0.4946</td><td>0.4538</td><td>0.4531</td><td>0.5114</td><td>0.5029</td><td>0.4956</td><td>0.7194</td><td>0.654</td><td>0.2188</td><td>0.2547</td></tr><tr><td>BRISQUE [47]</td><td>0.5736</td><td>0.5401</td><td>0.6005</td><td>0.6211</td><td>0.7150</td><td>0.7016</td><td>0.8021</td><td>0.8056</td><td>0.3201</td><td>0.3561</td></tr><tr><td>BMPRI [46]</td><td>0.5154</td><td>0.4583</td><td>0.4868</td><td>0.5229</td><td>0.6577</td><td>0.6546</td><td>0.7501</td><td>0.7544</td><td>0.2737</td><td>0.3146</td></tr><tr><td>CNNIQA [31]</td><td>0.6163</td><td>0.6144</td><td>0.6269</td><td>0.6008</td><td>0.6852</td><td>0.6837</td><td>0.7959</td><td>0.7988</td><td>0.3059</td><td>0.2850</td></tr><tr><td>WaDIQAm-NR [4]</td><td>0.6526</td><td>0.6359</td><td>0.6916</td><td>0.7304</td><td>0.7294</td><td>0.7538</td><td>0.8397</td><td>0.8449</td><td>0.4346</td><td>0.4303</td></tr><tr><td>SFA [38]</td><td>0.8202</td><td>0.8253</td><td>0.8037</td><td>0.8213</td><td>0.8882</td><td>0.8966</td><td>0.9057</td><td>0.9069</td><td>0.5415</td><td>0.6260</td></tr><tr><td>DB-CNN [89]</td><td>0.8450</td><td>0.8590</td><td>0.8443</td><td>0.8624</td><td>0.8780</td><td>0.8867</td><td>0.9099</td><td>0.9133</td><td>0.5537</td><td>0.6518</td></tr><tr><td>HyperIQA [60]</td><td>0.8544</td><td>0.8585</td><td>0.8546</td><td>0.8709</td><td>0.9075</td><td>0.9205</td><td>0.9155</td><td>0.9188</td><td>0.5354</td><td>0.6228</td></tr><tr><td>PaQ-2-PiQ* [79]</td><td>-</td><td>-</td><td>0.840</td><td>0.850</td><td>0.870</td><td>0.880</td><td>-</td><td>-</td><td>0.571</td><td>0.623</td></tr><tr><td>CONRTIQUE* [44]</td><td>-</td><td>-</td><td>0.854</td><td>0.890</td><td>0.896</td><td>0.901</td><td>-</td><td>-</td><td>0.580</td><td>0.641</td></tr><tr><td>UNIQUE* [90]</td><td>0.858</td><td>0.873</td><td>0.854</td><td>0.890</td><td>0.896</td><td>0.901</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MUSIQ* [32]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.916</td><td>0.928</td><td>0.917</td><td>0.921</td><td>0.566</td><td>0.661</td></tr><tr><td>TReS* [21]</td><td>-</td><td>-</td><td>0.846</td><td>0.877</td><td>0.915</td><td>0.928</td><td>-</td><td>-</td><td>0.554</td><td>0.625</td></tr><tr><td>ResNet50</td><td>0.8423</td><td>0.8521</td><td>0.8527</td><td>0.8807</td><td>0.9121</td><td>0.9270</td><td>0.9161</td><td>0.9207</td><td>0.5514</td><td>0.6354</td></tr><tr><td>QPT-ResNet50</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td><td>0.9271</td><td>0.9413</td><td>0.9250</td><td>0.9279</td><td>0.6104†</td><td>0.6770</td></tr></table>",
+        "bbox": [
+            138,
+            142,
+            831,
+            380
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7c531eaee968ea33a79c66d01d447870069826bfd049e7e579320d495aae2bf8.jpg",
+        "table_caption": [
+            "Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td rowspan=\"2\">Pre-trained Type</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td><td colspan=\"2\">KonIQ10K</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td rowspan=\"2\">HyperIQA</td><td>Original</td><td>0.8665</td><td>0.8883</td><td>0.8553</td><td>0.8716</td><td>0.8990</td><td>0.9190</td></tr><tr><td>QPT</td><td>0.8982+3.17%</td><td>0.9061+1.78%</td><td>0.8743+1.90%</td><td>0.8732+0.16%</td><td>0.9066+0.76%</td><td>0.9241+0.51%</td></tr><tr><td rowspan=\"2\">TRes</td><td>Original</td><td>0.7541</td><td>0.7918</td><td>0.8436</td><td>0.8793</td><td>0.8958</td><td>0.9097</td></tr><tr><td>QPT</td><td>0.7936+3.95%</td><td>0.8037+1.19%</td><td>0.8666+2.30%</td><td>0.8882+0.89%</td><td>0.9052+0.94%</td><td>0.9150+0.53%</td></tr></table>",
+        "bbox": [
+            96,
+            434,
+            867,
+            527
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/42cb970374eb50b5925a166828bba9ad6874ddea271275a54f61d113d3fbe7db.jpg",
+        "table_caption": [
+            "Table 5. Cross-dataset evaluation. Results of SRCC are reported."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Train</td><td>Test</td><td>DBCNN</td><td>HyperIQA</td><td>CONTRIQUE</td><td>QPT</td></tr><tr><td>KIQ10k</td><td>CLIVE</td><td>0.755</td><td>0.785</td><td>0.731</td><td>0.8208</td></tr><tr><td>KIQ10k</td><td>BID</td><td>0.816</td><td>0.819</td><td>-</td><td>0.8247</td></tr><tr><td>CLIVE</td><td>BID</td><td>0.762</td><td>0.756</td><td>-</td><td>0.8449</td></tr><tr><td>CLIVE</td><td>KIQ10k</td><td>0.754</td><td>0.772</td><td>0.676</td><td>0.7494</td></tr></table>",
+        "bbox": [
+            81,
+            566,
+            462,
+            633
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/832513cb052b86691f2537b2679141af30e3ec6dfeb6995c7b48b17e96cf3d17.jpg",
+        "table_caption": [
+            "Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Percentage of ImageNet</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>20%</td><td>0.8311</td><td>0.8305</td><td>0.8115</td><td>0.8203</td></tr><tr><td>50%</td><td>0.8760</td><td>0.8973</td><td>0.8868</td><td>0.9007</td></tr><tr><td>100%</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>",
+        "bbox": [
+            84,
+            689,
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+            767
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
+            76,
+            784,
+            240,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use  $20\\%$ ,  $50\\%$  and  $100\\%$  percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the",
+        "bbox": [
+            75,
+            809,
+            470,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/534709f66f8a01e2fa9623b9d37218d588935827053838443732b211e0f948fa.jpg",
+        "table_caption": [
+            "Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Network</td><td rowspan=\"2\">Params</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>MBViTV2-100</td><td>4.90</td><td>0.8746</td><td>0.8799</td><td>0.8640</td><td>0.8914</td></tr><tr><td>MBViTV2-150</td><td>10.59</td><td>0.8782</td><td>0.8976</td><td>0.8702</td><td>0.8970</td></tr><tr><td>MBViTV2-200</td><td>18.45</td><td>0.8821</td><td>0.8960</td><td>0.8894</td><td>0.9006</td></tr><tr><td>ResNet-18</td><td>11.69</td><td>0.8679</td><td>0.8805</td><td>0.8610</td><td>0.8795</td></tr><tr><td>ResNet-34</td><td>21.80</td><td>0.8742</td><td>0.9001</td><td>0.8780</td><td>0.8871</td></tr><tr><td>ResNet-50</td><td>25.56</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>",
+        "bbox": [
+            501,
+            579,
+            885,
+            699
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only  $50\\%$  of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61].",
+        "bbox": [
+            496,
+            717,
+            890,
+            792
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream",
+        "bbox": [
+            496,
+            794,
+            893,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "22308",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3ba41b7b697a9a2d847b95a99bfec60c99fcf52ad21271f697b95046ad0203ba.jpg",
+        "table_caption": [
+            "Table 8. Impact on the composition of negative samples."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Inter</td><td rowspan=\"2\">Intra</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>✓</td><td>✓</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr><tr><td>✓</td><td>×</td><td>0.8702</td><td>0.9051</td><td>0.8721</td><td>0.8994</td></tr><tr><td>×</td><td>✓</td><td>0.8399</td><td>0.8357</td><td>0.8084</td><td>0.8142</td></tr><tr><td>×</td><td>×</td><td>0.7078</td><td>0.7731</td><td>0.7495</td><td>0.7493</td></tr></table>",
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+        "type": "image",
+        "img_path": "images/6202046e3b964be34837536ae12cbffbb5b7de5b85c844f1a5df9b041d499ed0.jpg",
+        "image_caption": [
+            "(a) Results in BID"
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+        "img_path": "images/26cf8107b5392dfa02cb357907d1f25db978effc89a468d0ba144b42c15e1676.jpg",
+        "image_caption": [
+            "(b) Results in CLIVE",
+            "Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially."
+        ],
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+    {
+        "type": "text",
+        "text": "performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of  $\\{53\\mathrm{h}, 61\\mathrm{h}, 75\\mathrm{h}\\}$ , MBViTV2s of  $\\{66\\mathrm{h}, 92\\mathrm{h}, 109\\mathrm{h}\\}$ , respectively). We did not use larger networks out of tradeoffs, which can be tried in future work.",
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+    {
+        "type": "text",
+        "text": "Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e.,  $K - 1$ ), the number of inter-sample ones (i.e.,  $N \\cdot K$ ), which contain both different content and degradation types, is larger.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results.",
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+    {
+        "type": "text",
+        "text": "4.5. Comparisons with other pretext tasks",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations.",
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+    {
+        "type": "text",
+        "text": "Linear probing evaluation. In this way, the weights of",
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+        "type": "table",
+        "img_path": "images/404c36d40aaded9abc81940101e22f87f200ff8b93887377b94499098db25358.jpg",
+        "table_caption": [
+            "Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>skip</td><td>shuffle</td><td>two-order</td><td>SRCC</td><td>PLCC</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>0.8875</td><td>0.9109</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>0.8828</td><td>0.9075</td></tr><tr><td>✓</td><td>×</td><td>×</td><td>0.8745</td><td>0.9029</td></tr><tr><td>×</td><td>×</td><td>×</td><td>0.8626</td><td>0.8864</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/077c848e92ec4eaf8a8d1be882a85911740269667737c004307fc0a28c061ce4.jpg",
+        "table_caption": [
+            "Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Pretext task</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>Supervised</td><td>0.7678</td><td>0.7860</td><td>0.7128</td><td>0.7668</td></tr><tr><td>MoCo</td><td>0.7367</td><td>0.7357</td><td>0.6796</td><td>0.7154</td></tr><tr><td>QPT</td><td>0.8242</td><td>0.8175</td><td>0.7613</td><td>0.7938</td></tr></table>",
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+    },
+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 11. Comparisons of end-to-end fine-tuning evaluation using different pretext tasks in BID and CLIVE."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Pretext task</td><td colspan=\"2\">BID</td><td colspan=\"2\">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>w/o</td><td>0.7078</td><td>0.7731</td><td>0.7495</td><td>0.7493</td></tr><tr><td>Supervised</td><td>0.8423</td><td>0.8521</td><td>0.8527</td><td>0.8807</td></tr><tr><td>MoCo</td><td>0.8531</td><td>0.8724</td><td>0.8494</td><td>0.8615</td></tr><tr><td>QPT</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "encoder are frozen for feature extraction directly. As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by  $8.75\\%$  of SRCC in BID and  $8.17\\%$  in CLIVE.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. By introducing diverse degradation types and compositions, we construct a degradation space that contains  $2 \\times 10^{7}$  possible degradations, to simulate more complicated and realistic distorted images. To constrain the learning process, we proposed the QC-Loss that treats patch pairs extracted from the same degraded images as positive ones. And other pairs are noted as negative ones, including degradation-based and content-based ones. After pre-trained on ImageNet using QPT, BIQA models obtain significant improvements on five BIQA benchmark datasets. Moreover, QPT can be easily integrated with current SOTA methods by replacing their pre-trained weights, showing good generalization ability.",
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+        "type": "page_number",
+        "text": "22309",
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+    },
+    {
+        "type": "text",
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2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/8d41dca5-5365-455a-824a-8a417d4e7839_origin.pdf

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2023/Quality-Aware Pre-Trained Models for Blind Image Quality Assessment/full.md

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+# Quality-aware Pre-trained Models for Blind Image Quality Assessment
+
+Kai Zhao†, Kun Yuan†, Ming Sun, Mading Li and Xing Wen Kuaishou Technology
+
+{zhaokai05,yuankun03,sunming03,limading,wenxing}@kuaishou.com
+
+# Abstract
+
+Blind image quality assessment (BIQA) aims to automatically evaluate the perceived quality of a single image, whose performance has been improved by deep learning-based methods in recent years. However, the paucity of labeled data somewhat restrains deep learning-based BIQA methods from unleashing their full potential. In this paper, we propose to solve the problem by a pretext task customized for BIQA in a self-supervised learning manner, which enables learning representations from orders of magnitude more data. To constrain the learning process, we propose a quality-aware contrastive loss based on a simple assumption: the quality of patches from a distorted image should be similar, but vary from patches from the same image with different degradations and patches from different images. Further, we improve the existing degradation process and form a degradation space with the size of roughly  $2 \times 10^{7}$ . After pre-trained on ImageNet using our method, models are more sensitive to image quality and perform significantly better on downstream BIQA tasks. Experimental results show that our method obtains remarkable improvements on popular BIQA datasets.
+
+# 1. Introduction
+
+With the arrival of the mobile internet era, billions of images are generated, uploaded and shared on various social media platforms, including Twitter, TikTok, etc [30]. As an essential indicator, image quality can help these service providers filter and deliver high-quality images to users, thereby improving Quality of Experience. Therefore, huge efforts [12,20,22,24,52,73] have been devoted to establishing an image quality assessment (IQA) method consistent with human viewers. In real-world scenarios, there usually exists no access to the reference images and the quality of reference images is suspicious. Thus, blind IQA (BIQA) methods are more attractive and applicable, despite full-reference IQA has achieved prospective results [33].
+
+![](images/db40156e128a461ecd37c539efa1d54a46b49714b55d52f4c1dafc1fd816ed7d.jpg)  
+Figure 1. The two images in the first row are sampled from BIQA dataset CLIVE [20]. Although they have the same semantic meaning, their perceptual qualities are quite different: their mean opinion scores (MOS) are 31.83 and 86.35. The second row shows modified versions of the first two images and their MOSs (rated by 7 people). After different operations, the quality dramatically changed, while semantic meaning remains unchanged.
+
+Recently, deep learning-based BIQA methods have made tremendous improvements on in-the-wild IQA benchmarks [17, 29, 79]. However, this problem is far from resolved and is hindered by the paucity of labeled data [34]. The largest (by far) available BIQA dataset, FLIVE [79], contains nearly 40,000 real-world distorted images. By comparison, the very popular entry-level image recognition dataset, CIFAR-100 [35], contains 60,000 labeled images. Accordingly, existing BIQA datasets are too small to train deep learning-based models effectively.
+
+Researchers present several methods to tackle this challenge. A straight-forward way is to sample local patches and assign the label of the whole image (i.e., mean opinion score, MOS) to the patches [4, 31, 32, 38, 60, 89, 90]. However, the perceived scores of local image patches tend to differ from the score of the entire image [79, 89]. Another common strategy is to leverage domain knowledge from large-scale datasets (e.g., ImageNet [14]) for other computer vision tasks [6, 32]. Nevertheless, these pre-trained models can be sub-optimal for BIQA tasks: images with the same content share the same semantic label, whereas, their quality may be different (Fig. 1). Some researchers
+
+propose to train a model on synthetic images with artificial degradation and then regress the model onto small-scale target BIQA datasets [43, 73, 89]. However, images generated by rather simple degradation process with limited distortion types/levels are far from authentic. Further, synthetic images are regularly distorted from limited pristine images of high quality, so the image content itself only has a marginal effect on the image quality. Yet in real-world scenarios, the image quality is closely related to its content, due to viewers' preferences for divergent contents [38, 62].
+
+Self-supervised learning (SSL) or unsupervised learning is another potential choice to overcome the problem of lacking adequate training data, for its ability to utilize an amount of unlabeled data. Such technique is proven to be effective in many common computer vision tasks [2]. However, different from models for these tasks which mainly focus on high-level information, representations learned for BIQA should be sensitive to all kinds of low-level distortions and high-level contents, as well as interactions between them. There are few research focused on such area in the literature, let alone a deep SSL designed for BIQA with state-of-the-art performance [44].
+
+In this work, we propose a novel SSL mechanism that distinguishes between samples with different perceptual qualities, generating Quality-aware Pre-Trained (QPT) models for downstream BIQA tasks. Specifically, we suppose the quality of patches from a distorted image should be similar, but vary from patches from different images (i.e., content-based negative) and the same image with different degradations (i.e., degradation-based negative). Moreover, inspired by recent progress in image restoration, we introduce shuffle order [84], high-order [70] and a skip operation to the image degradation process, to simulate real-world distortions. In this way, models pre-trained on ImageNet are expected to extract quality-aware features, and boost downstream BIQA performances. We summarize the contributions of this work as follows:
+
+- We design a more complex degradation process suitable for BIQA. It not only considers a mixture of multiple degradation types, but also incorporates with shuffle order, high-order and a skip operation, resulting in a much larger degradation space. For a dataset with a size of  $10^{7}$ , our method can generate more than  $2 \times 10^{14}$  possible pairs for contrastive learning.  
+- To fully exploit the abundant information hidden beneath such an amount of data, we propose a novel SSL framework to generate QPT models for BIQA based on MoCoV2 [8]. By carefully designing positive/negative samples and customizing quality-aware contrastive loss, our approach enables models to learn quality-aware information rather than regular semantic-aware representation from massive unlabeled images.
+
+- Extensive experiments on five BIQA benchmark datasets (sharing the same pre-trained weight of QPT) demonstrate that our proposed method significantly outperforms other counterparts, which indicates the effectiveness and generalization ability of QPT. It is also worth noting that the proposed method can be easily integrated with current SOTA methods by replacing their pre-trained weights.
+
+# 2. Related Work
+
+In this section, we provide a brief review of major works on BIQA and recent advances in contrastive learning and image degradation modeling.
+
+# 2.1. Blind Image Quality Assessment
+
+Before the rise of deep learning, natural scene statistics (NSS) theory dominates the realm of BIQA, which assumes that pristine natural images obey certain statistics distribution and various distortions will break such statistical regularity [59]. Based on this theory, various hand-crafted features are proposed in different domains, including spatial [47, 48], frequency [49, 54] and gradient [85]. Meanwhile, some learning-based methods [46, 78] have also been preliminarily explored. Typically, they estimate the subjective quality using support vector regression and features learned by visual codebooks [77].
+
+In recent years, a variety of deep learning-based methods have been studied for BIQA and significantly boost the in-the-wild performance [21, 28, 38, 53, 67]. As a pioneer work, a shallow network [31] consisting of only three layers is built to solve BIQA in an end-to-end manner. After that, later works naturally expand the BIQA model by deepening the network depth [4, 42] or utilizing more effective building blocks [60, 91]. Recently, transformer-based BIQA methods [32, 76, 80, 92] are sprouting up, based on the assumption that transformer can compensate the missing ability of CNNs to capture non-local information [16].
+
+Except for elaborate model design, a few research are devoted to solving the chief obstacle in BIQA, the paucity of labeled data. Some of them try to make full use of existing supervisory signals, such as rank learning [37, 39], multi-task learning [17] and mixed-dataset training [62, 90]. Meanwhile, others turn to large-scale pre-training [32, 42, 82], which generates a large number of distorted images labeled by specifications of degradation process [89] or quality scores estimated from FR models [43].
+
+In comparison, our proposed method is based on contrastive learning without needing any explicit supervisory signal, thereby fully utilizing plenty of real-world images.
+
+# 2.2. Self-supervised Learning
+
+SSL, as a form of unsupervised learning, is used to learn a good data representation for the downstream true purpose
+
+[2]. A very straightforward idea to conduct such learning is minimizing the difference between a model's output and a fixed target, such as reconstructing the input pixels [69] or predicting the pre-defined categories [15, 86]. Motivated by the successes of masked language modeling in natural language processing, masked image modeling [26, 75] is becoming a hot trend in computer vision.
+
+Unlike the above methods, the goal of contrastive learning is to learn such an embedding space, where similar samples are assembled while dissimilar pairs are repelled [30]. Specifically, contrastive learning generally involves two aspects: pretext tasks and training objectives. Owing to the flexibility of contrastive learning, a wide range of pretext tasks have been proposed, such as colorization [86, 87], multi-view coding [64], and instance discrimination [27, 74]. When it comes to training objectives, the major trend is the move from only one positive and one negative sample [10, 55] to multiple positive and negative pairs [18, 25, 66]. Especially, InfoNCE [66] has become the most popular choice [5, 9, 27].
+
+Notably, all of the above works can be classified as semantic-aware pre-training, because they encourage views (augmentations) of the same image to have a similar representation while ignoring the changes of perceived image quality. In this work, we redesign a quality-aware pretext task for BIQA, which will be discussed in Sec. 3.3.
+
+# 2.3. Image Degradation Modelling
+
+Most of the previous works focus on several classical distortion types [56, 57, 72, 83] to extract distortion-specific features. As the importance of BIQA is rising, more distortion types have been developed and applied to synthesize distorted images [40]. DipIQ [41] summarizes common distortion operations, such as noise, blur and compression, and further subdivides each with five levels. DB-CNN [89] introduces additional five distortion types. Recently, many works [21, 34, 91] point out that the above methods are too simple to simulate real-world images with complex and mixed distortions, due to the synthesized image only with a specific distortion type and level. In this work, we combine multiple degradation tricks [70, 84] proposed in the field of image restoration to form a much larger degradation space and generate distorted images that are more realistic.
+
+# 3. Method
+
+To excavate the potential of the "pre-training and finetuning" paradigm on BIQA for better performance, we present QPT models by pre-training on ImageNet. In Sec. 3.1, we will briefly review some related SSL frameworks. In Sec. 3.2, we will detail the degradation process for generating distorted images that contain quality-related information. In Sec. 3.3, we will give the definition of quality-aware pretext task and optimization objective.
+
+# 3.1. Reviewing the Framework of SSL
+
+SSL enables learning representations from orders of magnitude more data, which addresses the obstacle for BIQA in establishing large-scale annotated datasets. SSL methods can be roughly divided into generative-based [26, 68, 75] and contrastive-based [7, 23, 27]. Among them, MAE [26], as a generative-based method, develops an asymmetric encoder-decoder architecture for image reconstruction. MoCo [27], as a contrastive-based method, builds a dynamic dictionary with a queue and a moving-averaged encoder for contrastive learning. Relatively, contrastive learning is more suitable for BIQA, for which can easily measure quality ranking between samples. Due to the fact that the quality of an image is related to various complicated factors [65, 71], a large number of images are needed to ensure the diversity of negative samples [7]. Empirically, we choose MoCo, since it provides a memory-efficient framework to establish a large and consistent set.
+
+In brief, MoCo builds a dictionary using a momentum queue to enlarge available size for comparison, where samples are progressively replaced with incoming mini-batch ones. And keys in the dictionary are updated through a momentum-based moving average of the encoder network, maintaining consistency with query samples. MoCo adopts the instance-level discrimination task [74] as its pretext task (i.e., a query matches a key if they are encoded views of the same image). Then, a contrastive loss, named InfoNCE, is adopted to distinguish the positive key from negative ones in a softmax manner, which can be noted as:
+
+$$
+\mathcal {L} _ {\text {I n f o N C E}} = - \log \frac {\exp (q \cdot k _ {+} / \tau)}{\sum_ {i = 0} ^ {N} \exp (q \cdot k _ {i} / \tau)}, \tag {1}
+$$
+
+where  $q$  is an encoded query,  $k_{i}$  is the  $i$ -th encoded key of a dictionary consisting of  $N$  samples, and  $k_{+}$  is a single key that matches  $q$ . And  $\tau$  is a temperature hyper-parameter.
+
+# 3.2. Degradation Space
+
+To obtain utilizable quality-related information in self-supervised scenarios, a simple way is to generate image pairs using controllable degradations manually. Before designing specific degradation types, several observations need to be mentioned: First, there exist many factors affecting the perceptual quality of an image (e.g., content, distortions, compression). For example, an image with unmeaningful content is often classified as a low-quality one [36]. Also, distortions (e.g., blurriness [13], noise [58] and sharpness [81]) introduced during the image production phase and compression artifacts introduced by transcoding or transmission, will degrade the overall quality. Second, the aforementioned factors, as a complicated composition, are always involved in practical scenarios [1, 58]. An image may go through various processes of shooting, editing,
+
+![](images/b1232fd1c076a3948f9f6d6900587cad67094a7c8f5aa47b7f22ea694026bc4b.jpg)  
+Figure 2. Illustration of generating distorted images using different compositions of degradation. Compared with the process of fixed sequence, the introduced skip, shuffle and high-order largely increase the degradation space, covering diverse and realistic distortions.
+
+compression, and transmission, resulting in more complicated distortions. These scenarios increase the difficulty of BIQA tasks. Thus a good pre-trained model for IQA should take these into account, covering diverse distortions using suitable degradations as large and realistic as possible.
+
+Based on these observations, we design the degradation space from the perspective of individual operations and their compositions. For the first observation, we introduce a variety of degradation types to simulate real distortions, which can be divided into three categories: (1) geometric deformation, which simulates distortions introduced during editing process or adaptation on various display equipment, including 4 operations of scale jitter [32], horizontal flip, down-sampling and up-sampling [50]; (2) color change [63], which can be caused by lightness, chroma, and hue differences in the shooting or codec process, including 2 operations of color jitter and grayscale; (3) texture adjustment, which can be captured from environmental interference or transmission, including 3 operations of adding noise, fuzzification [19] and JPEG compression [11]. Given an image  $\mathbf{y}$ , the process can be formulated as:
+
+$$
+\mathbf {x} = \mathcal {D} (\mathbf {y}; w, p), \tag {2}
+$$
+
+where  $\mathcal{D}$  denotes the function of degradation.  $w$  represents hyper-parameters of the degradation (e.g., scale size, location, brightness intensity, etc.). And  $p\in \{0,1\}$  indicates whether this operation is performed. For the second observation, we propose a sequence, consisting of randomly chosen degradations, for more complicated types (e.g., a list of {scale jitter, color jitter, adding noise}), where each operation can be skipped, and the order can be shuffled:
+
+$$
+\mathbf {x} = \mathcal {D} ^ {o} (\mathbf {y}) = \mathcal {D} _ {o} \left(\dots \mathcal {D} _ {1} (\mathbf {y}; w _ {1}, p _ {1}) \dots ; w _ {o}, p _ {o}\right), \tag {3}
+$$
+
+where  $o$  is the number of selected degradations. Furthermore, to simulate multiple transfers, we adopt a high-order
+
+degradation type, involving multiple repeated processes of  $\mathcal{D}^o (\mathbf{x})$ , where each process performs with the same procedure but different hyper-parameters. Empirically, we employ a degenerate approach with at most two orders, as it could resolve most real cases while keeping simplicity. The illustration of the overall process is shown in Fig. 2.
+
+The degradation space formed by our operations is much larger than those in existing super-resolution (SR) methods [70,84], which reconstruct high-resolution images from low-resolution ones. Since BIQA does not require pixel-level aligned pairs like SR, more operations like geometric deformation/color change can be used. Moreover, SR requires that the source images should be high-quality and the distributions of target and source images should be as consistent as possible. These factors limit the number of available compositions. Without these restrictions, in our method, the size of degradation space can be expanded substantially. Theoretically, for a space containing 9 degradation types, the number of discrete compositions is  $2 \times \sum_{i=1}^{9} \mathbf{C}_{9}^{i} \times \mathbf{A}_{i}^{i} \approx 2 \times 10^{7}$ .
+
+# 3.3. Quality-aware Pretext Task
+
+Different from the classical semantic-aware pretext task (i.e., treating each image instance as a distinct class) [3, 74], we propose a new quality-aware pretext task that distinguishes between samples with different perceptual qualities.
+
+Suppose we have  $N$  images  $\mathbf{y}^{(1)},\dots ,\mathbf{y}^{(N)}$ . As shown in Fig. 3, each image  $\mathbf{y}^{(n)}$  will be differently augmented by  $K$  degradation compositions, obtaining different "views"  $\mathbf{x}_1^{(n)},\dots ,\mathbf{x}_K^{(n)}$  that own consistent content but with different perceptual qualities. Then we extract a "query" (or "anchor") and a "key" patch that originates from the same view  $\mathbf{x}_k^{(n)}$  but with different locations, denoted  $\mathbf{x}_{k,i}^{(n)}$  and  $\mathbf{x}_{k,j}^{(n)}$  respectively. The query and key are considered as a positive pair due to their consistent content and degrada
+
+![](images/70f2387e572644c152be2fa6cbfc89b14cf7e9b18708f4e96acbd26651b06331.jpg)  
+Figure 3. The framework of Quality-aware Pretext Task (QPT). First, images are augmented by diverse degradations. Second, patches will be extracted from various views to form patch pairs. Pairs generated from the same view but different locations are treated as positive pairs. And other pairs are noted as negative pairs, including degradation-based and content-based. Then, the patches are transformed into encoded features by a network. Last, these feature pairs are constrained using a Quality-aware Contrastive Loss (QC-Loss).
+
+Table 1. Comparison of two types of pretext tasks, where  $\tilde{k}$  represents a degradation/augmentation type different from  $k$ ,  $\tilde{n}$  is an image different from  $n$ , and * denotes an arbitrary value.  
+
+<table><tr><td>Pretext task</td><td>Positive Pair</td><td>Negative Pair</td></tr><tr><td>semantic-aware</td><td>(x(nk,i), x(nk,j))</td><td>(x(n)*, x(n*))</td></tr><tr><td>quality-aware</td><td>(x(nk,i), x(nk,j))</td><td>(x(n)*, x(n*), x(nk,*))</td></tr></table>
+
+tion type. And otherwise pairs are treated as negative ones, which can be divided into two parts. First, for the same image, patches extracted from different "views" are denoted as degradation-based negative pairs. Their content is the same, but the way it degenerates is different, resulting in inconsistent qualities. To ensure the quality of patches generated from a single image as consistent as possible, we set the lower bound for the area ratio during random crop to be 0.5. So patches generated from the same image share similar content rather than contrast regions (e.g., smooth and textured ones). Besides, for different images, regardless of whether their degradation types are the same, they are considered content-based negative pairs due to different contents. Notably, there may exist some noise (i.e., different contents, similar quality) under this partition, but it is negligible due to the very small proportions. To count the number of negative pairs with similar quality, we perform JND tests proposed in LPIPS [88] on 500 generated patches, indicating around  $10\%$ . Correctly assigned pairs still dominate. The difference between quality-level and instance-level discrimination tasks is given in Tab. 1.
+
+Let  $\mathcal{F}$  denote the transformation of the encoder network. Given an input patch  $\mathbf{x}_{k,i}^{(n)}$ , the encoded feature can be noted as  $\mathbf{f}_{k,i}^{(n)} = \mathcal{F}(\mathbf{x}_{k,i}^{(n)}) / ||\mathcal{F}(\mathbf{x}_{k,i}^{(n)})||$ , after a  $\mathcal{L}_2$  normalization
+
+for computing the dot-product similarity. Then our method can be optimized using a Quality-aware Contrastive Loss (QC-Loss), which is formulated as follows:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {Q C}} = - \beta \cdot \log \sum_ {k = 1} ^ {K} \frac {\exp \left(\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k , j} ^ {(n)} / \tau\right)}{\sum_ {\tilde {k} \neq k} ^ {K} \exp \left(\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {\tilde {k} , j} ^ {(n)} / \tau\right)} \tag {4} \\ - \log \sum_ {k = 1} ^ {K} \frac {\exp (\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k , j} ^ {(n)} / \tau)}{\sum_ {\bar {n} \neq n} ^ {N} \sum_ {k ^ {\prime} = 1} ^ {K} \exp (\mathbf {f} _ {k , i} ^ {(n)} \cdot \mathbf {f} _ {k ^ {\prime} , j} ^ {(\bar {n})} / \tau)}, \\ \end{array}
+$$
+
+where the first part denotes distinguishing degradation-based negative pairs, and the second part is for content-based negative pairs.  $\beta$  is a coefficient for balancing.
+
+To further construct more image pairs containing abundant content and texture information, we adopt the well-known ImageNet as the baseline dataset for pre-training. Compared with IQA datasets, whose number of available data is relatively small (as shown in Tab. 2), ImageNet contains over 1 million of natural images from 1,000 diverse categories. Numerous samples and huge degradation space together contribute to generating  $2 \times 10^{14}$  possible pairs during the pre-training phase.
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Criteria
+
+Datasets. Our method is evaluated on five public BIQA datasets, including BID [12], CLIVE [20], KonIQ10K [29], SPAQ [17] and FLIVE [79]. BID is a blur image dataset that contains 586 images with realistic blur distortions (e.g., out-of-focus, simple motion, complex motion blur). CLIVE consists of 1,162 images with diverse authentic distortions captured by mobile devices. KonIQ10K contains 10,073
+
+Table 2. Details of selected BIQA datasets.  
+
+<table><tr><td>Dataset</td><td>Size</td><td>Resolution</td><td>MOS Range</td></tr><tr><td>BID [12]</td><td>586</td><td>480P~2112P</td><td>0~5</td></tr><tr><td>CLIVE [20]</td><td>1,162</td><td>500P~640P</td><td>0~100</td></tr><tr><td>KonIQ10K [29]</td><td>10,073</td><td>768P</td><td>0~100</td></tr><tr><td>SPAQ [17]</td><td>11,125</td><td>1080P~4368P</td><td>0~100</td></tr><tr><td>FLIVE [79]</td><td>39,810</td><td>160P~700P</td><td>0~100</td></tr></table>
+
+images which are selected from YFCC-100M. And the selected images cover a wide and uniform range of distortions in terms of quality indicators such as brightness, colorfulness, contrast, noise, sharpness, etc. SPAQ consists of 11,125 images captured by different mobile devices, covering a large variety of scene categories. FLIVE is the largest in-the-wild IQA dataset by far, which contains 39,810 real-world distorted images with diverse contents, sizes and aspect ratios. Details are given in Tab. 2.
+
+Evaluation criteria. Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank-Order Correlation Coefficient (SRCC) are selected as criteria to measure the accuracy and monotonicity, respectively. They are in the range of [0, 1]. A larger PLCC means a more accurate numerical fit with MOS scores. A larger SRCC shows a more accurate ranking between samples. For all datasets, following [21, 32], we split the dataset into a  $80\%$  training set and a  $20\%$  testing set randomly.
+
+# 4.2. Implementation Details
+
+Our experiments are performed using PyTorch [51], and are all conducted on 8 Nvidia V100 GPUs. Following the classical pre-training and fine-tuning paradigm, we run the whole experiments in two stages:
+
+Pre-training. We inherit most settings from MoCoV2 [8], while modify the pretext task and degradation process for the quality-aware purpose. Specifically, we use a ResNet50 [28] with an extra two-layer MLP as the encoder and train it on ImageNet. We use SGD optimizer with weight decay of 0.0001, momentum of 0.9 and a mini-batch size of 256. The initial learning rate is 0.03 and multiplied by 0.1 at 120 and 160 epoch. The hyper-parameters,  $\beta$  and  $\tau$  in Eq. (4), are empirically set to 0.4 and 0.2 in our experiments. It takes about 75 hours training ResNet50, for 200 epochs.
+
+Fine-tuning. Following the scheme from [62], we resize the smaller edge of images to 340 while maintaining aspect ratio, and randomly sample and horizontally flip patches with size  $320 \times 320$  pixels. We use AdamW optimizer with weight decay of 0.01 and mini-batch size of 64. The Learning rate is initialized with 0.0002, and decayed by the cosine annealing strategy. For BID and CLIVE, experiments
+
+are trained for 100 epochs. And for other three datasets, the number is 200. By default, we select last epoch for weight initialization and evaluation. During test stage, we take five crops (i.e., four corners and a center patch) from an image, and average their corresponding prediction scores to get the final prediction score. To reduce the randomness in training/test set splitting, following [21, 60, 91], we repeat train/test procedures 10 times for each dataset, and report the median SRCC and PLCC results.
+
+# 4.3. Comparison with SOTA BIQA Methods
+
+We report the performance of SOTA BIQA methods in Tab. 3. Generally, our method pushes the current SOTA results a big step forward (using the same pre-trained weight generated by QPT), improving the best results to  $0.8875(+3.0\%)$  of SRCC and  $0.9109(+4.6\%)$  of PLCC in BID,  $0.8947(+4.0\%)$  of SRCC and  $0.9141(+2.4\%)$  of PLCC in CLIVE,  $0.9271(+1.1\%)$  of SRCC and  $0.9413(+1.3\%)$  of PLCC in KonIQ10K,  $0.9250(+0.8\%)$  of SRCC and  $0.9279(+0.7\%)$  of PLCC in SPAQ, and  $0.5746(+0.9\%)$  of SRCC and  $0.6748(+1.4\%)$  of PLCC in FLIVE. Notably, these results are achieved using an ordinary architecture of ResNet-50, showing the power of utilizing QPT models. Besides, we also report the results of naive ResNet-50 (i.e., using ImageNet supervised pre-training).
+
+Specifically, QPT models surpass traditional methods (e.g., NIQE [48], ILNIQE [85], BRISQUE [47] and BMPRI [46]) that rely on hand-crafted features in large margins. Compared with earlier CNN-based methods (e.g., CN-NIQA [31], WaDIQaM-NR [4] and SFA [38]), QPT shows the advantages of big data pre-training. For HyperIQA [60] that utilized a self-adaptive hyper network architecture to estimate content understanding, perception rule learning and quality predicting, QPT-ResNet50 obtains higher results without fine-designed architectures. Compared with current SOTA Transformer-based methods (e.g., MUSIQ [32] and TReS [21]), QPT models still outperform them, showing the effectiveness of quality-ware pretext training.
+
+Due to the flexibility of QPT, it can be easily integrated with current SOTA methods by replacing their pre-trained weights. We reproduced two SOTA methods (i.e., HyperIQA and TReS) based on their official open-source code, giving the results in Tab. 4. The results of the comparison are based on a consistent dataset partitioning and training hyper-parameters, following official implementation. It can be seen that QPT further boosts SOTA methods effectively (e.g., a even better result with 0.8982 of SRCC in BID can be achieved), showing satisfactory generalization ability. We further give the corss-dataset evaluation in Tab. 5. Compared with the most competitive methods, QPT takes the lead in three scenarios.
+
+Table 3. Performance of existing SOTA methods and the proposed QPT models on five in-the-wild BIQA datasets. The “ $\star$ ” means missing corresponding results in the original paper. The best and second-best results are bolded and underlined. With the inherent learned knowledge in QPT models, a widely-used ResNet50 can outperform existing SOTA methods.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">BID</td><td colspan="2">CLIVE</td><td colspan="2">KonIQ10K</td><td colspan="2">SPAQ</td><td colspan="2">FLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>NIQE [48]</td><td>0.4772</td><td>0.4713</td><td>0.4536</td><td>0.4676</td><td>0.5260</td><td>0.4745</td><td>0.6973</td><td>0.6850</td><td>0.1048</td><td>0.1409</td></tr><tr><td>ILNIQE [85]</td><td>0.4946</td><td>0.4538</td><td>0.4531</td><td>0.5114</td><td>0.5029</td><td>0.4956</td><td>0.7194</td><td>0.654</td><td>0.2188</td><td>0.2547</td></tr><tr><td>BRISQUE [47]</td><td>0.5736</td><td>0.5401</td><td>0.6005</td><td>0.6211</td><td>0.7150</td><td>0.7016</td><td>0.8021</td><td>0.8056</td><td>0.3201</td><td>0.3561</td></tr><tr><td>BMPRI [46]</td><td>0.5154</td><td>0.4583</td><td>0.4868</td><td>0.5229</td><td>0.6577</td><td>0.6546</td><td>0.7501</td><td>0.7544</td><td>0.2737</td><td>0.3146</td></tr><tr><td>CNNIQA [31]</td><td>0.6163</td><td>0.6144</td><td>0.6269</td><td>0.6008</td><td>0.6852</td><td>0.6837</td><td>0.7959</td><td>0.7988</td><td>0.3059</td><td>0.2850</td></tr><tr><td>WaDIQAm-NR [4]</td><td>0.6526</td><td>0.6359</td><td>0.6916</td><td>0.7304</td><td>0.7294</td><td>0.7538</td><td>0.8397</td><td>0.8449</td><td>0.4346</td><td>0.4303</td></tr><tr><td>SFA [38]</td><td>0.8202</td><td>0.8253</td><td>0.8037</td><td>0.8213</td><td>0.8882</td><td>0.8966</td><td>0.9057</td><td>0.9069</td><td>0.5415</td><td>0.6260</td></tr><tr><td>DB-CNN [89]</td><td>0.8450</td><td>0.8590</td><td>0.8443</td><td>0.8624</td><td>0.8780</td><td>0.8867</td><td>0.9099</td><td>0.9133</td><td>0.5537</td><td>0.6518</td></tr><tr><td>HyperIQA [60]</td><td>0.8544</td><td>0.8585</td><td>0.8546</td><td>0.8709</td><td>0.9075</td><td>0.9205</td><td>0.9155</td><td>0.9188</td><td>0.5354</td><td>0.6228</td></tr><tr><td>PaQ-2-PiQ* [79]</td><td>-</td><td>-</td><td>0.840</td><td>0.850</td><td>0.870</td><td>0.880</td><td>-</td><td>-</td><td>0.571</td><td>0.623</td></tr><tr><td>CONRTIQUE* [44]</td><td>-</td><td>-</td><td>0.854</td><td>0.890</td><td>0.896</td><td>0.901</td><td>-</td><td>-</td><td>0.580</td><td>0.641</td></tr><tr><td>UNIQUE* [90]</td><td>0.858</td><td>0.873</td><td>0.854</td><td>0.890</td><td>0.896</td><td>0.901</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MUSIQ* [32]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.916</td><td>0.928</td><td>0.917</td><td>0.921</td><td>0.566</td><td>0.661</td></tr><tr><td>TReS* [21]</td><td>-</td><td>-</td><td>0.846</td><td>0.877</td><td>0.915</td><td>0.928</td><td>-</td><td>-</td><td>0.554</td><td>0.625</td></tr><tr><td>ResNet50</td><td>0.8423</td><td>0.8521</td><td>0.8527</td><td>0.8807</td><td>0.9121</td><td>0.9270</td><td>0.9161</td><td>0.9207</td><td>0.5514</td><td>0.6354</td></tr><tr><td>QPT-ResNet50</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td><td>0.9271</td><td>0.9413</td><td>0.9250</td><td>0.9279</td><td>0.6104†</td><td>0.6770</td></tr></table>
+
+Table 4. Improving the performance of existing SOTA methods by replacing their pre-trained weights with QPT models directly. Experiments are conducted based on their open-source code, using the consistent dataset partitioning and training hyper-parameters.  
+
+<table><tr><td rowspan="2">Methods</td><td rowspan="2">Pre-trained Type</td><td colspan="2">BID</td><td colspan="2">CLIVE</td><td colspan="2">KonIQ10K</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td rowspan="2">HyperIQA</td><td>Original</td><td>0.8665</td><td>0.8883</td><td>0.8553</td><td>0.8716</td><td>0.8990</td><td>0.9190</td></tr><tr><td>QPT</td><td>0.8982+3.17%</td><td>0.9061+1.78%</td><td>0.8743+1.90%</td><td>0.8732+0.16%</td><td>0.9066+0.76%</td><td>0.9241+0.51%</td></tr><tr><td rowspan="2">TRes</td><td>Original</td><td>0.7541</td><td>0.7918</td><td>0.8436</td><td>0.8793</td><td>0.8958</td><td>0.9097</td></tr><tr><td>QPT</td><td>0.7936+3.95%</td><td>0.8037+1.19%</td><td>0.8666+2.30%</td><td>0.8882+0.89%</td><td>0.9052+0.94%</td><td>0.9150+0.53%</td></tr></table>
+
+Table 5. Cross-dataset evaluation. Results of SRCC are reported.  
+
+<table><tr><td>Train</td><td>Test</td><td>DBCNN</td><td>HyperIQA</td><td>CONTRIQUE</td><td>QPT</td></tr><tr><td>KIQ10k</td><td>CLIVE</td><td>0.755</td><td>0.785</td><td>0.731</td><td>0.8208</td></tr><tr><td>KIQ10k</td><td>BID</td><td>0.816</td><td>0.819</td><td>-</td><td>0.8247</td></tr><tr><td>CLIVE</td><td>BID</td><td>0.762</td><td>0.756</td><td>-</td><td>0.8449</td></tr><tr><td>CLIVE</td><td>KIQ10k</td><td>0.754</td><td>0.772</td><td>0.676</td><td>0.7494</td></tr></table>
+
+Table 6. Impact of data amount for the pretext task of QPT, using different percentages of the ImageNet dataset, in BID and CLIVE.  
+
+<table><tr><td rowspan="2">Percentage of ImageNet</td><td colspan="2">BID</td><td colspan="2">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>20%</td><td>0.8311</td><td>0.8305</td><td>0.8115</td><td>0.8203</td></tr><tr><td>50%</td><td>0.8760</td><td>0.8973</td><td>0.8868</td><td>0.9007</td></tr><tr><td>100%</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>
+
+# 4.4. Ablation Studies
+
+Impact of data amount for QPT. To evaluate the effectiveness of the quality-aware pretext task, we use  $20\%$ ,  $50\%$  and  $100\%$  percentages of the ImageNet dataset, analyzing the impact on the number of used data for downstream results. As given in Tab. 6, the larger the number used in the pre-training process, the better the performance on the
+
+Table 7. Impact of encoder capacity for QPT, using different series of networks, in BID and CLIVE.  
+
+<table><tr><td rowspan="2">Network</td><td rowspan="2">Params</td><td colspan="2">BID</td><td colspan="2">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>MBViTV2-100</td><td>4.90</td><td>0.8746</td><td>0.8799</td><td>0.8640</td><td>0.8914</td></tr><tr><td>MBViTV2-150</td><td>10.59</td><td>0.8782</td><td>0.8976</td><td>0.8702</td><td>0.8970</td></tr><tr><td>MBViTV2-200</td><td>18.45</td><td>0.8821</td><td>0.8960</td><td>0.8894</td><td>0.9006</td></tr><tr><td>ResNet-18</td><td>11.69</td><td>0.8679</td><td>0.8805</td><td>0.8610</td><td>0.8795</td></tr><tr><td>ResNet-34</td><td>21.80</td><td>0.8742</td><td>0.9001</td><td>0.8780</td><td>0.8871</td></tr><tr><td>ResNet-50</td><td>25.56</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>
+
+downstream IQA datasets. Still, it is quite a surprise that our method obtains SOTA results with only  $50\%$  of the data. Furthermore, training larger-scale data is an open question and can be investigated in future work, where QPT may benefit from JFT-300M [61].
+
+Impact of encoder capacity for QPT. To verify the effect of model capacity on feature modeling, we select two series of networks for analysis, including the widely-used CNN architectures of ResNet and an emerging Transformer-based architectures of MobileViTV2 [45]. As shown in Tab. 7, increasing the model size can help improve the ability of feature representation, resulting in better downstream
+
+Table 8. Impact on the composition of negative samples.  
+
+<table><tr><td rowspan="2">Inter</td><td rowspan="2">Intra</td><td colspan="2">BID</td><td colspan="2">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>✓</td><td>✓</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr><tr><td>✓</td><td>×</td><td>0.8702</td><td>0.9051</td><td>0.8721</td><td>0.8994</td></tr><tr><td>×</td><td>✓</td><td>0.8399</td><td>0.8357</td><td>0.8084</td><td>0.8142</td></tr><tr><td>×</td><td>×</td><td>0.7078</td><td>0.7731</td><td>0.7495</td><td>0.7493</td></tr></table>
+
+![](images/6202046e3b964be34837536ae12cbffbb5b7de5b85c844f1a5df9b041d499ed0.jpg)  
+(a) Results in BID
+
+![](images/26cf8107b5392dfa02cb357907d1f25db978effc89a468d0ba144b42c15e1676.jpg)  
+(b) Results in CLIVE  
+Figure 4. Evaluation results of SRCC under different fixed compositions of degradations in a first-order manner. The diagonal entries denote single class degradation type, and off-diagonals represent composition of two-class degradation applied sequentially.
+
+performance. It should be pointed out that large models will also increase the time consumption of the pre-training phase (i.e., ResNets of  $\{53\mathrm{h}, 61\mathrm{h}, 75\mathrm{h}\}$ , MBViTV2s of  $\{66\mathrm{h}, 92\mathrm{h}, 109\mathrm{h}\}$ , respectively). We did not use larger networks out of tradeoffs, which can be tried in future work.
+
+Impact of different compositions of negative samples. To evaluate the effectiveness of negative samples and the proposed QC Loss, we give the results in Tab. 8. The highest result is achieved when both types of negative samples are present. And the absence of inter-sample negative pairs leads to a larger performance drop. This is due to the fact that compared with intra-sample negative pairs (i.e.,  $K - 1$ ), the number of inter-sample ones (i.e.,  $N \cdot K$ ), which contain both different content and degradation types, is larger.
+
+Ablation on the degradation space. Experiments are performed to evaluate the impact of different degradations and compositions. In Fig. 4, we give the results under different compositions of degradation types in a first-order manner. Trying all combinations is impractical due to the huge degradation space. Experiments are performed in a coarse-grained manner. The results show that there is a clear effect difference between the degradation types of a fixed form. More flexible and larger space are needed to cover different downstream scenarios. We further evaluate the strategy of composition as shown in Fig. 2. In Tab. 9, a combination of the three strategies yielded the best results.
+
+# 4.5. Comparisons with other pretext tasks
+
+We further compare QPT with other pretext methods, including train-from-scratch (i.e., w/o pre-training weights), supervised and MoCo. We extract features from the encoder output for both fine-tuning and linear probing evaluations.
+
+Linear probing evaluation. In this way, the weights of
+
+Table 9. Ablation on the degradation space (different formulation type in Eq. (3) of complicated degradation models) in BID.  
+
+<table><tr><td>skip</td><td>shuffle</td><td>two-order</td><td>SRCC</td><td>PLCC</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>0.8875</td><td>0.9109</td></tr><tr><td>✓</td><td>✓</td><td>×</td><td>0.8828</td><td>0.9075</td></tr><tr><td>✓</td><td>×</td><td>×</td><td>0.8745</td><td>0.9029</td></tr><tr><td>×</td><td>×</td><td>×</td><td>0.8626</td><td>0.8864</td></tr></table>
+
+Table 10. Comparisons of linear probing evaluation using different pretext tasks in BID and CLIVE.  
+
+<table><tr><td rowspan="2">Pretext task</td><td colspan="2">BID</td><td colspan="2">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>Supervised</td><td>0.7678</td><td>0.7860</td><td>0.7128</td><td>0.7668</td></tr><tr><td>MoCo</td><td>0.7367</td><td>0.7357</td><td>0.6796</td><td>0.7154</td></tr><tr><td>QPT</td><td>0.8242</td><td>0.8175</td><td>0.7613</td><td>0.7938</td></tr></table>
+
+Table 11. Comparisons of end-to-end fine-tuning evaluation using different pretext tasks in BID and CLIVE.  
+
+<table><tr><td rowspan="2">Pretext task</td><td colspan="2">BID</td><td colspan="2">CLIVE</td></tr><tr><td>SRCC</td><td>PLCC</td><td>SRCC</td><td>PLCC</td></tr><tr><td>w/o</td><td>0.7078</td><td>0.7731</td><td>0.7495</td><td>0.7493</td></tr><tr><td>Supervised</td><td>0.8423</td><td>0.8521</td><td>0.8527</td><td>0.8807</td></tr><tr><td>MoCo</td><td>0.8531</td><td>0.8724</td><td>0.8494</td><td>0.8615</td></tr><tr><td>QPT</td><td>0.8875</td><td>0.9109</td><td>0.8947</td><td>0.9141</td></tr></table>
+
+encoder are frozen for feature extraction directly. As given in Tab. 10, QPT obtains the best performance, surpassing MoCo by  $8.75\%$  of SRCC in BID and  $8.17\%$  in CLIVE.
+
+End-to-end fine-tuning evaluation. Linear probing has been a popular protocol in the past few years. However, it misses the opportunity of pursuing strong but nonlinear features which is indeed a strength of deep learning [26]. We also give the fine-tuning results in Tab. 11. QPT still achieves the best results. Generally, higher results can be obtained than linear probing. These results further prove the effectiveness of QPT over instance-level discrimination or supervised classification pretext tasks in IQA scenarios.
+
+# 5. Conclusion
+
+In this paper, we proposed the QPT to generate pretrained models for downstream BIQA tasks, alleviating the obstacle of insufficient annotated data. By introducing diverse degradation types and compositions, we construct a degradation space that contains  $2 \times 10^{7}$  possible degradations, to simulate more complicated and realistic distorted images. To constrain the learning process, we proposed the QC-Loss that treats patch pairs extracted from the same degraded images as positive ones. And other pairs are noted as negative ones, including degradation-based and content-based ones. After pre-trained on ImageNet using QPT, BIQA models obtain significant improvements on five BIQA benchmark datasets. Moreover, QPT can be easily integrated with current SOTA methods by replacing their pre-trained weights, showing good generalization ability.
+
+# References
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+            "Figure 1. The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks."
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+        "text": "The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods.",
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+        "text": "uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows:",
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+        "list_items": [
+            "- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization.",
+            "- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result.",
+            "- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55].",
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+        "type": "text",
+        "text": "Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner.",
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+        "type": "text",
+        "text": "Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "5948",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Visual Fidelity for Image Style Transfer",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Image style transfer aims to transfer a content image  $c$ , e.g., a photo, to a stylized image  $y$  by a given style reference  $s$ , e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Style fidelity: The style similarity between  $y$  and  $s$ , which is often evaluated by the Gram matrix [13, 34].",
+            "- Content fidelity: The content similarity between  $y$  and  $c$ , which is often evaluated by the perceptual loss [28] or the LPIPS distance [62].",
+            "- Visual fidelity: The realness of the generated image  $y$ . Since all real artwork images belong to a distribution  $\\mathcal{T}$ , a generated image  $y$  tends to have a higher visual fidelity if it is closer to distribution  $\\mathcal{T}$ ."
+        ],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm  $(\\alpha = 0)$  faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution  $\\mathcal{T}$  in the representation space, where the centroids of all clusters form an artwork codebook  $\\mathcal{Z}_{art}$ . When making inferences, we replace the feature map at each position with its nearest centroid in  $\\mathcal{Z}_{art}$ . In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/ea0e806e62a1fc5ccb96922919a21ca5a693d33b46dfdcc3492e9b0dcfa18a8b.jpg",
+        "image_caption": [
+            "Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer  $w / o$  and  $w/$  latent feature quantizing, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation  $y$  to be close to one of the centroids of the artwork distribution  $\\mathcal{T}$  but far away from the reference  $s$ . We introduce more details of QuantArt in the following Section 4.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. Our Approach",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Framework Overview",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level  $\\alpha \\in [0,1]$  between the SGA outputs. In the following, we discuss more details of QuantArt.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.2. Learning Auto-Encoders and Codebooks",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We first extract the features of the content image  $c$  and the style reference  $s$  with two convolutional encoders  $E_{C}$  and  $E_{S}$ , then decode the features back into images  $c_{rec}$  and  $s_{rec}$  with two convolutional decoders  $D_{C}$  and  $D_{S}$ , respec",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "5949",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "image",
+        "img_path": "images/ac25ffe5b4ab261433e08b77ad601a9d322b24f4884808a2e54416059d33fcfb.jpg",
+        "image_caption": [
+            "(a) Training Stage-1: learning the auto-encoders"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ac2d2a1f0fbd65a1b319b91a45858f1b3a822d9d1adb4ced8ebae617da6563fd.jpg",
+        "image_caption": [
+            "(b) Training Stage-2: learning the SGA modules"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/d1280cbf44fcdffee8a747dc2454d6a529fe42a215bd417e1ad5cf3bb1376029.jpg",
+        "image_caption": [
+            "(c) Inference Stage"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "tively as",
+        "bbox": [
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+            441
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nc _ {r e c} = D _ {C} \\left(E _ {C} (c)\\right), \\quad s _ {r e c} = D _ {S} \\left(E _ {S} (s)\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This is distinct from the general neural style transfer methods, which use the VGG [48] or ResNet [18] network pretrained on natural image datasets (e.g., ImageNet [7]) as the image encoder to extract features of both content and style images. To optimize encoder  $E_{C}$  and decoder  $D_{C}$ , the reconstruction loss is",
+        "bbox": [
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+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {A E} \\left(E _ {C}, D _ {C}\\right) = \\left| \\left| c _ {r e c} - c \\right| \\right| + \\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            86,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{adv}$  is the adversarial training loss and  $\\mathbb{D}_C$  is the corresponding discriminator network,",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {a d v} \\left(E _ {C}, D _ {C}, \\mathbb {D} _ {C}\\right) = \\log \\mathbb {D} _ {C} (c) + \\log \\left(1 - \\mathbb {D} _ {C} \\left(c _ {r e c}\\right)\\right). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$E_{S}$  and  $D_{S}$  are also optimized by the reconstruction loss  $\\mathcal{L}_{AE}(E_S,D_S)$  as formulated in Eq. 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we build two codebooks  $\\mathcal{Z}_{photo},\\mathcal{Z}_{art}\\in \\mathbb{R}^{N\\times d}$  to model the distributions of the photo dataset and artwork dataset, where  $N$  is the number of entries in the codebook and  $d$  is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {c} = \\hat {E} _ {C} (c), \\quad z _ {s} = \\hat {E} _ {S} (s). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We then apply vector quantization [52] to the latent features to get the quantized features  $\\hat{z}_c$  and  $\\hat{z}_s$ , where the vector quantization operator  $Q_{\\mathcal{Z}}(z)$  is formulated as",
+        "bbox": [
+            76,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ _ {\\mathcal {Z}} (z) := \\underset {\\mathbf {z} _ {k} \\in \\mathcal {Z}} {\\arg \\min } \\| z - \\mathbf {z} _ {k} \\|, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/cb46f7ecfb30c4d4905d235429f0f9382bea836832666ccdfbecf1fcbed1de7e.jpg",
+        "image_caption": [
+            "Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively.  $\\mathbb{Q}$  denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters  $\\alpha$ ,  $\\beta \\in [0,1]$ .",
+            "Figure 4. The vector quantization operator  $Q_{\\mathcal{Z}}(z)$  in Eq. 5."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            529,
+            430,
+            857,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{z}_k$  is the  $k$ -th entry in the codebook  $\\mathcal{Z}$ . As illustrated in Fig. 4,  $z$  is replaced with the nearest neighbour entry in the codebook  $\\mathcal{Z}$  via  $Q_{\\mathcal{Z}}(z)$ . The quantized features  $\\hat{z}_c$  and  $\\hat{z}_s$  are collected from codebooks  $\\mathcal{Z}_{photo}$  and  $\\mathcal{Z}_{art}$  as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {z} _ {c} = Q _ {\\mathcal {Z} _ {\\text {p h o t o}}} \\left(z _ {c}\\right), \\quad \\hat {z} _ {s} = Q _ {\\mathcal {Z} _ {\\text {a r t}}} \\left(z _ {s}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The quantized features  $\\hat{z}_c$  and  $\\hat{z}_s$  are decoded into images  $\\hat{c}_{rec}$  and  $\\hat{s}_{rec}$  via the decoders  $\\hat{D}_C$  and  $\\hat{D}_S$ , as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {c} _ {r e c} = \\hat {D} _ {C} (\\hat {z} _ {c}), \\quad \\hat {s} _ {r e c} = \\hat {D} _ {S} (\\hat {z} _ {s}). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            576,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By following [52], we optimize the codebook  $\\mathcal{Z}_{\\text{photo}}$  jointly with the reconstruction loss in Eq. 2. The reconstruction loss for encoder  $\\hat{E}_C$ , decoder  $\\hat{D}_C$ , and codebook  $\\mathcal{Z}_{\\text{photo}}$  is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\hat {A E}} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}, \\mathcal {Z} _ {\\text {p h o t o}}\\right) = \\mathcal {L} _ {A E} \\left(\\hat {E} _ {C}, \\hat {D} _ {C}\\right) + \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left. \\left| \\left| \\left| \\mathbf {s g} \\left[ z _ {c} \\right] - \\hat {z} _ {c} \\right| \\right| \\right| + \\left| \\left| \\mathbf {s g} \\left[ \\hat {z} _ {c} \\right] - z _ {c} \\right| \\right| \\right|,\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            660,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathfrak{sg}[\\cdot ]$  indicates the stop gradient operator. The second term in Eq. 8 optimizes the codebook  $\\mathcal{Z}_{photo}$ , while, the third term in Eq. 8 forces the latent feature  $z_{c}$  to be close to the nearest neighbor entry in  $\\mathcal{Z}_{photo}$ .  $\\hat{E}_S$ ,  $\\hat{D}_S$ , and  $\\mathcal{Z}_{art}$  are",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5950",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/160f7f6d0f3d8ada59a5ab01001c878a8323a7adfe37719c6c6e5c63c755a993.jpg",
+        "image_caption": [
+            "Figure 5. The SGA module proposed for feature style transfer."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            127,
+            90,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "also optimized by the loss function  $\\mathcal{L}_{\\hat{A}E}(\\hat{E}_S, \\hat{D}_S, \\mathcal{Z}_{art})$  as formulated in Eq. 8.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Style Transfer with Style Guided Attention",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature  $z_{c} \\in \\mathbb{R}^{d}$  and style reference feature  $z_{s} \\in \\mathbb{R}^{d}$  as inputs, then outputs the stylized feature vector  $z_{y} \\in \\mathbb{R}^{d}$ . It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query  $q$ , key  $k$ , and value  $v$  as inputs,",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t n} (q, k, v) = \\operatorname {s o f t m a x} \\left(f _ {q} (q) f _ {k} (k)\\right) f _ {v} (v) + q, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{q}, f_{k}, f_{v}$  are the embedding layers. The first attention block is a self-attention block that all its input heads  $q, k, v$  accept the transformed content feature  $\\tilde{z}_{c} = \\mathrm{ResBlock}(z_{c})$ . The second attention block takes  $\\tilde{z}_{c}$  as  $q$ , and the style reference feature  $z_{s}$  as  $k$  and  $v$ . The output of the SGA module is formulated as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {y} = \\operatorname {S G A} \\left(z _ {c}, z _ {s}\\right) = \\operatorname {A t t n} \\left(\\operatorname {A t t n} \\left(\\tilde {z} _ {c}, \\tilde {z} _ {c}, \\tilde {z} _ {c}\\right), z _ {s}, z _ {s}\\right). \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for  $M$  times to achieve a better style transfer performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The objective function for  $\\mathrm{SGA}(z_c, z_s)$  includes the content loss  $\\mathcal{L}_{\\text {content }}$ , style loss  $\\mathcal{L}_{\\text {style }}$ , and adversarial training loss  $\\mathcal{L}_{\\text {featadv }}$",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {S G A} = \\mathcal {L} _ {\\text {c o n t e n t}} + \\mathcal {L} _ {\\text {s t y l e}} + \\mathcal {L} _ {\\text {f e a t a d v}} \\tag {11}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where",
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+        ],
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {c o n t e n t}} = \\left| \\left| z _ {y} - z _ {c} \\right| \\right|, \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {s t y l e}} = \\left| \\left| \\mu \\left(z _ {y}\\right) - \\mu \\left(z _ {s}\\right) \\right| \\right| + \\left| \\left| \\sigma \\left(z _ {y}\\right) - \\sigma \\left(z _ {s}\\right) \\right| \\right|, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t a d v}} = \\log \\mathbb {D} _ {S G A} \\left(z _ {s}\\right) + \\log \\left(1 - \\mathbb {D} _ {S G A} \\left(z _ {y}\\right)\\right). \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$\\mu (\\cdot)$  and  $\\sigma (\\cdot)$  denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss  $\\mathcal{L}_{featadv}$  is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We adopt another SGA module to transfer the quantized features  $\\hat{z}_c$  and  $\\hat{z}_s$ , as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {z} _ {y} = Q _ {\\mathcal {Z} _ {a r t}} \\left(\\mathrm {S} \\hat {\\mathrm {G A}} \\left(\\hat {z} _ {c}, \\hat {z} _ {s}\\right)\\right). \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$\\hat{\\mathrm{SGA}} (\\cdot ,\\cdot)$  and  $\\mathrm{SGA}(\\cdot ,\\cdot)$  have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook  $Q_{\\mathcal{Z}_{art}}$  to ensure that the output is on the latent space of the decoder  $\\hat{D}_S$ . The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {S \\hat {G} A} = \\mathcal {L} _ {S G A} + | | \\operatorname {s g} [ \\hat {z} _ {y} ] - z _ {y} ] | | \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Inference",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature  $z_{y}$  and stylized quantized feature  $\\hat{z}_{y}$  by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {t e s t} = \\oplus_ {\\alpha} \\left(\\oplus_ {\\beta} \\left(\\hat {z} _ {y}, \\hat {z} _ {c}\\right), \\oplus_ {\\beta} \\left(z _ {y}, z _ {c}\\right)\\right), \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $z_{c}$  and  $\\hat{z}_{c}$  are the content features, and  $\\oplus$  is the weighted sum operator as  $\\oplus_{p}(a,b) = pa + (1 - p)b$ .  $z_{test}$  is decoded into a stylized image with a fused decoder  $\\bar{D}_S = \\oplus_\\alpha (\\hat{D}_S, D_S)$ .  $\\beta$  controls the style fidelity, and a larger  $\\alpha$  results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt  $(\\alpha, \\beta)$  provides a simple and easy-to-understand handle grip for users to adjust the style transfer results.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5951",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            89,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experiment Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the \"genre\" tag of \"landscape\" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to  $256 \\times 256$  pixels.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of  $16 \\times 16$  and a feature dimension of 256. The codebook has  $N = 1024$  entries and an entry dimension of  $d = 256$ . The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of  $4.5 \\times 10^{-6}$ , and a training epoch of 50. The loss weights of  $\\mathcal{L}_{AE}$ ,  $\\mathcal{L}_{codebook}$ ,  $\\mathcal{L}_{content}$ ,  $\\mathcal{L}_{style}$ , and  $\\mathcal{L}_{adv}$  are set to 1, 1, 1, 10, and 0.8, respectively.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Multi-Fidelity Image Style Transfer",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our QuantArt  $(\\alpha, \\beta)$  method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations  $(\\alpha, \\beta)$ . When the style fidelity  $\\beta = 0$ , the model simply reconstructs the input content image. With  $\\beta = 1$  and visual fidelity  $\\alpha \\rightarrow 1$ , the generated images look more vivid but lose some texture details in the style reference. Note that neither  $\\alpha = 0$  or  $\\alpha = 1$  performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparing with State-of-the-Art Methods",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/0ea38468e5bfb276d569aad85470814cc8b043d7aaccf68370804f3491193cb7.jpg",
+        "image_caption": [
+            "Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters  $\\alpha$  and  $\\beta$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23].",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with  $\\alpha = 0$  faithfully transfers the texture from input style images, while QuantArt with  $\\alpha = 1$  paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "5952",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/e964907757c64c85ee7a27697627f8715b94151b611710cbc5ad040647f0e637.jpg",
+        "image_caption": [
+            "Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b8031b1d9c0d7d137e10bbc43c159f0de46daaf27a75aa6ca842e763f474e160.jpg",
+        "table_caption": [
+            "Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Metric ↓</td><td rowspan=\"2\">AdaIN</td><td rowspan=\"2\">WCT</td><td rowspan=\"2\">LinearWCT</td><td rowspan=\"2\">ArtFlow</td><td rowspan=\"2\">EFDM</td><td rowspan=\"2\">StyleSwap</td><td rowspan=\"2\">AvatarNet</td><td rowspan=\"2\">SANet</td><td rowspan=\"2\">AdaAttN</td><td rowspan=\"2\">StyTR2</td><td colspan=\"3\">Ours (α,β)</td></tr><tr><td>(0,0)</td><td>(0,1)</td><td>(1,1)</td></tr><tr><td>LPIPS ↓</td><td>0.681</td><td>0.695</td><td>0.657</td><td>0.603</td><td>0.652</td><td>0.607</td><td>0.706</td><td>0.686</td><td>0.633</td><td>0.514</td><td>0.159</td><td>0.565</td><td>0.581</td></tr><tr><td>Gram loss (×103) ↓</td><td>0.163</td><td>0.282</td><td>0.172</td><td>0.101</td><td>0.402</td><td>1.357</td><td>0.718</td><td>0.120</td><td>0.246</td><td>0.386</td><td>-</td><td>0.395</td><td>0.864</td></tr><tr><td>FID ↓</td><td>36.618</td><td>65.193</td><td>48.156</td><td>28.899</td><td>51.070</td><td>74.168</td><td>58.178</td><td>27.080</td><td>25.894</td><td>30.893</td><td>-</td><td>25.590</td><td>17.787</td></tr><tr><td>ArtFID ↓</td><td>63.240</td><td>112.229</td><td>81.452</td><td>47.936</td><td>86.007</td><td>120.803</td><td>100.964</td><td>47.356</td><td>43.910</td><td>48.284</td><td>-</td><td>41.623</td><td>29.695</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7a1f2709943b9df147ab823a32df2c9faa3d8daa8a328e5939b374777b5934ec.jpg",
+        "table_caption": [
+            "Table 2. Inference time (seconds) of a  ${256} \\times  {256}$  image with a NVIDIA Tesla V100 GPU."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ArtFlow</td><td>StyleSwap</td><td>AvatarNet</td><td>SANet</td><td>AdaAttN</td><td>StyTR2</td><td>Ours</td></tr><tr><td>0.068</td><td>0.043</td><td>0.124</td><td>0.007</td><td>0.050</td><td>0.055</td><td>0.045</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods.",
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+        "type": "text",
+        "text": "5.4. Human Evaluation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Since image style transfer is a highly subjective task, we further examine our model with human evaluation.",
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+        "type": "text",
+        "text": "User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of  $43.5\\%$ ,  $51.9\\%$ , and  $40.2\\%$ , respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms.",
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+        "type": "text",
+        "text": "Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion",
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+        "type": "page_number",
+        "text": "5953",
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+    {
+        "type": "image",
+        "img_path": "images/5ea829693dccf9eccfff22df3be7907edaa320f041d58d5fefd289eb61864477.jpg",
+        "image_caption": [
+            "Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "img_path": "images/ec0c8b7c38d60a90feb3b500c505578a52640aecf1be85c0ed716e51f816b71f.jpg",
+        "image_caption": [
+            "Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only  $40.6\\%$  participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions."
+        ],
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+    {
+        "type": "image",
+        "img_path": "images/613c40009b5f91ef1043a14331813d61d890f57bce3b95c76aa289865b6bab3d.jpg",
+        "image_caption": [],
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+    {
+        "type": "text",
+        "text": "test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of  $i$  a real artwork image  $s$  and  $ii$  a photo stylized according to the reference of  $s$ . The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material.",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/6c91ee916ea84960fa663fccc51d51c496db39f08518208c4df8ce24a2c31ef4.jpg",
+        "table_caption": [
+            "Table 3. An ablation study of the design choices of QuantArt."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Complete model, α = 1, code size 16×16</td><td>LPIPS ↓</td><td>Gram ↓</td><td>FID ↓</td></tr><tr><td>0.581</td><td>0.864</td><td>17.787</td></tr><tr><td>Remove Quantization in SGA</td><td>0.545</td><td>0.993</td><td>18.757</td></tr><tr><td>Remove all Quantizations (i.e., α = 0)</td><td>0.565</td><td>0.395</td><td>25.590</td></tr><tr><td>Code size 8×8</td><td>0.656</td><td>1.078</td><td>27.741</td></tr><tr><td>Code size 32×32</td><td>0.513</td><td>0.798</td><td>28.663</td></tr><tr><td>Remove self-attention in SGA</td><td>0.584</td><td>0.883</td><td>19.025</td></tr><tr><td>Remove ResBlock in SGA</td><td>0.608</td><td>1.841</td><td>27.177</td></tr><tr><td>Replace SGA with StyTR2 decoder layer [8]</td><td>0.539</td><td>0.875</td><td>26.299</td></tr><tr><td>Shared encoders</td><td>0.588</td><td>0.788</td><td>30.806</td></tr><tr><td>Shared encoders and decoders</td><td>0.593</td><td>0.891</td><td>35.830</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.5. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a  $16 \\times 16$  patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of  $16 \\times 16$  is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. The experiments on Photo-to-Artwork, Artwork-to-Artwork, and Photo-to-Photo transfer settings have shown that our method achieves higher visual fidelity along with comparable content and style fidelities compared with the state-of-the-art methods.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by NIH grant 5U54CA225088-03. The computations in this paper were run on the FASRC Cannon cluster supported by Harvard.",
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+        "type": "page_number",
+        "text": "5954",
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+    {
+        "type": "text",
+        "text": "References",
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2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/4935fc7e-77d7-46b7-8112-ea03d0af8f8a_origin.pdf

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2023/QuantArt_ Quantizing Image Style Transfer Towards High Visual Fidelity/full.md

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+# QuantArt: Quantizing Image Style Transfer Towards High Visual Fidelity
+
+Siyu Huang\*
+
+Jie An\*
+
+$^{1}$ Harvard University
+
+Donglai Wei<sup>3</sup>
+
+$^{2}$ University of Rochester
+
+Jiebo Luo
+
+Hanspeter Pfister
+
+3Boston College
+
+{huang, pfister}@seas.harvard.com
+
+{jan6,jluo}@cs.ROchester.edu
+
+donglai.wei@bc.edu
+
+![](images/42bc59bb7f4a090c0a7d01879c5b898b0bdfe8704f57ddb9a7a2b4eeb8bf2ba8.jpg)  
+Figure 1. The proposed QuantArt method produces impressive arbitrary style transfer results on various image style transfer tasks.
+
+# Abstract
+
+The mechanism of existing style transfer algorithms is by minimizing a hybrid loss function to push the generated image toward high similarities in both content and style. However, this type of approach cannot guarantee visual fidelity, i.e., the generated artworks should be indistinguishable from real ones. In this paper, we devise a new style transfer framework called QuantArt for high visual-fidelity stylization. QuantArt pushes the latent representation of the generated artwork toward the centroids of the real artwork distribution with vector quantization. By fusing the quantized and continuous latent representations, QuantArt allows flexible control over the generated artworks in terms of content preservation, style similarity, and visual fidelity. Experiments on various style transfer settings show that our QuantArt framework achieves significantly higher visual fidelity compared with the existing style transfer methods.
+
+# 1. Introduction
+
+Image style transfer aims at transferring the artistic style of a reference image to a content image, where the output image should have the style (e.g., colors, textures, strokes,
+
+and tones) of the reference and the content information of the content image. Great advances [4, 5, 13, 14, 39, 40, 63] have been made in the area of image style transfer, where the arbitrary style transfer (AST) has become one of the main research focuses. Given a trained model, AST algorithms [8, 26, 33] can perform style transfer on arbitrary unseen content-style pairs in a zero-shot manner, such that it enables more practical applications<sup>1</sup>.
+
+Existing AST algorithms, including the statistics-based methods [1,26,35,60] and the patch-based methods [6,47], deliver remarkable style transfer results by matching the artistic style information of the stylized image and the style reference. However, taking the high-fidelity artwork generation as the ultimate goal of image style transfer, all existing methods can still be improved since there are few mechanisms to guarantee a high artistic fidelity of the stylized image. A few existing work [3,59] accommodate the adversarial loss [15] into the style transfer framework to enhance the image quality. However, the performance improvement is hindered by the heterogeneous optimization objectives of high image quality and faithful image stylization.
+
+In this work, we introduce visual fidelity as a new eval
+
+uation dimension of style transfer. It is formulated as the similarity between the stylized image and the real artwork dataset, and it is orthogonal to the two widely studied evaluation dimensions including style similarity and content preservation. Motivated by the vector-quantized image representation [11,45,52], if the latent feature of generation is closer to one of the cluster centers in the real distribution, it is harder for humans to distinguish it from the real images, i.e., having better visual fidelity. We propose to learn an artwork codebook, i.e., a global dictionary, to save the discrete cluster centers of all artworks. The continuous representations of images are converted to the discrete encodings in the artwork codebook via vector quantization, ensuring that it is not only close to the given style reference but also close to one of the learned cluster centers in the real distribution.
+
+We further propose a framework called Quantizing Artistic Style Transfer (QuantArt) to achieve flexible control of the three evaluation dimensions mentioned above. QuantArt first extracts both content and style features using separate encoders, respectively. Next, it applies vector quantization to both content and style features to fetch discrete codes in the learned codebooks. Then, the content and style codes are transferred to the stylized feature with a specially designed feature style transfer module called Style-Guided Attention. Before feeding into the decoder, the stylized feature is quantized again with the artwork codebook, ensuring a high visual-fidelity stylization by approaching the cluster centers of the real artwork distribution. By fusing the continuous and quantized stylized features with the content features before the decoder, QuantArt allows users to arbitrarily trade off between the style similarity, visual fidelity, and content reservation of the style transfer results. In the experiments, the proposed method significantly increases the visual fidelity of generations in various image style transfer settings including photo-to-art, art-to-art, photo-to-photo, and art-to-photo (see Fig. 1). The contribution of the proposed method can be summarized as follows:
+
+- We define visual fidelity as a new evaluation dimension of style transfer and propose a high visual-fidelity style transfer algorithm based on vector quantization.  
+- We design a framework based on both discrete and continuous style transfer architectures, which allow users to flexibly control style similarity, content preservation, and visual fidelity of the stylization result.  
+- The extensive experiments demonstrate that our method achieves higher visual fidelity and comparable style similarity with respect to the state-of-the-art style transfer methods.
+
+# 2. Related Work
+
+Image style transfer. Image style transfer is a challenging topic that has been studied for decades [20, 27, 34, 55].
+
+Gatys et al. [13] first adopted convolutional neural networks (CNNs) for image style transfer by matching the statistics of content and style features extracted by CNNs. Among the neural style transfer (NST) algorithms [13, 14, 40], arbitrary style transfer (AST) [5, 6, 25, 26, 63] has drawn much attention from researchers in recent years due to its zero-shot image stylization manner.
+
+Existing AST algorithms can be generally categorized into two types: the statistics-based methods [10, 51] and the patch-based methods [12, 16, 37, 54]. The statistics-based methods minimize the distance of global feature statistics between the generation and the style image, where the feature statistics can be Gram matrices [13, 14], histograms [19, 46], wavelets [44, 60], mean-standard statistics [9, 26], and covariance matrices [35]. The statistics-based methods are highly efficient in capturing the global style information. The patch-based methods search for appropriate patches in style images to reconstruct the transferred images. StyleSwap [6] and Avatar-Net [47] are two typical patch-based methods, which iteratively swap the content feature patches with the nearest-matched feature patches of the reference image. Compared to the statistics-based approaches, the patch-based methods produce better texture synthesis quality as they directly adopt patches from style images. However, it requires the content and style images to have similar local semantic structures.
+
+In general, the existing AST algorithms aim at matching the styles of the generation and the reference, where the visual fidelity of the generation cannot be guaranteed. In this work, we introduce visual fidelity as a new evaluation dimension of style transfer and propose a novel AST framework, i.e., QuantArt, to enhance the visual fidelity of generations via pushing the latent feature toward the centroids of artwork distributions. QuantArt can also alleviate the stylization artifact issue, as the outlier styles are replaced with the nearest style centroid in the latent space.
+
+Photorealistic style transfer. The proposed method can also handle the photorealistic style transfer task. The artistic style transfer algorithms often fail for this task, since the stylized image would contain warping distortions that are redundant for the photorealism scenario. Motivated by this, several methods [2,23,57,58] have been specially designed. Luan et al. [40] first introduced a locally affine transformation as the photorealism loss term. PhotoWCT [36] proposes a closed-form post-processing algorithm to further smooth the stylized results. WCT² [60] eliminates the post-processing stage via the Wavelet Corrected Transfer module. Distinct from these approaches, our method does not require to impose any additional regularization or post-processing step for photorealistic style transfer, thanks to the highly effective quantized image representation.
+
+Vector-quantized image representation. The vector-quantized generative models [11, 61] are originally devel
+
+oped for compact yet effective image modeling. VQVAE [45, 52] devises a vector-quantized autoencoder to represent an image with a set of discrete tokens. VQGAN [11] improves VQVAE with the adversarial learning scheme [15]. This work adopts vector quantization as an efficient learnable implementation of artwork distribution clustering. The vector quantization pushes the latent feature to be closer to the real artwork distribution, resulting in higher visual-fidelity image stylization.
+
+# 3. Visual Fidelity for Image Style Transfer
+
+Image style transfer aims to transfer a content image  $c$ , e.g., a photo, to a stylized image  $y$  by a given style reference  $s$ , e.g., an artwork image. Existing image style transfer algorithms mainly focus on either content preservation or style similarity between the generated and input images. However, we argue that the visual realness of generated images is also a vital factor for style transfer performance. We formulate the three critical performance indicators of image style transfer as
+
+- Style fidelity: The style similarity between  $y$  and  $s$ , which is often evaluated by the Gram matrix [13, 34].  
+- Content fidelity: The content similarity between  $y$  and  $c$ , which is often evaluated by the perceptual loss [28] or the LPIPS distance [62].  
+- Visual fidelity: The realness of the generated image  $y$ . Since all real artwork images belong to a distribution  $\mathcal{T}$ , a generated image  $y$  tends to have a higher visual fidelity if it is closer to distribution  $\mathcal{T}$ .
+
+Many existing literature [26, 32, 39, 42, 47] shows that there is a trade-off between the style fidelity and content fidelity in image style transfer. Analogous to this, there is a trade-off between visual fidelity and style fidelity. As an example shown in the bottom of Fig. 2, the neural style transfer algorithm  $(\alpha = 0)$  faithfully renders the style textures of the tree in the reference image. However, it lowers the visual fidelity of the generated image.
+
+To increase the visual fidelity of neural style transfer, in this work we propose a novel framework named QuantArt to learn to cluster the artwork distribution  $\mathcal{T}$  in the representation space, where the centroids of all clusters form an artwork codebook  $\mathcal{Z}_{art}$ . When making inferences, we replace the feature map at each position with its nearest centroid in  $\mathcal{Z}_{art}$ . In this way, the feature of the generated artwork is pushed closer to the real artwork distribution, thus leading to better visual fidelity. This nearest centroid search and replacing operation is implemented by the vector quantization used in [11, 45, 52]. Besides, the idea of pushing the latent feature closer to the centroid of real distribution is partially motivated by the low-temperature sampling used in GANs [15, 24, 30, 66] and diffusion models [17, 22]. As
+
+![](images/ea0e806e62a1fc5ccb96922919a21ca5a693d33b46dfdcc3492e9b0dcfa18a8b.jpg)  
+Figure 2. (Top left) This work introduces visual fidelity as an orthogonal evaluation dimension to content fidelity and style fidelity. (Top right) Our style transfer method enables a trade-off between style and visual fidelities via quantizing the generation in the style space. (Bottom) An example of image style transfer  $w / o$  and  $w/$  latent feature quantizing, respectively.
+
+illustrated in the top right part of Fig. 2, one can increase the visual fidelity by pushing the generation  $y$  to be close to one of the centroids of the artwork distribution  $\mathcal{T}$  but far away from the reference  $s$ . We introduce more details of QuantArt in the following Section 4.
+
+# 4. Our Approach
+
+# 4.1. Framework Overview
+
+In this work, we propose a novel framework dubbed Quantizing Artistic Style Transfer (QuantArt) to enhance the visual fidelity of generations in image style transfer. As illustrated in Fig. 3, QuantArt adopts four auto-encoders to extract the continuous/quantized features of photo/artwork images respectively, two codebooks to store the cluster centers of photo and artwork distributions, and two SGA modules to transfer the styles of feature representations. The training of QuantArt consists of two stages. In the first training stage (see Fig. 3(a)), we learn the auto-encoders and the codebooks by reconstructing the photo and artwork images, respectively. In the second training stage (see Fig. 3(b)), we train the SGA modules based on the extracted feature representations. In the inference phase, as illustrated in Fig. 3(c), users can easily trade off the style and visual fidelity of generations by adjusting the discretization level  $\alpha \in [0,1]$  between the SGA outputs. In the following, we discuss more details of QuantArt.
+
+# 4.2. Learning Auto-Encoders and Codebooks
+
+We first extract the features of the content image  $c$  and the style reference  $s$  with two convolutional encoders  $E_{C}$  and  $E_{S}$ , then decode the features back into images  $c_{rec}$  and  $s_{rec}$  with two convolutional decoders  $D_{C}$  and  $D_{S}$ , respec
+
+![](images/ac25ffe5b4ab261433e08b77ad601a9d322b24f4884808a2e54416059d33fcfb.jpg)  
+(a) Training Stage-1: learning the auto-encoders
+
+![](images/ac2d2a1f0fbd65a1b319b91a45858f1b3a822d9d1adb4ced8ebae617da6563fd.jpg)  
+(b) Training Stage-2: learning the SGA modules
+
+![](images/d1280cbf44fcdffee8a747dc2454d6a529fe42a215bd417e1ad5cf3bb1376029.jpg)  
+(c) Inference Stage
+
+tively as
+
+$$
+c _ {r e c} = D _ {C} \left(E _ {C} (c)\right), \quad s _ {r e c} = D _ {S} \left(E _ {S} (s)\right). \tag {1}
+$$
+
+This is distinct from the general neural style transfer methods, which use the VGG [48] or ResNet [18] network pretrained on natural image datasets (e.g., ImageNet [7]) as the image encoder to extract features of both content and style images. To optimize encoder  $E_{C}$  and decoder  $D_{C}$ , the reconstruction loss is
+
+$$
+\mathcal {L} _ {A E} \left(E _ {C}, D _ {C}\right) = \left| \left| c _ {r e c} - c \right| \right| + \mathcal {L} _ {a d v} \left(E _ {C}, D _ {C}, \mathbb {D} _ {C}\right), \tag {2}
+$$
+
+where  $\mathcal{L}_{adv}$  is the adversarial training loss and  $\mathbb{D}_C$  is the corresponding discriminator network,
+
+$$
+\mathcal {L} _ {a d v} \left(E _ {C}, D _ {C}, \mathbb {D} _ {C}\right) = \log \mathbb {D} _ {C} (c) + \log \left(1 - \mathbb {D} _ {C} \left(c _ {r e c}\right)\right). \tag {3}
+$$
+
+$E_{S}$  and  $D_{S}$  are also optimized by the reconstruction loss  $\mathcal{L}_{AE}(E_S,D_S)$  as formulated in Eq. 2.
+
+Next, we build two codebooks  $\mathcal{Z}_{photo},\mathcal{Z}_{art}\in \mathbb{R}^{N\times d}$  to model the distributions of the photo dataset and artwork dataset, where  $N$  is the number of entries in the codebook and  $d$  is the dimension of each entry. To enable a better representation performance of the quantized features, we use two extra encoders to extract the features, respectively as
+
+$$
+z _ {c} = \hat {E} _ {C} (c), \quad z _ {s} = \hat {E} _ {S} (s). \tag {4}
+$$
+
+We then apply vector quantization [52] to the latent features to get the quantized features  $\hat{z}_c$  and  $\hat{z}_s$ , where the vector quantization operator  $Q_{\mathcal{Z}}(z)$  is formulated as
+
+$$
+Q _ {\mathcal {Z}} (z) := \underset {\mathbf {z} _ {k} \in \mathcal {Z}} {\arg \min } \| z - \mathbf {z} _ {k} \|, \tag {5}
+$$
+
+![](images/cb46f7ecfb30c4d4905d235429f0f9382bea836832666ccdfbecf1fcbed1de7e.jpg)  
+Figure 3. The training and inference pipelines of QuantArt. (a) The first training stage, where we learn the auto-encoders and codebooks for photo and artwork images, respectively.  $\mathbb{Q}$  denotes the vector quantization operator in Eq. 5. (b) The second training stage, where we learn the SGA-based style transfer modules. The dashed lines denote the parameters of encoders and the codebooks are frozen in this stage. (c) In the inference phase, one can trade off the content, style and visual fidelities by simply adjusting the parameters  $\alpha$ ,  $\beta \in [0,1]$ .  
+Figure 4. The vector quantization operator  $Q_{\mathcal{Z}}(z)$  in Eq. 5.
+
+where  $\mathbf{z}_k$  is the  $k$ -th entry in the codebook  $\mathcal{Z}$ . As illustrated in Fig. 4,  $z$  is replaced with the nearest neighbour entry in the codebook  $\mathcal{Z}$  via  $Q_{\mathcal{Z}}(z)$ . The quantized features  $\hat{z}_c$  and  $\hat{z}_s$  are collected from codebooks  $\mathcal{Z}_{photo}$  and  $\mathcal{Z}_{art}$  as
+
+$$
+\hat {z} _ {c} = Q _ {\mathcal {Z} _ {\text {p h o t o}}} \left(z _ {c}\right), \quad \hat {z} _ {s} = Q _ {\mathcal {Z} _ {\text {a r t}}} \left(z _ {s}\right), \tag {6}
+$$
+
+The quantized features  $\hat{z}_c$  and  $\hat{z}_s$  are decoded into images  $\hat{c}_{rec}$  and  $\hat{s}_{rec}$  via the decoders  $\hat{D}_C$  and  $\hat{D}_S$ , as
+
+$$
+\hat {c} _ {r e c} = \hat {D} _ {C} (\hat {z} _ {c}), \quad \hat {s} _ {r e c} = \hat {D} _ {S} (\hat {z} _ {s}). \tag {7}
+$$
+
+By following [52], we optimize the codebook  $\mathcal{Z}_{\text{photo}}$  jointly with the reconstruction loss in Eq. 2. The reconstruction loss for encoder  $\hat{E}_C$ , decoder  $\hat{D}_C$ , and codebook  $\mathcal{Z}_{\text{photo}}$  is
+
+$$
+\mathcal {L} _ {\hat {A E}} \left(\hat {E} _ {C}, \hat {D} _ {C}, \mathcal {Z} _ {\text {p h o t o}}\right) = \mathcal {L} _ {A E} \left(\hat {E} _ {C}, \hat {D} _ {C}\right) + \tag {8}
+$$
+
+$$
+\left. \left| \left| \left| \mathbf {s g} \left[ z _ {c} \right] - \hat {z} _ {c} \right| \right| \right| + \left| \left| \mathbf {s g} \left[ \hat {z} _ {c} \right] - z _ {c} \right| \right| \right|,
+$$
+
+where  $\mathfrak{sg}[\cdot ]$  indicates the stop gradient operator. The second term in Eq. 8 optimizes the codebook  $\mathcal{Z}_{photo}$ , while, the third term in Eq. 8 forces the latent feature  $z_{c}$  to be close to the nearest neighbor entry in  $\mathcal{Z}_{photo}$ .  $\hat{E}_S$ ,  $\hat{D}_S$ , and  $\mathcal{Z}_{art}$  are
+
+![](images/160f7f6d0f3d8ada59a5ab01001c878a8323a7adfe37719c6c6e5c63c755a993.jpg)  
+Figure 5. The SGA module proposed for feature style transfer.
+
+also optimized by the loss function  $\mathcal{L}_{\hat{A}E}(\hat{E}_S, \hat{D}_S, \mathcal{Z}_{art})$  as formulated in Eq. 8.
+
+After training the Stage-1 models, we can compute the continuous features and quantized features for the content and style images. In the following Section 4.3, we discuss how to perform feature-level style transfer based on the extracted features.
+
+# 4.3. Style Transfer with Style Guided Attention
+
+To perform effective style transfer for both the continuous and quantized features, we propose a feature-level style transfer module dubbed style-guided attention (SGA). Fig. 5 shows an illustration of the SGA module. The module takes the content feature  $z_{c} \in \mathbb{R}^{d}$  and style reference feature  $z_{s} \in \mathbb{R}^{d}$  as inputs, then outputs the stylized feature vector  $z_{y} \in \mathbb{R}^{d}$ . It consists of three blocks including a ResBlock used in ResNet-18 [18] and two attention blocks [53] each with a residual connection. The attention block accepts the query  $q$ , key  $k$ , and value  $v$  as inputs,
+
+$$
+\operatorname {A t t n} (q, k, v) = \operatorname {s o f t m a x} \left(f _ {q} (q) f _ {k} (k)\right) f _ {v} (v) + q, \tag {9}
+$$
+
+where  $f_{q}, f_{k}, f_{v}$  are the embedding layers. The first attention block is a self-attention block that all its input heads  $q, k, v$  accept the transformed content feature  $\tilde{z}_{c} = \mathrm{ResBlock}(z_{c})$ . The second attention block takes  $\tilde{z}_{c}$  as  $q$ , and the style reference feature  $z_{s}$  as  $k$  and  $v$ . The output of the SGA module is formulated as
+
+$$
+z _ {y} = \operatorname {S G A} \left(z _ {c}, z _ {s}\right) = \operatorname {A t t n} \left(\operatorname {A t t n} \left(\tilde {z} _ {c}, \tilde {z} _ {c}, \tilde {z} _ {c}\right), z _ {s}, z _ {s}\right). \tag {10}
+$$
+
+Compared with the existing attention-based style transfer modules [39, 42], our SGA module adopts an additional self-attention block to model the global information of the quantized codes. Our attention block also enables a residual connection between the input and output to better preserve the content details. In practice, we repeat the SGA module for  $M$  times to achieve a better style transfer performance.
+
+The objective function for  $\mathrm{SGA}(z_c, z_s)$  includes the content loss  $\mathcal{L}_{\text {content }}$ , style loss  $\mathcal{L}_{\text {style }}$ , and adversarial training loss  $\mathcal{L}_{\text {featadv }}$
+
+$$
+\mathcal {L} _ {S G A} = \mathcal {L} _ {\text {c o n t e n t}} + \mathcal {L} _ {\text {s t y l e}} + \mathcal {L} _ {\text {f e a t a d v}} \tag {11}
+$$
+
+where
+
+$$
+\mathcal {L} _ {\text {c o n t e n t}} = \left| \left| z _ {y} - z _ {c} \right| \right|, \tag {12}
+$$
+
+$$
+\mathcal {L} _ {\text {s t y l e}} = \left| \left| \mu \left(z _ {y}\right) - \mu \left(z _ {s}\right) \right| \right| + \left| \left| \sigma \left(z _ {y}\right) - \sigma \left(z _ {s}\right) \right| \right|, \tag {13}
+$$
+
+$$
+\mathcal {L} _ {\text {f e a t a d v}} = \log \mathbb {D} _ {S G A} \left(z _ {s}\right) + \log \left(1 - \mathbb {D} _ {S G A} \left(z _ {y}\right)\right). \tag {14}
+$$
+
+$\mu (\cdot)$  and  $\sigma (\cdot)$  denote the channel-wise mean and standard deviation of feature maps, respectively. Note that since the encoders and decoders are not optimized in Stage-2, the content and style losses can be directly computed on the features without using an extra pre-trained network to extract features [13, 26, 28]. The adversarial loss  $\mathcal{L}_{featadv}$  is also computed on the features, and it forces the SGA output to be more close to the distribution of style reference features.
+
+We adopt another SGA module to transfer the quantized features  $\hat{z}_c$  and  $\hat{z}_s$ , as
+
+$$
+\hat {z} _ {y} = Q _ {\mathcal {Z} _ {a r t}} \left(\mathrm {S} \hat {\mathrm {G A}} \left(\hat {z} _ {c}, \hat {z} _ {s}\right)\right). \tag {15}
+$$
+
+$\hat{\mathrm{SGA}} (\cdot ,\cdot)$  and  $\mathrm{SGA}(\cdot ,\cdot)$  have the same network architecture but different parameters. The output of the SGA module is further quantized by the art codebook  $Q_{\mathcal{Z}_{art}}$  to ensure that the output is on the latent space of the decoder  $\hat{D}_S$ . The optimization objective of SGA follows Eq. 11 with an additional codebook loss, as
+
+$$
+\mathcal {L} _ {S \hat {G} A} = \mathcal {L} _ {S G A} + | | \operatorname {s g} [ \hat {z} _ {y} ] - z _ {y} ] | | \tag {16}
+$$
+
+# 4.4. Inference
+
+Fig. 3(c) illustrates the inference procedure of QuantArt framework. We first extract the continuous and quantized features of input photo and artwork images using the corresponding encoders. Then, the features are transformed to the stylized continuous feature  $z_{y}$  and stylized quantized feature  $\hat{z}_{y}$  by using the corresponding SGA modules. To trade off between the content, style reference, and visual fidelity, we have
+
+$$
+z _ {t e s t} = \oplus_ {\alpha} \left(\oplus_ {\beta} \left(\hat {z} _ {y}, \hat {z} _ {c}\right), \oplus_ {\beta} \left(z _ {y}, z _ {c}\right)\right), \tag {17}
+$$
+
+where  $z_{c}$  and  $\hat{z}_{c}$  are the content features, and  $\oplus$  is the weighted sum operator as  $\oplus_{p}(a,b) = pa + (1 - p)b$ .  $z_{test}$  is decoded into a stylized image with a fused decoder  $\bar{D}_S = \oplus_\alpha (\hat{D}_S, D_S)$ .  $\beta$  controls the style fidelity, and a larger  $\alpha$  results in higher visual fidelity. In practice, a good trade-off of the fidelity terms depends on both the input images and individual users' preferences. QuantArt  $(\alpha, \beta)$  provides a simple and easy-to-understand handle grip for users to adjust the style transfer results.
+
+Extension to more style transfer tasks. In Section 4.3, we take the artistic image style transfer task as an example to discuss the learning of SGA modules. In addition to artistic style transfer, QuantArt can be applied to other image style transfer tasks such as artwork-to-artwork style transfer and photorealistic style transfer, via training the SGA modules on the basis of the learned auto-encoders and codebooks discussed in Section 4.2.
+
+# 5. Experiments
+
+# 5.1. Experiment Settings
+
+Dataset. For photo-artwork, photo-photo, and artwork-artwork style transfer tasks, we use the MS-COCO [38] as the photo dataset and the WikiArt [41] as the artwork dataset, by following the existing artistic/photorealistic style transfer methods [1, 26, 36, 39]. For face-to-artwork style transfer, we use the FFHQ [30] as the photo dataset and the MetFaces [29] as the artwork dataset. For artwork-to-photo transfer, we let the 12k images with the "genre" tag of "landscape" in the WikiArt [41] be the artwork dataset, and the LandscapesHQ [49] be the photo dataset, to ensure a semantic alignment between artistic and realistic domains [50]. All input images are resized to  $256 \times 256$  pixels.
+
+Network architecture and training. The encoder/decoder of QuantArt consists of four blocks, where each block contains two ResBlocks [18] and a downsampling/upsampling layer. The intermediate feature has a spatial size of  $16 \times 16$  and a feature dimension of 256. The codebook has  $N = 1024$  entries and an entry dimension of  $d = 256$ . The style transfer model consists of six SGA modules. We implement QuantArt on the PyTorch framework [43]. For both two training stages, we use an Adam optimizer [31] with a batch size of 32, a learning rate of  $4.5 \times 10^{-6}$ , and a training epoch of 50. The loss weights of  $\mathcal{L}_{AE}$ ,  $\mathcal{L}_{codebook}$ ,  $\mathcal{L}_{content}$ ,  $\mathcal{L}_{style}$ , and  $\mathcal{L}_{adv}$  are set to 1, 1, 1, 10, and 0.8, respectively.
+
+# 5.2. Multi-Fidelity Image Style Transfer
+
+Our QuantArt  $(\alpha, \beta)$  method produces diverse stylization results to meet the preferences of content, style, and visual fidelities for different users. Taking the Photo-to-Artwork style transfer task as an example, Fig. 6 shows a trilinear interpolation of the three fidelity terms by uniformly sampling parameter combinations  $(\alpha, \beta)$ . When the style fidelity  $\beta = 0$ , the model simply reconstructs the input content image. With  $\beta = 1$  and visual fidelity  $\alpha \rightarrow 1$ , the generated images look more vivid but lose some texture details in the style reference. Note that neither  $\alpha = 0$  or  $\alpha = 1$  performs the best for this example, revealing the necessity of flexibly adjusting the fidelity terms in practical application.
+
+# 5.3. Comparing with State-of-the-Art Methods
+
+For a comprehensive evaluation, we qualitatively and quantitatively compare our QuantArt framework with the state-of-the-art algorithms on tasks including artistic style transfer (i.e., Photo-to-Artwork, Artwork-to-Artwork) and photo-realistic style transfer (i.e., Photo-to-Photo).
+
+Methods for comparison. For artistic style transfer, we compare three lines of methods: 1) The feature statistics-based methods, including AdaIN [26], WCT [35], LinearWCT [33], DSTN [23], ArtFlow [1], EFDM [64], and CAST [65]; 2) The patch swapping methods, includ
+
+![](images/0ea38468e5bfb276d569aad85470814cc8b043d7aaccf68370804f3491193cb7.jpg)  
+Figure 6. QuantArt achieves smooth interpolation among content, style, and visual fidelities by adjusting the parameters  $\alpha$  and  $\beta$ .
+
+ing StyleSwap [6] and AvatarNet [47]; 3) The attention-based methods, including SANet [42], AdaAttn [39], and StyTR2 [8]. For photorealistic style transfer, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and DSTN [23].
+
+Qualitative results. As shown in Fig. 7, on all three tasks, QuantArt with  $\alpha = 0$  faithfully transfers the texture from input style images, while QuantArt with  $\alpha = 1$  paints realistic textures thanks to the learned style codebook. For the Photo-to-Photo example, the content image does not have clearly visible textures, and it is challenging for other methods to hallucinate texture details when the scene in the style reference is lit up.
+
+Quantitative results. We further quantitatively compare the performances of the state-of-the-art methods on the Photo-to-Artwork task. We randomly sample 10K images from the MS-COCO [38] and WikiArt [41] datasets, respectively, forming a total of 10K pairs of evaluation images. We use the LPIPS loss [62] to measure the content fidelity between the content and generated images. We use the style loss with a pretrained VGG-19 network [8, 26] to measure the style fidelity between the style and generated images. We compute the FID metric [21] between the style dataset and all the generated images to measure the visual fidelity of algorithms. We also adopt a recently proposed metric ArtFID = (1 + LPIPS) · (1 + FID) [56] to evaluate the overall stylization performance. For a fair comparison, we compare our methods QuantArt(0,1) and QuantArt(1,1) with the previous methods. QuantArt(0,0) serves as a baseline to show the image reconstruction performance. As shown in Table 1, both our methods QuantArt(0,1) and QuantArt(1,1) achieve competitive performances compared with the baseline methods on all metrics. Specifically, QuantArt(1,1) performs better than other methods for FID and ArtFID, indicating that it can significantly enhance the visual fidelity
+
+![](images/e964907757c64c85ee7a27697627f8715b94151b611710cbc5ad040647f0e637.jpg)  
+Figure 7. Comparisons of the state-of-the-art methods for artistic image style transfer, i.e., Photo-to-Artwork and Artwork-to-Artwork, and photorealistic image style transfer, i.e., Photo-to-Photo. Zoom in to view the details.
+
+Table 1. Quantitative comparison of the universal style transfer methods. The best and second best results are highlighted, respectively.  
+
+<table><tr><td rowspan="2">Metric ↓</td><td rowspan="2">AdaIN</td><td rowspan="2">WCT</td><td rowspan="2">LinearWCT</td><td rowspan="2">ArtFlow</td><td rowspan="2">EFDM</td><td rowspan="2">StyleSwap</td><td rowspan="2">AvatarNet</td><td rowspan="2">SANet</td><td rowspan="2">AdaAttN</td><td rowspan="2">StyTR2</td><td colspan="3">Ours (α,β)</td></tr><tr><td>(0,0)</td><td>(0,1)</td><td>(1,1)</td></tr><tr><td>LPIPS ↓</td><td>0.681</td><td>0.695</td><td>0.657</td><td>0.603</td><td>0.652</td><td>0.607</td><td>0.706</td><td>0.686</td><td>0.633</td><td>0.514</td><td>0.159</td><td>0.565</td><td>0.581</td></tr><tr><td>Gram loss (×103) ↓</td><td>0.163</td><td>0.282</td><td>0.172</td><td>0.101</td><td>0.402</td><td>1.357</td><td>0.718</td><td>0.120</td><td>0.246</td><td>0.386</td><td>-</td><td>0.395</td><td>0.864</td></tr><tr><td>FID ↓</td><td>36.618</td><td>65.193</td><td>48.156</td><td>28.899</td><td>51.070</td><td>74.168</td><td>58.178</td><td>27.080</td><td>25.894</td><td>30.893</td><td>-</td><td>25.590</td><td>17.787</td></tr><tr><td>ArtFID ↓</td><td>63.240</td><td>112.229</td><td>81.452</td><td>47.936</td><td>86.007</td><td>120.803</td><td>100.964</td><td>47.356</td><td>43.910</td><td>48.284</td><td>-</td><td>41.623</td><td>29.695</td></tr></table>
+
+Table 2. Inference time (seconds) of a  ${256} \times  {256}$  image with a NVIDIA Tesla V100 GPU.  
+
+<table><tr><td>ArtFlow</td><td>StyleSwap</td><td>AvatarNet</td><td>SANet</td><td>AdaAttN</td><td>StyTR2</td><td>Ours</td></tr><tr><td>0.068</td><td>0.043</td><td>0.124</td><td>0.007</td><td>0.050</td><td>0.055</td><td>0.045</td></tr></table>
+
+of style transfer results. QuantArt(0,1) performs better than QuantArt(1,1) on the Gram loss, empirically demonstrating the trade-off between style and visual fidelities. In Table 2, the inference time of our method is comparable with most of the benchmark universal style transfer methods.
+
+# 5.4. Human Evaluation
+
+Since image style transfer is a highly subjective task, we further examine our model with human evaluation.
+
+User study on method performance. We perform a user study to subjectively evaluate the performance of different methods on three image style transfer tasks. On Photo-to-Artwork and Artwork-to-Artwork, we compare
+
+AvatarNet [47], ArtFlow [1], StyTr2 [8], and our QuantArt(1,1). On Photo-to-Photo, we compare PhotoWCT [36], WCT² [60], LinearWCT [33], and QuantArt(1,1). In each example, we show the input image, style reference, and style transfer results of the four comparison methods. The user study participants are asked to select one of the four stylizations to their preference. We show 12 examples to every participant, where each style transfer task has 4 examples. We have collected effective responses from a total of 59 participants. As shown in Fig. 8, our method significantly outperforms the prior arts on all three tasks with an average preference ratio of  $43.5\%$ ,  $51.9\%$ , and  $40.2\%$ , respectively. The results also indicate that the visual fidelity is an important evaluation metrics for human to assess the style transfer algorithms.
+
+Confusion test on visual fidelity. We further perform a novel user study, dubbed artistic style transfer confusion
+
+![](images/5ea829693dccf9eccfff22df3be7907edaa320f041d58d5fefd289eb61864477.jpg)  
+Figure 8. User study results on three image style transfer tasks. We show the percentages of methods preferred by the participants.
+
+![](images/ec0c8b7c38d60a90feb3b500c505578a52640aecf1be85c0ed716e51f816b71f.jpg)  
+Figure 9. (Left) An example of our Artistic Style Transfer Confusion Test. Only  $40.6\%$  participants successfully distinguished the real artwork in this example. The answer can be found in our supplementary material. (Right) The statistical results with a total of 61 participants, where each participant is asked 20 questions.
+
+![](images/613c40009b5f91ef1043a14331813d61d890f57bce3b95c76aa289865b6bab3d.jpg)
+
+test, to subjectively evaluate the visual fidelity of the stylized images. The left part of Fig. 9 shows an example question of the test. Within each question of the test, we ask the participant to select the real artwork from a pair of  $i$  a real artwork image  $s$  and  $ii$  a photo stylized according to the reference of  $s$ . The test is more challenging compared with the previous tests designed for image style transfer [65], since the fake image should follow the artistic style of the paired real image. We generate a total of 50 images using QuantArt(1,1). The content images are randomly selected from the FFHQ [30], LandscapeHQ [49], or MS-COCO [38] dataset. The style images are randomly selected from the WikiArt [41] or MetFaces [29] dataset. To avoid image contents that would lead to unfair comparison, such as the hairstyles of middle ages in the reference image or the modern articles in the content image, we manually filter 36 examples from the 50 examples. Each participant is requested to answer 20 questions, where they can choose either one of the two presented images, or skip the question if she/he feels difficult to make a choice. We have collected effective responses from 61 participants.
+
+We plot the histogram of participants over the number of correct selections in the right part of Fig. 9. The distribution of the participants roughly follow the normal distribution with the mean number of correct selections 10.31, close to the random guess result (10). It indicates that our method can generate highly realistic artistic images which are difficult for human to identify from the real ones. More examples of this artistic confusion test can be found in the supplementary material.
+
+Table 3. An ablation study of the design choices of QuantArt.  
+
+<table><tr><td rowspan="2">Complete model, α = 1, code size 16×16</td><td>LPIPS ↓</td><td>Gram ↓</td><td>FID ↓</td></tr><tr><td>0.581</td><td>0.864</td><td>17.787</td></tr><tr><td>Remove Quantization in SGA</td><td>0.545</td><td>0.993</td><td>18.757</td></tr><tr><td>Remove all Quantizations (i.e., α = 0)</td><td>0.565</td><td>0.395</td><td>25.590</td></tr><tr><td>Code size 8×8</td><td>0.656</td><td>1.078</td><td>27.741</td></tr><tr><td>Code size 32×32</td><td>0.513</td><td>0.798</td><td>28.663</td></tr><tr><td>Remove self-attention in SGA</td><td>0.584</td><td>0.883</td><td>19.025</td></tr><tr><td>Remove ResBlock in SGA</td><td>0.608</td><td>1.841</td><td>27.177</td></tr><tr><td>Replace SGA with StyTR2 decoder layer [8]</td><td>0.539</td><td>0.875</td><td>26.299</td></tr><tr><td>Shared encoders</td><td>0.588</td><td>0.788</td><td>30.806</td></tr><tr><td>Shared encoders and decoders</td><td>0.593</td><td>0.891</td><td>35.830</td></tr></table>
+
+# 5.5. Ablation Study
+
+As shown in Table 3, we conduct the following ablation studies to justify the design choices of the proposed framework. 1) The effectiveness of vector quantization. By removing the quantization operators in SGA or removing all the quantization operators, the Gram loss decreases while the FID increases. It is aligned with our motivation that vector quantization trades-off the style fidelity with visual fidelity. 2) Code patch size. Each code in QuantArt corresponds to a  $16 \times 16$  patch of the feature maps. Either increasing or decreasing the results in an increase of FID, indicating that the code size of  $16 \times 16$  is a good choice for image style transfer. 3) Components in SGA. Removing either the self-attention or ResBlock in SGA results in a worse FID. Removing the ResBlock additionally results in a significant increase of Gram loss. Replacing SGA with the decoder layer of StyTR2 [8] leads to a worse FID. 4) Shared auto-encoders. QuantArt adopts separate auto-encoders to extract the continuous and quantized feature representations, respectively (see Fig. 3). The FID drastically increases when we share the encoders or auto-encoders for continuous and quantized representations. Therefore, in this work we use separate auto-encoders for feature extraction.
+
+# 6. Conclusion
+
+In this paper, we study the problem of enhancing the visual fidelity of image style transfer. We have proposed a quantizing style transfer algorithm to make the latent feature of the generated artwork closer to the real distribution. However, the algorithm may result in a generation that displays fewer style details of the reference image. To address this limitation, we have further presented a style transfer framework called QuantArt, which consists of a continuous branch and a quantized branch, to allow users to arbitrarily control the content preservation, style similarity, and visual fidelity of generated artworks. The experiments on Photo-to-Artwork, Artwork-to-Artwork, and Photo-to-Photo transfer settings have shown that our method achieves higher visual fidelity along with comparable content and style fidelities compared with the state-of-the-art methods.
+
+Acknowledgements. This work was supported by NIH grant 5U54CA225088-03. The computations in this paper were run on the FASRC Cannon cluster supported by Harvard.
+
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+        "type": "text",
+        "text": "Taehyeong  $\\mathrm{Kim}^{3\\dagger}$",
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+    {
+        "type": "text",
+        "text": "Chul Lee",
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+    {
+        "type": "text",
+        "text": "Jin young Choi",
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+    {
+        "type": "text",
+        "text": "$^{1}$ AI Lab, CTO Division, LG Electronics, South Korea",
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+    {
+        "type": "text",
+        "text": "$^{2}$ ASRI, Dept. of Electrical and Computer Engineering, Seoul National University, South Korea",
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+    {
+        "type": "text",
+        "text": "$^{3}$ Dept. of Biosystems Engineering, Seoul National University, South Korea",
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+    {
+        "type": "text",
+        "text": "{hoseok.do, eunkyung.ryu, clee.lee}  $@$  lge.com, {hoseok03, taehyeong.kim, jychoi}  $@$  snu.ac.kr",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "While 3D-based GAN techniques have been successfully applied to render photo-realistic 3D images with a variety of attributes while preserving view consistency, there has been little research on how to fine-control 3D images without limiting to a specific category of objects of their properties. To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24,",
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/4f1e089957a4f5afcd2ebab912a669f305db80ccb8a17b9b534093268daeac94.jpg",
+        "image_caption": [
+            "Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention.",
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+    },
+    {
+        "type": "text",
+        "text": "Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "†Work done during at LG Electronics",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "8529",
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+    },
+    {
+        "type": "text",
+        "text": "tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective.",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Latent Space Image Manipulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. 3D Object Manipulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM).",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3. Efficient Geometry-Aware 3D GANs (EG3D)",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature  $z$  into intermediate latent feature  $w$ , then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature  $w$ . Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature  $w_{s}$ , which is obtained from a source image  $I_{s}$ , is manipulated to target latent feature  $w_{t}$ . Then, from  $w_{t}$ , EG3D generates the viewpoint-wise target image  $I_{t}^{n}$  whose quantity vector is estimated by  $\\hat{Q}_t^n$ . For multi-view consistency, the quantifier is trained so that every  $\\hat{Q}_t^n$  follows the target quantity vector  $Q_{t}$  and the variance of  $\\hat{Q}_t^n$  is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature  $w_{s}$  to the target  $w_{t}$",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "8530",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/b24e269e9ea4abf3566d9de1f36de188c122501d211e89cd3e9aba054a0ca214.jpg",
+        "image_caption": [
+            "Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "in the latent space, referring to  $Q_{t}$  and the estimated source quantity vector  $\\hat{Q}_s$ . For training the navigator, the estimated attribute quantity vector  $\\hat{Q}_t$  is defined by the average of  $\\hat{Q}_t^n$  over  $n$ , which is used to form a loss (i.e., the squared error between  $Q_{t}$  and  $\\hat{Q}_t$  for accurate manipulation), while preserving the identity of  $I_{s}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1.Custom Attribute Quantifier",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity  $q$  of the custom attribute from the image  $x$ . We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset  $\\mathcal{D}_a$ , and the consistency dataset  $\\mathcal{D}_c$ . The former is used to train user-defined attributes, and the latter is used to train multi-view consistency.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Attribute Dataset Custom attributes are specified with a small amount of labeled dataset  $\\mathcal{D}_a$  provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset  $\\mathcal{D}_a = \\{x_a,q_a\\}$  with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in  $\\mathcal{D}_a$ , we first equally divide the quantity range of [0, 1] into  $M$  groups and divide the dataset  $\\mathcal{D}_a$  into  $M$  groups in the order of attribute change. Each group comprises  $\\Omega_{a}$  images. Then, the quantity label  $q_{a}$  for each image in the  $m$ -th group  $G_{m}$  in  $\\mathcal{D}_a$  is assigned to the value of  $\\frac{m - 1}{M - 1}$ . To mitigate the lack of samples in  $\\mathcal{D}_a$ , synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in  $G_{m}$  with that in  $G_{m + 1}$  using Cutmix of the combination ratio  $\\gamma$ , the quantity label  $q_{a}$  is assigned to  $\\frac{m - \\gamma}{M - 1}$ . Since  $\\gamma$  is sampled from the uniform distribution [0, 1], the dense",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "quantity labels are sufficient to train the quantifier for regression, yielding any quantity in  $[0,1]$ . Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Consistency Dataset We construct the consistency dataset  $\\mathcal{D}_c = \\{x_c\\}$  using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset  $\\mathcal{D}_c$  is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature  $w$ , we generate  $V$  images  $\\{x_c^1, x_c^2, \\dots, x_c^V\\}$  using different  $V$  camera viewpoints. Finally, the consistency dataset  $\\mathcal{D}_c$  is constructed using  $\\Omega_c$  random latent features, so it consists of multi-view images of  $\\Omega_c$  different objects.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated  $\\hat{q}_a$  and label  $q_{a}$  for an input sample  $x_{a}$  in  $\\mathcal{D}_a$ . The second term is the variance for the estimated  $\\hat{q}_c$  vector for  $V$  multiview images for a single object in the consistency dataset, where  $\\hat{q}_c^v$  is the estimated quantity of  $x_c^v$  in  $\\mathcal{D}_c$ . Quantifier training loss  $\\mathcal{L}_q$  is given by",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {q} = \\sum_ {x _ {a} \\in \\mathcal {D} _ {a}} \\left(q _ {a} - \\hat {q} _ {a}\\right) ^ {2} + \\lambda_ {c} \\sum_ {v = 1} ^ {V} \\sum_ {x _ {c} ^ {v} \\in \\mathcal {D} _ {c}} \\left(\\hat {q} _ {c} ^ {v} - \\bar {\\hat {q}} _ {c} ^ {v}\\right) ^ {2}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{\\hat{q}}_c^v$  is the mean of  $\\hat{q}_c^v$  over all  $v$ , and  $\\lambda_c$  is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of  $M$  images sampled, one from each group in  $\\mathcal{D}_a$ , and  $M$  objects sampled from  $\\mathcal{D}_c$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "8531",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For  $K$  attributes estimation,  $K$  quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar  $q^{(k)}$  from the  $k$ -th quantifier is concatenated to create  $K$ -dimensional quantity vector  $Q = [q^{(1)}, q^{(2)}, \\dots, q^{(K)}]$ . A quantity vector can be designed by a combination of various quantifiers, depending on an application.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Multi-Attribute Navigator",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space  $\\mathcal{W}+$ , where the source feature  $w_{s}$  is changed into the target feature  $w_{t}$  with the guidance of  $\\hat{Q}_s$  and  $Q_{t}$ . We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature  $f_{Q}$ . Second, layer-wise attention controller (LAC) estimates which layer among the  $L$  layer-wise mappers (LWMs) to attend each attribute manipulation.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "AFR converts  $\\hat{Q}_s$  and  $Q_{t}$  to a 512-dimensional attribute quantity feature  $f_{Q}$ . First,  $\\hat{Q}_s$  and  $Q_{t}$  are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature  $f_{Q}$ . The input vector with 1024 dimensions is generated by concatenating  $w_{s}$  and  $f_{Q}$ , and then, the input vector is fed to each LWM. From the input vector,  $l$ -th LWM generates  $w_{\\Delta}^{l}$ , which represents the movement on the latent space for  $l$ -th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "LAC outputs the layer-wise attention vector  $a = [a_1, a_2, \\dots, a_L]$  from attribute quantity feature  $f_{Q}$ . And the target latent feature  $w_{t}$  is generated as follows:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\\Delta} ^ {l}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw _ {t} = \\left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \\dots , w _ {t} ^ {L} \\right]. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of  $[0,1]$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Loss and Training The navigator is trained such that  $\\hat{Q}_t$  follows  $Q_t$ , while the identity between  $I_s$  and  $I_t$  is preserved. To this end, we randomly generate  $Q_t$  during the",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select  $J$  attributes to train out of a total of  $K$  attributes at every training iteration. That is, training attribute set  $\\mathcal{T}$  is generated as follows:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {T} = \\left\\{\\tau_ {1}, \\tau_ {2}, \\dots , \\tau_ {J} \\right\\} \\subset \\{1, 2, \\dots , K \\}. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Then,  $Q_{t}$  is generated by replacing  $J$  elements of  $\\hat{Q}_{s}$  with  $J$  random target values  $(q_{t})$ . To ensure that the navigator performs well within the entire range of [0, 1], we use  $q_{t}$  randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For view consistency in manipulation, we generate multi-view target images from  $w_{t}$ . Using  $N$  random camera viewpoint  $p_t^n$ ,  $N$  multi-view images  $I_{t}^{n}$  are generated. And target quantity vector  $\\hat{Q}_t^n$  is calculated from  $I_{t}^{n}$ , then  $\\hat{Q}_t$  is calculated as the average of  $\\hat{Q}_t^n$  vectors.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With the random target attribute quantity  $Q_{t}$  and random source latent  $w_{s}$ , we train the navigator by minimizing the losses, which can be grouped into three main subsets:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {n} = \\mathcal {L} _ {Q} \\left(Q _ {t}, \\hat {Q} _ {t}\\right) + \\mathcal {L} _ {i d} \\left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\\right) + \\mathcal {L} _ {a} (a). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The quantity loss  $\\mathcal{L}_Q$  guides the navigator to manipulate the image according to the target attribute quantity.  $J$ -dimensional quantity vector  $Q^{\\prime}$  for training attributes set  $\\mathcal{T}$  is generated as follows:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ ^ {\\prime} = \\left[ q ^ {(\\tau_ {1})}, q ^ {(\\tau_ {2})}, \\dots , q ^ {(\\tau_ {J})} \\right]. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "And the quantity loss consists of two MSE terms between quantity vectors as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {Q} = \\left\\| Q _ {t} ^ {\\prime} - \\hat {Q} _ {t} ^ {\\prime} \\right\\| _ {2} ^ {2} + \\lambda_ {q} \\left\\| Q _ {t} - \\hat {Q} _ {t} \\right\\| _ {2} ^ {2}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{q}$  is the hyper-parameter for balancing the loss. In quantity loss, the first term is for  $J$  attributes in  $\\mathcal{T}$  and the second term is for all  $K$  attributes. Because random target quantities are given for  $J$  attributes out of a total of  $K$  attributes,  $K - J$  attributes of  $Q_{t}$  are from  $\\hat{Q}_s$ . Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The identity loss  $\\mathcal{L}_{id}$  is designed by",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {i d} = \\left\\| w _ {t} - w _ {s} \\right\\| _ {2} ^ {2} + \\frac {\\lambda_ {L}}{N} \\sum_ {n = 1} ^ {N} \\operatorname {L P I P S} \\left(I _ {s}, I _ {t} ^ {n}\\right), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{L}$  is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The third term,  $\\mathcal{L}_n$ , is a regularization loss for layer-wise attention as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {a} = | \\alpha - \\bar {a} |, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{a}$  denotes the average of  $a_{l}$  over  $l$ , and  $\\alpha$  is the hyperparameter for the target average value of attention.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "8532",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/1bc818af15eef30a32286bc9eb5235e9dd86ade081db26e7aad42c1f4ba9117c.jpg",
+        "image_caption": [
+            "Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Custom Attribute Quantifier For the attribute dataset  $\\mathcal{D}_a$  of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed  $\\mathcal{D}_a$  for each attribute. We constructed each  $\\mathcal{D}_a$  for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each  $\\mathcal{D}_a$  for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed  $\\mathcal{D}_a$ , each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing  $\\mathcal{D}_a$  are provided in the supplement. For the consistency dataset  $\\mathcal{D}_c$ , we used  $V = 10$ ,  $\\Omega_c = 10,000$ . We trained the quantifier for 50 epochs with a batch size of  $M$ . We set",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/341b0542f1919a8cdf8b1f792a347285b30d6eb91d097c1108646a4ff5de9409.jpg",
+        "image_caption": [
+            "Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes.  $(\\dagger =$  custom attributes implemented via manually constructed  $D_{a}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\lambda_{c}$  to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate  $w_{s}$  with truncation factor  $\\phi = 0.7$  during navigator training. We set hyper-parameters  $\\lambda_{q} = 0.5$ ,  $\\lambda_{L} = 0.1$ ,  $\\alpha = 0.5$ , and  $N = 2$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2.Custom Attribute Manipulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity  $q_{t}$  normalized in the range [0,1]. Regardless of the source attribute quantity  $\\hat{q}_{s}$  of the source image  $I_{s}$ , the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When  $q_{t}$  approaches 0, they are both expressionless; when  $q_{t}$  approaches 1, they both smile broadly.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "8533",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/50d956ab4bffc06e87b6ad9701b55a46a8981de876e054d71e9d334b0312a7d1.jpg",
+        "image_caption": [
+            "Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Comparisons",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The resultant image  $I_{\\theta}^{\\phi}$  was manipulated from the source image  $I^{\\phi}$  using the  $\\theta$ -th target value  $(\\phi = 1, \\dots, \\Phi, \\theta =$",
+        "bbox": [
+            75,
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/73b423b5074fcaf092c0a66855729c51355ded3a1a2853e5539dd2c115c0dfa2.jpg",
+        "image_caption": [
+            "Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/3466cac5575d1ee5658ac4d4ed68d65c58f7d97649fba66d58cec73a3f281c35.jpg",
+        "image_caption": [
+            "Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            503,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "$1, \\dots, \\Theta)$ . In addition, we used Face++ [1] to measure  $r_{\\theta}^{\\phi}$  which is the resultant attribute quantity of  $I_{\\theta}^{\\phi}$ .",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "*StyleFlow originally used Microsoft Face API [22] as a quantifier, but Microsoft no longer supports it. Therefore, we used Face++ [1] as a quantifier for StyleFlow implementation on EG3D.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "8534",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4fcf46b25655e84ff5299b8070eaffcec964ddcd7d705009f376bcd6f2f43582.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Age</td><td colspan=\"4\">Smile</td><td colspan=\"2\">Gender</td><td colspan=\"2\">Eyeglasses</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>Acc. ↑</td><td>Ed↓</td><td>Acc. ↑</td><td>Ed↓</td></tr><tr><td>StyleFlow</td><td>8.40</td><td>0.373</td><td>21.3</td><td>2.304</td><td>37.38</td><td>0.382</td><td>29.9</td><td>4.859</td><td>83%</td><td>0.586</td><td>96%</td><td>0.510</td></tr><tr><td>StyleFlow+Q</td><td>10.46</td><td>0.331</td><td>22.1</td><td>2.304</td><td>27.49</td><td>0.320</td><td>34.4</td><td>2.635</td><td>78%</td><td>0.670</td><td>79%</td><td>0.486</td></tr><tr><td>Ours</td><td>8.03</td><td>0.245</td><td>32.6</td><td>2.235</td><td>21.50</td><td>0.210</td><td>51.0</td><td>2.255</td><td>95%</td><td>0.537</td><td>96%</td><td>0.468</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "across multiple manipulated views.",
+        "bbox": [
+            75,
+            252,
+            312,
+            267
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation  $\\sigma_{m,\\theta}$  of the  $\\theta$ -th resultant quantities  $\\{r_\\theta^1,\\dots ,r_\\theta^\\Phi \\}$ , the evaluation metric  $\\sigma_{m}$  is the mean of  $\\sigma_{m,\\theta}$ . Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance  $E_{d}$  between the embeddings of two manipulated images, which were generated using two adjacent target values, as",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nE _ {d} = \\frac {1}{(\\Theta - 1) \\Phi} \\sum_ {\\theta = 1} ^ {\\Theta - 1} \\sum_ {\\phi = 1} ^ {\\Phi} \\| F \\left(I _ {\\theta + 1} ^ {\\phi}\\right) - F \\left(I _ {\\theta} ^ {\\phi}\\right) \\|, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where  $F$  is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio  $\\rho$  between attribute manipulation and identity preservation as  $\\frac{(r_{\\Theta} - r_1)}{(\\Theta - 1)E_d}$ . Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images  $\\{I_\\theta^{\\phi,1}, I_\\theta^{\\phi,2}, I_\\theta^{\\phi,3}\\}$  and measured the resultant attribute quantities  $\\{r_\\theta^{\\phi,1}, r_\\theta^{\\phi,2}, r_\\theta^{\\phi,3}\\}$ . From the standard deviation  $\\sigma_{v,\\theta}^{\\phi}$  of the resultant attribute quantities, the evaluation metric  $\\sigma_v$  is the mean of  $\\sigma_{v,\\theta}^{\\phi}$ .",
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+        "type": "text",
+        "text": "We conducted experiments with  $\\Phi = 100$  and  $\\Theta = 8$ . As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++.",
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+        "type": "text",
+        "text": "Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case).",
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+        "table_caption": [
+            "Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness  $(\\sigma_{m})$ , manipulation accuracy (Acc.), identity preservation  $(E_{d})$ , manipulation efficiency  $(\\rho)$ , and view consistency  $(\\sigma_{v})$ . Our method gives the best results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Age</td><td colspan=\"3\">Smile</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td></tr><tr><td>Talk-to-Edit</td><td>14.3</td><td>0.221</td><td>32.9</td><td>22.6</td><td>0.212</td><td>40.9</td></tr><tr><td>StyleFlow</td><td>16.9</td><td>0.195</td><td>28.4</td><td>29.1</td><td>0.099</td><td>88.9</td></tr><tr><td>Ours</td><td>10.9</td><td>0.225</td><td>47.2</td><td>20.2</td><td>0.103</td><td>96.6</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness  $(\\sigma_{m})$ , identity preservation  $(E_{d})$ , and manipulation efficiency  $(\\rho)$ .",
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+        "img_path": "images/b24c83074bb6cf30e6be56200cd916e06c304a23144a2ed51d4a06396f8be75f.jpg",
+        "image_caption": [
+            "Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength."
+        ],
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+        "type": "text",
+        "text": "Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations.",
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+        "type": "text",
+        "text": "As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness  $\\sigma_{m}$ . In the  $E_{d}$  score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score  $\\rho$ . This result implies that our method better preserves identity when an attribute changes by the same quantity.",
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+        "type": "page_number",
+        "text": "8535",
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+    {
+        "type": "table",
+        "img_path": "images/26ce4651b79af4022ffb8a6f8a817136cffda45cbc391f02c34bb9a421c8d573.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Model</td><td>σm↓</td><td>Acc.↑</td><td>Ed↓</td></tr><tr><td rowspan=\"2\">Design</td><td>w/o LAC module</td><td>15.84</td><td>96.0%</td><td>0.415</td></tr><tr><td>w/o AFR module</td><td>15.37</td><td>89.0%</td><td>0.387</td></tr><tr><td rowspan=\"2\">Training</td><td>w/o entireatts. in LQ</td><td>14.78</td><td>87.5%</td><td>0.405</td></tr><tr><td>w/o intermediate Qt</td><td>15.65</td><td>97.0%</td><td>0.402</td></tr><tr><td></td><td>Full model</td><td>14.76</td><td>95.5%</td><td>0.365</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness  $(\\sigma_{m})$ , accuracy, and identity preservation  $(E_{d})$ .",
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+    {
+        "type": "text",
+        "text": "In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength.",
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+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in  $\\mathcal{L}_Q$ , intermediate target quantity). In the ablation study on the LAC module, we generated  $w_{t}$  by adding  $w_{\\Delta}$  to  $w_{s}$ . In the ablation study on the AFR module, we generated  $f_{Q}$  by concatenating  $\\hat{Q}_{s}$  and  $Q_{t}$ , then repeating it. When entire attributes are not used in  $\\mathcal{L}_Q$ , we trained the navigator with  $\\lambda_q = 0$ . When an intermediate target quantity is not used, we trained the navigator by randomly sampling  $q_{t}$  value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness  $\\sigma_{m}$  from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from  $87.5\\%$  to  $95.5\\%$ . Using intermediate target quantity in navigator training improved the manipulation exactness  $\\sigma_{m}$  from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended.",
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+    {
+        "type": "image",
+        "img_path": "images/bcda9631a4a613ddff274b065263ff8380d2e3c2b2918692c26231ed06e72270.jpg",
+        "image_caption": [
+            "Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation  $\\sigma_v$  (a lower value is better)."
+        ],
+        "image_footnote": [],
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+    },
+    {
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+        "img_path": "images/0053102007f163eb5229b4e49f7c77e4883b10d9358053ef1d7e7459895bfb0f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset  $\\mathcal{D}_c$  by setting  $\\lambda_c = 0$ . In the ablation study on the navigator, we trained the navigator without multi-view images by setting  $N = 1$ . Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of  $[0,1]$ . This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments.",
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+    {
+        "type": "text",
+        "text": "Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement.",
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+    },
+    {
+        "type": "text",
+        "text": "Further discussion of the potential negative social impacts is provided in the supplement.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]",
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+        "type": "page_number",
+        "text": "8536",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+            "[45] Yiyu Zhuang, Hao Zhu, Xusen Sun, and Xun Cao. Mofan-erf: Morphable facial neural radiance field. arXiv preprint arXiv:2112.02308, 2021. 2"
+        ],
+        "bbox": [
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+            892,
+            527
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "8538",
+        "bbox": [
+            482,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 9
+    }
+]

2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_model.json

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+[
+    [
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+                0.131,
+                0.885,
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+            "angle": 0,
+            "content": "Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.11,
+                0.18,
+                0.221,
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+            ],
+            "angle": 0,
+            "content": "Hoseok Do1,2"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.259,
+                0.18,
+                0.391,
+                0.2
+            ],
+            "angle": 0,
+            "content": "EunKyung Yoo"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.43,
+                0.18,
+                0.574,
+                0.2
+            ],
+            "angle": 0,
+            "content": "Taehyeong \\(\\mathrm{Kim}^{3\\dagger}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.605,
+                0.181,
+                0.688,
+                0.198
+            ],
+            "angle": 0,
+            "content": "Chul Lee"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.728,
+                0.181,
+                0.859,
+                0.199
+            ],
+            "angle": 0,
+            "content": "Jin young Choi"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "\\(^{1}\\)AI Lab, CTO Division, LG Electronics, South Korea"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.111,
+                0.224,
+                0.859,
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+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)ASRI, Dept. of Electrical and Computer Engineering, Seoul National University, South Korea"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.242,
+                0.78,
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+            ],
+            "angle": 0,
+            "content": "\\(^{3}\\)Dept. of Biosystems Engineering, Seoul National University, South Korea"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.186,
+                0.262,
+                0.778,
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+            ],
+            "angle": 0,
+            "content": "{hoseok.do, eunkyung.ryu, clee.lee} \\(@\\) lge.com, {hoseok03, taehyeong.kim, jychoi} \\(@\\) snu.ac.kr"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
+                0.312,
+                0.314,
+                0.329
+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.345,
+                0.474,
+                0.572
+            ],
+            "angle": 0,
+            "content": "While 3D-based GAN techniques have been successfully applied to render photo-realistic 3D images with a variety of attributes while preserving view consistency, there has been little research on how to fine-control 3D images without limiting to a specific category of objects of their properties. To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.604,
+                0.21,
+                0.62
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.63,
+                0.47,
+                0.797
+            ],
+            "angle": 0,
+            "content": "Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.798,
+                0.47,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24,"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
+                0.307,
+                0.875,
+                0.518
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.522,
+                0.895,
+                0.606
+            ],
+            "angle": 0,
+            "content": "Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.613,
+                0.893,
+                0.87
+            ],
+            "angle": 0,
+            "content": "26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.894,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.096,
+                0.887,
+                0.296,
+                0.9
+            ],
+            "angle": 0,
+            "content": "†Work done during at LG Electronics"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8529"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.501
+            ],
+            "angle": 0,
+            "content": "tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.51,
+                0.228,
+                0.525
+            ],
+            "angle": 0,
+            "content": "2. Related Works"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.533,
+                0.377,
+                0.55
+            ],
+            "angle": 0,
+            "content": "2.1. Latent Space Image Manipulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.555,
+                0.473,
+                0.844
+            ],
+            "angle": 0,
+            "content": "StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.849,
+                0.303,
+                0.866
+            ],
+            "angle": 0,
+            "content": "2.2. 3D Object Manipulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.871,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.258
+            ],
+            "angle": 0,
+            "content": "new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.258,
+                0.895,
+                0.379
+            ],
+            "angle": 0,
+            "content": "There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.387,
+                0.88,
+                0.403
+            ],
+            "angle": 0,
+            "content": "2.3. Efficient Geometry-Aware 3D GANs (EG3D)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.41,
+                0.895,
+                0.653
+            ],
+            "angle": 0,
+            "content": "EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature \\( z \\) into intermediate latent feature \\( w \\), then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature \\( w \\). Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.665,
+                0.593,
+                0.681
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.69,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature \\( w_{s} \\), which is obtained from a source image \\( I_{s} \\), is manipulated to target latent feature \\( w_{t} \\). Then, from \\( w_{t} \\), EG3D generates the viewpoint-wise target image \\( I_{t}^{n} \\) whose quantity vector is estimated by \\( \\hat{Q}_t^n \\). For multi-view consistency, the quantifier is trained so that every \\( \\hat{Q}_t^n \\) follows the target quantity vector \\( Q_{t} \\) and the variance of \\( \\hat{Q}_t^n \\) is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature \\( w_{s} \\) to the target \\( w_{t} \\)"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8530"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.891,
+                0.299
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.307,
+                0.893,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.374,
+                0.47,
+                0.466
+            ],
+            "angle": 0,
+            "content": "in the latent space, referring to \\( Q_{t} \\) and the estimated source quantity vector \\( \\hat{Q}_s \\). For training the navigator, the estimated attribute quantity vector \\( \\hat{Q}_t \\) is defined by the average of \\( \\hat{Q}_t^n \\) over \\( n \\), which is used to form a loss (i.e., the squared error between \\( Q_{t} \\) and \\( \\hat{Q}_t \\) for accurate manipulation), while preserving the identity of \\( I_{s} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.475,
+                0.334,
+                0.491
+            ],
+            "angle": 0,
+            "content": "3.1.Custom Attribute Quantifier"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.499,
+                0.471,
+                0.635
+            ],
+            "angle": 0,
+            "content": "The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity \\( q \\) of the custom attribute from the image \\( x \\). We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset \\( \\mathcal{D}_a \\), and the consistency dataset \\( \\mathcal{D}_c \\). The former is used to train user-defined attributes, and the latter is used to train multi-view consistency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.473,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Attribute Dataset Custom attributes are specified with a small amount of labeled dataset \\(\\mathcal{D}_a\\) provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset \\(\\mathcal{D}_a = \\{x_a,q_a\\}\\) with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in \\(\\mathcal{D}_a\\), we first equally divide the quantity range of [0, 1] into \\(M\\) groups and divide the dataset \\(\\mathcal{D}_a\\) into \\(M\\) groups in the order of attribute change. Each group comprises \\(\\Omega_{a}\\) images. Then, the quantity label \\(q_{a}\\) for each image in the \\(m\\)-th group \\(G_{m}\\) in \\(\\mathcal{D}_a\\) is assigned to the value of \\(\\frac{m - 1}{M - 1}\\). To mitigate the lack of samples in \\(\\mathcal{D}_a\\), synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in \\(G_{m}\\) with that in \\(G_{m + 1}\\) using Cutmix of the combination ratio \\(\\gamma\\), the quantity label \\(q_{a}\\) is assigned to \\(\\frac{m - \\gamma}{M - 1}\\). Since \\(\\gamma\\) is sampled from the uniform distribution [0, 1], the dense"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.374,
+                0.892,
+                0.45
+            ],
+            "angle": 0,
+            "content": "quantity labels are sufficient to train the quantifier for regression, yielding any quantity in \\([0,1]\\). Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.893,
+                0.624
+            ],
+            "angle": 0,
+            "content": "Consistency Dataset We construct the consistency dataset \\(\\mathcal{D}_c = \\{x_c\\}\\) using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset \\(\\mathcal{D}_c\\) is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature \\(w\\), we generate \\(V\\) images \\(\\{x_c^1, x_c^2, \\dots, x_c^V\\}\\) using different \\(V\\) camera viewpoints. Finally, the consistency dataset \\(\\mathcal{D}_c\\) is constructed using \\(\\Omega_c\\) random latent features, so it consists of multi-view images of \\(\\Omega_c\\) different objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.628,
+                0.895,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated \\(\\hat{q}_a\\) and label \\(q_{a}\\) for an input sample \\(x_{a}\\) in \\(\\mathcal{D}_a\\). The second term is the variance for the estimated \\(\\hat{q}_c\\) vector for \\(V\\) multiview images for a single object in the consistency dataset, where \\(\\hat{q}_c^v\\) is the estimated quantity of \\(x_c^v\\) in \\(\\mathcal{D}_c\\). Quantifier training loss \\(\\mathcal{L}_q\\) is given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.514,
+                0.773,
+                0.892,
+                0.817
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {q} = \\sum_ {x _ {a} \\in \\mathcal {D} _ {a}} \\left(q _ {a} - \\hat {q} _ {a}\\right) ^ {2} + \\lambda_ {c} \\sum_ {v = 1} ^ {V} \\sum_ {x _ {c} ^ {v} \\in \\mathcal {D} _ {c}} \\left(\\hat {q} _ {c} ^ {v} - \\bar {\\hat {q}} _ {c} ^ {v}\\right) ^ {2}, \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\(\\bar{\\hat{q}}_c^v\\) is the mean of \\(\\hat{q}_c^v\\) over all \\(v\\), and \\(\\lambda_c\\) is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of \\(M\\) images sampled, one from each group in \\(\\mathcal{D}_a\\), and \\(M\\) objects sampled from \\(\\mathcal{D}_c\\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8531"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.198
+            ],
+            "angle": 0,
+            "content": "For \\(K\\) attributes estimation, \\(K\\) quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar \\(q^{(k)}\\) from the \\(k\\)-th quantifier is concatenated to create \\(K\\)-dimensional quantity vector \\(Q = [q^{(1)}, q^{(2)}, \\dots, q^{(K)}]\\). A quantity vector can be designed by a combination of various quantifiers, depending on an application."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.205,
+                0.317,
+                0.22
+            ],
+            "angle": 0,
+            "content": "3.2. Multi-Attribute Navigator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.228,
+                0.47,
+                0.439
+            ],
+            "angle": 0,
+            "content": "Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space \\(\\mathcal{W}+\\), where the source feature \\(w_{s}\\) is changed into the target feature \\(w_{t}\\) with the guidance of \\(\\hat{Q}_s\\) and \\(Q_{t}\\). We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature \\(f_{Q}\\). Second, layer-wise attention controller (LAC) estimates which layer among the \\(L\\) layer-wise mappers (LWMs) to attend each attribute manipulation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.44,
+                0.47,
+                0.62
+            ],
+            "angle": 0,
+            "content": "AFR converts \\(\\hat{Q}_s\\) and \\(Q_{t}\\) to a 512-dimensional attribute quantity feature \\(f_{Q}\\). First, \\(\\hat{Q}_s\\) and \\(Q_{t}\\) are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature \\(f_{Q}\\). The input vector with 1024 dimensions is generated by concatenating \\(w_{s}\\) and \\(f_{Q}\\), and then, the input vector is fed to each LWM. From the input vector, \\(l\\)-th LWM generates \\(w_{\\Delta}^{l}\\), which represents the movement on the latent space for \\(l\\)-th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.621,
+                0.47,
+                0.667
+            ],
+            "angle": 0,
+            "content": "LAC outputs the layer-wise attention vector \\( a = [a_1, a_2, \\dots, a_L] \\) from attribute quantity feature \\( f_{Q} \\). And the target latent feature \\( w_{t} \\) is generated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.233,
+                0.672,
+                0.469,
+                0.69
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\\Delta} ^ {l}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.192,
+                0.693,
+                0.469,
+                0.711
+            ],
+            "angle": 0,
+            "content": "\\[\nw _ {t} = \\left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \\dots , w _ {t} ^ {L} \\right]. \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.717,
+                0.47,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of \\([0,1]\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.855,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Loss and Training The navigator is trained such that \\(\\hat{Q}_t\\) follows \\(Q_t\\), while the identity between \\(I_s\\) and \\(I_t\\) is preserved. To this end, we randomly generate \\(Q_t\\) during the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select \\( J \\) attributes to train out of a total of \\( K \\) attributes at every training iteration. That is, training attribute set \\( \\mathcal{T} \\) is generated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.561,
+                0.159,
+                0.892,
+                0.175
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {T} = \\left\\{\\tau_ {1}, \\tau_ {2}, \\dots , \\tau_ {J} \\right\\} \\subset \\{1, 2, \\dots , K \\}. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.183,
+                0.892,
+                0.29
+            ],
+            "angle": 0,
+            "content": "Then, \\( Q_{t} \\) is generated by replacing \\( J \\) elements of \\( \\hat{Q}_{s} \\) with \\( J \\) random target values \\( (q_{t}) \\). To ensure that the navigator performs well within the entire range of [0, 1], we use \\( q_{t} \\) randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.291,
+                0.892,
+                0.366
+            ],
+            "angle": 0,
+            "content": "For view consistency in manipulation, we generate multi-view target images from \\( w_{t} \\). Using \\( N \\) random camera viewpoint \\( p_t^n \\), \\( N \\) multi-view images \\( I_{t}^{n} \\) are generated. And target quantity vector \\( \\hat{Q}_t^n \\) is calculated from \\( I_{t}^{n} \\), then \\( \\hat{Q}_t \\) is calculated as the average of \\( \\hat{Q}_t^n \\) vectors."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.366,
+                0.892,
+                0.411
+            ],
+            "angle": 0,
+            "content": "With the random target attribute quantity \\( Q_{t} \\) and random source latent \\( w_{s} \\), we train the navigator by minimizing the losses, which can be grouped into three main subsets:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.418,
+                0.892,
+                0.435
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {n} = \\mathcal {L} _ {Q} \\left(Q _ {t}, \\hat {Q} _ {t}\\right) + \\mathcal {L} _ {i d} \\left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\\right) + \\mathcal {L} _ {a} (a). \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.44,
+                0.892,
+                0.5
+            ],
+            "angle": 0,
+            "content": "The quantity loss \\(\\mathcal{L}_Q\\) guides the navigator to manipulate the image according to the target attribute quantity. \\(J\\)-dimensional quantity vector \\(Q^{\\prime}\\) for training attributes set \\(\\mathcal{T}\\) is generated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.596,
+                0.506,
+                0.892,
+                0.525
+            ],
+            "angle": 0,
+            "content": "\\[\nQ ^ {\\prime} = \\left[ q ^ {(\\tau_ {1})}, q ^ {(\\tau_ {2})}, \\dots , q ^ {(\\tau_ {J})} \\right]. \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.531,
+                0.892,
+                0.561
+            ],
+            "angle": 0,
+            "content": "And the quantity loss consists of two MSE terms between quantity vectors as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.57,
+                0.566,
+                0.892,
+                0.585
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {Q} = \\left\\| Q _ {t} ^ {\\prime} - \\hat {Q} _ {t} ^ {\\prime} \\right\\| _ {2} ^ {2} + \\lambda_ {q} \\left\\| Q _ {t} - \\hat {Q} _ {t} \\right\\| _ {2} ^ {2}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.59,
+                0.892,
+                0.696
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{q}\\) is the hyper-parameter for balancing the loss. In quantity loss, the first term is for \\(J\\) attributes in \\(\\mathcal{T}\\) and the second term is for all \\(K\\) attributes. Because random target quantities are given for \\(J\\) attributes out of a total of \\(K\\) attributes, \\(K - J\\) attributes of \\(Q_{t}\\) are from \\(\\hat{Q}_s\\). Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.52,
+                0.696,
+                0.758,
+                0.711
+            ],
+            "angle": 0,
+            "content": "The identity loss \\(\\mathcal{L}_{id}\\) is designed by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.545,
+                0.717,
+                0.892,
+                0.758
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {i d} = \\left\\| w _ {t} - w _ {s} \\right\\| _ {2} ^ {2} + \\frac {\\lambda_ {L}}{N} \\sum_ {n = 1} ^ {N} \\operatorname {L P I P S} \\left(I _ {s}, I _ {t} ^ {n}\\right), \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.763,
+                0.892,
+                0.824
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda_{L}\\) is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.824,
+                0.892,
+                0.851
+            ],
+            "angle": 0,
+            "content": "The third term, \\(\\mathcal{L}_n\\), is a regularization loss for layer-wise attention as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.646,
+                0.85,
+                0.892,
+                0.865
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {a} = | \\alpha - \\bar {a} |, \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\( \\bar{a} \\) denotes the average of \\( a_{l} \\) over \\( l \\), and \\( \\alpha \\) is the hyperparameter for the target average value of attention."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8532"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.089,
+                0.468,
+                0.389
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.393,
+                0.47,
+                0.464
+            ],
+            "angle": 0,
+            "content": "Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.477,
+                0.21,
+                0.494
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.503,
+                0.295,
+                0.519
+            ],
+            "angle": 0,
+            "content": "4.1. Implementation Details"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.527,
+                0.47,
+                0.633
+            ],
+            "angle": 0,
+            "content": "We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.645,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Custom Attribute Quantifier For the attribute dataset \\(\\mathcal{D}_a\\) of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed \\(\\mathcal{D}_a\\) for each attribute. We constructed each \\(\\mathcal{D}_a\\) for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each \\(\\mathcal{D}_a\\) for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed \\(\\mathcal{D}_a\\), each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing \\(\\mathcal{D}_a\\) are provided in the supplement. For the consistency dataset \\(\\mathcal{D}_c\\), we used \\(V = 10\\), \\(\\Omega_c = 10,000\\). We trained the quantifier for 50 epochs with a batch size of \\(M\\). We set"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.089,
+                0.892,
+                0.365
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.369,
+                0.892,
+                0.443
+            ],
+            "angle": 0,
+            "content": "Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes. \\((\\dagger =\\) custom attributes implemented via manually constructed \\(D_{a}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.456,
+                0.892,
+                0.488
+            ],
+            "angle": 0,
+            "content": "\\(\\lambda_{c}\\) to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.49,
+                0.892,
+                0.567
+            ],
+            "angle": 0,
+            "content": "Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate \\( w_{s} \\) with truncation factor \\( \\phi = 0.7 \\) during navigator training. We set hyper-parameters \\( \\lambda_{q} = 0.5 \\), \\( \\lambda_{L} = 0.1 \\), \\( \\alpha = 0.5 \\), and \\( N = 2 \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.576,
+                0.783,
+                0.592
+            ],
+            "angle": 0,
+            "content": "4.2.Custom Attribute Manipulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.599,
+                0.892,
+                0.81
+            ],
+            "angle": 0,
+            "content": "As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity \\( q_{t} \\) normalized in the range [0,1]. Regardless of the source attribute quantity \\( \\hat{q}_{s} \\) of the source image \\( I_{s} \\), the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When \\( q_{t} \\) approaches 0, they are both expressionless; when \\( q_{t} \\) approaches 1, they both smile broadly."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.811,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8533"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.081,
+                0.089,
+                0.468,
+                0.243
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.246,
+                0.47,
+                0.289
+            ],
+            "angle": 0,
+            "content": "Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.298,
+                0.469,
+                0.328
+            ],
+            "angle": 0,
+            "content": "cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.33,
+                0.47,
+                0.631
+            ],
+            "angle": 0,
+            "content": "To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.644,
+                0.218,
+                0.66
+            ],
+            "angle": 0,
+            "content": "4.3. Comparisons"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.668,
+                0.469,
+                0.819
+            ],
+            "angle": 0,
+            "content": "In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.82,
+                0.469,
+                0.851
+            ],
+            "angle": 0,
+            "content": "The resultant image \\(I_{\\theta}^{\\phi}\\) was manipulated from the source image \\(I^{\\phi}\\) using the \\(\\theta\\)-th target value \\((\\phi = 1, \\dots, \\Phi, \\theta =\\)"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.076,
+                0.863,
+                0.469,
+                0.9
+            ],
+            "angle": 0,
+            "content": "*StyleFlow originally used Microsoft Face API [22] as a quantifier, but Microsoft no longer supports it. Therefore, we used Face++ [1] as a quantifier for StyleFlow implementation on EG3D."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.088,
+                0.892,
+                0.357
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.361,
+                0.892,
+                0.43
+            ],
+            "angle": 0,
+            "content": "Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.504,
+                0.446,
+                0.891,
+                0.628
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.636,
+                0.892,
+                0.678
+            ],
+            "angle": 0,
+            "content": "Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.692,
+                0.891,
+                0.727
+            ],
+            "angle": 0,
+            "content": "\\(1, \\dots, \\Theta)\\). In addition, we used Face++ [1] to measure \\(r_{\\theta}^{\\phi}\\) which is the resultant attribute quantity of \\(I_{\\theta}^{\\phi}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.735,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8534"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.093,
+                0.09,
+                0.875,
+                0.18
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"4\">Age</td><td colspan=\"4\">Smile</td><td colspan=\"2\">Gender</td><td colspan=\"2\">Eyeglasses</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>Acc. ↑</td><td>Ed↓</td><td>Acc. ↑</td><td>Ed↓</td></tr><tr><td>StyleFlow</td><td>8.40</td><td>0.373</td><td>21.3</td><td>2.304</td><td>37.38</td><td>0.382</td><td>29.9</td><td>4.859</td><td>83%</td><td>0.586</td><td>96%</td><td>0.510</td></tr><tr><td>StyleFlow+Q</td><td>10.46</td><td>0.331</td><td>22.1</td><td>2.304</td><td>27.49</td><td>0.320</td><td>34.4</td><td>2.635</td><td>78%</td><td>0.670</td><td>79%</td><td>0.486</td></tr><tr><td>Ours</td><td>8.03</td><td>0.245</td><td>32.6</td><td>2.235</td><td>21.50</td><td>0.210</td><td>51.0</td><td>2.255</td><td>95%</td><td>0.537</td><td>96%</td><td>0.468</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.188,
+                0.894,
+                0.232
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness \\((\\sigma_{m})\\), manipulation accuracy (Acc.), identity preservation \\((E_{d})\\), manipulation efficiency \\((\\rho)\\), and view consistency \\((\\sigma_{v})\\). Our method gives the best results."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.253,
+                0.313,
+                0.268
+            ],
+            "angle": 0,
+            "content": "across multiple manipulated views."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.268,
+                0.47,
+                0.435
+            ],
+            "angle": 0,
+            "content": "Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation \\(\\sigma_{m,\\theta}\\) of the \\(\\theta\\)-th resultant quantities \\(\\{r_\\theta^1,\\dots ,r_\\theta^\\Phi \\}\\), the evaluation metric \\(\\sigma_{m}\\) is the mean of \\(\\sigma_{m,\\theta}\\). Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance \\(E_{d}\\) between the embeddings of two manipulated images, which were generated using two adjacent target values, as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.104,
+                0.441,
+                0.47,
+                0.484
+            ],
+            "angle": 0,
+            "content": "\\[\nE _ {d} = \\frac {1}{(\\Theta - 1) \\Phi} \\sum_ {\\theta = 1} ^ {\\Theta - 1} \\sum_ {\\phi = 1} ^ {\\Phi} \\| F \\left(I _ {\\theta + 1} ^ {\\phi}\\right) - F \\left(I _ {\\theta} ^ {\\phi}\\right) \\|, \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.49,
+                0.47,
+                0.652
+            ],
+            "angle": 0,
+            "content": "where \\(F\\) is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio \\(\\rho\\) between attribute manipulation and identity preservation as \\(\\frac{(r_{\\Theta} - r_1)}{(\\Theta - 1)E_d}\\). Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images \\(\\{I_\\theta^{\\phi,1}, I_\\theta^{\\phi,2}, I_\\theta^{\\phi,3}\\}\\) and measured the resultant attribute quantities \\(\\{r_\\theta^{\\phi,1}, r_\\theta^{\\phi,2}, r_\\theta^{\\phi,3}\\}\\). From the standard deviation \\(\\sigma_{v,\\theta}^{\\phi}\\) of the resultant attribute quantities, the evaluation metric \\(\\sigma_v\\) is the mean of \\(\\sigma_{v,\\theta}^{\\phi}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.652,
+                0.47,
+                0.743
+            ],
+            "angle": 0,
+            "content": "We conducted experiments with \\(\\Phi = 100\\) and \\(\\Theta = 8\\). As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.75,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.502,
+                0.251,
+                0.89,
+                0.343
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"3\">Age</td><td colspan=\"3\">Smile</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td></tr><tr><td>Talk-to-Edit</td><td>14.3</td><td>0.221</td><td>32.9</td><td>22.6</td><td>0.212</td><td>40.9</td></tr><tr><td>StyleFlow</td><td>16.9</td><td>0.195</td><td>28.4</td><td>29.1</td><td>0.099</td><td>88.9</td></tr><tr><td>Ours</td><td>10.9</td><td>0.225</td><td>47.2</td><td>20.2</td><td>0.103</td><td>96.6</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.499,
+                0.349,
+                0.894,
+                0.42
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness \\((\\sigma_{m})\\), identity preservation \\((E_{d})\\), and manipulation efficiency \\((\\rho)\\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.436,
+                0.892,
+                0.571
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.577,
+                0.893,
+                0.634
+            ],
+            "angle": 0,
+            "content": "Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.657,
+                0.892,
+                0.793
+            ],
+            "angle": 0,
+            "content": "Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness \\(\\sigma_{m}\\). In the \\(E_{d}\\) score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score \\(\\rho\\). This result implies that our method better preserves identity when an attribute changes by the same quantity."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.482,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8535"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.08,
+                0.089,
+                0.477,
+                0.198
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Model</td><td>σm↓</td><td>Acc.↑</td><td>Ed↓</td></tr><tr><td rowspan=\"2\">Design</td><td>w/o LAC module</td><td>15.84</td><td>96.0%</td><td>0.415</td></tr><tr><td>w/o AFR module</td><td>15.37</td><td>89.0%</td><td>0.387</td></tr><tr><td rowspan=\"2\">Training</td><td>w/o entireatts. in LQ</td><td>14.78</td><td>87.5%</td><td>0.405</td></tr><tr><td>w/o intermediate Qt</td><td>15.65</td><td>97.0%</td><td>0.402</td></tr><tr><td></td><td>Full model</td><td>14.76</td><td>95.5%</td><td>0.365</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.201,
+                0.471,
+                0.258
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness \\((\\sigma_{m})\\), accuracy, and identity preservation \\((E_{d})\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.272,
+                0.471,
+                0.468
+            ],
+            "angle": 0,
+            "content": "In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.482,
+                0.231,
+                0.499
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.507,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in \\(\\mathcal{L}_Q\\), intermediate target quantity). In the ablation study on the LAC module, we generated \\(w_{t}\\) by adding \\(w_{\\Delta}\\) to \\(w_{s}\\). In the ablation study on the AFR module, we generated \\(f_{Q}\\) by concatenating \\(\\hat{Q}_{s}\\) and \\(Q_{t}\\), then repeating it. When entire attributes are not used in \\(\\mathcal{L}_Q\\), we trained the navigator with \\(\\lambda_q = 0\\). When an intermediate target quantity is not used, we trained the navigator by randomly sampling \\(q_{t}\\) value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness \\(\\sigma_{m}\\) from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from \\(87.5\\%\\) to \\(95.5\\%\\). Using intermediate target quantity in navigator training improved the manipulation exactness \\(\\sigma_{m}\\) from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.505,
+                0.092,
+                0.687,
+                0.179
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.695,
+                0.099,
+                0.888,
+                0.158
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.185,
+                0.892,
+                0.227
+            ],
+            "angle": 0,
+            "content": "Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation \\(\\sigma_v\\) (a lower value is better)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.247,
+                0.892,
+                0.414
+            ],
+            "angle": 0,
+            "content": "View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset \\(\\mathcal{D}_c\\) by setting \\(\\lambda_c = 0\\). In the ablation study on the navigator, we trained the navigator without multi-view images by setting \\(N = 1\\). Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.431,
+                0.619,
+                0.446
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.622
+            ],
+            "angle": 0,
+            "content": "Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of \\([0,1]\\). This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.633,
+                0.892,
+                0.769
+            ],
+            "angle": 0,
+            "content": "Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.77,
+                0.891,
+                0.8
+            ],
+            "angle": 0,
+            "content": "Further discussion of the potential negative social impacts is provided in the supplement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "8536"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.09,
+                0.174,
+                0.105
+            ],
+            "angle": 0,
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2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/79420605-e587-4a04-9757-13abf9958858_origin.pdf

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2023/Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis/full.md

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+# Quantitative Manipulation of Custom Attributes on 3D-Aware Image Synthesis
+
+Hoseok Do1,2
+
+EunKyung Yoo
+
+Taehyeong  $\mathrm{Kim}^{3\dagger}$
+
+Chul Lee
+
+Jin young Choi
+
+$^{1}$ AI Lab, CTO Division, LG Electronics, South Korea
+
+$^{2}$ ASRI, Dept. of Electrical and Computer Engineering, Seoul National University, South Korea
+
+$^{3}$ Dept. of Biosystems Engineering, Seoul National University, South Korea
+
+{hoseok.do, eunkyung.ryu, clee.lee}  $@$  lge.com, {hoseok03, taehyeong.kim, jychoi}  $@$  snu.ac.kr
+
+# Abstract
+
+While 3D-based GAN techniques have been successfully applied to render photo-realistic 3D images with a variety of attributes while preserving view consistency, there has been little research on how to fine-control 3D images without limiting to a specific category of objects of their properties. To fill such research gap, we propose a novel image manipulation model of 3D-based GAN representations for a fine-grained control of specific custom attributes. By extending the latest 3D-based GAN models (e.g., EG3D), our user-friendly quantitative manipulation model enables a fine yet normalized control of 3D manipulation of multi-attribute quantities while achieving view consistency. We validate the effectiveness of our proposed technique both qualitatively and quantitatively through various experiments.
+
+# 1. Introduction
+
+Recent advances in neural rendering [23,34,38] are making it easy to reproduce virtual 3D objects from real-world objects. Neural rendering approach is not fully scalable in practice since it heavily relies on input images and thereby can not fully represent every possible form, style, and state variation of all real and unreal objects. 3D generative adversarial networks (GANs) models, on the other hand, are more generalizable and extensible since these can not only reproduce 3D objects at scale but also allow easier configurations based on the user's intention [5,32,37], making them more suitable for various 3D image synthesis tasks.
+
+Image manipulation on the latent space of 2D GAN has been extensively studied in recent years [2, 28, 29, 33, 39]. StyleGAN2 [15] has been the dominant technique used due to its flexibility to represent different styles and disentangled latent spaces. More recently, 3D-based GAN [24,
+
+![](images/4f1e089957a4f5afcd2ebab912a669f305db80ccb8a17b9b534093268daeac94.jpg)  
+Figure 1. An example of quantitative image manipulation for the face tiredness attribute. Attributes expressed as complex facial features, such as tiredness, are not easy to define explicitly. Our method assigns user-defined attributes based on a small number of image samples, allowing quantitative manipulation of 3D objects according to the user's desired state changes.
+
+26, 32] for multi-view image synthesis using neural rendering [23, 25] has gained popularity. For instance, those models [5, 10, 27] equipped with StyleGAN2 modules can generate photo-realistic 3D images with a variety of attributes while preserving view consistency. Nevertheless, the existing works do not well explore a fine-grained manipulation of custom attributes (e.g., capturing tiredness in a face, consisting of multiple and complex facial expressions, as shown in Figure 1) of 3D objects that are synthesized using 3D-based GAN models, and therefore it deserves more thorough research. While there have been some attempts [29, 33, 39] to use the latent spaces generated by GAN models to manipulate generated and real images, these approaches mainly focus on 2D objects and they are not user-friendly because users need to individually determine the appropriate manipulation scale for every use according to every specific intention.
+
+Achieving view consistency during 3D image manipulation in the latent spaces is crucial to achieve the quanti
+
+tative manipulation of custom attributes. Previously, each attribute in a multi-view image for an object was inconsistently estimated across viewpoints [8, 16, 17]. We alleviate such multi-view inconsistency problem by treating each attribute in each multi-view image as the same. That is, our 3D manipulation model is based on a 3D-based GAN model like EG3D [5], also equipped with two operators: 1) attribute quantifier that estimates the quantity of attribute to be edited, and 2) navigator that explores across the latent space to generate a manipulated image. Since the attribute quantifier guides the navigator, the manipulation quality of the navigator depends on the performance of quantifier. As quantifier, an off-the-shelf pre-trained regression model [1, 22] for a specific attribute is often used. It is not always easy to construct the pre-trained quantifier, especially for uncommon custom attributes. Hence, to better deal with custom attributes, our navigator manipulates the image by only assigning the target quantity without exploring the direction and scale of changes of the latent features. The attribute quantifier is first trained on a small number of custom image samples and then evaluates a user-defined attribute as a normalized quantity in the range [0, 1]. Using the quantifier, the navigator is then trained to generate and manipulate images corresponding to target custom attributes. We evaluate our approach in various attributes of 3D and 2D objects, including human faces, confirming that our method is qualitatively and quantitatively effective.
+
+# 2. Related Works
+
+# 2.1. Latent Space Image Manipulation
+
+StyleGAN2 [15] can generate realistic images with various styles by learning from the styles of dataset images, and effective manipulation is possible because various attributes are disentangled. Some researchers [11, 29, 33, 39] have tried to find the direction for image manipulation in the latent space. GANSpace [11] finds meaningful directions in an unsupervised manner through principal component analysis. StyleCLIP [29] uses contrastive language-image pretraining (CLIP) [30] for text-driven image manipulation. In these methods of finding direction, the moving distance along the direction should be determined heuristically after finding the direction vector for manipulation. To mitigate this issue, StyleFlow [2] proposes a conditional exploration method of GAN's latent space using conditional normalizing flows. Because StyleFlow is based on an open-source algorithm of semantic attributes, it is not easy to extend new attributes. In contrast, our method can accurately manipulate images within the normalized range of attribute variation with a relatively small amount of labeled data.
+
+# 2.2. 3D Object Manipulation
+
+There have been several studies using GAN to generate 3D-aware images [5, 10, 27, 35]. The 3D GANs introduce
+
+new architectures by combining NeRF [23] with GAN. The vast majority of studies about 3D GAN have utilized StyleGAN2, and these models have a structure that is easy to manipulate, like 2D StyleGAN2. However, attribute manipulation based on these models has not yet been actively studied. Some of the manipulation studies that used 3D GAN were limited to the face and used a 3D morphable model (3DMM) [3, 36]-based method [19, 21, 44, 45]. Because we wanted to ensure that our methodology can be used in a domain-agnostic manner, we did not use a domain-specific pre-trained model (e.g., 3DMM).
+
+There have been some NeRF editing studies [13, 37, 41, 41]. CoNeRF [13] provides fine-grained control over 3D neural representations from a single video. Inspired by the CoNerf approach, we extend a fine-grained control scheme to the 3D GAN model. Compared to CoNeRF, which combines parts of a video to generate a novel image, our method is based on generative models and can therefore manipulate diverse novel attributes.
+
+# 2.3. Efficient Geometry-Aware 3D GANs (EG3D)
+
+EG3D [5] introduced a 3D GAN framework for 3D-aware image synthesis. By decoupling feature generator and neural renderer, EG3D leverages StyleGAN2 for efficiency and expressiveness. Using a StyleGAN2 backbone, EG3D transforms the random latent feature  $z$  into intermediate latent feature  $w$ , then generates a feature map. The feature map forms a tri-plane representation, and then the output image is generated using a neural renderer, followed by a super-resolution module, which uses a StyleGAN2 backbone and latent feature  $w$ . Because EG3D is designed with a StyleGAN2 backbone, it allows for various manipulations in the latent space. Researchers have studied various approaches for attribute manipulation in the latent space of StyleGAN2, but have not considered 3D structure. To mitigate this issue, we propose a novel approach to 3D image manipulation considering multi-view consistency.
+
+# 3. Method
+
+We design a custom attribute quantifier to estimate the normalized quantity of an image to provide user-friendly attribute handling and a navigator to manipulate a 3D object's custom attribute for 3D-aware image synthesis. The overall scheme of our method is depicted in Figure 2. On the latent space of EG3D, a source latent feature  $w_{s}$ , which is obtained from a source image  $I_{s}$ , is manipulated to target latent feature  $w_{t}$ . Then, from  $w_{t}$ , EG3D generates the viewpoint-wise target image  $I_{t}^{n}$  whose quantity vector is estimated by  $\hat{Q}_t^n$ . For multi-view consistency, the quantifier is trained so that every  $\hat{Q}_t^n$  follows the target quantity vector  $Q_{t}$  and the variance of  $\hat{Q}_t^n$  is minimized. By using multiple trained quantifiers, the multi-attribute navigator takes on the role of moving the source latent feature  $w_{s}$  to the target  $w_{t}$
+
+![](images/b24e269e9ea4abf3566d9de1f36de188c122501d211e89cd3e9aba054a0ca214.jpg)  
+Figure 2. Overall scheme of the proposed method. The quantifiers that estimate the attribute quantities of the source and target images are first trained using the custom dataset. The navigator then manipulates the latent feature for efficient geometry-aware 3D (EG3D) [5] to generate the target image from a source latent feature given along with a target attribute quantity. The navigator is trained so that the generated 3D-aware images are close to the target attribute quantity, yet do not lose their identity.
+
+in the latent space, referring to  $Q_{t}$  and the estimated source quantity vector  $\hat{Q}_s$ . For training the navigator, the estimated attribute quantity vector  $\hat{Q}_t$  is defined by the average of  $\hat{Q}_t^n$  over  $n$ , which is used to form a loss (i.e., the squared error between  $Q_{t}$  and  $\hat{Q}_t$  for accurate manipulation), while preserving the identity of  $I_{s}$ .
+
+# 3.1.Custom Attribute Quantifier
+
+The quantifier, which consists of a feature encoder and a linear regression model, aims to estimate the quantity  $q$  of the custom attribute from the image  $x$ . We use the pretrained image encoder of CLIP [30] as the feature encoder, and the linear regression model comprises a fully connected layer. The quantifier is trained using two datasets simultaneously: the attribute dataset  $\mathcal{D}_a$ , and the consistency dataset  $\mathcal{D}_c$ . The former is used to train user-defined attributes, and the latter is used to train multi-view consistency.
+
+Attribute Dataset Custom attributes are specified with a small amount of labeled dataset  $\mathcal{D}_a$  provided by the user. To train the quantifier for an attribute such as age, we construct an attribute dataset  $\mathcal{D}_a = \{x_a,q_a\}$  with fine-grained quantity labels in a range of [0, 1] to express various attributes on a normalized scale. To assign quantity labels to the images in  $\mathcal{D}_a$ , we first equally divide the quantity range of [0, 1] into  $M$  groups and divide the dataset  $\mathcal{D}_a$  into  $M$  groups in the order of attribute change. Each group comprises  $\Omega_{a}$  images. Then, the quantity label  $q_{a}$  for each image in the  $m$ -th group  $G_{m}$  in  $\mathcal{D}_a$  is assigned to the value of  $\frac{m - 1}{M - 1}$ . To mitigate the lack of samples in  $\mathcal{D}_a$ , synthetic samples are augmented using Cutmix [42] between images of adjacent groups. For the image augmented by combining an image in  $G_{m}$  with that in  $G_{m + 1}$  using Cutmix of the combination ratio  $\gamma$ , the quantity label  $q_{a}$  is assigned to  $\frac{m - \gamma}{M - 1}$ . Since  $\gamma$  is sampled from the uniform distribution [0, 1], the dense
+
+quantity labels are sufficient to train the quantifier for regression, yielding any quantity in  $[0,1]$ . Furthermore, we also augment data samples by random color jittering. Color jittering contributes to reducing the bias that is a potential concern in visual recognition.
+
+Consistency Dataset We construct the consistency dataset  $\mathcal{D}_c = \{x_c\}$  using EG3D to train the quantifier that estimates a quantity consistently regardless of the viewpoint. The consistency dataset  $\mathcal{D}_c$  is constructed using EG3D without the additional annotation cost. We utilize EG3D to generate multi-view image samples for a large number of objects. From one random latent feature  $w$ , we generate  $V$  images  $\{x_c^1, x_c^2, \dots, x_c^V\}$  using different  $V$  camera viewpoints. Finally, the consistency dataset  $\mathcal{D}_c$  is constructed using  $\Omega_c$  random latent features, so it consists of multi-view images of  $\Omega_c$  different objects.
+
+Loss and Training We design a loss function for training the quantifier that can estimate user-defined attributes while maintaining multi-view consistency. The first term of the loss is the mean squared error (MSE) between the estimated  $\hat{q}_a$  and label  $q_{a}$  for an input sample  $x_{a}$  in  $\mathcal{D}_a$ . The second term is the variance for the estimated  $\hat{q}_c$  vector for  $V$  multiview images for a single object in the consistency dataset, where  $\hat{q}_c^v$  is the estimated quantity of  $x_c^v$  in  $\mathcal{D}_c$ . Quantifier training loss  $\mathcal{L}_q$  is given by
+
+$$
+\mathcal {L} _ {q} = \sum_ {x _ {a} \in \mathcal {D} _ {a}} \left(q _ {a} - \hat {q} _ {a}\right) ^ {2} + \lambda_ {c} \sum_ {v = 1} ^ {V} \sum_ {x _ {c} ^ {v} \in \mathcal {D} _ {c}} \left(\hat {q} _ {c} ^ {v} - \bar {\hat {q}} _ {c} ^ {v}\right) ^ {2}, \tag {1}
+$$
+
+where  $\bar{\hat{q}}_c^v$  is the mean of  $\hat{q}_c^v$  over all  $v$ , and  $\lambda_c$  is a hyperparameter for balancing among the two loss terms. For the efficiency of training, we use a mini-batch of  $M$  images sampled, one from each group in  $\mathcal{D}_a$ , and  $M$  objects sampled from  $\mathcal{D}_c$ .
+
+For  $K$  attributes estimation,  $K$  quantifiers are trained individually on a custom attribute. For inference, each attribute quantity scalar  $q^{(k)}$  from the  $k$ -th quantifier is concatenated to create  $K$ -dimensional quantity vector  $Q = [q^{(1)}, q^{(2)}, \dots, q^{(K)}]$ . A quantity vector can be designed by a combination of various quantifiers, depending on an application.
+
+# 3.2. Multi-Attribute Navigator
+
+Design Using the pre-trained quantifier, the navigator controls the attribute change in the latent space, following the given target attribute quantity. To this end, the navigator manipulates the feature in the 512-dimensional latent space  $\mathcal{W}+$ , where the source feature  $w_{s}$  is changed into the target feature  $w_{t}$  with the guidance of  $\hat{Q}_s$  and  $Q_{t}$ . We design the navigator shown in Figure 2 to handle multiple attributes effectively. First, the attribute feature representative (AFR) enables more precise adjustment of attribute features by expanding the quantity information with positional encoding. AFR also represents multi-attribute feature in the attribute quantity feature  $f_{Q}$ . Second, layer-wise attention controller (LAC) estimates which layer among the  $L$  layer-wise mappers (LWMs) to attend each attribute manipulation.
+
+AFR converts  $\hat{Q}_s$  and  $Q_{t}$  to a 512-dimensional attribute quantity feature  $f_{Q}$ . First,  $\hat{Q}_s$  and  $Q_{t}$  are concatenated and mapped to higher dimensional space using the positional encoding proposed by NeRF [23]. Then, a fully connected layer maps the positional encoded feature to a 512-dimensional attribute quantity feature  $f_{Q}$ . The input vector with 1024 dimensions is generated by concatenating  $w_{s}$  and  $f_{Q}$ , and then, the input vector is fed to each LWM. From the input vector,  $l$ -th LWM generates  $w_{\Delta}^{l}$ , which represents the movement on the latent space for  $l$ -th layer of EG3D. An LWM follows the architecture of StyleGAN2's mapping network with four layers.
+
+LAC outputs the layer-wise attention vector  $a = [a_1, a_2, \dots, a_L]$  from attribute quantity feature  $f_{Q}$ . And the target latent feature  $w_{t}$  is generated as follows:
+
+$$
+w _ {t} ^ {l} = w _ {s} + a _ {l} w _ {\Delta} ^ {l}, \tag {2}
+$$
+
+$$
+w _ {t} = \left[ w _ {t} ^ {1}, w _ {t} ^ {2}, \dots , w _ {t} ^ {L} \right]. \tag {3}
+$$
+
+Because each layer of StyleGAN2 is responsible for different levels of an image's style, different attributes have different layers that are appropriate for manipulation. The LAC module, which learns layer-wise attention, is more effective for custom attribute manipulation compared to prior studies [2, 29], which manually specify the appropriate layers for each attribute. LAC is a two-layer MLP with sigmoid activation in the last layer to output in the range of  $[0,1]$ .
+
+Loss and Training The navigator is trained such that  $\hat{Q}_t$  follows  $Q_t$ , while the identity between  $I_s$  and  $I_t$  is preserved. To this end, we randomly generate  $Q_t$  during the
+
+training. To enable the navigator to manipulate multiple attributes simultaneously, we randomly select  $J$  attributes to train out of a total of  $K$  attributes at every training iteration. That is, training attribute set  $\mathcal{T}$  is generated as follows:
+
+$$
+\mathcal {T} = \left\{\tau_ {1}, \tau_ {2}, \dots , \tau_ {J} \right\} \subset \{1, 2, \dots , K \}. \tag {4}
+$$
+
+Then,  $Q_{t}$  is generated by replacing  $J$  elements of  $\hat{Q}_{s}$  with  $J$  random target values  $(q_{t})$ . To ensure that the navigator performs well within the entire range of [0, 1], we use  $q_{t}$  randomly sampled from the uniform distribution on [0, 1] during the navigator's training. Hence, the navigator can be trained to move the source latent feature to a point in the latent space representing an intermediate target quantity.
+
+For view consistency in manipulation, we generate multi-view target images from  $w_{t}$ . Using  $N$  random camera viewpoint  $p_t^n$ ,  $N$  multi-view images  $I_{t}^{n}$  are generated. And target quantity vector  $\hat{Q}_t^n$  is calculated from  $I_{t}^{n}$ , then  $\hat{Q}_t$  is calculated as the average of  $\hat{Q}_t^n$  vectors.
+
+With the random target attribute quantity  $Q_{t}$  and random source latent  $w_{s}$ , we train the navigator by minimizing the losses, which can be grouped into three main subsets:
+
+$$
+\mathcal {L} _ {n} = \mathcal {L} _ {Q} \left(Q _ {t}, \hat {Q} _ {t}\right) + \mathcal {L} _ {i d} \left(w _ {t}, w _ {s}, I _ {t}, I _ {s}\right) + \mathcal {L} _ {a} (a). \tag {5}
+$$
+
+The quantity loss  $\mathcal{L}_Q$  guides the navigator to manipulate the image according to the target attribute quantity.  $J$ -dimensional quantity vector  $Q^{\prime}$  for training attributes set  $\mathcal{T}$  is generated as follows:
+
+$$
+Q ^ {\prime} = \left[ q ^ {(\tau_ {1})}, q ^ {(\tau_ {2})}, \dots , q ^ {(\tau_ {J})} \right]. \tag {6}
+$$
+
+And the quantity loss consists of two MSE terms between quantity vectors as
+
+$$
+\mathcal {L} _ {Q} = \left\| Q _ {t} ^ {\prime} - \hat {Q} _ {t} ^ {\prime} \right\| _ {2} ^ {2} + \lambda_ {q} \left\| Q _ {t} - \hat {Q} _ {t} \right\| _ {2} ^ {2}, \tag {7}
+$$
+
+where  $\lambda_{q}$  is the hyper-parameter for balancing the loss. In quantity loss, the first term is for  $J$  attributes in  $\mathcal{T}$  and the second term is for all  $K$  attributes. Because random target quantities are given for  $J$  attributes out of a total of  $K$  attributes,  $K - J$  attributes of  $Q_{t}$  are from  $\hat{Q}_s$ . Hence, the second term can lead to both preserving the source attribute quantity and manipulating it to the target attribute quantity.
+
+The identity loss  $\mathcal{L}_{id}$  is designed by
+
+$$
+\mathcal {L} _ {i d} = \left\| w _ {t} - w _ {s} \right\| _ {2} ^ {2} + \frac {\lambda_ {L}}{N} \sum_ {n = 1} ^ {N} \operatorname {L P I P S} \left(I _ {s}, I _ {t} ^ {n}\right), \tag {8}
+$$
+
+where  $\lambda_{L}$  is the hyper-parameter for balancing the loss, and LPIPS denotes the learned perceptual image patch similarity [43] calculated by the distance between the activation of two images.
+
+The third term,  $\mathcal{L}_n$ , is a regularization loss for layer-wise attention as
+
+$$
+\mathcal {L} _ {a} = | \alpha - \bar {a} |, \tag {9}
+$$
+
+where  $\bar{a}$  denotes the average of  $a_{l}$  over  $l$ , and  $\alpha$  is the hyperparameter for the target average value of attention.
+
+![](images/1bc818af15eef30a32286bc9eb5235e9dd86ade081db26e7aad42c1f4ba9117c.jpg)  
+Figure 3. Quantitative manipulation results of faces for age, smile, and tiredness attributes. The image in the first column is the source, and the following four images are the manipulated images with gradually increased target quantity. The image in the last column is the 3D shape manipulated with the target quantity 1.0.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+We evaluated our results on 3D GAN, EG3D [5]. We tested face and cat categories, each pre-trained using the FFHQ [14] and AFHQv2 [6] datasets, respectively. We experimented with the face category's age, smile, gender, eyeglasses, tiredness, pain, thinness, drunkenness, and eyebrow attributes. In the cat category, we experimented with age, eye, and fur attributes.
+
+Custom Attribute Quantifier For the attribute dataset  $\mathcal{D}_a$  of attributes, we used either a public dataset or constructed it manually from an unlabeled dataset. We used the FFHQ-Aging [28] dataset for age and gender attributes, and we used the KDEF-dyn [4] dataset and CelebAMask-HQ [20] dataset for smile and eyeglasses, respectively. For custom attributes that had no attribute dataset, we manually constructed  $\mathcal{D}_a$  for each attribute. We constructed each  $\mathcal{D}_a$  for attributes of cats by manually sampling from the AFHQv2 dataset. We constructed each  $\mathcal{D}_a$  for tiredness, pain, thinness, drunkenness, and eyebrow attributes by web-crawling images and annotating labels. When we manually constructed  $\mathcal{D}_a$ , each dataset size was up to 100 samples, taking an average of 20 minutes. Details for constructing  $\mathcal{D}_a$  are provided in the supplement. For the consistency dataset  $\mathcal{D}_c$ , we used  $V = 10$ ,  $\Omega_c = 10,000$ . We trained the quantifier for 50 epochs with a batch size of  $M$ . We set
+
+![](images/341b0542f1919a8cdf8b1f792a347285b30d6eb91d097c1108646a4ff5de9409.jpg)  
+Figure 4. Various custom attribute manipulation results. The image in the first column is the source, and the following three images are the results of each manipulation for a single custom attribute. The image in the last column is the multi-attribute result of simultaneously manipulating the three prior attributes.  $(\dagger =$  custom attributes implemented via manually constructed  $D_{a}$
+
+$\lambda_{c}$  to 0 until 10 epochs, then linearly increased it to 0.01 until 25 epochs, and kept it at 0.01 until the end of training.
+
+Navigator We trained the navigator with 30,000 iterations with a batch size of 16 on 4 Tesla V100 GPUs. We used EG3D to randomly generate  $w_{s}$  with truncation factor  $\phi = 0.7$  during navigator training. We set hyper-parameters  $\lambda_{q} = 0.5$ ,  $\lambda_{L} = 0.1$ ,  $\alpha = 0.5$ , and  $N = 2$ .
+
+# 4.2.Custom Attribute Manipulation
+
+As shown in Figure 3, the faces were gradually manipulated for the attributes of age and smile according to the target attribute quantity  $q_{t}$  normalized in the range [0,1]. Regardless of the source attribute quantity  $\hat{q}_{s}$  of the source image  $I_{s}$ , the attribute quantity of the manipulated image changed according to the target attribute quantity. Comparing the source images in the examples of smile attributes, a woman (third row) smiles and a man (fourth row) is expressionless, which means that the source attribute quantity is different. In our results, the manipulated images of the two people's faces have similar facial expressions depending on the target attribute quantity. When  $q_{t}$  approaches 0, they are both expressionless; when  $q_{t}$  approaches 1, they both smile broadly.
+
+Figure 4 shows that our model can manipulate faces for various custom attributes and can also manipulate multiple attributes simultaneously. We show more results of the quantitative manipulations for these attributes in the supplement. Figure 5 represents gradually manipulated images of cats with custom attributes such as fur, eye, and age. Be
+
+![](images/50d956ab4bffc06e87b6ad9701b55a46a8981de876e054d71e9d334b0312a7d1.jpg)  
+Figure 5. Quantitative manipulation results of cats for custom attributes (fur, eye, and age). The image in the first column is the source, and following five are the manipulated images.
+
+cause we did not use any domain-specific pre-trained models, our method provides a domain-agnostic technique.
+
+To demonstrate the expandability of our method, we apply our method to StyleGAN2, which has pre-trained models in various categories. Face and cat categories were tested, pre-trained using the Stanford Cars [18] dataset and the LSUN Church [40] dataset, respectively. As shown in Figure 6, cars are gradually manipulated for the attributes of year and type, and churches are gradually manipulated for the cloudiness attribute. The manipulated results are independent of the source attribute quantity, as were the cases for faces in Figure 3. In the case of the car year attribute, it is difficult to intuitively describe the changes in appearance according to the year attribute quantity. However, our method can visualize the changes. In detail, the newer the car is, the more emphasized the horizontal lines on the grill, the sharper the headlights, and the more curved the overall design. This result shows that our approach can be used in a similar manner as GANalyze [9], which visualizes abstract concepts such as memorability through GAN. Implementation details and more experimental results of StyleGAN2 are provided in the supplement.
+
+# 4.3. Comparisons
+
+In this section, we compare our method with other quantitative manipulation methods. For quantitative comparison, we experimented with image manipulation of the faces on age, smile, gender, and eyeglasses attributes. We compared the performance of our approach with that of StyleFlow [2], which proposes a quantitative manipulation. We also implemented StyleFlow+Q, which uses our custom quantifier, while StyleFlow uses a pre-trained model as a quantifier*. Details for implementing StyleFlow on EG3D are provided in the supplement.
+
+The resultant image  $I_{\theta}^{\phi}$  was manipulated from the source image  $I^{\phi}$  using the  $\theta$ -th target value  $(\phi = 1, \dots, \Phi, \theta =$
+
+![](images/73b423b5074fcaf092c0a66855729c51355ded3a1a2853e5539dd2c115c0dfa2.jpg)  
+Figure 6. Quantitative manipulation results of cars for year and type attributes, and churches for cloudiness attribute in StyleGAN2. The image in the first column is the source, and the following six are the manipulated images with the target quantity increased from 0.0 to 1.0.
+
+![](images/3466cac5575d1ee5658ac4d4ed68d65c58f7d97649fba66d58cec73a3f281c35.jpg)  
+Figure 7. Qualitative comparison for age and smile attributes manipulation in EG3D. Competing methods fail to preserve identity when manipulated to Old and No-smile.
+
+$1, \dots, \Theta)$ . In addition, we used Face++ [1] to measure  $r_{\theta}^{\phi}$  which is the resultant attribute quantity of  $I_{\theta}^{\phi}$ .
+
+Quantitative Comparisons Image manipulation seeks to accomplish two primary objectives that are often conflict: 1) To modify an image to achieve specific intended attributes, and 2) to maintain original image's identity. To evaluate our approach to the objectives, we employed five metrics. Manipulation exactness and accuracy are both metrics employed to evaluate the success of the first objective, while identity preservation serves as the metric to access the achievement of the second objective. Manipulation efficiency measures success in both objectives, and identity preservation is a metric for evaluating consistency
+
+<table><tr><td rowspan="2">Method</td><td colspan="4">Age</td><td colspan="4">Smile</td><td colspan="2">Gender</td><td colspan="2">Eyeglasses</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σv↓</td><td>Acc. ↑</td><td>Ed↓</td><td>Acc. ↑</td><td>Ed↓</td></tr><tr><td>StyleFlow</td><td>8.40</td><td>0.373</td><td>21.3</td><td>2.304</td><td>37.38</td><td>0.382</td><td>29.9</td><td>4.859</td><td>83%</td><td>0.586</td><td>96%</td><td>0.510</td></tr><tr><td>StyleFlow+Q</td><td>10.46</td><td>0.331</td><td>22.1</td><td>2.304</td><td>27.49</td><td>0.320</td><td>34.4</td><td>2.635</td><td>78%</td><td>0.670</td><td>79%</td><td>0.486</td></tr><tr><td>Ours</td><td>8.03</td><td>0.245</td><td>32.6</td><td>2.235</td><td>21.50</td><td>0.210</td><td>51.0</td><td>2.255</td><td>95%</td><td>0.537</td><td>96%</td><td>0.468</td></tr></table>
+
+across multiple manipulated views.
+
+Specifically, we defined the metrics as follows: 1) Manipulation exactness refers to the consistency of results for the same input target value. From the standard deviation  $\sigma_{m,\theta}$  of the  $\theta$ -th resultant quantities  $\{r_\theta^1,\dots ,r_\theta^\Phi \}$ , the evaluation metric  $\sigma_{m}$  is the mean of  $\sigma_{m,\theta}$ . Regarding 2) manipulation accuracy, we measured the ratio of correctly manipulated images for binary-class attributes (e.g., gender, eyeglasses). For 3) identity preservation, we determined the average Euclidean distance  $E_{d}$  between the embeddings of two manipulated images, which were generated using two adjacent target values, as
+
+$$
+E _ {d} = \frac {1}{(\Theta - 1) \Phi} \sum_ {\theta = 1} ^ {\Theta - 1} \sum_ {\phi = 1} ^ {\Phi} \| F \left(I _ {\theta + 1} ^ {\phi}\right) - F \left(I _ {\theta} ^ {\phi}\right) \|, \tag {10}
+$$
+
+where  $F$  is the embedding of the pre-trained face recognition model [7]. The metric of 4) manipulation efficiency refers to trade-off ratio  $\rho$  between attribute manipulation and identity preservation as  $\frac{(r_{\Theta} - r_1)}{(\Theta - 1)E_d}$ . Lastly, 5) view consistency was calculated across multiple manipulated views. In each manipulation case, we generated three multi-view images  $\{I_\theta^{\phi,1}, I_\theta^{\phi,2}, I_\theta^{\phi,3}\}$  and measured the resultant attribute quantities  $\{r_\theta^{\phi,1}, r_\theta^{\phi,2}, r_\theta^{\phi,3}\}$ . From the standard deviation  $\sigma_{v,\theta}^{\phi}$  of the resultant attribute quantities, the evaluation metric  $\sigma_v$  is the mean of  $\sigma_{v,\theta}^{\phi}$ .
+
+We conducted experiments with  $\Phi = 100$  and  $\Theta = 8$ . As shown in Table 1, our approach outperforms the competing methods in all evaluation metrics. StyleFlow and StyleFlow+Q show similar performance, implying that our custom quantifier has reasonable performance compared to a public pre-trained model, Face++.
+
+Qualitative Comparisons Age and smile attributes were tested for qualitative comparison, as shown in Figure 7. StyleFlow+Q sometimes significantly changes the source identity (e.g., gender and eyeglasses status are changed in both Old and No-smile manipulation cases). StyleFlow also sometimes changes the source identity, and the manipulation performance is worse than others in the Smile case. Our method can manipulate images while preserving the source identity with better manipulation performance (e.g., broadly smiling in the Smile manipulation case).
+
+Table 1. Quantitative comparison with competing methods in EG3D. We evaluated the manipulation performance on age, smile, gender, and eyeglass attributes using five evaluation metrics: manipulation exactness  $(\sigma_{m})$ , manipulation accuracy (Acc.), identity preservation  $(E_{d})$ , manipulation efficiency  $(\rho)$ , and view consistency  $(\sigma_{v})$ . Our method gives the best results.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Age</td><td colspan="3">Smile</td></tr><tr><td>σm↓</td><td>Ed↓</td><td>ρ↑</td><td>σm↓</td><td>Ed↓</td><td>ρ↑</td></tr><tr><td>Talk-to-Edit</td><td>14.3</td><td>0.221</td><td>32.9</td><td>22.6</td><td>0.212</td><td>40.9</td></tr><tr><td>StyleFlow</td><td>16.9</td><td>0.195</td><td>28.4</td><td>29.1</td><td>0.099</td><td>88.9</td></tr><tr><td>Ours</td><td>10.9</td><td>0.225</td><td>47.2</td><td>20.2</td><td>0.103</td><td>96.6</td></tr></table>
+
+Table 2. Quantitative comparison with competing methods in StyleGAN2. We evaluated the manipulation performance on age and smile attributes using three evaluation metrics: manipulation exactness  $(\sigma_{m})$ , identity preservation  $(E_{d})$ , and manipulation efficiency  $(\rho)$ .
+
+![](images/b24c83074bb6cf30e6be56200cd916e06c304a23144a2ed51d4a06396f8be75f.jpg)  
+Figure 8. Comparison between models regarding the degree of image manipulation according to the manipulation strength (left: age attribute; right: smile attribute). Red boxes denote unnatural manipulated images due to excessive manipulation strength.
+
+Comparisons in 2D We compare our method with four baselines in StyleGAN2. For quantitative comparison, we compare our method with StyleFlow [2] and Talk-toEdit [12], which propose quantitative manipulations. For qualitative comparison, we compare our method with StyleCLIP [29] and GANSpace [11], which provide direction for attribute manipulation. The experiment was conducted by manipulating the age and smile attributes of the FFHQ test dataset using the authors' official implementations.
+
+As shown in Table 2, our approach outperforms Style-Flow and Talk-to-Edit in manipulation exactness  $\sigma_{m}$ . In the  $E_{d}$  score, StyleFlow is slightly better than ours, and Talk-to-Edit is similar to ours, but our approach outperforms both methods in terms of the efficiency score  $\rho$ . This result implies that our method better preserves identity when an attribute changes by the same quantity.
+
+<table><tr><td></td><td>Model</td><td>σm↓</td><td>Acc.↑</td><td>Ed↓</td></tr><tr><td rowspan="2">Design</td><td>w/o LAC module</td><td>15.84</td><td>96.0%</td><td>0.415</td></tr><tr><td>w/o AFR module</td><td>15.37</td><td>89.0%</td><td>0.387</td></tr><tr><td rowspan="2">Training</td><td>w/o entireatts. in LQ</td><td>14.78</td><td>87.5%</td><td>0.405</td></tr><tr><td>w/o intermediate Qt</td><td>15.65</td><td>97.0%</td><td>0.402</td></tr><tr><td></td><td>Full model</td><td>14.76</td><td>95.5%</td><td>0.365</td></tr></table>
+
+Table 3. Ablation study on quantitative manipulation. We experimented on four attributes (age, smile, gender, and eyeglasses) and reported the mean values of exactness  $(\sigma_{m})$ , accuracy, and identity preservation  $(E_{d})$ .
+
+In Figure 8, we compare the degree of image change according to the gradual increase in the manipulation strength. For each manipulation, we set the manipulation strength using the values suggested in their provided code. Each method enables natural manipulation of the attribute by using the appropriate strength; however, the appropriate strength varies for each attribute and source. In GANSpace, a greater strength is suitable for the smile attribute, and a lesser strength is suitable for the age attribute, which is the opposite in StyleCLIP. Our approach can manipulate attributes in a normalized range, so ours can generate naturally manipulated images without exploring the manipulation strength.
+
+# 4.4. Ablation Study
+
+Quantitative Manipulation We conducted several ablation experiments on our method. Four ablation factors were selected from our navigator: two from the design (LAC, AFR) and two from the training scheme (entire attributes in  $\mathcal{L}_Q$ , intermediate target quantity). In the ablation study on the LAC module, we generated  $w_{t}$  by adding  $w_{\Delta}$  to  $w_{s}$ . In the ablation study on the AFR module, we generated  $f_{Q}$  by concatenating  $\hat{Q}_{s}$  and  $Q_{t}$ , then repeating it. When entire attributes are not used in  $\mathcal{L}_Q$ , we trained the navigator with  $\lambda_q = 0$ . When an intermediate target quantity is not used, we trained the navigator by randomly sampling  $q_{t}$  value from zero or one. We evaluated the results using the mean values of evaluation metrics in Section 4.3. As shown in Table 3, the full model exhibits the best performance in evaluation exactness and identity preservation. An ablation study on the LAC module shows slightly better accuracy but worse performance in exactness and identity preservation. The AFR module improved the performance of manipulation exactness  $\sigma_{m}$  from 15.37 to 14.76. Using entire attributes in navigator training improved the performance of accuracy from  $87.5\%$  to  $95.5\%$ . Using intermediate target quantity in navigator training improved the manipulation exactness  $\sigma_{m}$  from 15.65 to 14.76. By training the navigator with a random intermediate target quantity, the navigator could move the source latent feature to the target more precisely, as intuitively intended.
+
+![](images/bcda9631a4a613ddff274b065263ff8380d2e3c2b2918692c26231ed06e72270.jpg)  
+Figure 9. Ablation study on view consistency. We experimented on two attributes (age, smile) and reported the viewpoint-wise standard deviation  $\sigma_v$  (a lower value is better).
+
+![](images/0053102007f163eb5229b4e49f7c77e4883b10d9358053ef1d7e7459895bfb0f.jpg)
+
+View Consistency We conducted another ablation study on view consistency performance. Two ablation factors were selected, one from the quantifier and one from the navigator. In the ablation study on the quantifier, we trained the quantifier without consistency dataset  $\mathcal{D}_c$  by setting  $\lambda_c = 0$ . In the ablation study on the navigator, we trained the navigator without multi-view images by setting  $N = 1$ . Furthermore, we also experimented with a case without both factors of the quantifier and navigator. As shown in Figure 9, each factor in the quantifier and navigator for multi-view consistency contributes to the view consistency.
+
+# 5. Conclusion
+
+Using our method, users can easily manipulate custom attributes of the source 3D image with only a target attribute quantity in the range of  $[0,1]$ . This goal was achieved by introducing a novel attribute quantifier that can estimate the normalized attribute quantity from a given image. The navigator enables fine-control manipulation of multi-attribute quantities using the attribute quantifier. Our method achieved 3D-aware image manipulation via using a consistent attribute quantity in multi-view. We validated the effectiveness of our method both qualitatively and quantitatively through various experiments.
+
+Limitations Since our study is based on the latent space of a pre-trained GAN model, the performance of manipulation is limited by that of the pre-trained model. EG3D has fewer pre-trained models than StyleGAN2, so examples are limited, but it is expected to expand as various pre-trained models are released. Moreover, we used images generated from random latent features as a source rather than real images. Examples of real image manipulation using the inversion method [31] are provided in the supplement.
+
+Further discussion of the potential negative social impacts is provided in the supplement.
+
+Acknowledgement This work was supported by IITP grant funded by Korea government(MSIT) [No.B0101-15-0266, Development of High Performance Visual BigData Discovery Platform for Large-Scale Realtime Data Analysis; NO.2021-0-01343, Artificial Intelligence Graduate School Program (Seoul National University)]
+
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+        "text": "Matteo Farina<sup>1</sup> Luca Magri<sup>2</sup> Willi Menapace<sup>1</sup>",
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+        "text": "Elisa Ricci $^{1,3}$  Vladislav Golyanik $^{4}$  Federica Arrigoni $^{2}$",
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+        "text": "<sup>1</sup>University of Trento <sup>2</sup>Politecnico di Milano <sup>3</sup>Fondazione Bruno Kessler <sup>4</sup>MPI for Informatics, SIC",
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+        "text": "Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.",
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+        "text": "1. Introduction",
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+        "text": "Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them.",
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+        "type": "text",
+        "text": "Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro",
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+            "Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49]."
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+        "type": "text",
+        "text": "vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including  $\\mathcal{NP}$ -hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC?",
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+        "text": "Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal",
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "text",
+        "text": "lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data.",
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+        "text": "Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few.",
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+        "text": "This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF.",
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+        "text": "Contributions. In summary, the primary technical contributions of this paper are the following:",
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+            "- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs;",
+            "- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models;",
+            "- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware."
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+        "text": "The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively.",
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+        "text": "The QUBO formulation in a binary search space is an optimization problem of the following form:",
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+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {y} \\in \\mathbb {R} ^ {d}} \\mathbf {y} ^ {\\mathsf {T}} Q \\mathbf {y} + \\mathbf {s} ^ {\\mathsf {T}} \\mathbf {y}, \\tag {1}\n$$\n",
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+        "type": "text",
+        "text": "where  $\\mathbb{B}^d$  denotes the set of binary vectors of length  $d$ ,  $Q \\in \\mathbb{R}^{d \\times d}$  is a real symmetric matrix and, in a QUBO with  $d$  variables, their linear coefficients are packed into  $\\mathbf{s} \\in \\mathbb{R}^d$ . When the problem is subject to linear constraints of the form  $A\\mathbf{y} = \\mathbf{b}$ , a common approach is to relax such constraints and reformulate the QUBO as:",
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+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {y} \\in \\mathbb {B} ^ {d}} \\mathbf {y} ^ {\\top} Q \\mathbf {y} + \\mathbf {s} ^ {\\top} \\mathbf {y} + \\lambda | | A \\mathbf {y} - \\mathbf {b} | | _ {2} ^ {2}, \\tag {2}\n$$\n",
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+        "text": "where  $\\lambda$  must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to:",
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+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {y} \\in B ^ {d}} \\mathbf {y} ^ {\\top} \\tilde {Q} \\mathbf {y} + \\tilde {\\mathbf {s}} ^ {\\top} \\mathbf {y} \\tag {3}\n$$\n",
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+        "type": "text",
+        "text": "where the following simple substitutions are implied:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {Q} = Q + \\lambda A ^ {\\mathsf {T}} A, \\quad \\tilde {\\mathbf {s}} = \\mathbf {s} - 2 \\lambda A ^ {\\mathsf {T}} \\mathbf {b} \\tag {4}\n$$\n",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For the proof, the reader can refer to, e.g., Birdal et al. [6].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector  $\\mathbf{y}$ ), while each coupler models an element of  $Q$  (i.e., the coupler between the physical qubits  $i$  and  $j$  maps to entry  $Q_{ij}$ ). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having  $d$  nodes (called logical qubits $^1$ ), corresponding to the  $d$  entries of  $\\mathbf{y}$  and edges corresponding to the non-zero entries of  $Q$ .",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_footnote",
+        "text": "Hereafter we will sometimes omit the term \"logical\" or \"physical\" as it will be clear from the context which type of qubits are being involved.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "13641",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. The Proposed Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem formulation",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Consider a set of data points  $X = \\{x_{1},\\dots,x_{n}\\}$  and a set  $\\Theta = \\{\\theta_1,\\ldots ,\\theta_m\\}$  of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from  $\\Theta$  the \"best\" models that describe all the data  $X$ . Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Choice of Optimization Objective",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by  $P$  and defined as:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP [ i, j ] = \\left\\{ \\begin{array}{l l} 1 & \\text {i f e r r o r} \\left(x _ {i}, \\theta_ {j}\\right) <   \\epsilon \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where:  $x_{i}$  and  $\\theta_{j}$  are the  $i$ -th point in the dataset and the  $j$ -th sampled model respectively; error expresses the residual of point  $x_{i}$  w.r.t. model  $\\theta_{j}$  and  $\\epsilon$  is the inlier threshold to assign the point to the model.  $P$  is a matrix of size is  $n \\times m$ , where  $n$  and  $m$  are the number of points and models, respectively. Intuitively, the columns of  $P$  represent the consensus sets of models, while the rows are points' preference sets.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of  $P$  that explain all the rows. More formally:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} \\geqslant \\mathbb {1} _ {n} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            609,
+            672,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbb{1}$  denotes a vector of ones (whose length is given as subscript) and  $\\mathbf{z}$  is a binary vector representing which models (i.e., columns of the preference matrix  $P$ ) are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "13642",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by  $k$ ) is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly  $k$  models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work:",
+        "bbox": [
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+            301,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\mathbb {1} _ {m} ^ {\\mathsf {T}} \\mathbf {z} \\quad \\text {s . t .} P \\mathbf {z} = \\mathbb {1} _ {n}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. QUBO Formulation",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nQ = 0, \\quad \\mathbf {s} = \\mathbb {1} _ {m}, \\quad A = P, \\quad \\mathbf {b} = \\mathbb {1} _ {n} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where optimization is carried out over  $\\mathbf{z} \\in \\mathbb{B}^m$ , that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {Q} = \\lambda P ^ {\\mathsf {T}} P, \\quad \\tilde {\\mathbf {s}} = \\mathbb {1} _ {m} - 2 \\lambda P ^ {\\mathsf {T}} \\mathbb {1} _ {n} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            699,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where no matrix of quadratic coefficients is present in  $\\widetilde{Q}$  as the considered formulation only contains linear terms, i.e.,  $Q = 0$ . Hence, Problem (7) can be turned into a QUBO of the form (3), namely:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\mathbf {z} \\in \\mathbb {B} ^ {m}} \\lambda \\mathbf {z} ^ {\\top} (P ^ {\\top} P) \\mathbf {z} + \\left(\\mathbb {1} _ {m} - 2 \\lambda P ^ {\\top} \\mathbb {1} _ {n}\\right) ^ {\\top} \\mathbf {z}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            133,
+            792,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 DEQUMF"
+        ],
+        "code_body": "Require:  $P,s$    \nwhile  $|P$  .columns  $\\vert >s$  do subproblems  $= \\text{ColumnPartition}(P,s)$ $i\\gets 0$    \nwhile  $i <   |$  subproblems|do  $\\mathcal{J}_i\\gets$  models in the  $i$  -th subproblem  $P_{\\mathcal{I}_i}\\gets P$  retaining only the  $\\mathcal{J}_i$  columns  $\\mathbf{z}_i = \\mathrm{QUMF}(P_{\\mathcal{I}_i})$  remove from  $P$  columns  $P_{\\mathcal{I}_i}[:,1 - \\mathbf{z}_i]$ $i\\gets i + 1$    \nend while   \nend while   \n $\\mathbf{z}\\gets \\mathrm{QUMF}(P)$    \nreturn  $P[:,\\mathbf{z}]$",
+        "bbox": [
+            500,
+            107,
+            803,
+            305
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Iterative Decomposed Set-Cover",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of  $m$ . In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix  $P$  and reduces the dimension of the problem to fit the number of available physical qubits.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix  $P$ , at each iteration we partition the columns of  $P$  into multiple submatrices  $P_{\\mathcal{J}_i}$ , where  $\\mathcal{J}_i$  indicates the set of selected column indices and  $|\\mathcal{J}_i| = s$ . We choose the subproblem size  $s$  so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by  $P_{\\mathcal{J}_i}$  is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector  $\\mathbf{z}_i$  that represents the subset of selected models for the current subproblem. Note that models not selected in  $\\mathbf{z}_i$  are unlikely to be solutions to the original problem since, by construction,  $\\mathbf{z}_i$  maximizes the coverage on all points with only the restricted subset of models  $\\mathcal{J}_i$ . Then, after all subproblems have been solved, we prune  $P$  by retaining only the columns that are selected in the corresponding optimal  $\\mathbf{z}_i$ . This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We iteratively apply the above procedure until the number of remaining columns in  $P$  falls below  $s$ , at which point the problem is directly and reliably solved using QUMF.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            814,
+            640,
+            829
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "13643",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/7974b62aff55b9686262afa416fda5adb67ad6385a2a793ec744d99befaf0f52.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of the iterative pruning technique applied to  $P$  in DEQUMF over consecutive iterations. At time  $t$ ,  $P$  is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time  $t + 1$ , models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            88,
+            433,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Multi-Model Fitting",
+        "text_level": 1,
+        "bbox": [
+            76,
+            398,
+            269,
+            416
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods.",
+        "bbox": [
+            75,
+            422,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50].",
+        "bbox": [
+            75,
+            483,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5].",
+        "bbox": [
+            75,
+            604,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective<sup>2</sup>. However, there are sub",
+        "bbox": [
+            75,
+            785,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals.",
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Quantum Computer Vision",
+        "text_level": 1,
+        "bbox": [
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+            257
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All available approaches can be classified into single QUBO (\"one sweep\") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "2The same objective is considered but constraints are different: RANSACOV [29] allows for overlapping models, resulting in an inequality constraint, see Problem (6); instead, we consider disjoint models, using an equality constraint, see Problem (7). For a fair comparison, we slightly modify RANSACOV, replacing the inequality with an equality constraint.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "13644",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4).",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs.",
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+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/fcc2996690464e415e76d60e81fea03f4dd8a3a6afc5952afa587cac738f4d6a.jpg",
+        "image_caption": [
+            "Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points  $n$  is fixed to  $n = 30$ , the number of ground-truth structures is fixed to  $k = 5$ , and the number of sampled models  $m$  is arranged on the x-axis."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/619b7500bcc91c415825961aeb7cebdf7c7724f9f8b038a27fdef64f56e84587.jpg",
+        "image_caption": [
+            "Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44]."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of  $20\\mu s$",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Selection of  $\\lambda$ . In every experiment, we set  $\\lambda = 1.1$ . This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for  $\\lambda$  by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for  $\\lambda$  generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.1. Synthetic Data",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions.",
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+    },
+    {
+        "type": "text",
+        "text": "Small-scale Data. In this experiment, we select a subset of  $n = 30$  points. The number of ground-truth models is fixed to  $k = 5$ , and additional  $m - k$  excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>3</sup>We refer to optimal solution probability as the ratio between the anneals ended in a globally optimal state and the total number of anneals.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "13645",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/b1d0c7c65a8de500bfb6816dcef9456944eab3bf387f56d4b33115b8f8ef4fa4.jpg",
+        "image_caption": [
+            "Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points  $n$  is fixed to  $n = 250$ , the number of ground-truth structures is fixed to  $k = 5$ , and the number of sampled models  $m$  (corresponding to the dimension of the search space) is arranged on the x-axis."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online $^4$ , that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the  $k = 5$  ground-truth models) as well as all of the  $n = 250$",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29].",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range  $[0,10]\\%$  for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Real Data",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach<sup>5</sup> perform reasonably well, with DEQUMF (SA) being on par with the state of the art.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>5</sup>We are not able to run QUMF on Traffic2 due to the limited amount of GPU time available in our monthly subscription combined with the large dimension of the dataset, hence results are not reported.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "4https://fusiello.github.io/demo/cov/index.html",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "13646",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ffa7645a9363dc96703d2bf7013f6576a9a7ca69ab66a5ad671ff1497a898627.jpg",
+        "table_caption": [
+            "Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>Multi-X [4]</td><td>J-Linkage [44]</td><td>T-Linkage [28]</td><td>RPA [30]</td><td>RANSACOV [29]</td><td>QUMF (SA)</td><td>DEQUMF</td><td>DEQUMF (SA)</td></tr><tr><td rowspan=\"2\">Traffic3 [45]</td><td>mean</td><td>0.32</td><td>1.58</td><td>0.48</td><td>0.19</td><td>0.35</td><td>5.14</td><td>8.74</td><td>0.55</td></tr><tr><td>median</td><td>0</td><td>0.34</td><td>0.19</td><td>0</td><td>0.19</td><td>2.85</td><td>7.50</td><td>0.28</td></tr><tr><td rowspan=\"2\">Traffic2 [45]</td><td>mean</td><td>0.09</td><td>1.75</td><td>1.31</td><td>0.14</td><td>0.54</td><td>6.04</td><td>-</td><td>0.10</td></tr><tr><td>median</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>3.17</td><td>-</td><td>0</td></tr><tr><td rowspan=\"2\">York [15]</td><td>mean</td><td>-</td><td>2.85</td><td>1.44</td><td>1.08</td><td>0.19</td><td>12.29</td><td>-</td><td>0.74</td></tr><tr><td>median</td><td>-</td><td>1.80</td><td>0</td><td>0</td><td>0</td><td>3.78</td><td>-</td><td>0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/6abed28e600689162ff25dafc369b56d246880e045c7ba4bdb9e0f953fba51bf.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>RANSACOV [29]</td><td>QUMF (SA)</td><td>DEQUMF</td><td>DEQUMF (SA)</td></tr><tr><td>mean</td><td>9.79</td><td>3.85</td><td>16.22</td><td>0.77</td></tr><tr><td>median</td><td>7.97</td><td>3.54</td><td>11.0</td><td>0.18</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3. Comparison with Quantum State-of-the-art",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online<sup>6</sup>, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider  $10\\%$  and  $20\\%$  of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Limitations",
+        "text_level": 1,
+        "bbox": [
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+            821,
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+            837
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate",
+        "bbox": [
+            76,
+            847,
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+            877
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/899d8c2d8f1036da7ad55186c19fe50bccebfb4b55f052aa7a4c129939cb5159.jpg",
+        "table_caption": [
+            "Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Algorithm</td><td colspan=\"3\">Outlier ratio</td></tr><tr><td>10%</td><td>20%</td><td>Full sequences</td></tr><tr><td>QUMF (SA)</td><td>7.22</td><td>11.34</td><td>13.23</td></tr><tr><td>DEQUMF</td><td>2.41</td><td>10.53</td><td>16.17</td></tr><tr><td>DEQUMF (SA)</td><td>6.26</td><td>8.28</td><td>10.83</td></tr><tr><td>HQC-RF [17]</td><td>3.71</td><td>37.0</td><td>45.84</td></tr></table>",
+        "bbox": [
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+            234,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49].",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/cca06efa4822d1a5eeafcc75d43abbb4354bc89338573e739da3c9a71476f8fa.jpg",
+        "image_caption": [
+            "DEQUMF (SA)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            430
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/2718e7988b4c7a55ad82a54a0355278d565bf2da9c76213bd044f29b0d0c68e6.jpg",
+        "image_caption": [
+            "HQC-RF [17]",
+            "Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with  $20\\%$  outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves  $8.49\\%$  error."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            696,
+            375,
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+            430
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work.",
+        "bbox": [
+            496,
+            536,
+            890,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            646,
+            617,
+            661
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research.",
+        "bbox": [
+            496,
+            672,
+            890,
+            762
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN.",
+        "bbox": [
+            496,
+            787,
+            890,
+            898
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{6}$ https://github.com/dadung/HQC-robust-fitting",
+        "bbox": [
+            93,
+            886,
+            450,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "13647",
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
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2023/Quantum Multi-Model Fitting/aabc5258-c568-488e-9b55-06bc7747cb81_origin.pdf

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2023/Quantum Multi-Model Fitting/full.md

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+# Quantum Multi-Model Fitting
+
+Matteo Farina<sup>1</sup> Luca Magri<sup>2</sup> Willi Menapace<sup>1</sup>
+
+Elisa Ricci $^{1,3}$  Vladislav Golyanik $^{4}$  Federica Arrigoni $^{2}$
+
+<sup>1</sup>University of Trento <sup>2</sup>Politecnico di Milano <sup>3</sup>Fondazione Bruno Kessler <sup>4</sup>MPI for Informatics, SIC
+
+# Abstract
+
+Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multimodel fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.
+
+# 1. Introduction
+
+Since the data volumes that AI technologies are required to process are continuously growing every year, the pressure to devise more powerful hardware solutions is also increasing. To face this challenge, a promising direction currently pursued both in academic research labs and in leading companies is to exploit the potential of quantum computing. Such paradigm leverages quantum mechanical effects for computations and optimization, accelerating several important problems such as prime number factorization, database search [36] and combinatorial optimization [33]. The reason for such acceleration is that quantum computers leverage quantum parallelism of qubits, i.e., the property that a quantum system can be in a superposition of multiple (exponentially many) states and perform calculations simultaneously on all of them.
+
+Among the two quantum computing models, i.e., gate-based and Adiabatic Quantum Computers (AQCs), the latter recently gained attention in the computer vision community thanks to advances in experimental hardware realizations [2, 6, 17, 34, 41, 51, 53]. At the present, AQCs pro
+
+![](images/fd51112c3082f1c75d16cc57985fc1ad1a29c5de439eb310cb472cbc369f7b5a.jpg)  
+Figure 1. Left: Differences between our method and HQC-RF [17]. While HQC-RF considers only a single model and is tested on quantum hardware with synthetic data, QUMF is also evaluated on real data on real quantum hardware. Although devised for multiple models, our method supports a single model likewise. Right: Qualitative results of QUMF on motion segmentation on the AdelaideRMF dataset [49].
+
+![](images/c73c3852b6acb3a794c6aa5a57af836b73e0ec7194e9fbdd27e1761dd9a37656.jpg)
+
+vide sufficient resources in terms of the number of qubits, qubit connectivity and admissible problem sizes which they can tackle [7], to be applied to a wide range of problems in computer vision. The AQC model is based on the adiabatic theorem of quantum mechanics [8] and designed for combinatorial problems (including  $\mathcal{NP}$ -hard) that are notoriously difficult to solve on classical hardware. Modern AQCs operate by optimizing objectives in the quadratic unconstrained binary optimization (QUBO) form (see Sec. 2). However, many relevant tasks in computer vision cannot be trivially expressed in this form. Hence, currently, two prominent research questions in the field are: 1) Which problems in computer vision could benefit from an AQC?, and 2) How can these problems be mapped to a QUBO form in order to use an AQC?
+
+Several efforts have been recently undertaken to bring classical vision problems in this direction. Notable examples are works on graph matching [40, 41], multi-image matching [6], point-set registration [20, 34], object detection [26], multi-object tracking [53], motion segmentation [2] and robust fitting [17]. Focusing on geometric model fitting, Doan et al. [17] proposed an iterative consensus maximization approach to robustly fit a single geometric model to noisy data. This work was the first to demonstrate the advantages of quantum hardware in robust single-model fitting with error bounds, which is an important and chal
+
+lenging problem with many applications in computer vision (e.g., template recognition in a point set). The authors proposed to solve a series of linear programs on an AQC and demonstrated promising results on synthetic data. They also showed experiments for fundamental matrix estimation and point triangulation using simulated annealing (SA) [25]. SA is a classical global optimization approach, that, in contrast to AQCs, can optimize arbitrary objectives and is a frequent choice when evaluating quantum approaches (see Sec. 2). HQC-RF [17] takes advantage of the hypergraph formalism to robustly fit a single model. It is not straightforward to extend it to the scenario where multiple models are required to explain the data.
+
+Multi-model fitting (MMF) is a relevant problem in many applications, such as 3D reconstruction, where it is employed to fit multiple rigid moving objects to initialize multi-body Structure from Motion [3, 37], or to produce intermediate interpretations of reconstructed 3D point clouds by fitting geometric primitives [32]. Other scenarios include face clustering, body-pose estimation, augmented reality and image stitching, to name a few.
+
+This paper proposes QUMF, i.e., the first quantum MMF approach. We propose to leverage the advantages of AQCs in optimizing combinatorial QUBO objectives to explain the data with multiple and disjoint geometric models. Importantly, QUMF does not assume the number of disjoint models to be known in advance. Note that the potential benefit from AQCs for MMF is higher than in the single-model case: when considering multiple models the search space scales exponentially with their number, making the combinatorial nature of the problem even more relevant. Furthermore, we show that QUMF can be easily applied to single-model fitting even though not explicitly designed for this task. We perform an extensive experimental evaluation on quantum hardware with many large-scale real datasets and obtain competitive results with respect to both classical and quantum methods. Figure 1 depicts a visual comparison between HQC-RF [17] and QUMF.
+
+Contributions. In summary, the primary technical contributions of this paper are the following:
+
+- We bring multi-model fitting, a fundamental computer vision problem with combinatorial nature, into AQCs;  
+- We introduce QUMF, demonstrating that it can be successfully used both for single and multiple models;  
+- We propose DEQUMF, a decomposition policy allowing our method to scale to large-scale problems, overcoming the limitations of modern quantum hardware.
+
+The following section provides the background on AQCs and how to use them to solve QUBO problems. After introducing QUMF and DEQUMF in Sec. 3, we discuss related work in Sec. 4. Experiments are given in Sec. 5. Limitations and Conclusion are reported in Sec. 6 and 7, respectively.
+
+# 2. Background
+
+The QUBO formulation in a binary search space is an optimization problem of the following form:
+
+$$
+\min  _ {\mathbf {y} \in \mathbb {R} ^ {d}} \mathbf {y} ^ {\mathsf {T}} Q \mathbf {y} + \mathbf {s} ^ {\mathsf {T}} \mathbf {y}, \tag {1}
+$$
+
+where  $\mathbb{B}^d$  denotes the set of binary vectors of length  $d$ ,  $Q \in \mathbb{R}^{d \times d}$  is a real symmetric matrix and, in a QUBO with  $d$  variables, their linear coefficients are packed into  $\mathbf{s} \in \mathbb{R}^d$ . When the problem is subject to linear constraints of the form  $A\mathbf{y} = \mathbf{b}$ , a common approach is to relax such constraints and reformulate the QUBO as:
+
+$$
+\min  _ {\mathbf {y} \in \mathbb {B} ^ {d}} \mathbf {y} ^ {\top} Q \mathbf {y} + \mathbf {s} ^ {\top} \mathbf {y} + \lambda | | A \mathbf {y} - \mathbf {b} | | _ {2} ^ {2}, \tag {2}
+$$
+
+where  $\lambda$  must be tuned to balance the contribution of the constraint term. Unravelling such a term leads to:
+
+$$
+\min  _ {\mathbf {y} \in B ^ {d}} \mathbf {y} ^ {\top} \tilde {Q} \mathbf {y} + \tilde {\mathbf {s}} ^ {\top} \mathbf {y} \tag {3}
+$$
+
+where the following simple substitutions are implied:
+
+$$
+\tilde {Q} = Q + \lambda A ^ {\mathsf {T}} A, \quad \tilde {\mathbf {s}} = \mathbf {s} - 2 \lambda A ^ {\mathsf {T}} \mathbf {b} \tag {4}
+$$
+
+For the proof, the reader can refer to, e.g., Birdal et al. [6].
+
+Adiabatic Quantum Computers (AQCs) are capable of solving QUBO problems. An AQC is organized as a fixed and architecture-dependent undirected graph, whose nodes correspond to physical qubits and whose edges correspond to couplers (defining the connectivity pattern among qubits) [14]. Such graph structure, in principle, can be mapped to a QUBO problem (1) as follows: each physical qubit represents an element of the solution (i.e., of the binary vector  $\mathbf{y}$ ), while each coupler models an element of  $Q$  (i.e., the coupler between the physical qubits  $i$  and  $j$  maps to entry  $Q_{ij}$ ). An additional weight term is assigned to each physical qubit, modelling the linear coefficients in s.
+
+Because AQC graphs are not fully connected, mapping an arbitrary QUBO to quantum hardware requires additional steps. This concept is easier to visualize if the notion of logical graph is introduced: the QUBO itself can also be represented with a graph, having  $d$  nodes (called logical qubits $^1$ ), corresponding to the  $d$  entries of  $\mathbf{y}$  and edges corresponding to the non-zero entries of  $Q$ .
+
+The logical graph undergoes minor embedding, where an algorithm such as [9] maps the logical graph to the physical one. During this process, a single logical qubit can be mapped to a set of physical qubits, i.e., a chain. All the physical qubits in a chain must be constrained to share the same state during annealing [38]. The magnitude of such
+
+constraint is called chain strength and the number of physical qubits in the chain is called chain length. An equivalent QUBO that can be directly embedded on the physical graph is obtained as the output of minor embedding.
+
+Then, optimization of the combinatorial objective takes place: we say that the AQC undergoes an annealing process. In this phase, the physical system transitions from a high-energy initial state to a low-energy final state, representing the solution of the mapped QUBO problem, according to the laws of quantum mechanics [18, 33]. At the end of the annealing, a binary assignment is produced for each physical qubit. A final postprocessing step is needed to go from physical qubits back to logical ones, thus obtaining a candidate solution for the original QUBO formulation (prior to minor embedding). Due to noise during the annealing process, the obtained solution may not correspond to the global optimum of the QUBO problem. In other terms, the annealing is inherently probabilistic and has to be repeated multiple times. The final solution is obtained as the one that achieves the minimum value of the objective function (lowest energy). Performing multiple annealings of the same QUBO form is called sampling.
+
+It is common practice [2, 17, 41, 53] to test the QUBO objective on classic computers using simulated annealing (SA) [25], a probabilistic optimization technique able to operate in the binary space. SA is probabilistic, so solutions are sampled multiple times, as it happens during quantum annealing. In contrast, SA operates on the original QUBO without embedding (i.e. directly on the logical graph) since no physical graph is involved. Importantly, SA can be used to evaluate performance on larger problem instances, in anticipation of larger AQC architectures.
+
+# 3. The Proposed Method
+
+In this section we derive our approach: first, we define an optimization function for the multi-model fitting task; then, we align it to the standard QUBO formulation, in order to enable quantum optimization; finally, we propose a decomposed version that can manage large-scale problems.
+
+# 3.1. Problem formulation
+
+Consider a set of data points  $X = \{x_{1},\dots,x_{n}\}$  and a set  $\Theta = \{\theta_1,\ldots ,\theta_m\}$  of tentative and redundant (parametric) models, which, in practice, are obtained by a random sample procedure as done in RANSAC [19]. Specifically, the models are instantiated by randomly selecting the minimum number of points necessary to unambiguously constrain the parameters of a model (e.g., 2 points for a line, 8 for a fundamental matrix). The aim of multi-model fitting is to extract from  $\Theta$  the "best" models that describe all the data  $X$ . Equivalently, MMF can be seen as a clustering problem, where points belonging to the same model must be grouped together. This is an ill-posed task since different
+
+interpretations of the same data are possible and recovering the best models requires the definition of a proper notion of optimality. To this end, the problem has been cast as the optimization of an objective function encoding different regularization strategies to disambiguate between interpretations and include additional prior about the data. The choice of the objective function is critical and determines the performance of the algorithm.
+
+# 3.2. Choice of Optimization Objective
+
+In this paper, we focus on the objective function of RANSACOV (Random Sample Coverage) [29] where MMF is treated as a set-cover problem. This choice is due to: i) the simplicity of the objective, which does not involve complex regularization terms as well as does not require to know in advance the number of models; ii) its combinatorial nature, that is well capitalized by a quantum formulation; iii) its generality, as this approach manages the broad situation of fitting multiple models, in contrast to previous work on quantum model fitting [17]. RANSACOV [29] casts MMF as an integer linear program. Such formulation is based on the notion of Preference-Consumus Matrix, which is commonly denoted by  $P$  and defined as:
+
+$$
+P [ i, j ] = \left\{ \begin{array}{l l} 1 & \text {i f e r r o r} \left(x _ {i}, \theta_ {j}\right) <   \epsilon \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {5}
+$$
+
+where:  $x_{i}$  and  $\theta_{j}$  are the  $i$ -th point in the dataset and the  $j$ -th sampled model respectively; error expresses the residual of point  $x_{i}$  w.r.t. model  $\theta_{j}$  and  $\epsilon$  is the inlier threshold to assign the point to the model.  $P$  is a matrix of size is  $n \times m$ , where  $n$  and  $m$  are the number of points and models, respectively. Intuitively, the columns of  $P$  represent the consensus sets of models, while the rows are points' preference sets.
+
+In this setup, selecting the subset of sampled models that best describe the data, is equivalent to selecting the minimum number of columns of  $P$  that explain all the rows. More formally:
+
+$$
+\min  _ {\mathbf {z} \in \mathbb {B} ^ {m}} \mathbb {1} _ {m} ^ {\mathsf {T}} \mathbf {z} \quad \text {s . t .} P \mathbf {z} \geqslant \mathbb {1} _ {n} \tag {6}
+$$
+
+where  $\mathbb{1}$  denotes a vector of ones (whose length is given as subscript) and  $\mathbf{z}$  is a binary vector representing which models (i.e., columns of the preference matrix  $P$ ) are selected. Solving (6) entails minimizing the number of selected models, while ensuring that each point is explained by at least one of them (as expressed by the inequality constraint). This problem is also known as set cover: we are looking for a cover of the data (i.e., a collection of sets whose union contains all the points) consisting of a minimum number of models, thus discouraging redundancy.
+
+Our goal is to express MMF as a QUBO, in order to make it suitable for optimization on an AQC and capitalize all the advantages of quantum computing. In general, posing a
+
+computer vision problem as a QUBO may not be straightforward, hence a careful choice of assumptions is essential. First, in this paper, we assume that the true number of models/clusters (denoted by  $k$ ) is unknown, so our approach is general. Second, we assume that outliers are not present in the data, i.e., there exist exactly  $k$  models that describe all the points. This is not a major limitation because, when outliers are present in the data, the models fitted to outliers could be easily recognized and discarded a-posteriori, using a-contrario reasoning [35], as usually done by MMF algorithms based on clustering [28, 42]. Third, we focus on the case where disjoint models are being sought, which is highly common in practical scenarios. In this situation, the inequality in (6) can be turned into an equality constraint.
+
+These assumptions allow to rewrite the problem in terms of disjoint set cover, which is the basis of our work:
+
+$$
+\min  _ {\mathbf {z} \in \mathbb {B} ^ {m}} \mathbb {1} _ {m} ^ {\mathsf {T}} \mathbf {z} \quad \text {s . t .} P \mathbf {z} = \mathbb {1} _ {n}. \tag {7}
+$$
+
+The above constraint, instead of ensuring that each point is explained by at least one selected model, forces each point to be explained by exactly one model, hence imposing the consensus sets of the selected models are disjoint. Problem (7) is the starting point of our QUBO formulation.
+
+# 3.3. QUBO Formulation
+
+Problem (7) is an integer linear program which is known to be NP-hard, hence it represents a suitable candidate to exploit the advantages of quantum optimization. To accomplish such a task, we need to turn (7) into a QUBO. Being a linear program, Problem (7) is, in particular, a special case of a quadratic program with linear equality constraints. Hence, if we pose constraints as soft ones (instead of hard ones), then we can rewrite (7) as (2) using the following correspondences:
+
+$$
+Q = 0, \quad \mathbf {s} = \mathbb {1} _ {m}, \quad A = P, \quad \mathbf {b} = \mathbb {1} _ {n} \tag {8}
+$$
+
+where optimization is carried out over  $\mathbf{z} \in \mathbb{B}^m$ , that represents the choice of a subset of optimal models. Putting together the equalities in (4) and (8), it follows that:
+
+$$
+\tilde {Q} = \lambda P ^ {\mathsf {T}} P, \quad \tilde {\mathbf {s}} = \mathbb {1} _ {m} - 2 \lambda P ^ {\mathsf {T}} \mathbb {1} _ {n} \tag {9}
+$$
+
+where no matrix of quadratic coefficients is present in  $\widetilde{Q}$  as the considered formulation only contains linear terms, i.e.,  $Q = 0$ . Hence, Problem (7) can be turned into a QUBO of the form (3), namely:
+
+$$
+\min  _ {\mathbf {z} \in \mathbb {B} ^ {m}} \lambda \mathbf {z} ^ {\top} (P ^ {\top} P) \mathbf {z} + \left(\mathbb {1} _ {m} - 2 \lambda P ^ {\top} \mathbb {1} _ {n}\right) ^ {\top} \mathbf {z}. \tag {10}
+$$
+
+Once a QUBO formulation has been obtained for a specific problem as in (10), an AQC can be leveraged to find an optimal solution, following the procedure from Sec. 2. This gives rise to our quantum approach for multi-model fitting, hereafter named QUMF.
+
+Algorithm 1 DEQUMF  
+Require:  $P,s$    
+while  $|P$  .columns  $\vert >s$  do subproblems  $= \text{ColumnPartition}(P,s)$ $i\gets 0$    
+while  $i <   |$  subproblems|do  $\mathcal{J}_i\gets$  models in the  $i$  -th subproblem  $P_{\mathcal{I}_i}\gets P$  retaining only the  $\mathcal{J}_i$  columns  $\mathbf{z}_i = \mathrm{QUMF}(P_{\mathcal{I}_i})$  remove from  $P$  columns  $P_{\mathcal{I}_i}[:,1 - \mathbf{z}_i]$ $i\gets i + 1$    
+end while   
+end while   
+ $\mathbf{z}\gets \mathrm{QUMF}(P)$    
+return  $P[:,\mathbf{z}]$
+
+# 3.4. Iterative Decomposed Set-Cover
+
+While the capabilities of quantum hardware are rapidly evolving [7, 24], current AQC architectures offer a limited number of physical qubits, thus the maximum dimension of the problems that can be solved is constrained in terms of  $m$ . In order to overcome this limitation, we present a decomposed approach that iteratively prunes out columns of the preference matrix  $P$  and reduces the dimension of the problem to fit the number of available physical qubits.
+
+Our iterative pruning procedure is named DEQUMF and is detailed in Algorithm 1. Instead of directly solving the problem encoded by the preference matrix  $P$ , at each iteration we partition the columns of  $P$  into multiple submatrices  $P_{\mathcal{J}_i}$ , where  $\mathcal{J}_i$  indicates the set of selected column indices and  $|\mathcal{J}_i| = s$ . We choose the subproblem size  $s$  so that the partitioned problems can be solved with high confidence by QUMF. Each subproblem encoded by  $P_{\mathcal{J}_i}$  is independently solved using QUMF (see Sec. 3.3), yielding an optimal binary vector  $\mathbf{z}_i$  that represents the subset of selected models for the current subproblem. Note that models not selected in  $\mathbf{z}_i$  are unlikely to be solutions to the original problem since, by construction,  $\mathbf{z}_i$  maximizes the coverage on all points with only the restricted subset of models  $\mathcal{J}_i$ . Then, after all subproblems have been solved, we prune  $P$  by retaining only the columns that are selected in the corresponding optimal  $\mathbf{z}_i$ . This has the effect of significantly decreasing the dimensionality of the search space (see Fig. 2).
+
+We iteratively apply the above procedure until the number of remaining columns in  $P$  falls below  $s$ , at which point the problem is directly and reliably solved using QUMF.
+
+# 4. Related Work
+
+The proposed approach is the first to address multimodel fitting using AQC. The most related work is HQC-RF [17] that leverages quantum computing as well for the scenario of single-model fitting.
+
+![](images/7974b62aff55b9686262afa416fda5adb67ad6385a2a793ec744d99befaf0f52.jpg)  
+Figure 2. Illustration of the iterative pruning technique applied to  $P$  in DEQUMF over consecutive iterations. At time  $t$ ,  $P$  is partitioned in different sub-problems of the same size (in the figure, 4 colour-coded problems with 6 models each) which are independently solved with QUMF. At time  $t + 1$ , models belonging to the sub-solutions (highlighted in red in the figure) are retained; the others are discarded.
+
+# 4.1. Multi-Model Fitting
+
+Robust fitting is a central problem in computer vision, and the case of multiple models counts several works that can be organized across two main directions, namely clustering-based and optimization-based methods.
+
+Clustering-based methods cast multi-model fitting as a clustering task where points belonging to the same model must be grouped together. Several procedural algorithms have been presented leveraging different schemes: hierarchical clustering [28, 31, 32, 44, 55], kernel fitting [10, 12], robust matrix factorization [30, 43], biclustering [16, 42], higher order clustering [1, 21, 23, 54] and hypergraph partitioning [27, 39, 47, 48, 50].
+
+Our approach falls instead in the category of optimization-based methods. Compared with procedural approaches based on clustering, methods based on the optimization of a precise objective function provide a quantitative criterion for evaluating the quality of the retrieved solution. In particular, our QUMF belongs to consensus-based approaches that generalize RANSAC by maximizing the consensus of the sought models. Sequential RANSAC [46], Multi-RANSAC [56] and RANSACOV [29] belong to this category as well. Other sophisticated techniques, that integrate consensus with additional priors, have also been proposed: Pearl [22], Multi-X [4] and Prog-X [5].
+
+Our approach is related to RANSACOV [29] as we consider the same data structure, i.e., the preference matrix, and a similar optimization objective<sup>2</sup>. However, there are sub
+
+stantial differences. RANSACOV addresses the task via integer linear programming, as Magri and Fusiello [29] use the MATLAB function intlinprog, which employs linear programming relaxation followed by rounding the found solution, in a combination with some heuristics. In case of failure it reduces to branch and bound. Our approach, instead, leverages quantum effects to optimize the objective directly in the space of qubits, where global optimality is expected with high probability after multiple anneals.
+
+# 4.2. Quantum Computer Vision
+
+Recently, many vision problems have been formulated for an AQC in QUBO forms, hence giving rise to the new field of Quantum Computer Vision (QCV). AQC are especially promising for problems involving combinatorial optimization (see Sec. 2) such as graph matching [40, 41], multi-image matching via permutation synchronization [6], single-model fitting [17], multi-object tracking [53], removing redundant boxes in object detection [26], and motion segmentation [2]. Moreover, solving non-combinatorial problems on quantum hardware is of high general interest as well, since new formulations have unique properties, can be compact and would allow seamless integration with other quantum approaches in future. Thus, several methods address point set alignment [20, 34] and approximate rotation matrices by the exponential map with power series.
+
+Depending on the problem, QUBO formulation can be straightforward [26, 40, 53] or require multiple analytical steps bringing the initial objective to the quadratic form [2, 6, 17]. In most cases, problem-specific constraints must be included in a QUBO as soft linear regularizers, as done in (2). This strategy is followed by the majority of works in the literature, including [2, 6, 17, 40, 53] and our approach. Alternatively, it has been recently shown that it is possible to tackle linearly-constrained QUBO problems via the Frank-Wolfe algorithm [52], which alleviates the need for hyper-parameter tuning, at the price of iteratively solving multiple QUBO problems and sub-linear convergence.
+
+All available approaches can be classified into single QUBO ("one sweep") and iterative methods. The first category prepares a single QUBO that is subsequently sampled on an AQC to obtain the final solution [2,6,20,26,40]. These methods can solve comparably small problems on current hardware: in the recent QuMoSeg [2], the maximum problem size solved with high accuracy has 200 qubits, which correspond to five images with two motions having ten points each. In QuantumSync [6], real experiments involve matching four keypoints in four images only. The second category of methods, instead, alternates between QUBO preparation on a CPU and QUBO sampling on an AQC, until convergence or a maximum number of iterations is reached [17,34,41]. This is done either to overcome the limit on the maximum problem size solvable on
+
+current quantum hardware [34, 41] or because the QUBO represents only a small portion of the whole problem, hence requiring additional (classical) steps as in Q-Match [41] and HQC-RF [17]. Closely related to iterative methods are decompositional approaches (e.g., [53]) that partition the original objective into QUBO subproblems. This paper proposes both a single QUBO method (see Sec. 3.3) and a decompositional, iterative pruning approach (see Sec. 3.4).
+
+Differences to HQC-RF. Most related to ours is a hybrid quantum-classical approach for robust fitting, HQC-RF [17], that can be regarded as a pioneer in bringing robust fitting into a QUBO-admissible form, thus paving the way to the adoption of AQCs for such a class of hard combinatorial problems. HQC-RF and our approach have substantial differences. First, although being both based on linear programs, the two formulations do not share common steps: HQC-RF considers the hypergraphs formalism, relying on multiple QUBOs in an iterative framework; our formulation, instead, is more compact as it involves a single QUBO in its one-sweep version. Second, HQC-RF considers a single model, whereas we consider the more general case of multiple models, which is relevant in practical applications and more challenging in terms of the search space and the number of unknowns involved. Extending Doan et al. [17] to MMF is not straightforward (it is not clear so far whether it is possible). Finally, HQC-RF is evaluated with an AQC on synthetic data only, whereas we test our method on several synthetic and real datasets on real quantum hardware, as shown in Sec. 5. Fig. 1 summarizes the core differences between HQC-RF [17] and our approach.
+
+Remark. Finally, it is also worth mentioning the technique for robust fitting (single model) by Chin et al. [11] evaluated on a simulator and designed for a different type of quantum hardware than AQC, i.e., a gate-based quantum computer (GQC). GQCs operate differently from AQCs, i.e., they execute unitary transformations on quantumly-encoded data, and currently possess a much smaller number of qubits compared to AQCs [24]. We focus on methods that can run on real quantum hardware. Unfortunately, modern AQCs cannot run algorithms designed for GQCs.
+
+# 5. Experiments
+
+In this section, we illustrate several experiments on synthetic and real datasets to evaluate the proposed approaches. The chosen metric is the misclassification error, that is the percentage of wrongly classified points, as it is common practice in this field. Our comparisons mainly concentrate on the classical RANSACOV [29] and the hybrid quantum-classical HQC-RF [17], which are the most related to our approaches, as explained in Sec. 4. Quantum experiments run on the DWave Advantage System 4.1, a modern AQC by DWave built with the Pegasus topology [7], comprising approximately 5000 physical qubits. Communication with the
+
+![](images/fcc2996690464e415e76d60e81fea03f4dd8a3a6afc5952afa587cac738f4d6a.jpg)  
+Figure 3. Misclassification Error for several methods on the Star5 dataset [44]. The number of points  $n$  is fixed to  $n = 30$ , the number of ground-truth structures is fixed to  $k = 5$ , and the number of sampled models  $m$  is arranged on the x-axis.
+
+![](images/619b7500bcc91c415825961aeb7cebdf7c7724f9f8b038a27fdef64f56e84587.jpg)  
+Figure 4. Relationship between physical qubits and logical qubits in embeddings produced with small-scale preference matrices from the Star5 dataset [44].
+
+AQC is managed via the Ocean software stack [13] and every experiment is executed with an annealing time of  $20\mu s$
+
+Selection of  $\lambda$ . In every experiment, we set  $\lambda = 1.1$ . This value is obtained with a two-step procedure: 1) Initially, following common practices (see, e.g., [2,6]), we perform an exhaustive grid search using QUMF to solve small-scale problems (encoded by at most 20 qubits), from which we get an initial guess for  $\lambda$  by looking at the optimal solution probability; 2) Then, we evaluate the initial guess further, solving problems encoded by at most 100 qubits with QUMF (SA), verifying whether or not the initial guess for  $\lambda$  generalizes well to larger problems, too. In this second step, the reference metric is the misclassification error.
+
+# 5.1. Synthetic Data
+
+We consider the synthetic Star5 dataset [44], that is used to fit five lines (depicting a star) given a set of 2D points. Outliers are removed to satisfy our assumptions.
+
+Small-scale Data. In this experiment, we select a subset of  $n = 30$  points. The number of ground-truth models is fixed to  $k = 5$ , and additional  $m - k$  excess models are sampled in order to study performances with increasing problem size. Note that this corresponds to including false models (i.e., columns) in the preference matrix, thereby representing noise. For each configuration, 20 preference ma
+
+![](images/b1d0c7c65a8de500bfb6816dcef9456944eab3bf387f56d4b33115b8f8ef4fa4.jpg)  
+Figure 5. Misclassification Error for several methods on the Star5 dataset [44]. The number of points  $n$  is fixed to  $n = 250$ , the number of ground-truth structures is fixed to  $k = 5$ , and the number of sampled models  $m$  (corresponding to the dimension of the search space) is arranged on the x-axis.
+
+trices are generated and averaged results are reported. We consider our single-QUBO quantum approach QUMF and its CPU counterpart QUMF (SA). We also compare our approaches with RANSACOV [29], whose code is available online $^4$ , that can be viewed as a baseline implementing a sophisticated integer programming solver. All the methods receive as input the same preference matrix and optimize the same objective, as already observed in Sec. 4.1.
+
+Results are given in Fig. 3, showing that QUMF can exactly solve problems up to 40 qubits, but it can not solve larger problems with high accuracy: this is an expected behaviour (in line with previous quantum papers, see Sec. 4.2), as current quantum hardware is limited and far from maturity. It is worth noting that our QUMF (SA) achieves excellent results (on par with RANSACOV) for all the analyzed problem sizes: considering that QUMF (SA) uses the same QUBO as QUMF, we can thus view the former as an indication on the performances the latter can achieve in the future thanks to the continuous improvements in the quantum hardware.
+
+Physical vs Logical Qubits. We analyze here how the allocation of QPU resources (physical qubits) grows with increasing problem size (logical qubits). Similarly to our previous experiment, we use synthetic preference matrices generated from the Star5 dataset with increasing number of columns. However, we consider here all of the 250 points in the dataset in order to study denser cases. Our analysis is displayed in Fig. 4, showing that physical qubits grow super-linearly with respect to logical ones. Such relationship makes it infeasible to allocate real world problems, as they typically require thousands of logical qubits. This finding, given the current state of the hardware, strengthens the need for a decomposition approach. Hence, we analyze our decomposition policy in the next paragraph.
+
+Large-scale Data. In this experiment, we consider up to 1000 models in the input preference matrix (also including the  $k = 5$  ground-truth models) as well as all of the  $n = 250$
+
+points in the Star5 dataset. Since QUMF is not able to manage such large-scale data, it is not considered here. Instead, it is used as a sub-component of our decomposed approach DEQUMF: each sub-problem has a dimension that can be solved with high accuracy by QUMF, namely 20 qubits. As a reference, we also include QUMF (SA) and its decomposed version DEQUMF (SA) as well as RANSACOV [29].
+
+Results are given in Fig. 5, showing that our DEQUMF (SA) achieves nearly zero misclassification error in all the cases, on par with RANSACOV. Average DEQUMF errors lie in the range  $[0,10]\%$  for all problem sizes, showing the great effectiveness of the decomposition principle. As for QUMF (SA), this specific dataset represents a failure case: after inspecting the solution, we hypothesize that a possible reason is the sparsity pattern of the preference matrix, causing the algorithm to select more models than needed.
+
+# 5.2. Real Data
+
+In this section, we test our framework on several real world datasets, each associated to a different task. Since these are large-scale problems, we do not consider QUMF but its CPU variant QUMF (SA).
+
+AdelaideRMF dataset [49]. From this benchmark, we consider the 15 sequences involving multiple fundamental matrices (which, in turn, can be used to perform motion segmentation in two images) and we remove outliers beforehand. All the analyzed methods are given the same preference matrices as input. Results are given in Tab. 2. Both QUMF (SA) and DEQUMF (SA) significantly outperform RANSACOV [29] in this scenario. In particular, DEQUMF (SA) performs better than its quantum version DEQUMF, in agreement with our previous experiments.
+
+Hopkins benchmark [45]. From this dataset, we consider the Traffic2 and Traffic3 sequences, which comprise 31 and 7 scenes, respectively. Here, the task is to fit multiple subspaces to point trajectories in the context of video motion segmentation. This benchmark provides outlier-free data, hence no pre-processing is needed. Results are given in Tab. 1: in addition to RANSACOV [29], other multimodel fitting approaches have been considered, whose results are taken from the respective papers. All the variants of our approach<sup>5</sup> perform reasonably well, with DEQUMF (SA) being on par with the state of the art.
+
+York Urban Line Segment Database [15]. This dataset contains 102 images used for vanishing point detection from multiple line segments without outliers. Results are presented in Table 1, following the same rationales as per the Hopkins benchmark. Such results are in line with our previous experiments: in particular, DEQUMF (SA) exhibits competitive performances with the state of the art.
+
+Table 1. Misclassification Error [%] on the Traffic3 and Traffic2 subsets of the Hopkins benchmark [45] and on the York DB [15].  
+
+<table><tr><td></td><td></td><td>Multi-X [4]</td><td>J-Linkage [44]</td><td>T-Linkage [28]</td><td>RPA [30]</td><td>RANSACOV [29]</td><td>QUMF (SA)</td><td>DEQUMF</td><td>DEQUMF (SA)</td></tr><tr><td rowspan="2">Traffic3 [45]</td><td>mean</td><td>0.32</td><td>1.58</td><td>0.48</td><td>0.19</td><td>0.35</td><td>5.14</td><td>8.74</td><td>0.55</td></tr><tr><td>median</td><td>0</td><td>0.34</td><td>0.19</td><td>0</td><td>0.19</td><td>2.85</td><td>7.50</td><td>0.28</td></tr><tr><td rowspan="2">Traffic2 [45]</td><td>mean</td><td>0.09</td><td>1.75</td><td>1.31</td><td>0.14</td><td>0.54</td><td>6.04</td><td>-</td><td>0.10</td></tr><tr><td>median</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>3.17</td><td>-</td><td>0</td></tr><tr><td rowspan="2">York [15]</td><td>mean</td><td>-</td><td>2.85</td><td>1.44</td><td>1.08</td><td>0.19</td><td>12.29</td><td>-</td><td>0.74</td></tr><tr><td>median</td><td>-</td><td>1.80</td><td>0</td><td>0</td><td>0</td><td>3.78</td><td>-</td><td>0</td></tr></table>
+
+<table><tr><td></td><td>RANSACOV [29]</td><td>QUMF (SA)</td><td>DEQUMF</td><td>DEQUMF (SA)</td></tr><tr><td>mean</td><td>9.79</td><td>3.85</td><td>16.22</td><td>0.77</td></tr><tr><td>median</td><td>7.97</td><td>3.54</td><td>11.0</td><td>0.18</td></tr></table>
+
+# 5.3. Comparison with Quantum State-of-the-art
+
+Our method is the first quantum solution to multi-model fitting, hence there are no quantum competitors in the literature. The most similar work to ours is HQC-RF [17], whose code is available online<sup>6</sup>, which addresses single-model fitting in the presence of outliers (see Sec. 4.2). HQC-RF has strong theoretical justifications, and the proposed algorithm terminates with either the globally optimal solution or a feasible solution paired with its error bound. Neither QUMF or DEQUMF have this property. On the other hand, our framework is general and can be used for a single model as well, allowing for an experimental comparison with HQC-RF [17]. Specifically, we exploit the information that only a single model is present in the data and we select, from the solution returned by set-cover, only the model with the maximum consensus set. All the other models in the solution are treated as outliers.
+
+We focus on fundamental matrix estimation and use the 4 sequences of the AdelaideRMF dataset [49] characterized by the presence of a single model. Since this is a large-scale dataset, we omit QUMF and consider QUMF (SA), DEQUMF and DEQUMF (SA), as previously done. We analyze how performances vary with different outlier ratios: we consider  $10\%$  and  $20\%$  of outliers, in addition to the evaluation on the original sequences, where no fixed outlier ratio is imposed. Results are summarized in Tab. 3.
+
+HQC-RF shows remarkable behaviour in controlled scenarios with low outlier ratios; however, it is worth noting that our method is more robust to higher outlier ratios, although not explicitly designed for single-model fitting. See also Fig. 6 for qualitative results of worst-case scenarios.
+
+# 6. Limitations
+
+Differently than current quantum methods for single-model robust fitting [17], our approach does not terminate
+
+Table 2. Misclassification Error [%] for several methods on the 15 multi-model sequences of the AdelaideRMF dataset [49].  
+
+<table><tr><td rowspan="2">Algorithm</td><td colspan="3">Outlier ratio</td></tr><tr><td>10%</td><td>20%</td><td>Full sequences</td></tr><tr><td>QUMF (SA)</td><td>7.22</td><td>11.34</td><td>13.23</td></tr><tr><td>DEQUMF</td><td>2.41</td><td>10.53</td><td>16.17</td></tr><tr><td>DEQUMF (SA)</td><td>6.26</td><td>8.28</td><td>10.83</td></tr><tr><td>HQC-RF [17]</td><td>3.71</td><td>37.0</td><td>45.84</td></tr></table>
+
+Table 3. Misclassification Error [%] for quantum methods on the single-model sequences of the AdelaideRMF dataset [49].
+
+![](images/cca06efa4822d1a5eeafcc75d43abbb4354bc89338573e739da3c9a71476f8fa.jpg)  
+DEQUMF (SA)
+
+![](images/2718e7988b4c7a55ad82a54a0355278d565bf2da9c76213bd044f29b0d0c68e6.jpg)  
+HQC-RF [17]  
+Figure 6. A sample of the worst results of the considered quantum methods on the book image pair from the AdealideRMF [49] with  $20\%$  outliers. Outliers and inliers are shown in red and green, respectively. On the right, HQC-RF [17] classifies all the points as outliers, whereas our method achieves  $8.49\%$  error.
+
+with a solution paired with its error bound. Additionally, the decomposition policy at the core of DEQUMF does not provide theoretical guarantees of global optimality, as globally optimal models may be discarded with locally optimal selection performed by QUMF. We believe it is worth trying to investigate this research question in future work.
+
+# 7. Conclusion
+
+We brought a new, very important problem into AQC-admissible form. Our method shows promising results on a variety of datasets for MMF and even surpasses the quantum SotA on single-model fitting, although not explicitly designed for such task. We believe it offers many avenues for future research.
+
+Acknowledgements. This paper is supported by FAIR (Future Artificial Intelligence Research) project, funded by the NextGenerationEU program within the PNRR-PE-AI scheme (M4C2, Investment 1.3, Line on Artificial Intelligence). This work was partially supported by the PRIN project LEGO-AI (Prot. 2020TA3K9N) and it was carried out in the Vision and Learning joint laboratory of FBK and UNITN.
+
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+        "type": "text",
+        "text": "Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification",
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+        "type": "text",
+        "text": "Jie Zhang $^{1}$ , Yongshan Zhang $^{2,1*}$ , Yicong Zhou $^{1*}$",
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+        "type": "text",
+        "text": "$^{1}$  Department of Computer and Information Science, University of Macau, Macau, China  $^{2}$  School of Computer Science, China University of Geosciences, Wuhan, China",
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+    {
+        "type": "text",
+        "text": "jiezh1997@gmail.com, yszhang.cug@gmail.com, yicongzhou@um.edu.m",
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+    {
+        "type": "text",
+        "text": "Abstract",
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+        "text": "Hyperspectral image (HSI) classification aims at assigning a unique label for every pixel to identify categories of different land covers. Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. In this pyramid framework, QSSPN progressively learns feature representations by cascading QSSN blocks and performs classification with a softmax classifier. It is the first attempt to introduce quantum theory in HSI processing model design. Substantial experiments are conducted on three HSI datasets to verify the superiority of the proposed QSSPN framework over the state-of-the-art methods.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. Each HSI contains two spatial dimensions and one spectral di",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f8e92293ecb73eba639865db402b61a405202b3924c0e52d8206f1a103228dcd.jpg",
+        "image_caption": [
+            "Figure 1. Performance comparison between the proposed QSSPN framework and existing methods. Average accuracies on Indian Pines dataset are presented."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49].",
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+        "text": "In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and  $K$ -nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "type": "page_footnote",
+        "text": "*Corresponding authors.",
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+        "page_idx": 0
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+    {
+        "type": "page_number",
+        "text": "9925",
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+    {
+        "type": "text",
+        "text": "in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks",
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+    {
+        "type": "text",
+        "text": "and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The contributions of this article are summarized as follows.",
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+    {
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+        "list_items": [
+            "- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising.",
+            "- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations.",
+            "- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion.",
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+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45].",
+        "bbox": [
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+        "text": "9926",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f55728ced1a6ba370d2c5c93235a61a3535ba4fc48139753d716f3d45a213148.jpg",
+        "image_caption": [
+            "Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            762,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in  $N$ -dimensional Hilbert space  $\\mathcal{H}^N$ . We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations  $\\left|\\cdot \\right\\rangle$  and  $\\langle \\cdot |$  denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors  $\\{\\left|\\phi_n\\right\\rangle \\}_{n = 1}^N$ , we can represent the states of quantum system  $|\\psi \\rangle$  as follows*:",
+        "bbox": [
+            496,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n| \\psi \\rangle = \\sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \\theta_ {n}} | \\phi_ {n} \\rangle , \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            611,
+            397,
+            890,
+            439
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $A_{n}$  is a probability amplitude satisfying  $\\sum_{N}|A_{n}|^{2} = 1$ ,  $i$  is the imaginary unit and  $\\theta_{n}$  indicates the phase. A simple example of basis state vectors for  $\\mathcal{H}^N$  is standard unit basis. Detailedly, the standard basis of  $\\mathcal{H}^2$  is formed by column vectors  $|0\\rangle_2 = [1,0]^T$  and  $|1\\rangle_2 = [0,1]^T$ . Here, we use the notation",
+        "bbox": [
+            498,
+            448,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left| n \\right\\rangle_ {N}, n = 0, 1, \\dots , N - 1 \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            602,
+            551,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to represent the standard basis of  $\\mathcal{H}^N$ . Accordingly,  $\\langle n|_N$  denotes the conjugate transpose of  $|n\\rangle_N$ . All components of  $|n\\rangle_N$  are 0 except the  $n$ -th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states.",
+        "bbox": [
+            496,
+            579,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The reversible unitary operator  $U$  describes the state's evolution in QC, mapping the initial states  $|\\psi_{initial}\\rangle$  to final states  $|\\psi_{final}\\rangle$ . These operators manipulate the phases  $\\theta_{n}$  and amplitudes  $A_{n}$  by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators  $\\{\\Pi_m = |\\phi_m\\rangle \\langle \\phi_m|\\}_{m = 1}^M$ . According to the Born rule [28],  $\\Pi_{m}$  projects the state  $|\\psi_{final}\\rangle$  to the corresponding basis state  $|\\phi_m\\rangle$  with a probability:",
+        "bbox": [
+            496,
+            640,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = T r \\left(\\Pi_ {m} \\rho\\right) = \\left\\langle \\phi_ {m} \\mid \\psi_ {\\text {f i n a l}} \\right\\rangle \\left\\langle \\psi_ {\\text {f i n a l}} \\mid \\phi_ {m} \\right\\rangle , \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            818,
+            890,
+            835
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|$  is the density matrix representation of  $|\\psi_{final}\\rangle$  and  $\\sum_{M}P(|\\phi_{m}\\rangle) = 1$ .  $|\\cdot \\rangle \\langle \\cdot |$  denotes the",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "*Only pure states are considered in this paper.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "9927",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e07cba4561baba1f2b8e0f9c2aea9c4e04b9ce0181a5c2168beb225e437b9a6e.jpg",
+        "image_caption": [
+            "Figure 3. Illustration of data mapping in QSSN. The state representation  $|\\psi \\rangle$  encodes data from original space to Hilbert space:  $\\mathcal{R} \\to \\mathcal{H}$ . The MFM outputs a feature vector mapped from  $|\\psi \\rangle$  to feature space:  $\\mathcal{H} \\to \\mathcal{F}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            98,
+            467,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "outer product and  $\\langle \\cdot |\\cdot \\rangle$  denotes the inner product of  $\\langle \\cdot |$  and  $|\\cdot \\rangle$  . Eq. (3) can be rewritten as:",
+        "bbox": [
+            76,
+            301,
+            470,
+            335
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} P \\left(\\left| \\phi_ {m} \\right\\rangle\\right) = \\left\\langle \\phi_ {m} \\right| \\rho \\left| \\phi_ {m} \\right\\rangle = \\left(\\left\\langle \\psi_ {f i n a l} \\mid \\phi_ {m} \\right\\rangle\\right) ^ {2} \\tag {4} \\\\ = \\sum_ {n _ {1}} ^ {N - 1} \\sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\\theta_ {n _ {1}} - \\theta_ {n _ {2}})} \\langle \\phi_ {m} | n _ {1} \\rangle \\langle n _ {2} | \\phi_ {m} \\rangle . \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            104,
+            342,
+            468,
+            406
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Here we neglect the subscript  $N$  of  $|n\\rangle_N$  for simplicity. In Eq. (4), the size of  $|n\\rangle$  is  $N$ . For the same measurement operator  $\\Pi_m \\sim |\\phi_m\\rangle$ , the output  $P(|\\phi_m\\rangle)$  depends on all pairs of  $A_{n_1}$  and  $A_{n_2}$  and their correlations  $(\\theta_{n_1} - \\theta_{n_2})$ . PVM yields values  $P_{res} = [P(|\\phi_1\\rangle), P(|\\phi_2\\rangle), \\ldots, P(|\\phi_M\\rangle)]$  corresponding to the selected projection operators  $\\{\\Pi_m\\}_{m=1}^M$ , reflecting the state of quantum system.",
+        "bbox": [
+            76,
+            414,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28].",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Quantum-Inspired Spectral-Spatial Network",
+        "text_level": 1,
+        "bbox": [
+            76,
+            590,
+            457,
+            606
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Let  $X \\in \\mathcal{R}^{H \\times W \\times B}$  be the HSI with  $H$  pixels in height,  $W$  pixels in width, and  $B$  spectral bands. Taking the  $(i,j)$ -th pixel as center, information in a small cuboid  $x_{i,j} \\in \\mathcal{R}^{P \\times P \\times B}$  with  $P \\times P$  pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad  $X$  with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification.",
+        "bbox": [
+            75,
+            611,
+            468,
+            762
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases  $\\Theta_{i,j} \\in R^{P \\times P \\times B}$  for all elements  $x_{i',j',k'}'$  in  $x_{i,j}$ . Phases play an important role in encoding data  $x_{i,j}$  in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class",
+        "bbox": [
+            75,
+            763,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase  $\\theta_{i',j',k'}$  for each element  $x_{i',j',k'}'$ . Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each  $x_{i',j',k'}'$ , the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have  $B$  channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in  $3\\times 3$  pixel windows. The following asymmetric convolution layers [37] with  $3\\times 1$  and  $1\\times 3$  kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases  $\\Theta_{i,j}$ . Before we encode each HSI cuboid into complex finite-dimensional Hilbert space  $\\mathcal{H}^K$  ( $K = P\\times P\\times B$ ), we reshape the HSI cuboid  $x_{i,j}$  and the corresponding phase cuboid  $\\Theta_{i,j}$  as follow:",
+        "bbox": [
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+            90,
+            892,
+            348
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} x ^ {v e c} = \\left[ x _ {0} ^ {\\prime}, \\dots , x _ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P} ^ {\\prime}, \\dots , x _ {K - 1} ^ {\\prime} \\right], \\tag {5} \\\\ \\Theta^ {v e c} = \\left[ \\theta_ {0}, \\dots , \\theta_ {i ^ {\\prime} + j ^ {\\prime} \\times P + k ^ {\\prime} \\times P \\times P}, \\dots , \\theta_ {K - 1} \\right], \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            356,
+            892,
+            391
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $i', j' \\in [0 : P - 1]$  and  $k' \\in [0 : B - 1]$ . Then phase vector  $x^{vec}$  and original data vector  $x^{vec}$  are used in the state vector representation  $|x_{i,j}\\rangle$  as follows:",
+        "bbox": [
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+            398,
+            892,
+            446
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left| x _ {i, j} \\right\\rangle = \\sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \\theta_ {n}} \\left| n \\right\\rangle_ {K}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            602,
+            455,
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+            498
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Eq. (6),  $A_{n}$  can be obtained as:",
+        "bbox": [
+            500,
+            507,
+            725,
+            522
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA _ {n} = \\sqrt {\\frac {x _ {n} ^ {v e c}}{\\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            617,
+            532,
+            890,
+            574
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $x_{n}^{vec}$  indicates the  $n$ -th element in  $x^{vec}$ . In Eq. (6),  $x_{i,j}$  can be represented by a complex vector  $|x_{i,j}\\rangle = [A_0e^{i\\theta_0}, A_1e^{i\\theta_1}, \\ldots, A_{K-1}e^{i\\theta_{K-1}}]$  in  $\\mathcal{H}^K$ . As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode  $x_{i,j}$  in  $|x_{i,j}\\rangle$  is neglecting the imaginary parts  $e^{i\\theta}$  (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations.",
+        "bbox": [
+            496,
+            583,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation  $(MO)$  to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as  $PVM(\\Pi_m,\\rho)$ : using a density matrix  $\\rho$  to represent the state of quantum system  $\\rho = |\\psi_{final}\\rangle \\langle \\psi_{final}|$  and then applying the matrix manipulation (matrix product and trace)",
+        "bbox": [
+            496,
+            779,
+            893,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9928",
+        "bbox": [
+            480,
+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with operators  $\\{\\Pi_m\\}_{m=1}^M$ . For each  $\\Pi_m$ , we get the probability  $P(|\\phi_m\\rangle)$ . Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by",
+        "bbox": [
+            76,
+            90,
+            468,
+            151
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} D _ {i, j} = \\left| x _ {i, j} \\right\\rangle \\left\\langle x _ {i, j} \\right| \\tag {8} \\\\ = \\sum_ {n = 0} ^ {K - 1} \\sum_ {n ^ {\\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\\prime}} e ^ {i \\left(\\theta_ {n} - \\theta_ {n ^ {\\prime}}\\right)} \\left| n ^ {\\prime} \\right\\rangle \\left\\langle n \\right|, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            145,
+            164,
+            467,
+            223
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $|n^{\\prime}\\rangle \\langle n|$  represents a square matrix with  $P\\times P\\times B$  rows and columns that all components are 0 except the  $(n,n^{\\prime})$ -th component is 1. Each term in the density matrix  $D_{i,j}$  is the multiplication of  $A_{n}$  and  $A_{n^{\\prime}}$  with a coefficient  $e^{i(\\theta_n - \\theta_{n^{\\prime}})}$ . Empirically, this is similar to fusing information of each pair of elements  $x_{n}^{vec}$  and  $x_{n^{\\prime}}^{vec}$ . Phases  $\\theta_{n}$  and  $\\theta_{n^{\\prime}}$  are predicted by PPM. We hope the imaginary part  $e^{i(\\theta_n - \\theta_{n^{\\prime}})}$  can dynamically modulate the correlations between  $x_{n}^{vec}$  and  $x_{n^{\\prime}}^{vec}$ . In each pair, the location and band of  $x_{n}^{vec}$  and  $x_{n^{\\prime}}^{vec}$  may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result  $P(|\\phi_m\\rangle)$  corresponding to  $\\Pi_{m}$ . Note that PVM has corresponding operations applied on physic devices. There are constraints of operations  $\\Pi_{m}$  in their mathematical formulation in quantum theory. We use an abstract representation of PVM as  $PVM(\\Pi_m,\\rho)\\rightarrow PVM(Operator_m,\\rho)$ . To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers  $FC_{m}$  with depth 3 as  $Operator_{m}$ . The MO generates a feature point as follows:",
+        "bbox": [
+            76,
+            232,
+            468,
+            580
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf e a _ {m} = M O \\left(F C _ {m}, D _ {i, j}\\right), \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            178,
+            590,
+            467,
+            607
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $D_{i,j}$  stores the fusion information of each element pair,  $x_{n}^{vec}$  and  $x_{n'}^{vec}$ .  $MO$  is an operation that feeds  $D_{i,j}$  into the operator  $FC_{m}$  to efficiently aggregate spatial and spectral information. Given  $M$  operators  $\\{FC_{m}\\}_{m=1}^{M}$ , we can get an  $M$ -dimensional feature vector  $F^{vec} = [fea_{1},fea_{2},\\ldots,fea_{M}]$ . Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus,  $M$  should be carefully designed for preserving important factors in data.",
+        "bbox": [
+            76,
+            617,
+            467,
+            752
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Following the steps above, QSSN extracts an  $M$ -dimensional feature vector from input cuboid  $x_{i,j}$  with the size of  $P \\times P \\times B$ . Furthermore, we introduce a new notation  $N$ -QSSN to denote the learned vector representation  $F^{vec}$  with the size of  $(P \\times P \\times N) \\times 1$ . The output feature vector  $F^{vec}$  is reshaped into a 3-D feature cuboid  $F^{cub}$  with the size of  $P \\times P \\times N$ . In  $N$ -QSSN, the size of  $M$  to denote the number of  $MO$  is determined by",
+        "bbox": [
+            76,
+            753,
+            467,
+            873
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM = P \\times P \\times N. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            210,
+            886,
+            467,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The outcome of  $N$ -QSSN  $F^{cub}$  has same spatial resolution as  $x_{i,j}$ . The input HSI cuboid  $x_{i,j}$  has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The  $N$ -QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the  $N$ -QSSN blocks.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. QSSN-based Pyramid Framework",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from  $x_{i,j}$ , followed by a classifier to identify the land-cover category of the center pixel (i.e., the  $(i,j)$ -th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks,  $N_{1}$ -QSSN and  $N_{2}$ -QSSN are stacked in a hierarchical manner. Specifically, for  $N_{1}$ -QSSN, we take an original cuboid with the size of  $P \\times P \\times B$  as input to learn the feature cuboid with the size of  $P \\times P \\times N_{1}$  as output. Sequentially, for  $N_{2}$ -QSSN, we use the feature representation with the size of  $P \\times P \\times N_{1}$  learned from  $N_{1}$ -QSSN as input to extract the feature cuboid with the size of  $P \\times P \\times N_{2}$  as output. In our setting,  $B > N_{1} > N_{2}$ , meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN-  $L$  to indicate QSSPN with  $L$  QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9929",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/e78b27c82abcc3fc36fc035ea7499e2a5cbf7a1cce9289a4971f1aa1faeee347.jpg",
+        "table_caption": [
+            "Table 1. Classification results and model analysis of different methods on HSI datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Datasets</td><td>Metrics</td><td>SSAN</td><td>SSRN</td><td>RvT</td><td>HiT</td><td>SSFTT</td><td>QSSPN-1</td><td>QSSPN-2</td><td>QSSPN-3</td></tr><tr><td rowspan=\"5\">IP</td><td>OA (%)</td><td>89.46</td><td>91.85</td><td>83.85</td><td>90.59</td><td>96.35</td><td>90.36</td><td>92.66</td><td>95.87</td></tr><tr><td>AA (%)</td><td>85.99</td><td>81.51</td><td>79.67</td><td>86.71</td><td>89.99</td><td>89.93</td><td>93.34</td><td>96.40</td></tr><tr><td>κ(%)</td><td>88.04</td><td>90.73</td><td>81.68</td><td>89.27</td><td>95.82</td><td>89.05</td><td>91.68</td><td>95.34</td></tr><tr><td>Params.</td><td>148.83K</td><td>735.88K</td><td>10.78M</td><td>49.60M</td><td>148.50K</td><td>910.50K</td><td>1.13M</td><td>1.17M</td></tr><tr><td>FLOPs</td><td>7.88M</td><td>212.48M</td><td>17.83M</td><td>345.88M</td><td>3.66M</td><td>34.54M</td><td>52.75M</td><td>55.59M</td></tr><tr><td rowspan=\"5\">PU</td><td>OA (%)</td><td>99.15</td><td>99.63</td><td>97.37</td><td>99.43</td><td>99.52</td><td>99.38</td><td>99.44</td><td>99.71</td></tr><tr><td>AA (%)</td><td>98.70</td><td>99.29</td><td>95.86</td><td>99.09</td><td>99.20</td><td>98.61</td><td>98.89</td><td>99.43</td></tr><tr><td>κ(%)</td><td>98.87</td><td>99.51</td><td>96.52</td><td>99.24</td><td>99.36</td><td>99.17</td><td>99.25</td><td>99.61</td></tr><tr><td>Params.</td><td>94.63K</td><td>396.99K</td><td>9.77M</td><td>42.41M</td><td>148.03K</td><td>609.16K</td><td>666.38K</td><td>700.52K</td></tr><tr><td>FLOPs</td><td>5.57M</td><td>108.04M</td><td>16.83M</td><td>190.85M</td><td>3.66M</td><td>10.25M</td><td>14.89M</td><td>17.66M</td></tr><tr><td rowspan=\"5\">SA</td><td>OA (%)</td><td>98.92</td><td>99.31</td><td>98.11</td><td>99.38</td><td>99.53</td><td>99.54</td><td>99.63</td><td>99.66</td></tr><tr><td>AA (%)</td><td>99.33</td><td>99.70</td><td>98.83</td><td>99.70</td><td>99.72</td><td>99.61</td><td>99.65</td><td>99.81</td></tr><tr><td>κ(%)</td><td>98.80</td><td>99.23</td><td>97.90</td><td>99.31</td><td>99.47</td><td>99.49</td><td>99.59</td><td>99.63</td></tr><tr><td>Params.</td><td>149.71K</td><td>750K</td><td>10.82M</td><td>50M</td><td>148.50K</td><td>926.90K</td><td>1.16M</td><td>1.20M</td></tr><tr><td>FLOPs</td><td>7.97M</td><td>216.84</td><td>17.80M</td><td>354.42M</td><td>3.66M</td><td>35.87M</td><td>54.82M</td><td>57.67M</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0a3d453e62156373300ea4c7b96c04c9def9c0a7a1279cab52f65154a92bb263.jpg",
+        "table_caption": [
+            "Table 2. Settings of channel reduction in QSSPN-L"
+        ],
+        "table_footnote": [
+            "*  $\\lfloor B / 2\\rfloor$  represents the greatest integer less than or equal to  $B / 2$ ."
+        ],
+        "table_body": "<table><tr><td>Models</td><td>Bands</td><td>N1</td><td>N2</td><td>N3</td></tr><tr><td>QSSPN-1</td><td>B</td><td>30</td><td>-</td><td>-</td></tr><tr><td>QSSPN-2</td><td>B</td><td>[B/2]*</td><td>30</td><td>-</td></tr><tr><td>QSSPN-3</td><td>B</td><td>[B/2]</td><td>50</td><td>30</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Experiment Details",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with  $145 \\times 145$  pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises  $512 \\times 217$  pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are  $610 \\times 340$  pixels with 103 bands to record nine classes of ground truths.",
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+    {
+        "type": "text",
+        "text": "Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Setup. We adopt the Adam [22] optimizer with learning rate  $1e^{-3}$  to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size  $9 \\times 9 \\times B$  for all methods. For all datasets, we randomly select  $10\\%$ ,  $5\\%$  and  $85\\%$  labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients  $(\\kappa)$ . Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Classification Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Tab. 1 reports the results of OA, AA and  $\\kappa$  on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves  $96.40\\%$  AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). On the Salinas and Pavia University",
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+    {
+        "type": "page_number",
+        "text": "9930",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/983bc1a0572e84ade2690e37efa08117c0568becc045568807257b4c0e76910f.jpg",
+        "image_caption": [
+            "(a) Ground truth"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f29871000e34acad89591d7d29526e7a246475530e3c708301cb9386d72c547.jpg",
+        "image_caption": [
+            "(b) RvT"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
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+            279,
+            165
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f2c52b8480dd822d494923b36535d1f42ad9d9b6b49c85655268ee4ab3734253.jpg",
+        "image_caption": [
+            "(c) HiT"
+        ],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9de2d9ef3efda918599785a4208421a40c341ad6b3a1b563898118588c577cb1.jpg",
+        "image_caption": [
+            "(d) SSAN"
+        ],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c93307d69ee867a99c21fafa59cd12bc70d11ecad4450a07e3735bd73640c98.jpg",
+        "image_caption": [
+            "(e)SSRN"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d544eba9f0b0a91fbec61b481443d5befb4339f286effb910122d996478add4.jpg",
+        "image_caption": [
+            "(f) QSSPN-1"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0e2a52ef3a4666ca26de0baeebb5c72a75ca2db8bbec4b786108474a3b157323.jpg",
+        "image_caption": [
+            "(g) QSSPN-2"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8e99060f463733fc1faa62206fdd7332da1429200b2c8e6ce678f462fa484605.jpg",
+        "image_caption": [
+            "(h) QSSPN-3"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/86a5ce48d8d8468be751198ee61df9747eefdc07460ef9345f9be007da4f1012.jpg",
+        "image_caption": [
+            "(a) Ground truth"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8d06af8208275af5b014ac6cdbf7e93214b63f85a9cfbc329a211fb870ea3376.jpg",
+        "image_caption": [
+            "(b) RvT"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/91d6478a19804e673b3f9a8eecdfde41eeb5e4b40aa1c12ead4d9b5025296fef.jpg",
+        "image_caption": [
+            "Figure 4. Classification maps of different methods for the Indian Pines dataset.",
+            "(c) HiT"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a9f9743234b2d1f88ead07c874e3408d1b1e2e3de4b61a7a5461d2f1c18a2aaa.jpg",
+        "image_caption": [
+            "(d) SSAN"
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+    {
+        "type": "image",
+        "img_path": "images/88aee164703f9470d2d6ca281a4f0b395e5a4453e170ff15a5a2af14e6267e42.jpg",
+        "image_caption": [
+            "(e) SSRN"
+        ],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8519a95fdd0c60f122a96c1112c1a315f799db8537d2730a774c7300db4693dd.jpg",
+        "image_caption": [
+            "(f) QSSPN-1"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4ed2d0528c3c03bd2de342a5fe14e3a30e2722566ee0037f7a46d3e8646104dd.jpg",
+        "image_caption": [
+            "(g) QSSPN-2"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ad3a407872a098030c7a4351a07c5f13ed534751d1f764947aa09a930eb4487.jpg",
+        "image_caption": [
+            "(h) QSSPN-3"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            215,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/9400aafd9a45c03ea4d8d2f156381249570fec071ea3e0ffa4a9e1d3905a0427.jpg",
+        "image_caption": [
+            "Figure 5. Classification maps of different methods for the Pavia University dataset.",
+            "(a) Original data",
+            "Figure 6. Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/378545ef6b20edd948cdafa28996a4e55c02d40dbd5446b6e6ee805749a1d20c.jpg",
+        "image_caption": [
+            "(b) Spectral-spatial representation"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "datasets, our methods obtain  $0.1\\%$  and  $0.3\\%$  improvement with respect to  $\\kappa$ , respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of  $\\{15\\%, 20\\%, 25\\%, 30\\%\\}$ . Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c53b855bef662a16dbe534cdf2f7c84dc480c6e3dd7bc4bfaeeca64b1aa182cc.jpg",
+        "image_caption": [
+            "Figure 7. OA of different models for the Indian Pines dataset with different training sizes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            521,
+            419,
+            836,
+            580
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "increases. Overall, QSSPN-3 surpasses other methods, achieving  $99.11\\%$  OA with a  $30\\%$  training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode,  $\\theta_{i',j',k'} = 0, i', j' \\in [0:P - 1], k' \\in [0:B - 1]$ ), the model has the worst performance compared with other models. The spatial phase mode (i.e.,  $\\theta_{i',j',0} = \\theta_{i',j',1} = \\dots = \\theta_{i',j',B - 1}$ ) considers spatial",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "9931",
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+        "img_path": "images/8b749d08ad8d7fb98b5baf4cb2d2e3884782fc679732be847d555dd64a94c700.jpg",
+        "table_caption": [
+            "Table 3. Effectiveness of phase on the Indian Pines dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Mode</td><td>Params.</td><td>FLOPs</td><td>OA (%)</td><td>κ (%)</td></tr><tr><td>No phase</td><td>717.13K</td><td>18.92M</td><td>86.86</td><td>85.10</td></tr><tr><td>Spatial phase</td><td>708.74K</td><td>18.22M</td><td>89.18</td><td>87.74</td></tr><tr><td>Spectral phase</td><td>705.68K</td><td>17.97M</td><td>88.66</td><td>87.09</td></tr><tr><td>All</td><td>1.13M</td><td>52.75M</td><td>92.66</td><td>91.68</td></tr></table>",
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+        "table_caption": [
+            "Table 4. Effectiveness of pyramid structure on the Indian Pines dataset."
+        ],
+        "table_footnote": [
+            "*  $L$  indicates the QSSPN-  $L$  model.",
+            "* Channel indicates the dimension of the learned feature cuboid for classification."
+        ],
+        "table_body": "<table><tr><td>L</td><td>Channel</td><td>Params.</td><td>FLOPs</td><td>OA (%)</td><td>κ (%)</td></tr><tr><td>1</td><td>10</td><td>571.18K</td><td>32.97M</td><td>82.72</td><td>80.45</td></tr><tr><td>1</td><td>30</td><td>910.5K</td><td>34.54M</td><td>90.36</td><td>89.05</td></tr><tr><td>1</td><td>50</td><td>1.26M</td><td>36.69M</td><td>91.63</td><td>90.49</td></tr><tr><td>2</td><td>30</td><td>1.14M</td><td>52.75M</td><td>91.93</td><td>90.84</td></tr><tr><td>3</td><td>30</td><td>1.17M</td><td>55.59M</td><td>92.93</td><td>91.96</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e.,  $\\theta_{0,0,k'} = \\theta_{0,1,k'} = \\dots = \\theta_{P-1,P-1,k'}$ ) only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance.",
+        "bbox": [
+            75,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Parameter Sensitivity Study",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks,",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "image",
+        "img_path": "images/ba16aad61381aafb9d2293491a56f955d0f5e3ea607e052d7f0e34a197ea59a1.jpg",
+        "image_caption": [
+            "(a) Indian Pines"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "image",
+        "img_path": "images/c031429a9e373234cb3888ce59df701a059dc83ce88f5ebeedd4ce1c00c9815d.jpg",
+        "image_caption": [
+            "(b) Salinas"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/22a84439773468dc4bc42d9e490ac214f42b5f9245ffc48bf91a2ff896047fee.jpg",
+        "image_caption": [
+            "(c) Indian Pines"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            222,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/cf729a5b1a18154005d0a56dd16b0f012ad4d2c98adfc7d6b326313d97faf048.jpg",
+        "image_caption": [
+            "(d) Salinas",
+            "Figure 8. OA of QSSPN with different patch sizes and depths."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            704,
+            222,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g.  $82.72\\%$  OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g.  $91.63\\%$  OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST).",
+        "bbox": [
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+        "type": "page_number",
+        "text": "9932",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/f89e1a74-57a2-4551-b632-b3352ab84a1f_origin.pdf

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2023/Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification/full.md

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+# Quantum-Inspired Spectral-Spatial Pyramid Network for Hyperspectral Image Classification
+
+Jie Zhang $^{1}$ , Yongshan Zhang $^{2,1*}$ , Yicong Zhou $^{1*}$
+
+$^{1}$  Department of Computer and Information Science, University of Macau, Macau, China  $^{2}$  School of Computer Science, China University of Geosciences, Wuhan, China
+
+jiezh1997@gmail.com, yszhang.cug@gmail.com, yicongzhou@um.edu.m
+
+# Abstract
+
+Hyperspectral image (HSI) classification aims at assigning a unique label for every pixel to identify categories of different land covers. Existing deep learning models for HSIs are usually performed in a traditional learning paradigm. Being emerging machines, quantum computers are limited in the noisy intermediate-scale quantum (NISQ) era. The quantum theory offers a new paradigm for designing deep learning models. Motivated by the quantum circuit (QC) model, we propose a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN consists of a phase-prediction module (PPM) and a measurement-like fusion module (FMF) inspired from quantum theory to dynamically fuse spectral and spatial information. Specifically, QSSN uses a quantum representation to represent an HSI cuboid and extracts joint spectral-spatial features using FMF. An HSI cuboid and its phases predicted by PPM are used in the quantum representation. Using QSSN as the building block, we further propose an end-to-end quantum-inspired spectral-spatial pyramid network (QSSPN) for HSI feature extraction and classification. In this pyramid framework, QSSPN progressively learns feature representations by cascading QSSN blocks and performs classification with a softmax classifier. It is the first attempt to introduce quantum theory in HSI processing model design. Substantial experiments are conducted on three HSI datasets to verify the superiority of the proposed QSSPN framework over the state-of-the-art methods.
+
+# 1. Introduction
+
+Hyperspectral images (HSIs) are always represented by three-order tensors that collected by remote sensors to record the characteristics reflected by land covers. Each HSI contains two spatial dimensions and one spectral di
+
+![](images/f8e92293ecb73eba639865db402b61a405202b3924c0e52d8206f1a103228dcd.jpg)  
+Figure 1. Performance comparison between the proposed QSSPN framework and existing methods. Average accuracies on Indian Pines dataset are presented.
+
+mension to reflect abundant spectral information and spatial context, making it different from color images. HSI classification aims to determine land-cover categories of areas represented by every pixel according to rich spatial and spectral information [21]. It has a broad range of applications, including target detection [42], mining [1] and agriculture [8]. Based on the recorded HSIs, samples in different categories may be extremely imbalanced in some data sets. This makes HSI classification very challenging [20, 49].
+
+In recent decades, a large number of HSI classification models have been proposed. Existing models can be divided into traditional learning methods and deep learning methods. Traditional classification models are simply adopted for HSIs, such as support vector machine (SVM) [27] and  $K$ -nearest neighbours (KNN) [19]. To achieve better results, advanced traditional learning models, e.g., extended morphological profile (EMP) [3] and extended multiattribute profile (EMAP) [7], first conduct feature extraction and then perform classification. These methods are two-step learning models that cannot achieve satisfactory performance. Deep learning models are promising to simultaneously conduct feature extraction and classification
+
+in an end-to-end manner [12, 34]. Benefiting from the developed technique, deep learning models for HSI classification are in blossom. A wide variety of models rely on convolutional neural networks (CNNs). Most existing models are designed to separately extract spatial and spectral features in different branches [18, 47]. To enrich the development of deep learning models, attention mechanic [26, 46], graph convolution network [45] and transformer learning [36, 43, 48] have been explored in recent works. These works make significant improvement in architecture design and classification performance. However, they separately aggregate spatial and spectral information in different modules, resulting in model redundancy and inefficient exploration of the correlation between spatial and spectral information. Besides, they are all developed from traditional learning paradigm.
+
+Different from traditional computers, quantum computers are emerging machines to perform quantum algorithms [2]. Quantum computing utilizes quantum theory to process data in quantum device [14, 28]. There are several models of quantum computation, such as quantum circuits, quantum annealing and adiabatic quantum computation. It has been proved that quantum computers outperform classical computers in solving certain problems [11, 33]. For example, Shor's algorithm can be used to solve the integer factorization problem much faster than algorithms running on the classical computer [33]. In the noisy intermediate-scale quantum (NISQ) era [31], quantum computers cannot perform complex quantum algorithms for practical applications. Fortunately, quantum computation provides a new mathematical formalism for computing. As a new learning paradigm, quantum machine learning (QML) adopts quantum computation to enhance classical machine learning models [4, 32]. Recently, quantum theory has been adopted in classical algorithms and deep learning models, with an expectation of improving computation efficiency and outcome quality [9, 38].
+
+Motivated by quantum theory, in this paper, we first introduce a quantum-inspired spectral-spatial network (QSSN) for HSI feature extraction. The proposed QSSN includes a phase-prediction module (PPM) and a measurement-like fusion module (MFM). Instead of fusing spatial and spectral information in different modules, we extract joint spatial-spectral features in the same operation. A small data cuboid taken from an HSI is represented by quantum-inspired state representation, and the amplitudes in a state vector are values in normalized input cuboid. The corresponding phases are predicted by PPM, dynamically modulating the spatial and spectral correlations. MFM simultaneously aggregates spatial and spectral information to generate a feature cuboid. Additionally, we design a quantum-inspired spectral-spatial pyramid network (QSSPN) framework with multiple cascaded QSSN blocks
+
+and a softmax classifier for HSI classification. Deep pyramid structure of QSSPN gradually decreases the channels of feature cuboids and extracts robust and expressive features from original data for classification. This is a simple but efficient end-to-end framework taking advantage from both quantum theory and deep neural network.
+
+The contributions of this article are summarized as follows.
+
+- As far as we know, QSSN and QSSPN are the first proposed quantum-inspired method for HSI feature extraction and classification. It shows that this quantum-inspired framework is promising.  
+- Motivated by QC in quantum theory, we propose a QSSN for HSI feature extraction. QSSN aggregates spatial-spectral information simultaneously using quantum-like representations and operations.  
+- Based on QSSN, we develop a QSSPN for HSI classification. In QSSPN, QSSN blocks stacked in a pyramid manner that can extract robust and discriminative features for classification. As shown in Fig. 1, QSSPN achieves the best classification accuracy with low model complexity.
+
+The rest of this paper is organized as follows: Sec. 2 reviews the related work about deep learning-based HSI classification and quantum-inspired deep learning methods. Sec. 3 introduces the detailed framework of QSSN and describes the proposed QSSPN for HSI classification. Sec. 4 presents the experimental results and analysis. Finally, Sec. 5 draws the conclusion.
+
+# 2. Related Work
+
+Deep learning-based HSI Classification. Deep learning models adapted from color image processing show priority in HSI processing [21, 29]. Autoencoder-based [15] models are unsupervised networks that are widely researched in HSI classification [5, 6]. These methods cannot efficiently capture the spatial-spectral correlations. Inspired by human vision system, local connectivity allows CNN to extract spatial information efficiently [23]. CNN-based HSI classification methods are widely researched [29, 44, 47]. Zhong et al. proposed 3D CNN with residual connection to improve the network trainability and classification accuracy [47]. Attention mechanic [41] is introduced for learning correlations among neighboring pixels and bands [26, 35, 46]. Mei et al. designed two attention-based branches to extract discriminant feature vectors from spatial and spectral aspects [26]. Frameworks based on graph convolution network and transformer have been also investigated in recent years. These methods show priorities in capturing subtle spectral discrepancies [36] and learning structural information [45].
+
+![](images/f55728ced1a6ba370d2c5c93235a61a3535ba4fc48139753d716f3d45a213148.jpg)  
+Figure 2. Illustration of the proposed QSSN and QSSPN framework. The yellow and blue boxes at the top are phase-prediction module (PPM) and measurement-like fusion module (MFM), respectively. The middle box shows the QSSN framework. The QSSPN framework is presented at the bottom.
+
+Quantum-Inspired Computation. The mathematical formalism of quantum theory has been adopted in various tasks, including natural language processing (NLP) [25], computer vision (CV) [38], information retrieval (IR) [39, 40] and multimodal analysis [9, 10, 24]. Van et al. pioneeringly exploited the quantum probability for object representation in IR tasks [40]. To achieve better outcome quality and interpretability, Li et al. introduced a quantum-inspired network in NLP models for semantic matching [25]. Quantum-motivated strategies are also exploited in multimodal information processing. Li et al. investigated multimodal feature fusion methods via quantum-like neural network for conversation emotion recognition [24]. Gkoumas et al. introduced a video semantic recognition network via fusing multimodal information at the decision level [10]. Moreover, the quantum-inspired methods are also developed in image processing tasks. Tang's work utilizes the wave-like function to represent an image, using phase to model the relationship between patches [38]. The proposed wave-multilayer perceptron achieves promising performance on various vision tasks, such as image classification and objection detection.
+
+# 3. Method
+
+This section presents the QSSPN framework for HSI classification based on QSSN. We first briefly discuss the QC model. Then, we describe the proposed QSSN model to extract joint spatial-spectral features. At last, using QSSN as the building block, we introduce the proposed QSSPN framework for HSI classification. Details of QSSN and QSSPN are shown in Fig. 2.
+
+# 3.1. Preliminaries
+
+Most quantum computers are constructed based on the QC model [2, 28]. The computation of QC includes state initialization, unitary evolution and measurement. The quantum device is first set to the initial state. Scientists manipulate the quantum state by applying unitary operators to quantum device. In this process, the initial state of the system is mapped to the final state, storing processing results in quantum device. For capturing classical information from quantum device, measurements are adopted to extract processing results from the final state to the classical representation. Mathematically, the state of quantum system can be represented by a state vector in  $N$ -dimensional Hilbert space  $\mathcal{H}^N$ . We adopt the Dirac notations in quantum theory to denote the states of quantum system [28]. The notations  $\left|\cdot \right\rangle$  and  $\langle \cdot |$  denote a Ket to represent a complex-valued unit vector and a Bra to indicate its conjugate transpose. Specifically, given a set of basis state vectors  $\{\left|\phi_n\right\rangle \}_{n = 1}^N$ , we can represent the states of quantum system  $|\psi \rangle$  as follows*:
+
+$$
+| \psi \rangle = \sum_ {n = 0} ^ {N - 1} A _ {n} e ^ {i \theta_ {n}} | \phi_ {n} \rangle , \tag {1}
+$$
+
+where  $A_{n}$  is a probability amplitude satisfying  $\sum_{N}|A_{n}|^{2} = 1$ ,  $i$  is the imaginary unit and  $\theta_{n}$  indicates the phase. A simple example of basis state vectors for  $\mathcal{H}^N$  is standard unit basis. Detailedly, the standard basis of  $\mathcal{H}^2$  is formed by column vectors  $|0\rangle_2 = [1,0]^T$  and  $|1\rangle_2 = [0,1]^T$ . Here, we use the notation
+
+$$
+\left| n \right\rangle_ {N}, n = 0, 1, \dots , N - 1 \tag {2}
+$$
+
+to represent the standard basis of  $\mathcal{H}^N$ . Accordingly,  $\langle n|_N$  denotes the conjugate transpose of  $|n\rangle_N$ . All components of  $|n\rangle_N$  are 0 except the  $n$ -th component is 1. In quantum theory, Eq. (1) represents the superposition of basis states.
+
+The reversible unitary operator  $U$  describes the state's evolution in QC, mapping the initial states  $|\psi_{initial}\rangle$  to final states  $|\psi_{final}\rangle$ . These operators manipulate the phases  $\theta_{n}$  and amplitudes  $A_{n}$  by applying specific physical operations to the quantum system. In QC, projection-valued measure (PVM) is a function that can collapse the system state from superposition of multiple basis states to one basis state. Mathematical formulation of PVM is a set of projection operators  $\{\Pi_m = |\phi_m\rangle \langle \phi_m|\}_{m = 1}^M$ . According to the Born rule [28],  $\Pi_{m}$  projects the state  $|\psi_{final}\rangle$  to the corresponding basis state  $|\phi_m\rangle$  with a probability:
+
+$$
+P \left(\left| \phi_ {m} \right\rangle\right) = T r \left(\Pi_ {m} \rho\right) = \left\langle \phi_ {m} \mid \psi_ {\text {f i n a l}} \right\rangle \left\langle \psi_ {\text {f i n a l}} \mid \phi_ {m} \right\rangle , \tag {3}
+$$
+
+where  $\rho = |\psi_{final}\rangle \langle \psi_{final}|$  is the density matrix representation of  $|\psi_{final}\rangle$  and  $\sum_{M}P(|\phi_{m}\rangle) = 1$ .  $|\cdot \rangle \langle \cdot |$  denotes the
+
+![](images/e07cba4561baba1f2b8e0f9c2aea9c4e04b9ce0181a5c2168beb225e437b9a6e.jpg)  
+Figure 3. Illustration of data mapping in QSSN. The state representation  $|\psi \rangle$  encodes data from original space to Hilbert space:  $\mathcal{R} \to \mathcal{H}$ . The MFM outputs a feature vector mapped from  $|\psi \rangle$  to feature space:  $\mathcal{H} \to \mathcal{F}$ .
+
+outer product and  $\langle \cdot |\cdot \rangle$  denotes the inner product of  $\langle \cdot |$  and  $|\cdot \rangle$  . Eq. (3) can be rewritten as:
+
+$$
+\begin{array}{l} P \left(\left| \phi_ {m} \right\rangle\right) = \left\langle \phi_ {m} \right| \rho \left| \phi_ {m} \right\rangle = \left(\left\langle \psi_ {f i n a l} \mid \phi_ {m} \right\rangle\right) ^ {2} \tag {4} \\ = \sum_ {n _ {1}} ^ {N - 1} \sum_ {n _ {2}} ^ {N - 1} A _ {n _ {1}} A _ {n _ {2}} e ^ {i (\theta_ {n _ {1}} - \theta_ {n _ {2}})} \langle \phi_ {m} | n _ {1} \rangle \langle n _ {2} | \phi_ {m} \rangle . \\ \end{array}
+$$
+
+Here we neglect the subscript  $N$  of  $|n\rangle_N$  for simplicity. In Eq. (4), the size of  $|n\rangle$  is  $N$ . For the same measurement operator  $\Pi_m \sim |\phi_m\rangle$ , the output  $P(|\phi_m\rangle)$  depends on all pairs of  $A_{n_1}$  and  $A_{n_2}$  and their correlations  $(\theta_{n_1} - \theta_{n_2})$ . PVM yields values  $P_{res} = [P(|\phi_1\rangle), P(|\phi_2\rangle), \ldots, P(|\phi_M\rangle)]$  corresponding to the selected projection operators  $\{\Pi_m\}_{m=1}^M$ , reflecting the state of quantum system.
+
+We loosely describe the quantum mechanic related to our method. A rigorous definition of quantum computing can be found in [28].
+
+# 3.2. Quantum-Inspired Spectral-Spatial Network
+
+Let  $X \in \mathcal{R}^{H \times W \times B}$  be the HSI with  $H$  pixels in height,  $W$  pixels in width, and  $B$  spectral bands. Taking the  $(i,j)$ -th pixel as center, information in a small cuboid  $x_{i,j} \in \mathcal{R}^{P \times P \times B}$  with  $P \times P$  pixels are considered for finding the joint spectral-spatial feature representation corresponding to the center pixel [21]. We pad  $X$  with 0 so that we can successfully take cuboids for edge pixels. As shown in the middle box of Fig. 2, QSSN is composed of PPM and MFM to learn spectral-spatial feature representations for HSI classification.
+
+Phase-Prediction Module (PPM). For HSI analysis, it is vital to take full advantage of spectral and spatial information. PPM utilizes spectral and spatial information to dynamically generate phases  $\Theta_{i,j} \in R^{P \times P \times B}$  for all elements  $x_{i',j',k'}'$  in  $x_{i,j}$ . Phases play an important role in encoding data  $x_{i,j}$  in Hilbert space. We hope that phases can correctly model the spectral-spatial correlations of all elements. Besides, we hope that samples encoded in Hilbert space have small intra-class distance and large inter-class
+
+distance. Hence, PPM should be able to capture discriminative information from original data and assign appropriate phase  $\theta_{i',j',k'}$  for each element  $x_{i',j',k'}'$ . Since 2D-CNN shows its priority in HSI analysis [29], we utilize the CNN blocks to construct PPM. PPM is a three-layer CNN. For predicting phase for each  $x_{i',j',k'}'$ , the shapes of input and output of each convolution layer are the same. This means that the kernels of each layer have  $B$  channels and zeropadding methods are adopted in each layer. The first CNN layer in PPM extracts features in  $3\times 3$  pixel windows. The following asymmetric convolution layers [37] with  $3\times 1$  and  $1\times 3$  kernel shapes fuse the information in a smaller region in the vertical and horizontal direction to predict the phases  $\Theta_{i,j}$ . Before we encode each HSI cuboid into complex finite-dimensional Hilbert space  $\mathcal{H}^K$  ( $K = P\times P\times B$ ), we reshape the HSI cuboid  $x_{i,j}$  and the corresponding phase cuboid  $\Theta_{i,j}$  as follow:
+
+$$
+\begin{array}{l} x ^ {v e c} = \left[ x _ {0} ^ {\prime}, \dots , x _ {i ^ {\prime} + j ^ {\prime} \times P + k ^ {\prime} \times P \times P} ^ {\prime}, \dots , x _ {K - 1} ^ {\prime} \right], \tag {5} \\ \Theta^ {v e c} = \left[ \theta_ {0}, \dots , \theta_ {i ^ {\prime} + j ^ {\prime} \times P + k ^ {\prime} \times P \times P}, \dots , \theta_ {K - 1} \right], \\ \end{array}
+$$
+
+where  $i', j' \in [0 : P - 1]$  and  $k' \in [0 : B - 1]$ . Then phase vector  $x^{vec}$  and original data vector  $x^{vec}$  are used in the state vector representation  $|x_{i,j}\rangle$  as follows:
+
+$$
+\left| x _ {i, j} \right\rangle = \sum_ {n = 0} ^ {K - 1} A _ {n} e ^ {i \theta_ {n}} \left| n \right\rangle_ {K}. \tag {6}
+$$
+
+In Eq. (6),  $A_{n}$  can be obtained as:
+
+$$
+A _ {n} = \sqrt {\frac {x _ {n} ^ {v e c}}{\sum_ {n ^ {*} = 0} ^ {K - 1} x _ {n ^ {*}} ^ {v e c}}}, \tag {7}
+$$
+
+where  $x_{n}^{vec}$  indicates the  $n$ -th element in  $x^{vec}$ . In Eq. (6),  $x_{i,j}$  can be represented by a complex vector  $|x_{i,j}\rangle = [A_0e^{i\theta_0}, A_1e^{i\theta_1}, \ldots, A_{K-1}e^{i\theta_{K-1}}]$  in  $\mathcal{H}^K$ . As for classification task, we hope to encode samples in the space that has large inter-class distance and small intra-class distance, as shown in Fig. 3. A simple strategy to encode  $x_{i,j}$  in  $|x_{i,j}\rangle$  is neglecting the imaginary parts  $e^{i\theta}$  (meaning 'no phase') or only using the same phases in spatial dimension (neglecting 'spectral phase') or spectral dimension (neglecting 'spatial phase'). Based on PPM, we adopt the imaginary parts to dynamically fuse spectral-spatial information in MFM. Compared to these simple strategies, our strategy is able to fully exploit the spatial and spectral correlations.
+
+Measurement-like Fusion Module (MFM). Motivated by PVM, we design a measurement-like operation  $(MO)$  to generate low-dimensional feature representations [49]. Recalling that in Eq. (3), for simplicity, the mathematical formulation of measurement can be described as  $PVM(\Pi_m,\rho)$ : using a density matrix  $\rho$  to represent the state of quantum system  $\rho = |\psi_{final}\rangle \langle \psi_{final}|$  and then applying the matrix manipulation (matrix product and trace)
+
+with operators  $\{\Pi_m\}_{m=1}^M$ . For each  $\Pi_m$ , we get the probability  $P(|\phi_m\rangle)$ . Motivated by quantum measurement, we first use the density matrix representation to denote the state vector by
+
+$$
+\begin{array}{l} D _ {i, j} = \left| x _ {i, j} \right\rangle \left\langle x _ {i, j} \right| \tag {8} \\ = \sum_ {n = 0} ^ {K - 1} \sum_ {n ^ {\prime} = 0} ^ {K - 1} A _ {n} A _ {n ^ {\prime}} e ^ {i \left(\theta_ {n} - \theta_ {n ^ {\prime}}\right)} \left| n ^ {\prime} \right\rangle \left\langle n \right|, \\ \end{array}
+$$
+
+where  $|n^{\prime}\rangle \langle n|$  represents a square matrix with  $P\times P\times B$  rows and columns that all components are 0 except the  $(n,n^{\prime})$ -th component is 1. Each term in the density matrix  $D_{i,j}$  is the multiplication of  $A_{n}$  and  $A_{n^{\prime}}$  with a coefficient  $e^{i(\theta_n - \theta_{n^{\prime}})}$ . Empirically, this is similar to fusing information of each pair of elements  $x_{n}^{vec}$  and  $x_{n^{\prime}}^{vec}$ . Phases  $\theta_{n}$  and  $\theta_{n^{\prime}}$  are predicted by PPM. We hope the imaginary part  $e^{i(\theta_n - \theta_{n^{\prime}})}$  can dynamically modulate the correlations between  $x_{n}^{vec}$  and  $x_{n^{\prime}}^{vec}$ . In each pair, the location and band of  $x_{n}^{vec}$  and  $x_{n^{\prime}}^{vec}$  may be different. Therefore, the density matrix can simultaneously fuse spatial and spectral information. Recalling that in Eq. (3), PVM generates numerical result  $P(|\phi_m\rangle)$  corresponding to  $\Pi_{m}$ . Note that PVM has corresponding operations applied on physic devices. There are constraints of operations  $\Pi_{m}$  in their mathematical formulation in quantum theory. We use an abstract representation of PVM as  $PVM(\Pi_m,\rho)\rightarrow PVM(Operator_m,\rho)$ . To learn a low-dimensional representation, we design an MFM with a deep learning framework to relieve the limitations and perform similar functions in PVMs. In MFM, we use fully-connected layers  $FC_{m}$  with depth 3 as  $Operator_{m}$ . The MO generates a feature point as follows:
+
+$$
+f e a _ {m} = M O \left(F C _ {m}, D _ {i, j}\right), \tag {9}
+$$
+
+where  $D_{i,j}$  stores the fusion information of each element pair,  $x_{n}^{vec}$  and  $x_{n'}^{vec}$ .  $MO$  is an operation that feeds  $D_{i,j}$  into the operator  $FC_{m}$  to efficiently aggregate spatial and spectral information. Given  $M$  operators  $\{FC_{m}\}_{m=1}^{M}$ , we can get an  $M$ -dimensional feature vector  $F^{vec} = [fea_{1},fea_{2},\ldots,fea_{M}]$ . Aggressive dimension reduction of feature cuboids may cause bottlenecks of deep learning models [37]. Thus,  $M$  should be carefully designed for preserving important factors in data.
+
+Following the steps above, QSSN extracts an  $M$ -dimensional feature vector from input cuboid  $x_{i,j}$  with the size of  $P \times P \times B$ . Furthermore, we introduce a new notation  $N$ -QSSN to denote the learned vector representation  $F^{vec}$  with the size of  $(P \times P \times N) \times 1$ . The output feature vector  $F^{vec}$  is reshaped into a 3-D feature cuboid  $F^{cub}$  with the size of  $P \times P \times N$ . In  $N$ -QSSN, the size of  $M$  to denote the number of  $MO$  is determined by
+
+$$
+M = P \times P \times N. \tag {10}
+$$
+
+The outcome of  $N$ -QSSN  $F^{cub}$  has same spatial resolution as  $x_{i,j}$ . The input HSI cuboid  $x_{i,j}$  has abundant band information but little spatial information. A few neighboring pixels are considered during feature extraction. Empirically, models are prone to ignore the spatial correlations. The  $N$ -QSSN preserves the spatial resolution in output, expecting QSSN to learn the location-sensitive information. Besides, it is possible to construct deep models based on the  $N$ -QSSN blocks.
+
+# 3.3. QSSN-based Pyramid Framework
+
+It has been proved that deep models have high-quality outcome in theory [16, 17] and practice [12, 34]. Recalling that QSSN consists of three convolution layers and three fully-connected layers. It can be treated as a building block to construct a deeper framework. To extract more robust and discriminative features, we use QSSN to develop a hierarchical framework for HSI classification, called QSSPN. Dually, we can cascade multiple QSSN blocks to extract deep features from  $x_{i,j}$ , followed by a classifier to identify the land-cover category of the center pixel (i.e., the  $(i,j)$ -th pixel). An example of the framework of QSSPN is shown in Fig. 2. The example model consists of two QSSN blocks and a linear classifier. For the two QSSN blocks,  $N_{1}$ -QSSN and  $N_{2}$ -QSSN are stacked in a hierarchical manner. Specifically, for  $N_{1}$ -QSSN, we take an original cuboid with the size of  $P \times P \times B$  as input to learn the feature cuboid with the size of  $P \times P \times N_{1}$  as output. Sequentially, for  $N_{2}$ -QSSN, we use the feature representation with the size of  $P \times P \times N_{1}$  learned from  $N_{1}$ -QSSN as input to extract the feature cuboid with the size of  $P \times P \times N_{2}$  as output. In our setting,  $B > N_{1} > N_{2}$ , meaning that the channel of feature maps are gradually reduced from the previous QSSN to the latter QSSN. The reduction of the channel of feature cuboids enables QSSPN to show the pyramid-like structure. Empirically, extreme decrease of the dimensionality of each QSSN may result in discarding important information [37]. Thus, we gently reduce the channels of each QSSN to find expressive and robust representations by aggregating spatial and spectral information.
+
+The output feature cuboids learned from the final QSSN are then flattened into a vector and fed into a classifier. A linear layer with a softmax function is adopted as a classifier in this work. Therefore, our proposed framework is end-to-end and easy to implement. For simplicity, we use QSSPN-  $L$  to indicate QSSPN with  $L$  QSSN layers. For example, the model with two QSSN layers shown in Fig. 2 can be denoted by QSSPN-2.
+
+Table 1. Classification results and model analysis of different methods on HSI datasets.  
+
+<table><tr><td>Datasets</td><td>Metrics</td><td>SSAN</td><td>SSRN</td><td>RvT</td><td>HiT</td><td>SSFTT</td><td>QSSPN-1</td><td>QSSPN-2</td><td>QSSPN-3</td></tr><tr><td rowspan="5">IP</td><td>OA (%)</td><td>89.46</td><td>91.85</td><td>83.85</td><td>90.59</td><td>96.35</td><td>90.36</td><td>92.66</td><td>95.87</td></tr><tr><td>AA (%)</td><td>85.99</td><td>81.51</td><td>79.67</td><td>86.71</td><td>89.99</td><td>89.93</td><td>93.34</td><td>96.40</td></tr><tr><td>κ(%)</td><td>88.04</td><td>90.73</td><td>81.68</td><td>89.27</td><td>95.82</td><td>89.05</td><td>91.68</td><td>95.34</td></tr><tr><td>Params.</td><td>148.83K</td><td>735.88K</td><td>10.78M</td><td>49.60M</td><td>148.50K</td><td>910.50K</td><td>1.13M</td><td>1.17M</td></tr><tr><td>FLOPs</td><td>7.88M</td><td>212.48M</td><td>17.83M</td><td>345.88M</td><td>3.66M</td><td>34.54M</td><td>52.75M</td><td>55.59M</td></tr><tr><td rowspan="5">PU</td><td>OA (%)</td><td>99.15</td><td>99.63</td><td>97.37</td><td>99.43</td><td>99.52</td><td>99.38</td><td>99.44</td><td>99.71</td></tr><tr><td>AA (%)</td><td>98.70</td><td>99.29</td><td>95.86</td><td>99.09</td><td>99.20</td><td>98.61</td><td>98.89</td><td>99.43</td></tr><tr><td>κ(%)</td><td>98.87</td><td>99.51</td><td>96.52</td><td>99.24</td><td>99.36</td><td>99.17</td><td>99.25</td><td>99.61</td></tr><tr><td>Params.</td><td>94.63K</td><td>396.99K</td><td>9.77M</td><td>42.41M</td><td>148.03K</td><td>609.16K</td><td>666.38K</td><td>700.52K</td></tr><tr><td>FLOPs</td><td>5.57M</td><td>108.04M</td><td>16.83M</td><td>190.85M</td><td>3.66M</td><td>10.25M</td><td>14.89M</td><td>17.66M</td></tr><tr><td rowspan="5">SA</td><td>OA (%)</td><td>98.92</td><td>99.31</td><td>98.11</td><td>99.38</td><td>99.53</td><td>99.54</td><td>99.63</td><td>99.66</td></tr><tr><td>AA (%)</td><td>99.33</td><td>99.70</td><td>98.83</td><td>99.70</td><td>99.72</td><td>99.61</td><td>99.65</td><td>99.81</td></tr><tr><td>κ(%)</td><td>98.80</td><td>99.23</td><td>97.90</td><td>99.31</td><td>99.47</td><td>99.49</td><td>99.59</td><td>99.63</td></tr><tr><td>Params.</td><td>149.71K</td><td>750K</td><td>10.82M</td><td>50M</td><td>148.50K</td><td>926.90K</td><td>1.16M</td><td>1.20M</td></tr><tr><td>FLOPs</td><td>7.97M</td><td>216.84</td><td>17.80M</td><td>354.42M</td><td>3.66M</td><td>35.87M</td><td>54.82M</td><td>57.67M</td></tr></table>
+
+Table 2. Settings of channel reduction in QSSPN-L  
+
+<table><tr><td>Models</td><td>Bands</td><td>N1</td><td>N2</td><td>N3</td></tr><tr><td>QSSPN-1</td><td>B</td><td>30</td><td>-</td><td>-</td></tr><tr><td>QSSPN-2</td><td>B</td><td>[B/2]*</td><td>30</td><td>-</td></tr><tr><td>QSSPN-3</td><td>B</td><td>[B/2]</td><td>50</td><td>30</td></tr></table>
+
+*  $\lfloor B / 2\rfloor$  represents the greatest integer less than or equal to  $B / 2$ .
+
+# 4. Experiments
+
+# 4.1. Experiment Details
+
+Datasets. We evaluate the proposed models on three HSI datasets, including Indian Pines (IP), Pavia University (PU) and Salinas (SA). The Indian Pines and Salinas datasets were collected by the airborne visible and infrared imaging spectrometer (AVIRIS) sensor. The Indian Pines dataset with  $145 \times 145$  pixels and 200 valid spectral bands contains 16 land-cover categories, recording a scene of the physiognomy from the Indian Pines test site in Northwest Indiana. In this dataset, samples in different classes are extremely imbalanced. The covered area of Salinas Valley comprises  $512 \times 217$  pixels and 204 spectral signatures in the Salinas dataset to describe 16 different ground truth categories. The Pavia University dataset was collected by the reflective optics system imaging spectrometer (ROSIS) sensor over the University of Pavia. There are  $610 \times 340$  pixels with 103 bands to record nine classes of ground truths.
+
+Compared methods. To validate the effectiveness of the proposed QSSPN framework, we utilize the following methods for comparison. We compare our model with advanced CNN-based and transformer-based models. The selected CNN-based models are spectral-spatial attention network (SSAN) [26] and spectral-spatial residual network (SSRN) [47]. As for the selected transformer-based mod
+
+els, there are robust vision transformer (RvT) [13], hyperspectral image transformer (HiT) [43] and spectral-spatial feature tokenization transformer (SSFTT) [36].
+
+Setup. We adopt the Adam [22] optimizer with learning rate  $1e^{-3}$  to update parameters of deep learning models in each training iteration. Models are trained through 200 epochs. The batch size is set to 64. Other settings of our proposed models are shown in Tab. 2. To make a fair comparison, we use the same input patch size  $9 \times 9 \times B$  for all methods. For all datasets, we randomly select  $10\%$ ,  $5\%$  and  $85\%$  labeled samples for model training, validation and testing, respectively. We train and test each model 10 times and report the average results. The performance is evaluated in terms of overall accuracy (OA), average accuracy (AA) and kappa coefficients  $(\kappa)$ . Different from OA, AA helps to see if a model is strong or weak when classifying specific classes. All the experiments are performed with Pytorch [30] on NVIDIA 3090 GPU and 48GB RAM.
+
+# 4.2. Classification Results
+
+Tab. 1 reports the results of OA, AA and  $\kappa$  on three HSI datasets. Our proposed QSSPN-3 achieves the best AA on three dataset. Specifically, QSSPN-3 achieves  $96.40\%$  AA with only 1.17M Parameters on the Indian Pines dataset. It is much better than the existing methods. As shown in Fig. 4 (a), samples of different classes on the Indian Pines dataset are extremely imbalanced. Without data augmentation strategies, there are a few classes that only have less than 6 samples for training most of the time, such as 'Grass-pasture-mowed' and 'Oats'. While for some classes, such as classes 'Corn-notill' and 'Soybean-mintill', there are hundreds of samples. This makes it difficult for models to learn from data. Our methods achieve high classification accuracies in each class regardless of the distribution of training samples (96.40% AA). On the Salinas and Pavia University
+
+![](images/983bc1a0572e84ade2690e37efa08117c0568becc045568807257b4c0e76910f.jpg)  
+(a) Ground truth
+
+![](images/6f29871000e34acad89591d7d29526e7a246475530e3c708301cb9386d72c547.jpg)  
+(b) RvT
+
+![](images/f2c52b8480dd822d494923b36535d1f42ad9d9b6b49c85655268ee4ab3734253.jpg)  
+(c) HiT
+
+![](images/9de2d9ef3efda918599785a4208421a40c341ad6b3a1b563898118588c577cb1.jpg)  
+(d) SSAN
+
+![](images/9c93307d69ee867a99c21fafa59cd12bc70d11ecad4450a07e3735bd73640c98.jpg)  
+(e)SSRN
+
+![](images/2d544eba9f0b0a91fbec61b481443d5befb4339f286effb910122d996478add4.jpg)  
+(f) QSSPN-1
+
+![](images/0e2a52ef3a4666ca26de0baeebb5c72a75ca2db8bbec4b786108474a3b157323.jpg)  
+(g) QSSPN-2
+
+![](images/8e99060f463733fc1faa62206fdd7332da1429200b2c8e6ce678f462fa484605.jpg)  
+(h) QSSPN-3
+
+![](images/86a5ce48d8d8468be751198ee61df9747eefdc07460ef9345f9be007da4f1012.jpg)  
+(a) Ground truth
+
+![](images/8d06af8208275af5b014ac6cdbf7e93214b63f85a9cfbc329a211fb870ea3376.jpg)  
+(b) RvT
+
+![](images/91d6478a19804e673b3f9a8eecdfde41eeb5e4b40aa1c12ead4d9b5025296fef.jpg)  
+Figure 4. Classification maps of different methods for the Indian Pines dataset.  
+(c) HiT
+
+![](images/a9f9743234b2d1f88ead07c874e3408d1b1e2e3de4b61a7a5461d2f1c18a2aaa.jpg)  
+(d) SSAN
+
+![](images/88aee164703f9470d2d6ca281a4f0b395e5a4453e170ff15a5a2af14e6267e42.jpg)  
+(e) SSRN
+
+![](images/8519a95fdd0c60f122a96c1112c1a315f799db8537d2730a774c7300db4693dd.jpg)  
+(f) QSSPN-1
+
+![](images/4ed2d0528c3c03bd2de342a5fe14e3a30e2722566ee0037f7a46d3e8646104dd.jpg)  
+(g) QSSPN-2
+
+![](images/8ad3a407872a098030c7a4351a07c5f13ed534751d1f764947aa09a930eb4487.jpg)  
+(h) QSSPN-3
+
+![](images/9400aafd9a45c03ea4d8d2f156381249570fec071ea3e0ffa4a9e1d3905a0427.jpg)  
+Figure 5. Classification maps of different methods for the Pavia University dataset.  
+(a) Original data  
+Figure 6. Distribution of original data and representation extracted by QSSN blocks in QSSPN-3 for the Indian Pines dataset.
+
+![](images/378545ef6b20edd948cdafa28996a4e55c02d40dbd5446b6e6ee805749a1d20c.jpg)  
+(b) Spectral-spatial representation
+
+datasets, our methods obtain  $0.1\%$  and  $0.3\%$  improvement with respect to  $\kappa$ , respectively. QSSPN-1 with only one QSSN block achieves competitive performance with low computation complexity. It implies that our proposed QSSN framework can efficiently aggregate spatial-spectral information. Fig. 4 and Fig. 5 visualize the classification maps of our proposed methods on the Indian Pines and Pavia University datasets, along with results of best CNN-based and transformer-based models and the ground-truth maps.
+
+To investigate the separability of data, we employ t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the distribution of original data and spectral-spatial features extracted by QSSN blocks in QSSPN-3 in Fig. 6. As shown in Fig. 6, the extracted feature embedding are more separable. It means that QSSN can learn expressive representations for HSI classification. To verify the learnability of the proposed framework, we further evaluate the performance of different models on the Indian Pines dataset by varying training sizes of  $\{15\%, 20\%, 25\%, 30\%\}$ . Fig. 7 shows the OA values achieved by different models. All models achieve higher performance when the training size
+
+![](images/c53b855bef662a16dbe534cdf2f7c84dc480c6e3dd7bc4bfaeeca64b1aa182cc.jpg)  
+Figure 7. OA of different models for the Indian Pines dataset with different training sizes.
+
+increases. Overall, QSSPN-3 surpasses other methods, achieving  $99.11\%$  OA with a  $30\%$  training size. It is a promising result, implying that our proposed framework cannot only learn from limited data, but also extract robust feature representations with sufficient training samples.
+
+# 4.3. Ablation Study
+
+Phases are used in representing a data cuboid by a state vector, dynamically modulating the spatial-spectral correlations between elements. To investigate the effectiveness of the phase module, we tabulate the classification results on the challenging Indian Pines dataset with QSSPN-2 for ablation study in Tab. 3. Without the phase information (i.e., the no phase mode,  $\theta_{i',j',k'} = 0, i', j' \in [0:P - 1], k' \in [0:B - 1]$ ), the model has the worst performance compared with other models. The spatial phase mode (i.e.,  $\theta_{i',j',0} = \theta_{i',j',1} = \dots = \theta_{i',j',B - 1}$ ) considers spatial
+
+Table 3. Effectiveness of phase on the Indian Pines dataset.  
+
+<table><tr><td>Mode</td><td>Params.</td><td>FLOPs</td><td>OA (%)</td><td>κ (%)</td></tr><tr><td>No phase</td><td>717.13K</td><td>18.92M</td><td>86.86</td><td>85.10</td></tr><tr><td>Spatial phase</td><td>708.74K</td><td>18.22M</td><td>89.18</td><td>87.74</td></tr><tr><td>Spectral phase</td><td>705.68K</td><td>17.97M</td><td>88.66</td><td>87.09</td></tr><tr><td>All</td><td>1.13M</td><td>52.75M</td><td>92.66</td><td>91.68</td></tr></table>
+
+Table 4. Effectiveness of pyramid structure on the Indian Pines dataset.  
+
+<table><tr><td>L</td><td>Channel</td><td>Params.</td><td>FLOPs</td><td>OA (%)</td><td>κ (%)</td></tr><tr><td>1</td><td>10</td><td>571.18K</td><td>32.97M</td><td>82.72</td><td>80.45</td></tr><tr><td>1</td><td>30</td><td>910.5K</td><td>34.54M</td><td>90.36</td><td>89.05</td></tr><tr><td>1</td><td>50</td><td>1.26M</td><td>36.69M</td><td>91.63</td><td>90.49</td></tr><tr><td>2</td><td>30</td><td>1.14M</td><td>52.75M</td><td>91.93</td><td>90.84</td></tr><tr><td>3</td><td>30</td><td>1.17M</td><td>55.59M</td><td>92.93</td><td>91.96</td></tr></table>
+
+*  $L$  indicates the QSSPN-  $L$  model.  
+* Channel indicates the dimension of the learned feature cuboid for classification.
+
+information and achieves better performance than the no phase mode. This implies that spatial phase can efficiently aggregate spatial information. However, this mode ignores abundant band information, making it perform worse than QSSPN. The spectral phase mode (i.e.,  $\theta_{0,0,k'} = \theta_{0,1,k'} = \dots = \theta_{P-1,P-1,k'}$ ) only considers the spectral correlations and has similar performance as the spatial phase mode. The QSSPN uses joint spatial-spectral phases, incurring the best performance.
+
+# 4.4. Parameter Sensitivity Study
+
+To better understand the proposed QSSPN framework, we study the parameter sensitivity of patch size for HSI cuboid and model depth for pyramid structure. The parameter sensitivity studies are conducted on the Indian Pines dataset with QSSPN-2 unless being specifically stated.
+
+Patch size for HSI cuboid. The patch size of the cuboid controls the size of input data. We investigate the effectiveness of patch size for classification. As shown in Figs. 8c and 8d, QSSPN achieves better accuracies with larger patches in most cases. We notice that the classification accuracy decreases when the size changes from 9 to 11 in Fig. 8c. It can be explained that as patch size increases, unrelated information and noise will increase. Besides, there is a trade-off between computation complexity and outcome quality. Large patches increase the computation cost with slight accuracy improvement.
+
+Model depth for pyramid structure. The model structure plays an important role in deep learning models. We investigate QSSPN by varying the number of QSSN blocks and the channels of the learned feature cuboids. As shown in Figs. 8a and 8b, with the increase of QSSN blocks,
+
+![](images/ba16aad61381aafb9d2293491a56f955d0f5e3ea607e052d7f0e34a197ea59a1.jpg)  
+(a) Indian Pines
+
+![](images/c031429a9e373234cb3888ce59df701a059dc83ce88f5ebeedd4ce1c00c9815d.jpg)  
+(b) Salinas
+
+![](images/22a84439773468dc4bc42d9e490ac214f42b5f9245ffc48bf91a2ff896047fee.jpg)  
+(c) Indian Pines
+
+![](images/cf729a5b1a18154005d0a56dd16b0f012ad4d2c98adfc7d6b326313d97faf048.jpg)  
+(d) Salinas  
+Figure 8. OA of QSSPN with different patch sizes and depths.
+
+QSSPN achieves higher performance. Tab. 4 investigates the correlations between the channels of feature cuboid and the depth of the model. The extreme compression of feature channels incurs poor performance (e.g.  $82.72\%$  OA with 10 channels). Large feature cuboids achieve higher classification accuracy (e.g.  $91.63\%$  OA with 50 channels). However, the computation complexity greatly increases from 571.18K parameters to 1.26M parameters. With the same output feature channel, QSSPN-3 achieves higher accuracy compared to QSSPN-1 and QSSPN-2. QSSPN decreases the feature channels in a pyramid manner to avoid the bottleneck of deep learning models. This indicates that QSSPN is able to extract discriminative and robust spatial-spectral features with a deep pyramid structure.
+
+# 5. Conclusion
+
+In this paper, motivated by quantum theory, we first proposed a QSSN framework for HSI feature extraction. In QSSN, phases are predicted by PPM to represent the state representation for an HSI cuboid, and joint spatial-spectral features are extracted from state-like representation by MFM. Furthermore, we designed a QSSPN framework based on QSSN for HSI classification. This pyramid framework can extract expressive and robust features for classification. Extensive experiments have demonstrated the superiority of QSSPN. In our future work, we will investigate effective and efficient quantum-inspired methods for other applications.
+
+Acknowledgements. This work was supported by the Science and Technology Development Fund, Macau SAR (File no. 0049/2022/A1), and by the University of Macau (File no. MYRG2022-00072-FST).
+
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+        "text": "Zikang Zhou $^{1,2}$  Jianping Wang $^{1,2}$  Yung-Hui Li $^{3}$  Yu-Kai Huang $^{4}$ $^{1}$ City University of Hong Kong  $^{2}$ City University of Hong Kong Shenzhen Research Institute  \n $^{3}$ Hon Hai Research Institute  $^{4}$ Carnegie Mellon University",
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+        "text": "zikanzhou2-c@my.cityu.edu.hk",
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+        "text": "Predicting the future trajectories of surrounding agents is essential for autonomous vehicles to operate safely. This paper presents QCNet, a modeling framework toward pushing the boundaries of trajectory prediction. First, we identify that the agent-centric modeling scheme used by existing approaches requires re-normalizing and re-encoding the input whenever the observation window slides forward, leading to redundant computations during online prediction. To overcome this limitation and achieve faster inference, we introduce a query-centric paradigm for scene encoding, which enables the reuse of past computations by learning representations independent of the global spacetime coordinate system. Sharing the invariant scene features among all target agents further allows the parallelism of multi-agent trajectory decoding. Second, even given rich encodings of the scene, existing decoding strategies struggle to capture the multimodality inherent in agents' future behavior, especially when the prediction horizon is long. To tackle this challenge, we first employ anchor-free queries to generate trajectory proposals in a recurrent fashion, which allows the model to utilize different scene contexts when decoding waypoints at different horizons. A refinement module then takes the trajectory proposals as anchors and leverages anchor-based queries to refine the trajectories further. By supplying adaptive and high-quality anchors to the refinement module, our query-based decoder can better deal with the multimodality in the output of trajectory prediction. Our approach ranks  $1^{st}$  on Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming all methods on all main metrics by a large margin. Meanwhile, our model can achieve streaming scene encoding and parallel multi-agent decoding thanks to the query-centric design ethos.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Making safe decisions for autonomous vehicles requires accurate predictions of surrounding agents' future trajectories. In recent years, learning-based methods have been",
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+    {
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+        "img_path": "images/49918b1b7df75fa3d356a17c43f25747238f528ddca67d6ad8e2f7e0c6ca5ef5.jpg",
+        "image_caption": [
+            "agent history",
+            "Figure 1. Illustration of our query-centric reference frame, where we build a local coordinate system for each spatial-temporal element, including map polygons and agent states at all time steps. In the attention-based encoder, all scene elements' queries are derived and updated in their local reference frames."
+        ],
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+        "img_path": "images/48b83e0e98bd6607728ccfee4ed95cf6072e635517f50389aea718dd7e6e509d.jpg",
+        "image_caption": [
+            "reference frame of agent state",
+            "$\\rightarrow$  reference frame of map polygon"
+        ],
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+    {
+        "type": "text",
+        "text": "widely used for trajectory prediction [14, 31, 37, 38, 46, 56]. Despite the considerable efforts made to enhance models' forecasting ability, there is still a long way to go before fully addressing the problem of trajectory prediction. Why is this task so challenging, and what inability lies in existing approaches? We attempt to answer these questions from the following two perspectives:",
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+    {
+        "type": "text",
+        "text": "(i) While the flourishing forecasting models have achieved impressive performance on trajectory prediction benchmarks [7, 13, 49], today's most advanced architectures specialized for this task [37, 38, 46, 56] fail to process the heterogeneous traffic scenes efficiently. In an autonomous driving system, data frames arrive at the prediction module sequentially as a stream of sparse scene context, including the high-definition vector map and the surrounding agents' kinematic states. A model must learn expressive representations of these scene elements to achieve accurate forecasts. With the continuing development of modeling techniques for sparse context encoding [14, 31, 50], the research community has witnessed rapid progress toward more powerful trajectory predictors. Notably, factorized attention-based Transformers [37, 38, 56] have recently raised prediction accuracy to an unprecedented level. However, they require learning attention-based representations for each spatial-",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "17863",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "temporal scene element and suffer from prohibitively high costs when processing dense traffic scenes. As every minimal delay may lead to catastrophic accidents in autonomous driving, the unmet need for real-time predictions has limited the applicability of state-of-the-art approaches.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(ii) The immense uncertainty in the output of trajectory prediction, which grows explosively as the prediction horizon lengthens, has troubled the research community constantly. For example, a vehicle at an intersection may turn or go straight depending on the driver's long-term goal. To avoid missing any potential behavior, a model must learn to capture the underlying multimodal distribution rather than simply predicting the most frequent mode. This learning task is challenging since only one possibility is logged in each training sample. To ease the learning difficulty, a body of works utilizes handcrafted anchors as guidance for multimodal prediction [6, 12, 39, 53, 55]. Their effectiveness, however, is subject to the quality of the anchors. Typically, these methods fail to work well when few anchors can precisely cover the ground truth. This problem is exacerbated in long-term prediction, where the search space for anchors is much larger. Some other works [10, 31, 38, 46, 56] circumvent this issue by directly predicting multiple trajectories, albeit at the risk of mode collapse and training instability [33, 41]. Due to the lack of spatial priors, these methods also fail to produce accurate long-term forecasts.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The analysis above drives us to propose a trajectory prediction framework, termed as QCNet, to overcome the limitations of previous solutions. First, we note that it is possible to achieve faster online inference while also benefiting from the power of factorized attention, but the agent-centric encoding scheme [25, 27, 46, 56] used by existing methods serves as an impediment. Each time a new data frame arrives, the observation window slides one step forward and overlaps with its predecessor substantially, which provides opportunities for models to reuse the previously computed encodings. However, agent-centric approaches require normalizing the input based on the latest agent states' positions, necessitating the re-encoding of scene elements whenever the observation window slides forward. To address this issue, we introduce a query-centric paradigm for scene encoding (see Fig. 1). The crux of our design ethos lies in processing all scene elements in their local spacetime reference frames and learning representations independent of the global coordinates. This strategy enables us to cache and reuse the previously computed encodings, spreading the computation across all observation windows and thereby reducing inference latency. The invariant scene features can also be shared among all target agents in the scene to enable the parallelism of multi-agent decoding. Second, to better utilize the scene encodings for multimodal and long-term prediction, we use anchor-free queries to retrieve the scene context recurrently and let them decode a short seg",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "ment of future waypoints at each recurrence. This recurrent mechanism eases the modeling burden on the queries by allowing them to focus on different scene contexts when predicting waypoints at different horizons. The high-quality trajectories predicted by the recurrent decoder serve as dynamic anchors in the subsequent refinement module, where we use anchor-based queries to refine the trajectory proposals based on the scene context. As a result, our query-based decoding pipeline incorporates the flexibility of anchor-free methods into anchor-based solutions, taking the best of both worlds to facilitate multimodal and long-term prediction.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our proposed query-centric encoding paradigm is the first that can exploit the sequential nature of trajectory prediction to achieve fast online inference. Besides, our query-based decoder exhibits superior performance for multimodal and long-term prediction. Experiments show that our approach achieves state-of-the-art results, ranking  $1^{\\text{st}}$  on two large-scale motion forecasting benchmarks [7, 49].",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Scene context fusion encodes rich information for trajectory prediction. Early work rasterizes world states as multichannel images and employs classic convolutional neural networks for learning [5,6,10,21]. Due to the lossy rendering, limited receptive field, and prohibitively high cost of raster-based methods, the research community has turned to a vector-based encoding scheme [14, 31, 50]. With the use of permutation-invariant set operators such as pooling [3, 12, 14, 20, 46], graph convolution [11, 31, 36, 53], and attention mechanism [24, 26, 30, 32, 34, 52], vector-based methods can efficiently aggregate sparse information in traffic scenes. Several powerful trajectory prediction models have recently adopted Transformers [47] with factorized attention as their encoders [18, 37, 38, 56]. Although these models improve efficiency by learning agent-centric representations hierarchically [56] or encoding the whole scene in a shared coordinate system [38], their scalability is still limited by the computational complexity of factorized attention. In comparison, our encoder inherits the representational power of factorized attention while achieving more efficient scene context fusion by using a query-centric encoding paradigm, which goes beyond agent-centric modeling and enables streaming trajectory prediction.",
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+    {
+        "type": "text",
+        "text": "Multimodal future distribution is a widely adopted output form of trajectory prediction, given that world states are partially observable and agents' intentions are highly uncertain. While generative models naturally fit multimodal prediction [20, 28, 40, 45], sampling from latent variables introduces test-time stochasticity, which is undesirable for safety-critical applications such as autonomous driving. Another line of research tackles multimodality by decoding a discrete set of trajectories from the encoded scene context [6, 10, 31, 55]. Since only one mode is ob-",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "17864",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "served in training data, predicting multiple diverse futures is challenging. Anchor-based methods achieve this with the guidance of anchors, which facilitate multimodal prediction by leveraging predefined maneuvers [12], candidate trajectories [6, 39], or map-adaptive goals [53, 55]. However, the quality of these anchors significantly impacts prediction performance. By contrast, anchor-free methods output multiple hypotheses freely at the risk of mode collapse and training instability [10, 31, 38, 46]. Our decoding pipeline takes advantage of both anchor-based and anchor-free solutions, with an anchor-free module generating adaptive anchors in a data-driven manner and an anchor-based module refining these anchors based on the scene context.",
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+    {
+        "type": "text",
+        "text": "3. Approach",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Input and Output Formulation",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Consider a scenario with  $A$  agents surrounding the autonomous vehicle. During online running, the perception module supplies a stream of agent states to the prediction module at a fixed interval, where each agent state is associated with its spatial-temporal position and geometric attributes. For example, the  $i$ -th agent's state at time step  $t$  comprises the spatial position  $\\mathbf{p}_i^t = (\\mathbf{p}_{i,x}^t,\\mathbf{p}_{i,y}^t)$ , the angular position  $\\theta_{i}^{t}$  (i.e., the yaw angle), the temporal position  $t$  (i.e., the time step), and the velocity  $\\mathbf{v}_i^t$ . We also add the motion vector  $\\mathbf{p}_i^t -\\mathbf{p}_i^{t - 1}$  to the geometric attributes similar to some baselines [31, 56]. Besides, the prediction module has access to  $M$  polygons on the high-definition map (e.g., lanes and crosswalks), where each map polygon is annotated with sampled points and semantic attributes (e.g., the user type of a lane). Given the map information and the agent states within an observation window of  $T$  time steps, the prediction module is tasked with forecasting  $K$  future trajectories for each target agent over a horizon of  $T^{\\prime}$  time steps and assigning a probability score for each forecast.",
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+    {
+        "type": "text",
+        "text": "3.2. Query-Centric Scene Context Encoding",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The first step of trajectory prediction is to encode the scene input. Recent research has found factorized attention incredibly effective for scene encoding [37, 38, 56]. These approaches let a query element attend to key/value elements along one axis at a time, which results in temporal attention, agent-map attention, and social attention (i.e., agent-agent attention) with the complexity of  $\\mathcal{O}(AT^2)$ ,  $\\mathcal{O}(ATM)$ , and  $\\mathcal{O}(A^2T)$ , respectively. Unlike typical encoding strategies that first apply a temporal network to squeeze the time dimension and then perform agent-map and agent-agent fusions at the current time step only, factorized attention conducts fusions at every past time step within the observation window. As a result, factorized attention can capture more information, such as how the relations between agents and map elements evolve over the observation horizon. How",
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+    {
+        "type": "text",
+        "text": "ever, its scalability is limited by the cubic complexity of each fusion operation. In extreme circumstances involving hundreds of agents and map elements, such models may fail to emit predictions promptly. We ask: is it possible to reduce the inference latency during online prediction while enjoying the representational power of factorized attention?",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Before diving into our solution, recall that trajectory prediction is a streaming processing task: when a new data frame arrives, we put it in the queue and drop the oldest one. Thus, the latest observation window has  $T - 1$  time steps overlapping with its predecessor. This fact motivates us to raise another question: can we reuse the overlapped time steps' encodings computed previously after the observation window slides forward? Unfortunately, this idea is infeasible owing to the normalization requirement for trajectory prediction: existing methods employ an agent-centric encoding paradigm for spatially roto-translation invariance [25, 27, 46, 56], where each agent is encoded in the local coordinate frame determined by its current time step's position and yaw angle. Each time the observation window slides forward, the \"current time step\" also shifts accordingly, and the geometric attributes of all scene elements need to be re-normalized based on the positions of the latest agent states. Due to the variation in input, we are forced to re-encode all time steps' elements even though the observation windows largely overlap.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Based on the analysis above, we identify that the evolving spacetime coordinate systems hinder the reuse of previously computed encodings. To address this issue, we introduce a query-centric encoding paradigm for learning representations independent of scene elements' global coordinates. Specifically, we establish a local spacetime coordinate system for each scene element that a query vector derives from, processing query elements' features in their local reference frames. Then, we inject the relative spatial-temporal positions into the key and value elements when performing attention-based scene context fusion. We elaborate on the encoding process in the following paragraphs.",
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+    },
+    {
+        "type": "text",
+        "text": "Local Spacetime Coordinate System. Figure 1 shows an example of scene elements' local coordinate systems. For the  $i$ -th agent's state at time step  $t$ , the local coordinate frame is determined by the reference spatial-temporal position  $(\\mathbf{p}_i^t, t)$  and the reference direction  $\\theta_i^t$ , where  $\\mathbf{p}_i^t$  and  $\\theta_i^t$  are the agent state's spatial and angular positions, respectively. For lanes and crosswalks, we choose the position and orientation at the entry point of the centerline as the reference. In this way, we build local coordinate systems canonically for all the scene elements considered, resulting in one dedicated local frame per map polygon and  $T$  reference frames per agent within any observation window.",
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+    {
+        "type": "text",
+        "text": "Scene Element Embedding. For each spatial-temporal scene element, such as an agent state or a lane, we compute the polar coordinates of all geometric attributes (e.g.,",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "17865",
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+    {
+        "type": "text",
+        "text": "the velocity and motion vector of an agent state, the positions of all sampled points on a lane) relative to the spatial point and direction referenced by the element's local frame. Then, we transform each polar coordinate into Fourier features [22, 35, 44] to facilitate learning high-frequency signals. For each agent state and each sampled point on the map, the Fourier features are concatenated with the semantic attributes (e.g., an agent's category) and passed through a multi-layer perceptron (MLP) to obtain an embedding. To further produce polygon-level representations for lanes and crosswalks, we apply attention-based pooling on the embeddings of sampled points within each map polygon. These operations result in agent embeddings of shape  $[A, T, D]$  and map embeddings of shape  $[M, D]$ , where  $D$  denotes the hidden feature dimension. Benefiting from modeling in local reference frames, the embedding of each agent state/map polygon has only one instance and can be reused in the subsequent observation windows. In contrast, agent-centric approaches have to copy all inputs multiple times, encode each copy relative to one of the  $A$  agents' current position and heading, and re-encode all inputs whenever the observation window slides forward, leading to much more overhead during online inference.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Relative Spatial-Temporal Positional Embedding. We prepare the relative positional embeddings for scene element pairs, which will be incorporated into the attention-based operators to help the model be aware of the difference between two elements' local coordinate frames. For an element with absolute spatial-temporal position  $(\\mathbf{p}_i^t,\\boldsymbol {\\theta}_i^t,t)$  and another with  $(\\mathbf{p}_j^s,\\boldsymbol {\\theta}_j^s,s)$ , we use a 4D descriptor to summarize their relative position, whose components are the relative distance  $\\left\\| \\mathbf{p}_j^s -\\mathbf{p}_i^t\\right\\| _2$ , the relative direction  $\\mathrm{atan2}(\\mathbf{p}_{j,y}^{s} - \\mathbf{p}_{i,y}^{t},\\mathbf{p}_{j,x}^{s} - \\mathbf{p}_{i,x}^{t}) - \\boldsymbol{\\theta}_{i}^{t}$ , the relative orientation  $\\boldsymbol{\\theta}_j^s -\\boldsymbol{\\theta}_i^t$  and the time gap  $s - t$ . Since we can easily reconstruct one element's absolute position from another with the help of the descriptor, we have preserved all spatial-temporal position information of the scene element pair. Then, we transform the 4D descriptor into Fourier features and pass them through an MLP to produce the relative positional embedding  $\\mathbf{r}_{j\\rightarrow i}^{s\\rightarrow t}$ . If any of the two scene elements are static (e.g., static map polygons), we can omit the superscript and denote the embedding as  $\\mathbf{r}_{j\\rightarrow i}$ .",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Self-Attention for Map Encoding. We employ self-attention to model the relationships among map elements, after which the updated map encodings will enrich the agent features and assist trajectory decoding. For the  $i$ -th map polygon, we derive a query vector from its embedding  $\\mathbf{m}_i$  and let it attend to the neighboring lanes and crosswalks  $\\{\\mathbf{m}_j\\}_{j\\in \\mathcal{N}_i}$ , where  $\\mathcal{N}_i$  denotes the neighbor set of the polygon. To incorporate spatial awareness for map encoding, we generate the  $j$ -th key/value vector from the concatenation of  $\\mathbf{m}_j$  and the relative positional embedding, i.e.,  $[\\mathbf{m}_j;\\mathbf{r}_{j\\rightarrow i}]$ . Since each triple of  $(\\mathbf{m}_i,\\mathbf{m}_j,\\mathbf{r}_{j\\rightarrow i})$  input to the attention",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4139b4329f7a463095a56cfdeca10d0337167b4ce19f34f758e29438f01a482b.jpg",
+        "image_caption": [
+            "Figure 2. Overview of the encoder in an online mode. After reusing the encodings computed in previous observation windows (blue), the complexity of factorized attention goes from  $\\mathcal{O}(AT^2) + \\mathcal{O}(ATM) + \\mathcal{O}(A^2T)$  to  $\\mathcal{O}(AT) + \\mathcal{O}(AM) + \\mathcal{O}(A^2)$ ."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "layer is independent of the global spacetime coordinate system, the output map encodings  $\\{\\mathbf{m}_i^{\\prime}\\}_{i = 1}^{M}$  are also invariant under transformations of the global reference frame. Thus, they can be shared across all agents and all time steps and can even be pre-computed offline, thereby avoiding redundant computation suffered by agent-centric modeling.",
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+    {
+        "type": "text",
+        "text": "Factorized Attention for Agent Encoding. To help the agent embeddings capture more information, we also consider factorized attention across agent time steps, among agents, and between agents and maps. Take the  $i$ -th agent at time step  $t$  as an example. Given the query vector derived from the agent state's embedding  $\\mathbf{a}_i^t$ , we employ temporal attention by computing the key and value vectors based on  $\\{[\\mathbf{a}_i^s;\\mathbf{r}_{i\\rightarrow i}^{s\\rightarrow t}]\\}_{s = t - \\tau}^{t - 1}$ , which are the  $i$ -th agent's embeddings from time step  $t - \\tau$  ( $0 < \\tau < T$ ) to time step  $t - 1$  and the corresponding relative positional embeddings. Likewise, the key and value vectors for agent-map and social attention are derived from  $\\{[\\mathbf{m}_j';\\mathbf{r}_{j\\rightarrow i}]\\}_{j\\in \\mathcal{N}_i}$  and  $\\{[\\mathbf{a}_j^t;\\mathbf{r}_{j\\rightarrow i}^{t\\rightarrow t}]\\}_{j\\in \\mathcal{N}_i}$ , respectively, where the neighbor set  $\\mathcal{N}_i$  is determined by a distance threshold of 50 meters. As a result of updating the initially invariant queries with invariant keys and values, the outputs of these layers are also invariant. We stack the temporal, the agent-map, and the social attention sequentially as one fusion block and repeat such blocks  $L_{\\mathrm{enc}}$  times.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Thanks to the query-centric modeling, all the agent and map encodings are unique and fixed no matter from which spacetime coordinate system we view them (i.e., roto-translation invariance for the space dimension and translation invariance for the time dimension), enabling the model to reuse past computations and operate streamingly. During online prediction, we can cache the encodings computed in previous observation windows and incrementally update the scene representation. As shown in Fig. 2, our model only performs factorized attention for the  $A$  incoming agent states when a new data frame arrives, resulting in temporal attention with  $\\mathcal{O}(AT)$  complexity, agent-map attention with  $\\mathcal{O}(AM)$  complexity, and social attention with  $\\mathcal{O}(A^2)$  complexity. All of these operations are an order less expensive than their non-streaming counterpart. Finally, we update the cached tensors using the newly computed encodings.",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "17866",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/55bc5cc5fc0a1dce8112241111669c479a13735df6797f1d2d1e5711525d06fd.jpg",
+        "image_caption": [
+            "Figure 3. Overview of the decoding pipeline. An anchor-free module generates trajectory proposals recurrently based on the encoded scene context. These proposals act as the anchors in the refinement module, where an anchor-based decoder refines the anchor trajectories and assigns a probability score for each hypothesis."
+        ],
+        "image_footnote": [],
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Query-Based Trajectory Decoding",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The second step of trajectory prediction is to utilize the scene encodings output by the encoder to decode  $K$  future trajectories for each target agent, which is non-trivial since the encoder returns only one set of feature embeddings. Inspired by the progress in object detection, some recent works [18, 32, 37, 46] employ DETR-like decoders [4] to deal with such a one-to-many problem, where multiple learnable queries cross-attend the scene encodings and decode trajectories. However, these models suffer from training instability and mode collapse like other anchor-free approaches. Moreover, they do not perform well in long-term prediction, where the forecasting task is much more challenging due to the explosive uncertainty in the distant future. Our query-based decoder overcomes these limitations by utilizing a recurrent, anchor-free proposal module to generate adaptive trajectory anchors, followed by an anchor-based module that further refines the initial proposals. An overview of our decoding pipeline is shown in Fig. 3. In the following, we will illustrate the components of the decoder in detail.",
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+    {
+        "type": "text",
+        "text": "Mode2Scene and Mode2Mode Attention. Both the proposal and refinement modules use a DETR-like architecture. Similar to the concept of object queries in DETR [4], each query takes charge of decoding one of the  $K$  trajectory modes. In the Mode2Scene attention, we use cross-attention layers to update the mode queries with multiple contexts, including the history encodings of the target agent, the map encodings, and the neighboring agents' encodings. Following the Mode2Scene attention, the  $K$  mode queries \"talk\" to each other via the Mode2Mode self-attention to improve the diversity of multiple modes.",
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+    {
+        "type": "text",
+        "text": "Reference Frames of Mode Queries. To predict the trajectories of multiple agents in parallel, we share the same set of scene encodings among all target agents in the scene. As these encodings are derived from their local spacetime coordinate systems, we need to project them into each target agent's current viewpoint to achieve the same effect as",
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+    {
+        "type": "text",
+        "text": "agent-centric modeling. To this end, we hallucinate a coordinate frame for each mode query based on the corresponding target agent's current position and yaw angle. When updating the query embeddings via Mode2Scene attention, the scene elements' positions relative to the queries are incorporated into the keys and values, which is similar to what we have done for the encoder.",
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+    {
+        "type": "text",
+        "text": "Anchor-Free Trajectory Proposal. We use learnable, anchor-free queries to propose initial trajectories. These proposals will later act as anchors in the refinement module. Compared with anchor-based methods that attempt to cover the ground truth with densely sampled handcrafted anchors [6, 19], our proposal module generates  $K$  adaptive anchors in a data-driven manner. Thanks to the cross-attention layers, the mode queries can retrieve the scene context and quickly narrow the search space for anchors. The self-attention layer further allows the queries to collaborate with each other when generating trajectory proposals.",
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+    {
+        "type": "text",
+        "text": "Over an extended prediction horizon, an agent can travel a long distance, and its surrounding environment may vary quickly. As a result, it is hard to summarize all information required for decoding a long sequence into a single query embedding. To ease the queries' burden of context extraction and improve the anchors' quality, we generalize the DETR-like decoder to a recurrent fashion. Using  $T_{\\mathrm{rec}}$  recurrent steps, the context-aware mode queries only decode  $T^{\\prime} / T_{\\mathrm{rec}}$  future waypoints via an MLP at the end of each recurrent step. At the subsequent recurrence, these queries become the input again and extract the scene context relevant to the next few waypoints' prediction. For efficiency,  $T_{\\mathrm{rec}}$  is far smaller than the prediction horizon  $T^{\\prime}$ . We also find that using much more recurrent steps is unnecessary.",
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+    },
+    {
+        "type": "text",
+        "text": "Anchor-Based Trajectory Refinement. Anchor-free decoding can be a two-edged sword: despite its flexibility, the unstable training process may lead to mode collapse occasionally. On the other hand, the randomly initialized mode queries must adapt to all target agents in all scenes and lack the scenario-specific bias, which may result in non-",
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "17867",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "compliant predictions, such as trajectories that violate the laws of motion or break the traffic rules conveyed by the high-definition map. We are thus motivated to employ an anchor-based module to refine the proposals further. Taking the output of the proposal module as anchors, we let the refinement module predict the offset to the proposed trajectories and estimate the likelihood of each hypothesis. This module also adopts a DETR-like architecture, but its mode queries are derived from the proposed trajectory anchors instead of randomly initialized. Specifically, a small GRU [8] is used to embed each trajectory anchor, and we take its final hidden state as the mode query. These anchor-based queries provide explicit spatial prior for the model, enabling the attention layers to localize the context of interest more easily.",
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+    },
+    {
+        "type": "text",
+        "text": "3.4. Training Objectives",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Following HiVT [56], we parameterize the  $i$ -th agent's future trajectory as a mixture of Laplace distributions:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf \\left(\\left\\{\\mathbf {p} _ {i} ^ {t} \\right\\} _ {t = 1} ^ {T ^ {\\prime}}\\right) = \\sum_ {k = 1} ^ {K} \\pi_ {i, k} \\prod_ {t = 1} ^ {T ^ {\\prime}} \\text {L a p l a c e} \\left(\\mathbf {p} _ {i} ^ {t} \\mid \\boldsymbol {\\mu} _ {i, k} ^ {t}, \\mathbf {b} _ {i, k} ^ {t}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where  $\\{\\pi_{i,k}\\}_{k=1}^{K}$  are the mixing coefficients, and the  $k$ -th mixture component's Laplace density at time step  $t$  is parameterized by the location  $\\pmb{\\mu}_{i,k}^t$  and the scale  $\\mathbf{b}_{i,k}^t$ . We then use a classification loss  $\\mathcal{L}_{\\mathrm{cls}}$  to optimize the mixing coefficients predicted by the refinement module. This loss minimizes the negative log-likelihood of Eq. (1), and we stop the gradients of the locations and scales to optimize the mixing coefficients only. On the other hand, we adopt the winner-take-all strategy [29] to optimize the locations and scales output by the proposal and refinement modules, which conducts backpropagation on the best-predicted proposal and its refinement only. For stabilization, the refinement module stops the gradients of the proposed trajectory anchors. The final loss function combines the trajectory proposal loss  $\\mathcal{L}_{\\mathrm{propose}}$ , the trajectory refinement loss  $\\mathcal{L}_{\\mathrm{refine}}$ , and the classification loss  $\\mathcal{L}_{\\mathrm{cls}}$  for end-to-end training:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {p r o p o s e}} + \\mathcal {L} _ {\\text {r e f i n e}} + \\lambda \\mathcal {L} _ {\\text {c l s}}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where we use  $\\lambda$  to balance regression and classification.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets. We use Argoverse 1 [7] and Argoverse 2 [49], two large-scale motion forecasting datasets, to test the efficacy of our approach. The Argoverse 1 dataset collects 323,557 sequences of data from Miami and Pittsburgh, while the Argoverse 2 dataset contains 250,000 scenarios spanning six cities. Both datasets have a sampled rate of  $10\\mathrm{Hz}$ . For the Argoverse 1 dataset, models need to predict agents' 3-second future trajectories given the 2-second",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "observations of history. The Argoverse 2 dataset, in comparison, is featured by improved data diversity, higher data quality, a larger observation window of 5 seconds, and a longer prediction horizon of 6 seconds. Using these two datasets, we intend to examine models' forecasting capability on various data distributions and prediction horizons.",
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+    {
+        "type": "text",
+        "text": "Metrics. Following the standard evaluation protocol, we adopt metrics including minimum Average Displacement Error  $(\\min\\mathrm{ADE}_K)$ , minimum Final Displacement Error  $(\\min\\mathrm{FDE}_K)$ , Brier-minimum Final Displacement Error (b-minFDE  $K$ ), and Miss Rate  $(\\mathrm{MR}_K)$  for evaluation. The metric  $\\min\\mathrm{ADE}_K$  calculates the  $\\ell_2$  distance in meters between the ground-truth trajectory and the best of  $K$  predicted trajectories as an average of all future time steps. On the other hand, the metric  $\\min\\mathrm{FDE}_K$  only concerns the prediction error at the final time step to emphasize long-term performance. To further measure the performance of uncertainty estimation, the metric b-minFDE  $K$  adds  $(1 - \\hat{\\pi})^2$  to the final-step error, where  $\\hat{\\pi}$  denotes the best-predicted trajectory's probability score that the model assigns. Moreover, the metric  $\\mathrm{MR}_K$  is used for counting the ratio of cases where  $\\min\\mathrm{FDE}_K$  exceeds 2 meters. As a common practice,  $K$  is selected as 1 and 6. If a model outputs more than  $K$  trajectories, only the predictions with the top- $K$  probability scores are considered during evaluation.",
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+    {
+        "type": "text",
+        "text": "4.2. Comparison with State of the Art",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We compare our method with the strongest baselines on the Argoverse 1 and the Argoverse 2 motion forecasting benchmarks [7, 49]. We first conduct experiments on the Argoverse 2 dataset [49], which favors solutions that work well on long-term prediction, given that its prediction horizon is as long as 6 seconds. The results are shown in Tab. 1. Even without ensembling, QCNet has already outperformed all previous approaches on the Argoverse 2 test set in terms of  $\\min\\mathrm{ADE}_6$ ,  $\\min\\mathrm{FDE}_6$ ,  $\\min\\mathrm{ADE}_1$ , and  $\\min\\mathrm{FDE}_1$ . After using ensembling techniques similar to other entries, QCNet surpasses all methods on all metrics by a large margin. We also evaluate our model on the Argoverse 1 dataset [7] to better understand the generalizability of our approach. Although the performance on the Argoverse 1 benchmark has saturated for years [49], Tab. 2 shows that QCNet significantly advances state-of-the-art on most metrics. As of the time we submitted the paper, QCNet ranks  $1^{st}$  on the leaderboards of Argoverse 1 and Argoverse 2, outperforming all published and unpublished works on the two benchmarks. Please refer to the supplementary material for more results on Argoverse 2 [49] and Waymo Open Motion Dataset [13].",
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+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Effects of Scene Context Fusion. We study the effects of scene context fusion in Tab. 3. The first question we answer is whether factorized attention is worth it. If no fac",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "17868",
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+    {
+        "type": "table",
+        "img_path": "images/501c3b5e59995674cb29ff64a9368d75b1dee593a121c6933d6f59ab185677c3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>b-minFDE6↓</td><td>minADE6↓</td><td>minFDE6↓</td><td>MR6↓</td><td>minADE1↓</td><td>minFDE1↓</td><td>MR1↓</td></tr><tr><td>THOMAS [17]</td><td>2.16</td><td>0.88</td><td>1.51</td><td>0.20</td><td>1.95</td><td>4.71</td><td>0.64</td></tr><tr><td>GoRela [9]</td><td>2.01</td><td>0.76</td><td>1.48</td><td>0.22</td><td>1.82</td><td>4.62</td><td>0.66</td></tr><tr><td>MTR [42]</td><td>1.98</td><td>0.73</td><td>1.44</td><td>0.15</td><td>1.74</td><td>4.39</td><td>0.58</td></tr><tr><td>GANet [48]</td><td>1.96</td><td>0.72</td><td>1.34</td><td>0.17</td><td>1.77</td><td>4.48</td><td>0.59</td></tr><tr><td>QML* [43]</td><td>1.95</td><td>0.69</td><td>1.39</td><td>0.19</td><td>1.84</td><td>4.98</td><td>0.62</td></tr><tr><td>BANet* [54]</td><td>1.92</td><td>0.71</td><td>1.36</td><td>0.19</td><td>1.79</td><td>4.61</td><td>0.60</td></tr><tr><td>QCNet (w/o ensemble)</td><td>1.91</td><td>0.65</td><td>1.29</td><td>0.16</td><td>1.69</td><td>4.30</td><td>0.59</td></tr><tr><td>QCNet (w/ ensemble)</td><td>1.78</td><td>0.62</td><td>1.19</td><td>0.14</td><td>1.56</td><td>3.96</td><td>0.55</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/a0d7cc45388c8146e08d96b9707384cd1c7e6af53343ef1b17382c30f6d10c5b.jpg",
+        "table_caption": [
+            "Table 1. Quantitative results on the Argoverse 2 motion forecasting leaderboard [1] ranked by b-minFDE<sub>6</sub>. Baselines that are known to have used ensembling are marked with symbol “*”. For each metric, the best result is in bold and the second best result is underlined."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>b-minFDE6↓</td><td>minADE6↓</td><td>minFDE6↓</td><td>MR6↓</td></tr><tr><td>LaneGCN [31]</td><td>2.06</td><td>0.87</td><td>1.36</td><td>0.16</td></tr><tr><td>mmTransformer [32]</td><td>2.03</td><td>0.84</td><td>1.34</td><td>0.15</td></tr><tr><td>DenseTNT [19]</td><td>1.98</td><td>0.88</td><td>1.28</td><td>0.13</td></tr><tr><td>TPCN [50]</td><td>1.93</td><td>0.82</td><td>1.24</td><td>0.13</td></tr><tr><td>SceneTransformer [38]</td><td>1.89</td><td>0.80</td><td>1.23</td><td>0.13</td></tr><tr><td>HOME+GOHOME [15, 16]</td><td>1.86</td><td>0.89</td><td>1.29</td><td>0.08</td></tr><tr><td>HiVT [56]</td><td>1.84</td><td>0.77</td><td>1.17</td><td>0.13</td></tr><tr><td>MultiPath++ [46]</td><td>1.79</td><td>0.79</td><td>1.21</td><td>0.13</td></tr><tr><td>GANet [48]</td><td>1.79</td><td>0.81</td><td>1.16</td><td>0.12</td></tr><tr><td>PAGA [11]</td><td>1.76</td><td>0.80</td><td>1.21</td><td>0.11</td></tr><tr><td>DCMS [51]</td><td>1.76</td><td>0.77</td><td>1.14</td><td>0.11</td></tr><tr><td>Wayformer [37]</td><td>1.74</td><td>0.77</td><td>1.16</td><td>0.12</td></tr><tr><td>Ours</td><td>1.69</td><td>0.73</td><td>1.07</td><td>0.11</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7113f9d51eec42e5179cb017446b62e5134cb6b11a6de4b276de47a76832ddff.jpg",
+        "table_caption": [
+            "Table 2. Quantitative results on the Argoverse 1 motion forecasting leaderboard [2]. The leaderboard is sorted by b-minFDE<sub>6</sub>."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">Online Inference (ms)</td><td rowspan=\"2\">minADE6↓</td><td rowspan=\"2\">minFDE6↓</td><td rowspan=\"2\">MR6↓</td></tr><tr><td>w/o reuse</td><td>w/ reuse</td></tr><tr><td>QCNet (Lenc = 0)</td><td>8±1</td><td>1±0</td><td>0.76</td><td>1.33</td><td>0.18</td></tr><tr><td>QCNet (Lenc = 1)</td><td>64±1</td><td>10±1</td><td>0.74</td><td>1.30</td><td>0.17</td></tr><tr><td>QCNet (Lenc = 2)</td><td>82±1</td><td>13±1</td><td>0.73</td><td>1.27</td><td>0.16</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Models' performance and inference latency evaluated on the Argoverse 2 validation set. We use an A40 GPU to measure encoders' online inference latency in the densest traffic scene involving 190 agents and 169 map polygons.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "torized attention-based fusion blocks are employed, the encoder does not involve information interactions along different axes of the scene. Even so, the decoder has access to all information required for predictions thanks to the Mode2Scene layers. As shown in the first row of Tab. 3, our model can offer solid prediction performance without fusing the scene context. But after feeding our decoder with the fused encodings, the model gains considerable improvement over its non-fusion variant. Moreover, increasing the number of fusion blocks yields better results on all metrics, demonstrating the effectiveness of factorized attention. However, the resulting inference latency is not amenable to real-time applications such as autonomous driving, making this modeling choice less appealing for widespread adoption. Fortunately, our query-centric paradigm allows the reuse of computations from previous observation windows during online prediction, which goes beyond agent-centric approaches such as HiVT [56]. As shown in Tab. 3, caching",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "and reusing the previously computed encodings drastically lowers the online inference latency in the densest traffic scene. Such a \"free lunch\" also provides headroom to design a more advanced decoder for stronger performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Component Study of the Decoder. As demonstrated in Tab. 4, all layers in the decoder contribute to the performance to a certain degree. First, although the factorized attention in the encoder has already brought context awareness to the agent features, we find that using the target agent's history encodings alone is insufficient for accurate trajectory proposals. We hypothesize that injecting the map and social information into the anchor-free decoder can explicitly provide the queries with the future context, enabling them to narrow the search space for initial trajectories. On the other hand, the map and social information can also help the anchor-based queries identify those unrealistic predictions, such as trajectories that break the traffic rules or collide with static objects on the road. As a result, the role of our refinement module is more than simply trajectory smoothing [23, 51]. Table 4 also shows that removing the Mode2Mode self-attention in either the proposal or the refinement module will harm the long-term accuracy and the diversity of multiple hypotheses.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 5 demonstrates the effects of the recurrent mechanism and the refinement module on different datasets. On Argoverse 1, most agents merely exhibit trivial behavior, and the scene context usually does not have significant variation within the 3-second prediction horizon. For this reason, our design choices only bring marginal improvement when evaluated on this dataset. However, on the more challenging Argoverse 2 dataset where the prediction horizon is 6 seconds, increasing the number of recurrent steps from 1 (i.e., no recurrence) to 3 leads to much better long-term performance, and the refinement module offers a dramatic improvement in terms of both accuracy and multimodality. We also notice that using much more recurrent steps is redundant: when increasing the number from 3 to 6, the model performance on Argoverse 2 cannot be further improved.",
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+    {
+        "type": "text",
+        "text": "4.4. Qualitative Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We present some qualitative results on the Argoverse 2 validation set. Comparing Fig. 4a and Fig. 4b, we can see",
+        "bbox": [
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+        "text": "17869",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Time</td><td colspan=\"3\">Proposal Module</td><td colspan=\"4\">Refinement Module</td><td rowspan=\"2\">b-minFDE6↓</td><td rowspan=\"2\">minADE6↓</td><td rowspan=\"2\">minFDE6↓</td><td rowspan=\"2\">MR6↓</td></tr><tr><td>Map</td><td>Social</td><td>Mode</td><td>Time</td><td>Map</td><td>Social</td><td>Mode</td></tr><tr><td>✓</td><td></td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>2.22</td><td>0.82</td><td>1.58</td><td>0.22</td></tr><tr><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>2.04</td><td>0.78</td><td>1.43</td><td>0.19</td></tr><tr><td>✓</td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>2.18</td><td>0.81</td><td>1.55</td><td>0.22</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td></td><td>2.06</td><td>0.79</td><td>1.48</td><td>0.21</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td></td><td>2.02</td><td>0.77</td><td>1.40</td><td>0.19</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>1.99</td><td>0.74</td><td>1.33</td><td>0.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>1.94</td><td>0.74</td><td>1.30</td><td>0.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>1.97</td><td>0.74</td><td>1.31</td><td>0.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>1.91</td><td>0.73</td><td>1.29</td><td>0.17</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>1.90</td><td>0.73</td><td>1.27</td><td>0.16</td></tr></table>",
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+        "type": "image",
+        "img_path": "images/5a164a7e5428f72ae5854a3bc49af38dbb05211ec118078dacf423d0b73467b9.jpg",
+        "image_caption": [
+            "(a) w/o recurrence & w/o refinement"
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+        "img_path": "images/c7c3957988cf9490b84c30f88d4fd7e4c85c85dfa2ec8140f1142881d53f7040.jpg",
+        "image_caption": [
+            "(b) w/ recurrence & w/o refinement"
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+        "type": "image",
+        "img_path": "images/0fe86ebba88ed038a8dbf7039b61872c2642ca8ed5c0064ab1eafb7b6270fa66.jpg",
+        "image_caption": [
+            "(c) w/ recurrence & w/ refinement",
+            "Figure 4. Qualitative results on the Argoverse 2 validation set. The target agents' bounding boxes and ground-truth trajectories are shown in purple, and models' predictions are shown in pink."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c8a86ef58e5e8bd591f6970774c5bc23bb0b2fd4da7b678e2011e80456d893ed.jpg",
+        "table_caption": [
+            "Table 4. Ablation study on the components of the decoder. Experimental results are based on the Argoverse 2 validation set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>#Recurrent Step</td><td>Refinement</td><td>b-minFDE6↓</td><td>minFDE6↓</td><td>MR6↓</td></tr><tr><td rowspan=\"4\">Argoverse 1 (3-sec pred.)</td><td>1 (3 sec/step)</td><td>×</td><td>1.58</td><td>0.92</td><td>0.09</td></tr><tr><td>2 (1.5 sec/step)</td><td>×</td><td>1.57</td><td>0.90</td><td>0.08</td></tr><tr><td>3 (1 sec/step)</td><td>×</td><td>1.56</td><td>0.90</td><td>0.08</td></tr><tr><td>3 (1 sec/step)</td><td>✓</td><td>1.55</td><td>0.89</td><td>0.08</td></tr><tr><td rowspan=\"5\">Argoverse 2 (6-sec pred.)</td><td>1 (6 sec/step)</td><td>×</td><td>2.10</td><td>1.47</td><td>0.20</td></tr><tr><td>2 (3 sec/step)</td><td>×</td><td>2.04</td><td>1.42</td><td>0.19</td></tr><tr><td>3 (2 sec/step)</td><td>×</td><td>2.02</td><td>1.40</td><td>0.19</td></tr><tr><td>3 (2 sec/step)</td><td>✓</td><td>1.90</td><td>1.27</td><td>0.16</td></tr><tr><td>6 (1 sec/step)</td><td>✓</td><td>1.90</td><td>1.27</td><td>0.16</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 5. Effects of the trajectory proposal and refinement modules on datasets with varying difficulty levels and prediction horizons.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "that the recurrent mechanism of the proposal module can reduce the prediction error in the long term. Figure 4c further demonstrates the effectiveness of the refinement module, which improves the diversity of multiple hypotheses and the smoothness of the predicted trajectories.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "This paper introduces QCNet, a neural architecture that overcomes some important challenges in trajectory prediction. Powered by the design ethos of query-centric modeling, QCNet maintains the representational capability of factorized attention while enjoying much faster inference. It achieves multimodal and long-term prediction by employing a recurrent, anchor-free trajectory proposal module and an anchor-based refinement module. QCNet exhibits unprecedented performance on large-scale trajectory prediction datasets, demonstrating the effectiveness of its designs.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This work was partially supported by Hong Kong Research Grant Council under GRF 11200220, Science and Technology Innovation Committee Foundation of Shenzhen under Grant No. JCYJ20200109143223052.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "17870",
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+    },
+    {
+        "type": "text",
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+]