Add Batch 15c72b69-dcfd-40bb-8599-bfaa46d023a9 data

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@@ -860,3 +860,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2025/Extrapolated Urban View Synthesis Benchmark/e65fa038-3ae6-4620-9f47-ad1a63db0abf_content_list.json

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+        "text": "Xiangyu Han $^{1,3*}$  Zhen Jia $^{1*}$  Boyi Li $^{2}$  Yan Wang $^{2}$  Boris Ivanovic $^{2}$  Yurong You $^{2}$  Lingjie Liu $^{3}$  Yue Wang $^{2,4}$  Marco Pavone $^{2,5}$  Chen Feng $^{1}$  Yiming Li $^{1,2\\dagger}$ $^{1}$ NYU  ${}^{2}$ NVIDIA  ${}^{3}$ UPenn  ${}^{4}$ USC  ${}^{5}$ Stanford",
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+            "Figure 1. Our key contributions. Previous evaluations for urban view synthesis have primarily focused on interpolated poses, as the lack of ground truth data has made it challenging to evaluate extrapolated poses. We address this gap by providing real-world data that enables both quantitative and qualitative evaluations of extrapolated view synthesis in urban scenes. The quantitative results reveal a significant performance drop in 3D Gaussian Splatting [25] when handling extrapolated views, highlighting the need for more robust NVS methods."
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+            "GT is available in our benchmark"
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Photorealistic simulators are essential for the training and evaluation of vision-centric autonomous vehicles (AVs). At their core is Novel View Synthesis (NVS), a crucial capability that generates diverse unseen viewpoints to accommodate the broad and continuous pose distribution of AVs. Recent advances in radiance fields, such as 3D Gaussian Splatting, achieve photorealistic rendering at real-time speeds and have been widely used in modeling large-scale driving scenes. However, their performance is commonly evaluated using an interpolated setup with highly correlated training and test views. In contrast, extrapolation, where test views largely deviate from training views, remains underexplored, limiting progress in generalizable simulation technology. To address this gap, we leverage publicly available AV datasets with multiple traversals,",
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+    {
+        "type": "text",
+        "text": "multiple vehicles, and multiple cameras to build the first Extrapolated Urban View Synthesis (EUVS) benchmark. Meanwhile, we conduct both quantitative and qualitative evaluations of state-of-the-art NVS methods across different evaluation settings. Our results show that current NVS methods are prone to overfitting to training views. Besides, incorporating diffusion priors and improving geometry cannot fundamentally improve NVS under large view changes, highlighting the need for more robust approaches and large-scale training. We have released the data to help advance self-driving and urban robotics simulation technology.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The development of vision-centric autonomous vehicles (AVs) relies heavily on photorealistic simulators, which provide controlled, reproducible, and scalable environments for training and evaluation of driving models [13, 44, 56]. These simulators enable AVs to learn and adapt to a variety",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This ICCV 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_footnote",
+        "text": "*Equal contribution.",
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author.",
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+    {
+        "type": "page_number",
+        "text": "28718",
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+    {
+        "type": "text",
+        "text": "of real-world scenarios, from crowded urban streets to adverse weather conditions, without the logistical and safety concerns of physical road testing. At the heart of these simulators is the capability for Novel View Synthesis (NVS)—a key technology that generates realistic images of unseen viewpoints, simulating the continuous changes in perspective that occur as AVs navigate through urban environments.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Recent advancements in radiance fields, particularly methods based on 3D Gaussian Splatting [25], have significantly improved the realism and efficiency of NVS. These approaches [8, 53, 64, 66] can produce photorealistic renderings at real-time speeds, making them highly attractive for large-scale driving scene simulation. However, despite their impressive results, the evaluation of NVS methods has predominantly focused on interpolated scenarios, where training and test viewpoints are closely related. While interpolation tests are valuable for assessing local consistency, they fall short in addressing the more critical challenge of extrapolation—where test viewpoints differ significantly from the training data. As shown in Figure 1, the interpolation test set demonstrates strong performance, with metrics such as PSNR, SSIM, and LPIPS remaining very close to the training set values. In contrast, the extrapolation test set, which includes additional translation and rotation changes relative to the training set, exhibits notable drops in performance. Specifically, the metric decreases relative to the training set are  $28\\%$  for PSNR,  $22\\%$  for SSIM, and  $50\\%$  for LPIPS. These results underscore the urgent need to explore and advance extrapolated view synthesis in complex urban scenes, as real-world driving often involves encountering scenarios with significant viewpoint shifts and diverse spatial transformations that deviate from training distributions. Several recent studies [20, 23] have investigated the generalization capabilities of NVS in 3D Gaussian Splatting. Although they show promising qualitative results, there is no comprehensive quantitative analysis due to the absence of standardized datasets. Moreover, their evaluations are primarily limited to specific scenarios or use cases, without investigating varying evaluation settings based on the degree of extrapolation. This gap underscores the urgent need for a benchmark that offers diverse and challenging datasets, enabling a rigorous and systematic assessment of NVS methods.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To establish a common platform for assessing the robustness of NVS methods, we introduce a comprehensive benchmark for quantitatively and qualitatively evaluating extrapolated novel view synthesis in large-scale urban scenes. Our benchmark leverages publicly available datasets, including NuPlan [4], MARS [30], and Argoverse2 [46], which feature multi-traversal, multi-agent and multi-camera sensory recordings. Multi-traversal data consists of asynchronous traversals of the same location, while multi-agent data refers to data collected simultaneously",
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+    {
+        "type": "text",
+        "text": "from multiple vehicles within the same area. These data provide diverse camera poses within a 3D scene, enabling the training and evaluation of extrapolated view synthesis in outdoor environments. For the experimental setup, we define three evaluation settings: (1) translation only, (2) rotation only, and (3) translation + rotation, as shown in Figure 4. In autonomous driving scenarios, Setting 1 corresponds to maneuvers such as lane changes, Setting 2 involves switching between cameras facing different directions, and Setting 3 addresses complex intersections, such as crossroads with diverse traversal paths. These settings represent common challenges in autonomous driving, and addressing them enables the synthesis of complete scenes from sparse image observations.",
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+        "text": "We conduct pose estimation and sparse reconstruction using COLMAP [39], which facilitates the initialization of Gaussian Splatting. We then evaluate state-of-the-art Gaussian Splatting-based approaches across each evaluation setting, identifying performance gaps both qualitatively and quantitatively in extrapolated urban view synthesis.",
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+    {
+        "type": "text",
+        "text": "In summary, our main contributions are as follows:",
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+        "list_items": [
+            "- We initiate the first comprehensive quantitative and qualitative study on the Extrapolated Urban View Synthesis (EUVS) problem, supported by a robust evaluation framework that categorizes evaluation settings (translation-only, rotation-only, and translation + rotation) while assessing performance using diverse metrics, including reconstruction accuracy and visual fidelity.",
+            "- We construct a novel dataset by integrating multitraversal, multi-agent, and multi-camera data from publicly available resources, totaling 90,810 frames across 345 videos. Our dataset effectively addresses the limitations of existing benchmarks, enabling rigorous and robust evaluation for extrapolated urban view synthesis.",
+            "- We benchmark state-of-the-art Gaussian Splitting-based and NeRF-based models and analyze key factors that influence the performance of extrapolated NVs, laying a solid foundation for future advancements in this challenging task. Data and code will be released upon acceptance."
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+        "text": "2. Related Works",
+        "text_level": 1,
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+    {
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+        "text": "Extrapolated View Synthesis. Extrapolated view synthesis aims to generate novel views beyond observed perspectives, addressing challenges in visual coherence for unseen regions. RapNeRF [60] proposes a random ray-casting policy that enables training on unseen views based on visible ones. Following work [54] enhances this approach by incorporating holistic priors. Besides, some generalizable models [6, 9, 45] have emerged, capable of generating extrapolated novel views from a limited number of input images. While these methods are designed for indoor scenes, several works address extrapolated view synthesis in outdoor driving scenarios, which typically involve forward-facing",
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "28719",
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+    },
+    {
+        "type": "text",
+        "text": "cameras and unbounded environments. To tackle the Setting 1 challenge in our benchmark and address the scarcity of lane change data, GGS [20] introduces a novel virtual lane generation module. In parallel, AutoSplat [26] tackles lane change in dynamic scenes by applying geometric and reflected consistency constraints. To address the Setting 1 or 2 challenge, FreeSim [15], VEGS [23], and SGD [58] enhance 3DGS [25] with diffusion priors to improve generalization ability. Yet existing methods suffer from two major limitations: (1) a lack of real data for quantitative evaluation, which confines them to quantitative analysis, and (2) a narrow focus on a specific setting in our benchmark, preventing a comprehensive and systematic exploration.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3D Gaussian Splatting. Recent advances in radiance fields, particularly NeRF [34] and 3DGS [25], have garnered significant attention due to their impressive advancements in NVs. NeRF employs an implicit representation through a multi-layer perceptron (MLP). Furthermore, 3DGS explicitly represents scenes using anisotropic 3D Gaussian ellipsoids, enabling high-quality real-time rendering. Several works have addressed issues such as difficulties with reflective surfaces [24], aliasing [57], etc. However, urban scenes introduce unique challenges due to their unbounded and dynamic nature. To address the challenge, several works separate dynamic and static elements in the scene by leveraging a composite dynamic Gaussian graph [53, 66], optical flow prediction [55, 64], etc. PVG [8] presents a unified representation model that simultaneously incorporates both dynamic and static components without relying on priors. To achieve realistic geometry and efficient rendering, 2DGS [22] collapses 3D Gaussians onto 2D planes, while hybrid approaches [41, 48] combine different Gaussians to better capture region-specific features. In summary, current urban NVS methods primarily focus on effectively handling dynamic elements and enhancing geometry representation, while the challenge of extrapolated view synthesis remains largely underexplored.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Autonomous Driving Simulators. Current simulators focus on three key challenges: parameter initialization [16, 42], traffic simulation [28, 51, 63], and sensor simulation [1, 13, 18, 27, 56, 62]. Sensor simulation is crucial for generating realistic sensory data that AVs depend on for perception and decision-making. Early sensor simulators [13, 40, 50] provide simulated environments that are valuable for research but lack visual realism. Recent studies have focused on data-driven simulators that extract data from real-world driving logs, creating more realistic and adaptable environments. These methods can be classified into two categories: generation-based and reconstruction-based approaches. The former rely on inputs such as text, video, and other data sources for simulation, supported by world models or prior knowledge [18, 27, 62]. Reconstruction-based simulations leverage real-world data",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "to ensure both visual fidelity and geometric consistency [47, 49, 56]. UniSim [56] is a pioneering example of this approach, utilizing NeRF-based scene representation to create dynamic scenes with geometric information that are both editable and controllable. Extrapolated view synthesis is essential for these simulators, as it enables the generation of realistic and consistent views from diverse angles.",
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+    {
+        "type": "text",
+        "text": "Autonomous Driving Datasets. High-quality datasets play a vital role in advancing autonomous driving research. The KITTI dataset [19], released in 2012, marked a major milestone, significantly accelerating advances in AVs [17, 33, 43]. Since then, many influential autonomous vehicle datasets have been developed to tackle challenges like adverse weather conditions [37], multimodal fusion [3, 4], repeated driving [4, 12], collaborative driving [29, 30, 52], and motion prediction [5, 14, 46], etc. We leverage publicly available datasets with multi-traversal, multi-agent, and multi-camera recordings, enabling a comprehensive and robust evaluation of extrapolated urban view synthesis.",
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+    {
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+        "text": "3. The EUVS Benchmark",
+        "text_level": 1,
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+        "text": "3.1. Dataset Curation",
+        "text_level": 1,
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+    {
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+        "text": "We leverage three publicly available, community-verified autonomous driving datasets—nuPlan [4], Argoverse 2 [46], and MARS [30]—to enhance adoption and foster trust through their established reliability. nuPlan [4] provides 1,200 hours of driving data from four cities, serving as the first large-scale planning benchmark. Argoverse 2 [46] supports multimodal perception and forecasting with 1,000 annotated 3D scenarios, 20,000 unlabeled lidar sequences, and 250,000 motion forecasting cases. MARS [30] enables collaborative driving research with multi-agent and multitraversal scenarios. The original datasets were not designed for evaluating extrapolated view synthesis, which requires our significant labor in data processing— $300+$  hours of manual traversal selection and  $800+$  hours of computing to run COLMAP. By integrating these datasets, our benchmark enables the evaluation of view synthesis across diverse and realistic urban environments under varying conditions. Figure 3 illustrates the distribution of the integrated datasets.",
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+        "text": "3.2. Evaluation Framework",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To systematically assess model performance in extrapolated urban view synthesis, our evaluation framework incorporates three evaluation settings and three data configurations. Data configurations include multi-traversal, multi-agent, and multi-camera, while evaluation settings are categorized into (1) translation only, (2) rotation only, and (3) translation + rotation, as illustrated in Figure 4.",
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+    {
+        "type": "text",
+        "text": "Setting 1. The translation-only experimental setup involves scenarios where the vehicle's position shifts without any change in orientation. This scenario is commonly observed",
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+        "img_path": "images/1709a7854bc488c0ae02b1c9a19f4299eefca5241f7ba846a7195561fb2aa78d.jpg",
+        "image_caption": [
+            "Figure 2. Dataset visualization. Our dataset features diverse scenes across various locations in different cities, sourced from multiple datasets. Typical driving scenarios include maneuvers such as lane changes, cross intersections, and T-junctions. Top: Each column displays images captured at the same location by different agents or traversals. Bottom: Each image displays the COLMAP points at a specific location, along with the corresponding camera poses."
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+        "image_caption": [
+            "Figure 3. Dataset distribution. Our dataset comprises 90,810 frames distributed over 104 cases, capturing a diverse array of multi-traversal paths, multi-agent interactions, and multi-camera perspectives across varying evaluation settings."
+        ],
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+    {
+        "type": "text",
+        "text": "in lane changes. We use traversals from different lanes in multi-traversal data, focusing on the three front cameras. The data is sourced from nuPlan [4] and Argoverse 2 [46].",
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+    {
+        "type": "text",
+        "text": "Setting 2. The second setting, rotation only, evaluates models on views with significant orientation changes. In vision-centric autonomous vehicles, this corresponds to transitions between cameras capturing different directions. We leverage multi-camera data from nuPlan [4], training on three forward-facing and three rear-facing cameras, while evaluating on two side-facing cameras.",
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+    {
+        "type": "text",
+        "text": "Setting 3. The third setting, combining translation and rotation, includes both positional shifts and orientation changes, posing the greatest challenge for NVS. To address this, we utilize multi-traversal driving data collected from the same location but across different traversal routes. For example, the training and test sets may include routes that approach an intersection from different directions. Typical route combinations feature scenarios such as intersections,",
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+    {
+        "type": "text",
+        "text": "T-junctions, and Y-junctions, as shown in Figure 2, ensuring diversity and comprehensive evaluation. The data for this setting is from MARS [30] and Argoverse 2 [46].",
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+        "text": "3.3. Algorithm Overview",
+        "text_level": 1,
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+    {
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+        "text": "Vanilla 3D Gaussian Splatting. 3D Gaussian Splatting (3DGS) [25] leverage 3D Gaussians to explicitly represent the scene, which achieves high quality while offering real-time rendering by avoiding unnecessary computation in the empty space. Building on this, 3DGM [31] leverages multitraversal consensus to differentiate transient and permanent elements, enabling joint 2D segmentation and 3D mapping without using any human supervision.",
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+    {
+        "type": "text",
+        "text": "Planar-based and Geometry Refined Gaussian Splat-ting. GaussianPro [11] builds on 3DGS [25] by introducing multi-frame geometric optimization, which guides the densi-sification of 3D Gaussians, enhancing scene consistency in complex geometries. It further refines geometry by encour",
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+            "(a) Evaluation Setting 1: Translation Only"
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+        "image_caption": [
+            "(b) Evaluation Setting 2: Rotation Only",
+            "(c) Evaluation Setting 3: Translation + Rotation",
+            "Figure 4. Qualitative and quantitative results across three evaluation settings. The performance drop from interpolation to extrapolation is significant in both qualitative and quantitative comparison. Different testing settings have distinct scenario characteristics, enabling the evaluation of a method's capabilities from various aspects, thus systematically assessing the overall performance of reconstruction algorithms, including geometric accuracy, hallucination ability, view consistency, and depth precision, etc."
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+        "type": "text",
+        "text": "aging Gaussian primitives to adopt flat structures. Similarly, 2DGS [22] projects the 3D volume into a set of 2D oriented planar Gaussian disks, enabling high-fidelity surface reconstruction. PGSR [7] introduces an unbiased depth rendering method and integrates single-view geometric, multiview photometric, and geometric regularization techniques to improve global geometry accuracy.",
+        "bbox": [
+            88,
+            574,
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+            680
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Gaussian Splatting with Diffusion Priors. VEGS [23] introduces a novel view generalization approach that harnesses pre-extracted surface normals to align 3D Gaussians while generating augmented camera views guided by diffusion priors. These diffusion priors serve a dual purpose: providing denoising loss guidance and supervising the training of augmented cameras. This process effectively mitigates floating artifacts and fragmented geometries, resulting in more accurate and coherent 3D representations.",
+        "bbox": [
+            88,
+            684,
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+            820
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Feature-Enhanced Gaussian Splatting. Feature 3DGS [65] extends 3D Gaussian Splatting with a Parallel N-dimensional Gaussian Rasterizer, allowing simultaneous rendering of radiance fields and high-dimensional semantic features. By embedding semantic features directly into 3D",
+        "bbox": [
+            89,
+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Gaussians, the approach enhances optimization, enabling better correspondence with scene semantics and achieving more detailed and accurate spatial representations.",
+        "bbox": [
+            511,
+            574,
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+            619
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "NeRF-based Method. Instant-NGP [35] uses a multiresolution hash encoding to map spatial coordinates into compact latent representations via hash tables. It efficiently encodes high-frequency details by combining trainable feature vectors with interpolation, enabling adaptive and scalable input encodings. Zip-NeRF [2] leverages multisampling with isotropic Gaussians for scale-aware features and introduces a smooth anti-aliasing loss to address z-aliasing. In addition, it incorporates a novel distance normalization technique to better manage close and distant objects, achieving high-quality rendering and fast training.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiment",
+        "text_level": 1,
+        "bbox": [
+            511,
+            805,
+            638,
+            821
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experiment Setup",
+        "text_level": 1,
+        "bbox": [
+            511,
+            830,
+            689,
+            848
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. All 3DGS-based methods are initialized only from sparse points obtained by COLMAP [39] and exclude lidar points. We employ Grounded-SAM-2",
+        "bbox": [
+            511,
+            854,
+            906,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "28722",
+        "bbox": [
+            478,
+            944,
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+            957
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/8762fe8aee21c2d60ceb89757fa613178e7395fb6bfa8c2867fa41b4fc7afd75.jpg",
+        "table_caption": [
+            "Table 1. Quantitative rendering results across three evaluation settings. In. denotes interpolation, while Ex. represents extrapolation. Different baselines excel in different settings, reflecting the comprehensiveness and completeness of the evaluation protocol."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Method</td><td colspan=\"3\">PSNR↑</td><td colspan=\"3\">SSIM↑</td><td colspan=\"3\">LPIPS↓</td><td colspan=\"3\">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td></tr><tr><td rowspan=\"9\">Setting 1</td><td>3DGS [25]</td><td>21.36</td><td>16.37</td><td>23.4%</td><td>0.8275</td><td>0.7203</td><td>13.0%</td><td>0.2041</td><td>0.2599</td><td>27.3%</td><td>0.6828</td><td>0.6039</td><td>11.6%</td></tr><tr><td>3DGM [31]</td><td>20.96</td><td>16.35</td><td>22.0%</td><td>0.8293</td><td>0.7248</td><td>12.6%</td><td>0.2003</td><td>0.2542</td><td>26.9%</td><td>0.6802</td><td>0.6087</td><td>10.5%</td></tr><tr><td>GSPro [11]</td><td>21.51</td><td>16.39</td><td>23.8%</td><td>0.8310</td><td>0.7189</td><td>13.5%</td><td>0.1804</td><td>0.2450</td><td>35.8%</td><td>0.7081</td><td>0.6130</td><td>13.4%</td></tr><tr><td>VEGS [23]</td><td>21.26</td><td>15.88</td><td>25.3%</td><td>0.8107</td><td>0.7047</td><td>13.1%</td><td>0.2498</td><td>0.3062</td><td>22.6%</td><td>0.6323</td><td>0.5521</td><td>12.7%</td></tr><tr><td>PGSR [7]</td><td>20.57</td><td>16.32</td><td>20.7%</td><td>0.8104</td><td>0.7102</td><td>12.4%</td><td>0.2262</td><td>0.2733</td><td>20.8%</td><td>0.6515</td><td>0.5848</td><td>10.2%</td></tr><tr><td>2DGS [22]</td><td>20.87</td><td>16.30</td><td>21.9%</td><td>0.8076</td><td>0.7103</td><td>12.0%</td><td>0.2438</td><td>0.2890</td><td>18.5%</td><td>0.6256</td><td>0.5644</td><td>9.8%</td></tr><tr><td>Feature 3DGS [65]</td><td>21.02</td><td>16.01</td><td>23.8%</td><td>0.8096</td><td>0.7243</td><td>10.5%</td><td>0.1876</td><td>0.2575</td><td>37.3%</td><td>0.6958</td><td>0.6122</td><td>12.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>19.68</td><td>14.06</td><td>28.6%</td><td>0.7856</td><td>0.6917</td><td>12.0%</td><td>0.2711</td><td>0.3418</td><td>26.1%</td><td>0.6318</td><td>0.5542</td><td>12.3%</td></tr><tr><td>Instant-NGP [35]</td><td>18.77</td><td>12.65</td><td>32.6%</td><td>0.7631</td><td>0.6252</td><td>18.1%</td><td>0.4874</td><td>0.5938</td><td>21.8%</td><td>0.5465</td><td>0.4837</td><td>11.5%</td></tr><tr><td></td><td>AVERAGE</td><td>20.67</td><td>15.59</td><td>24.6%</td><td>0.8083</td><td>0.7046</td><td>12.8%</td><td>0.2501</td><td>0.3134</td><td>25.3%</td><td>0.6505</td><td>0.5774</td><td>11.2%</td></tr><tr><td rowspan=\"9\">Setting 2</td><td>3DGS [25]</td><td>25.75</td><td>19.53</td><td>24.2%</td><td>0.8766</td><td>0.7511</td><td>14.3%</td><td>0.1536</td><td>0.2668</td><td>73.7%</td><td>0.7327</td><td>0.6319</td><td>13.8%</td></tr><tr><td>3DGM [31]</td><td>25.75</td><td>18.78</td><td>27.1%</td><td>0.8786</td><td>0.7464</td><td>15.0%</td><td>0.1556</td><td>0.2813</td><td>80.8%</td><td>0.7278</td><td>0.6344</td><td>12.8%</td></tr><tr><td>GSPro [11]</td><td>26.42</td><td>19.39</td><td>26.6%</td><td>0.8821</td><td>0.7470</td><td>15.3%</td><td>0.1329</td><td>0.2246</td><td>69.0%</td><td>0.7523</td><td>0.6487</td><td>13.8%</td></tr><tr><td>VEGS [23]</td><td>24.54</td><td>23.33</td><td>4.9%</td><td>0.8366</td><td>0.7949</td><td>5.0%</td><td>0.2301</td><td>0.2811</td><td>22.2%</td><td>0.6595</td><td>0.6133</td><td>7.0%</td></tr><tr><td>PGSR [7]</td><td>24.53</td><td>18.38</td><td>25.1%</td><td>0.8612</td><td>0.7119</td><td>17.3%</td><td>0.1555</td><td>0.2532</td><td>62.8%</td><td>0.7200</td><td>0.5817</td><td>19.2%</td></tr><tr><td>2DGS [22]</td><td>25.15</td><td>18.83</td><td>25.1%</td><td>0.8578</td><td>0.7204</td><td>16.0%</td><td>0.1756</td><td>0.2917</td><td>66.1%</td><td>0.6898</td><td>0.5785</td><td>16.1%</td></tr><tr><td>Feature 3DGS [65]</td><td>24.91</td><td>19.59</td><td>21.4%</td><td>0.8800</td><td>0.7864</td><td>10.6%</td><td>0.1377</td><td>0.2278</td><td>65.4%</td><td>0.7427</td><td>0.6464</td><td>13.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>29.06</td><td>17.36</td><td>40.3%</td><td>0.8660</td><td>0.6715</td><td>22.5%</td><td>0.2078</td><td>0.3582</td><td>72.4%</td><td>0.7479</td><td>0.5843</td><td>21.9%</td></tr><tr><td>Instant-NGP [35]</td><td>25.61</td><td>17.15</td><td>33.0%</td><td>0.8596</td><td>0.7212</td><td>16.1%</td><td>0.3340</td><td>0.5171</td><td>54.8%</td><td>0.7254</td><td>0.6182</td><td>14.8%</td></tr><tr><td></td><td>AVERAGE</td><td>25.75</td><td>19.15</td><td>25.6%</td><td>0.8665</td><td>0.7390</td><td>14.7%</td><td>0.1870</td><td>0.3002</td><td>62.5%</td><td>0.7220</td><td>0.6153</td><td>14.8%</td></tr><tr><td rowspan=\"9\">Setting 3</td><td>3DGS [25]</td><td>21.22</td><td>14.99</td><td>29.4%</td><td>0.8550</td><td>0.7169</td><td>16.1%</td><td>0.2252</td><td>0.4050</td><td>79.8%</td><td>0.7002</td><td>0.4774</td><td>31.8%</td></tr><tr><td>3DGM [31]</td><td>20.62</td><td>14.60</td><td>29.2%</td><td>0.8543</td><td>0.7233</td><td>15.3%</td><td>0.2254</td><td>0.4049</td><td>79.6%</td><td>0.6874</td><td>0.4672</td><td>32.0%</td></tr><tr><td>GSPro [11]</td><td>21.58</td><td>14.82</td><td>31.3%</td><td>0.8634</td><td>0.6996</td><td>19.0%</td><td>0.2010</td><td>0.3877</td><td>92.9%</td><td>0.7093</td><td>0.4541</td><td>36.0%</td></tr><tr><td>VEGS [23]</td><td>21.13</td><td>14.25</td><td>32.6%</td><td>0.8266</td><td>0.6475</td><td>21.7%</td><td>0.2359</td><td>0.4422</td><td>87.5%</td><td>0.6785</td><td>0.4442</td><td>34.5%</td></tr><tr><td>PGSR [7]</td><td>19.60</td><td>14.17</td><td>27.7%</td><td>0.8238</td><td>0.6984</td><td>15.2%</td><td>0.2934</td><td>0.4363</td><td>48.7%</td><td>0.5867</td><td>0.3787</td><td>35.5%</td></tr><tr><td>2DGS [22]</td><td>17.35</td><td>11.36</td><td>34.5%</td><td>0.7568</td><td>0.5447</td><td>28.0%</td><td>0.4296</td><td>0.5459</td><td>27.1%</td><td>0.3552</td><td>0.2327</td><td>34.5%</td></tr><tr><td>Feature 3DGS [65]</td><td>21.88</td><td>14.33</td><td>34.5%</td><td>0.8643</td><td>0.6386</td><td>26.1%</td><td>0.1400</td><td>0.3816</td><td>172.6%</td><td>0.7411</td><td>0.4669</td><td>37.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>20.61</td><td>14.42</td><td>30.0%</td><td>0.8383</td><td>0.6565</td><td>21.7%</td><td>0.2197</td><td>0.4546</td><td>106.9%</td><td>0.7108</td><td>0.3645</td><td>48.7%</td></tr><tr><td>Instant-NGP [35]</td><td>19.63</td><td>14.39</td><td>26.7%</td><td>0.8179</td><td>0.7104</td><td>13.1%</td><td>0.4956</td><td>0.6592</td><td>33.0%</td><td>0.6083</td><td>0.4157</td><td>31.7%</td></tr><tr><td></td><td>AVERAGE</td><td>20.40</td><td>14.15</td><td>30.6%</td><td>0.8334</td><td>0.6707</td><td>19.5%</td><td>0.2740</td><td>0.4575</td><td>70.0%</td><td>0.6419</td><td>0.4113</td><td>35.9%</td></tr></table>",
+        "bbox": [
+            91,
+            127,
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+            547
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/6d06a4968b2da68a66458dcb048216312f128e1bcba7c93697539170691d92d4.jpg",
+        "table_caption": [
+            "Table 2. Quantitative comparison of depth evaluation in extrapolated views in Setting 1. 3DGM [31] demonstrates superior performance on most evaluation metrics, while VEGS [23] and GSPro [11] excel in SqRel and Delta1, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Baseline</td><td>AbsRel ↓</td><td>RMSE ↓</td><td>SqRel ↓</td><td>Delta1 ↑</td><td>Delta2 ↑</td><td>Delta3 ↑</td></tr><tr><td>3DGS [25]</td><td>0.361</td><td>14.44</td><td>10.41</td><td>0.649</td><td>0.824</td><td>0.895</td></tr><tr><td>3DGM [31]</td><td>0.301</td><td>13.93</td><td>8.906</td><td>0.651</td><td>0.846</td><td>0.915</td></tr><tr><td>PGSR [7]</td><td>0.366</td><td>17.57</td><td>21.50</td><td>0.759</td><td>0.834</td><td>0.883</td></tr><tr><td>GSPro [11]</td><td>0.355</td><td>19.66</td><td>32.01</td><td>0.643</td><td>0.839</td><td>0.909</td></tr><tr><td>VEGS [23]</td><td>0.368</td><td>15.00</td><td>8.398</td><td>0.441</td><td>0.691</td><td>0.827</td></tr></table>",
+        "bbox": [
+            94,
+            627,
+            473,
+            718
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "[38] to mask out pixels corresponding to potentially movable objects during both training and evaluation and also exclude them from the initialization of 3DGS.",
+        "bbox": [
+            89,
+            732,
+            482,
+            777
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics. We use three widely-used metrics to evaluate visual quality: peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [61]. We also employ DINOv2 [36] feature cosine similarity to evaluate image quality in latent space. For geometry evaluation, we use depth metrics, including RMSE and  $\\delta_{1.25}$ . Additionally, we incorporate the Fréchet Inception Distance (FID) [21] to",
+        "bbox": [
+            89,
+            779,
+            483,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/9322a9ccabd85634e9bafa9debda576eff1aadb37c39e6137bb878f22d5237c2.jpg",
+        "table_caption": [
+            "Table 3. Perceptual quality metric of VEGS [23]. Our benchmark also incorporates the Fréchet Inception Distance (FID) to evaluate the inpainting ability of models with generative priors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Setting 1</td><td>Setting 2</td><td>Setting 3</td><td>AVERAGE</td></tr><tr><td>FID (In.) ↓</td><td>46.3</td><td>33.5</td><td>46.1</td><td>42.0</td></tr><tr><td>FID (Ex.) ↓</td><td>87.4</td><td>67.2</td><td>132.4</td><td>95.7</td></tr><tr><td>FID (Drop)</td><td>89%</td><td>101%</td><td>187%</td><td>126.7%</td></tr></table>",
+        "bbox": [
+            516,
+            613,
+            897,
+            679
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "evaluate the inpainting ability of models with strong priors.",
+        "bbox": [
+            511,
+            695,
+            903,
+            712
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Experimental Results",
+        "text_level": 1,
+        "bbox": [
+            511,
+            724,
+            718,
+            739
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1 presents the quantitative results across Settings 1-3, while Figure 5 illustrates the qualitative outcomes on the extrapolated test set. Table 3 and Table 2 present the perceptual quality and depth metrics. The results indicate that, while the metrics perform relatively well in the interpolated test set, there is a significant drop in performance in the extrapolated test set across all baselines.",
+        "bbox": [
+            511,
+            748,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Setting 1: Translation-only. In Setting 1, training views fully cover test views with moderate translational changes. (1) Results show a consistent drop in performance from",
+        "bbox": [
+            511,
+            854,
+            908,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "28723",
+        "bbox": [
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+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5481253f8bc9af45aa50f2778f2efc58a4a90a023e48c8b55a1490a87f41c2d2.jpg",
+        "image_caption": [
+            "Setting 1: Translation Only"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            99,
+            90,
+            395,
+            398
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/544945f12614aa72971e9dcd893b56c88f38ebbcc03e182571dfcb3fd272fe91.jpg",
+        "image_caption": [
+            "Setting 2: Rotation Only"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            398,
+            90,
+            620,
+            398
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a281b5f540c7d598c32ec069ca3181a039727fc9a85a60f86c9fbaf2d2c6fcb8.jpg",
+        "image_caption": [
+            "Setting 3: Rotation + Translation",
+            "Figure 5. Qualitative comparison of extrapolated view synthesis across different settings. For each setting, results from different methods are compared against the ground truth. Red boxes highlight areas where methods are limited in capturing fine details, such as road surfaces, sky regions, or object boundaries, demonstrating the challenges faced by each approach under varying movement complexities."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            624,
+            90,
+            890,
+            398
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "interpolation to extrapolation across all metrics, highlighting the challenge of generalization to views with variations. Relative drops vary by metric: PSNR falls  $23 - 25\\%$  (e.g., GSPro [11]:  $21.51 \\rightarrow 16.39$ ), with SSIM and LPIPS showing similar declines. (2) On the extrapolative test set, methods perform comparably: GSPro tops PSNR (16.39) and minimizes LPIPS (0.2450), while 3DGM [31] leads in SSIM (0.7248). Both yield similar feature cosine similarity; VEGS [23] and PGSR [7] lag slightly. Results suggest that although GSPro marginally outperforms others, differences are small, underscoring the need for improved solutions.",
+        "bbox": [
+            89,
+            469,
+            482,
+            636
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Setting 2: Rotation-only. In Setting 2, training views provide extensive coverage of the surrounding scene. However, most methods show poor generalization, with PSNR dropping by  $22.75\\%$ . Rotation changes are particularly challenging in textured regions (e.g., trees and intricate details), often resulting in blurring, while regions perpendicular to the vehicle remain difficult to capture. Additionally, distant areas pose reconstruction challenges, frequently leading to missing buildings and sky blackouts. Among the evaluated baselines, VEGS [23] and GSPro [11] stand out as the best-performing baselines in this setting: VEGS utilizes its diffusion prior for inpainting and refining missing regions, while GSPro's robust geometry handling improves generalization.",
+        "bbox": [
+            89,
+            640,
+            482,
+            835
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Setting 3: Translation + Rotation. In Setting 3, the view changes are the largest. (1) All methods exhibit notable performance drops from interpolation to extrapolation across metrics. For instance, 3DGS [25] experiences a PSNR",
+        "bbox": [
+            89,
+            839,
+            482,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "drop of  $29.4\\%$  ( $21.22 \\rightarrow 14.99$ ), while GSPro [11] undergoes a similar drop of  $31.3\\%$  ( $21.58 \\rightarrow 14.82$ ). (2) Feature 3DGS [65] and 3DGM [31] stand out as leading methods, excelling in LPIPS (0.3816) and SSIM (0.7233), respectively. However, overall performance remains limited, with PSNR consistently falling below 15, highlighting significant room for improvement in generating high-fidelity outputs for extrapolated views.",
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+        "type": "text",
+        "text": "5. Discussions",
+        "text_level": 1,
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+        "text": "Lighting Inconsistency Handling. Lighting inconsistencies are a widespread challenge in multi-traversal datasets due to varying illumination and weather conditions. To address this, we have taken specific measures. (1) Importantly, our multi-traversal dataset is manually curated to ensure that the lighting across images appears consistent to the eye. This step helps reduce the impact of extreme lighting changes and ensures a fairer evaluation of our method under controlled conditions. (2) One potential approach is to incorporate an appearance embedding for each image. We experiment with the Gaussian in the Wild (GS-W) baseline [59]. GS-W replaces traditional spherical harmonic-based color modeling with a method that separates intrinsic properties of each Gaussian point from dynamic appearance features of each image. This approach captures the stable, inherent appearance of objects while accommodating dynamic factors like highlights and shadows. Despite these efforts, our results, especially in Setting 3, still exhibit",
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+        "text": "28724",
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+        "img_path": "images/da6c60a73c394fcedf097463a5914d3d68971797e22304e6938efca9efb646be.jpg",
+        "image_caption": [
+            "(a) Mitigating lighting inconsistency by camera embedding."
+        ],
+        "image_footnote": [],
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+        "img_path": "images/9739511aa7f4910e80e89a9e7eb4c373e6276bbd22fcc5af6056f54a9bad3e71.jpg",
+        "image_caption": [
+            "(b) Qualitative dynamic scenes rendering comparison.",
+            "Figure 6. Qualitative results of dynamic baseline and lighting handling. We mitigate the lighting inconsistency issue by carefully selecting traversals under similar lighting conditions, and it can be further alleviated by introducing camera embeddings. We provide the quantitative evaluation of dynamic scene reconstruction methods in Setting 2."
+        ],
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+    {
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+        "img_path": "images/9bd9aca3939a6630077de23f5d942da933d8f5e31ba8ae7cc6252053785e3eac.jpg",
+        "table_caption": [
+            "Table 4. Quantitative performance of GS-W [59] in different settings. After learning the lighting features, the interpolated and extrapolated test metrics show significant improvement compared to other baselines. However, there is still a considerable drop from interpolation to extrapolation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Setting</td><td colspan=\"2\">PSNR ↑</td><td colspan=\"2\">SSIM ↑</td><td colspan=\"2\">LPIPS ↓</td><td colspan=\"2\">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td></tr><tr><td>Setting 1</td><td>28.15</td><td>20.22</td><td>0.89</td><td>0.78</td><td>0.15</td><td>0.23</td><td>0.71</td><td>0.64</td></tr><tr><td>Setting 2</td><td>30.10</td><td>21.21</td><td>0.91</td><td>0.82</td><td>0.13</td><td>0.20</td><td>0.76</td><td>0.67</td></tr><tr><td>Setting 3</td><td>28.62</td><td>19.36</td><td>0.87</td><td>0.73</td><td>0.15</td><td>0.31</td><td>0.74</td><td>0.50</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "a significant performance drop, as shown in Table 4 and Figure 6a, underscoring the limitations of Gaussian-based models in handling extrapolated, unseen scenarios.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dynamic Scenes. In addition to the static scene reconstruction methods that we evaluated in Table 1, some dynamic scene reconstruction techniques have recently emerged. We conduct evaluation for Setting 2 to assess these approaches, e.g., OmniRe [10]. It organizes rigid-deformable nodes and background nodes to capture dynamic scene structures and employs SMPL [32] for non-rigid object modeling. As illustrated in Figure 6b, the rendering results reveal a significant performance gap between the training and extrapolated test cameras. In the extrapolated test views, objects such as trees and stakes lose texture and geometric details, resulting in noticeably blurry outputs, whereas the training views maintain high fidelity. As shown in Table 5, the reconstruction metrics indicate an average drop of  $25\\%$  when transitioning from interpolated to extrapolated settings. The results highlight the challenges of extrapolated view synthesis in dynamic scenes and the need for further research.",
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+    {
+        "type": "text",
+        "text": "6. Conclusions, Limitations and Future Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Conclusions. We introduce the first benchmark enabling quantitative evaluation of extrapolated view synthesis, advancing photorealistic simulation for self-driving",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/b2139876ec7719c95af06b6d0d6930f0c541c57a706658d91c4bbc8487ee49b9.jpg",
+        "table_caption": [
+            "Table 5. Quantitative performance of OmniRe [10] in Setting 2. The experiment uses a single traversal with dynamic objects, showing a noticeable drop from interpolation to extrapolation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Setting</td><td colspan=\"2\">PSNR ↑</td><td colspan=\"2\">SSIM ↑</td><td colspan=\"2\">LPIPS ↓</td><td colspan=\"2\">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td></tr><tr><td>Setting 2</td><td>19.78</td><td>15.32</td><td>0.65</td><td>0.45</td><td>0.38</td><td>0.53</td><td>0.73</td><td>0.58</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "and robotics. Our benchmark integrates real-world multi-traversal, multi-agent, and multi-camera data, categorizes scenes into different evaluation settings, and evaluates state-of-the-art NVS models. Experimental results reveal that while some methods address specific challenges, current models demonstrate limited generalization, with significant overfitting to training views and suboptimal performance in extrapolated view synthesis. To support further research, we will release the dataset and benchmark, addressing the long-standing data scarcity and providing evaluation protocols. We believe the EUVS benchmark will catalyze meaningful advancements in self-driving and robotics innovation.",
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+    {
+        "type": "text",
+        "text": "Limitations and Future Work. Our benchmark does have limitations. First, although we provide the ground truth to enable quantitative evaluation for static scenes in all settings and the foreground objects evaluation in Setting 2, we lack the foreground evaluation in Settings 1 and 3. Future work will aim to expand our work to include the dynamic object evaluation in Settings 1 and 3 using multi-agent data. Secondly, although we carefully manually selected and ensured that the test trajectory viewpoints are well covered by training trajectories, a more in-depth evaluation of how observed and unseen regions differ is left for future work.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment. This work was supported in part through NSF grants 2238968 and 2121391, and the NYU IT High Performance Computing resources, services, and staff expertise. Yiming Li is supported by NVIDIA Graduate Fellowship (2024-2025).",
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+        "text": "28725",
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+    {
+        "type": "text",
+        "text": "References",
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2025/Extrapolated Urban View Synthesis Benchmark/e65fa038-3ae6-4620-9f47-ad1a63db0abf_origin.pdf

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2025/Extrapolated Urban View Synthesis Benchmark/full.md

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+# Extrapolated Urban View Synthesis Benchmark
+
+Xiangyu Han $^{1,3*}$  Zhen Jia $^{1*}$  Boyi Li $^{2}$  Yan Wang $^{2}$  Boris Ivanovic $^{2}$  Yurong You $^{2}$  Lingjie Liu $^{3}$  Yue Wang $^{2,4}$  Marco Pavone $^{2,5}$  Chen Feng $^{1}$  Yiming Li $^{1,2\dagger}$ $^{1}$ NYU  ${}^{2}$ NVIDIA  ${}^{3}$ UPenn  ${}^{4}$ USC  ${}^{5}$ Stanford
+
+https://ai4ce.github.io/EUVS-Benchmark
+
+![](images/2750e1de8e2e50beca42baa1099958d524968a043102410c836203c281dd0c6d.jpg)  
+Figure 1. Our key contributions. Previous evaluations for urban view synthesis have primarily focused on interpolated poses, as the lack of ground truth data has made it challenging to evaluate extrapolated poses. We address this gap by providing real-world data that enables both quantitative and qualitative evaluations of extrapolated view synthesis in urban scenes. The quantitative results reveal a significant performance drop in 3D Gaussian Splatting [25] when handling extrapolated views, highlighting the need for more robust NVS methods.
+
+![](images/fc9a854c63e2bee516fd917f4f42336948855da87e0a6a0784af664d4c075558.jpg)
+
+![](images/ce57cae050600ffb83d7b56b896254455bb4ea9f953c02cde065b1107a85d519.jpg)  
+GT is available in previous benchmark
+
+![](images/8e20560ca42402c382e700e53a8b707c1a96b5c1dba871c7051a5da554f6c2af.jpg)
+
+![](images/60d60ba9ab5eafe33b3d1185866f863d630b62c9e743fb06fe8a2c06ff73990e.jpg)  
+GT is available in our benchmark
+
+![](images/59d0e3a7f01289ad2105a343148fef98d14a6eaa7349ffc290cc04ae639af593.jpg)
+
+# Abstract
+
+Photorealistic simulators are essential for the training and evaluation of vision-centric autonomous vehicles (AVs). At their core is Novel View Synthesis (NVS), a crucial capability that generates diverse unseen viewpoints to accommodate the broad and continuous pose distribution of AVs. Recent advances in radiance fields, such as 3D Gaussian Splatting, achieve photorealistic rendering at real-time speeds and have been widely used in modeling large-scale driving scenes. However, their performance is commonly evaluated using an interpolated setup with highly correlated training and test views. In contrast, extrapolation, where test views largely deviate from training views, remains underexplored, limiting progress in generalizable simulation technology. To address this gap, we leverage publicly available AV datasets with multiple traversals,
+
+multiple vehicles, and multiple cameras to build the first Extrapolated Urban View Synthesis (EUVS) benchmark. Meanwhile, we conduct both quantitative and qualitative evaluations of state-of-the-art NVS methods across different evaluation settings. Our results show that current NVS methods are prone to overfitting to training views. Besides, incorporating diffusion priors and improving geometry cannot fundamentally improve NVS under large view changes, highlighting the need for more robust approaches and large-scale training. We have released the data to help advance self-driving and urban robotics simulation technology.
+
+# 1. Introduction
+
+The development of vision-centric autonomous vehicles (AVs) relies heavily on photorealistic simulators, which provide controlled, reproducible, and scalable environments for training and evaluation of driving models [13, 44, 56]. These simulators enable AVs to learn and adapt to a variety
+
+of real-world scenarios, from crowded urban streets to adverse weather conditions, without the logistical and safety concerns of physical road testing. At the heart of these simulators is the capability for Novel View Synthesis (NVS)—a key technology that generates realistic images of unseen viewpoints, simulating the continuous changes in perspective that occur as AVs navigate through urban environments.
+
+Recent advancements in radiance fields, particularly methods based on 3D Gaussian Splatting [25], have significantly improved the realism and efficiency of NVS. These approaches [8, 53, 64, 66] can produce photorealistic renderings at real-time speeds, making them highly attractive for large-scale driving scene simulation. However, despite their impressive results, the evaluation of NVS methods has predominantly focused on interpolated scenarios, where training and test viewpoints are closely related. While interpolation tests are valuable for assessing local consistency, they fall short in addressing the more critical challenge of extrapolation—where test viewpoints differ significantly from the training data. As shown in Figure 1, the interpolation test set demonstrates strong performance, with metrics such as PSNR, SSIM, and LPIPS remaining very close to the training set values. In contrast, the extrapolation test set, which includes additional translation and rotation changes relative to the training set, exhibits notable drops in performance. Specifically, the metric decreases relative to the training set are  $28\%$  for PSNR,  $22\%$  for SSIM, and  $50\%$  for LPIPS. These results underscore the urgent need to explore and advance extrapolated view synthesis in complex urban scenes, as real-world driving often involves encountering scenarios with significant viewpoint shifts and diverse spatial transformations that deviate from training distributions. Several recent studies [20, 23] have investigated the generalization capabilities of NVS in 3D Gaussian Splatting. Although they show promising qualitative results, there is no comprehensive quantitative analysis due to the absence of standardized datasets. Moreover, their evaluations are primarily limited to specific scenarios or use cases, without investigating varying evaluation settings based on the degree of extrapolation. This gap underscores the urgent need for a benchmark that offers diverse and challenging datasets, enabling a rigorous and systematic assessment of NVS methods.
+
+To establish a common platform for assessing the robustness of NVS methods, we introduce a comprehensive benchmark for quantitatively and qualitatively evaluating extrapolated novel view synthesis in large-scale urban scenes. Our benchmark leverages publicly available datasets, including NuPlan [4], MARS [30], and Argoverse2 [46], which feature multi-traversal, multi-agent and multi-camera sensory recordings. Multi-traversal data consists of asynchronous traversals of the same location, while multi-agent data refers to data collected simultaneously
+
+from multiple vehicles within the same area. These data provide diverse camera poses within a 3D scene, enabling the training and evaluation of extrapolated view synthesis in outdoor environments. For the experimental setup, we define three evaluation settings: (1) translation only, (2) rotation only, and (3) translation + rotation, as shown in Figure 4. In autonomous driving scenarios, Setting 1 corresponds to maneuvers such as lane changes, Setting 2 involves switching between cameras facing different directions, and Setting 3 addresses complex intersections, such as crossroads with diverse traversal paths. These settings represent common challenges in autonomous driving, and addressing them enables the synthesis of complete scenes from sparse image observations.
+
+We conduct pose estimation and sparse reconstruction using COLMAP [39], which facilitates the initialization of Gaussian Splatting. We then evaluate state-of-the-art Gaussian Splatting-based approaches across each evaluation setting, identifying performance gaps both qualitatively and quantitatively in extrapolated urban view synthesis.
+
+In summary, our main contributions are as follows:
+
+- We initiate the first comprehensive quantitative and qualitative study on the Extrapolated Urban View Synthesis (EUVS) problem, supported by a robust evaluation framework that categorizes evaluation settings (translation-only, rotation-only, and translation + rotation) while assessing performance using diverse metrics, including reconstruction accuracy and visual fidelity.  
+- We construct a novel dataset by integrating multitraversal, multi-agent, and multi-camera data from publicly available resources, totaling 90,810 frames across 345 videos. Our dataset effectively addresses the limitations of existing benchmarks, enabling rigorous and robust evaluation for extrapolated urban view synthesis.  
+- We benchmark state-of-the-art Gaussian Splitting-based and NeRF-based models and analyze key factors that influence the performance of extrapolated NVs, laying a solid foundation for future advancements in this challenging task. Data and code will be released upon acceptance.
+
+# 2. Related Works
+
+Extrapolated View Synthesis. Extrapolated view synthesis aims to generate novel views beyond observed perspectives, addressing challenges in visual coherence for unseen regions. RapNeRF [60] proposes a random ray-casting policy that enables training on unseen views based on visible ones. Following work [54] enhances this approach by incorporating holistic priors. Besides, some generalizable models [6, 9, 45] have emerged, capable of generating extrapolated novel views from a limited number of input images. While these methods are designed for indoor scenes, several works address extrapolated view synthesis in outdoor driving scenarios, which typically involve forward-facing
+
+cameras and unbounded environments. To tackle the Setting 1 challenge in our benchmark and address the scarcity of lane change data, GGS [20] introduces a novel virtual lane generation module. In parallel, AutoSplat [26] tackles lane change in dynamic scenes by applying geometric and reflected consistency constraints. To address the Setting 1 or 2 challenge, FreeSim [15], VEGS [23], and SGD [58] enhance 3DGS [25] with diffusion priors to improve generalization ability. Yet existing methods suffer from two major limitations: (1) a lack of real data for quantitative evaluation, which confines them to quantitative analysis, and (2) a narrow focus on a specific setting in our benchmark, preventing a comprehensive and systematic exploration.
+
+3D Gaussian Splatting. Recent advances in radiance fields, particularly NeRF [34] and 3DGS [25], have garnered significant attention due to their impressive advancements in NVs. NeRF employs an implicit representation through a multi-layer perceptron (MLP). Furthermore, 3DGS explicitly represents scenes using anisotropic 3D Gaussian ellipsoids, enabling high-quality real-time rendering. Several works have addressed issues such as difficulties with reflective surfaces [24], aliasing [57], etc. However, urban scenes introduce unique challenges due to their unbounded and dynamic nature. To address the challenge, several works separate dynamic and static elements in the scene by leveraging a composite dynamic Gaussian graph [53, 66], optical flow prediction [55, 64], etc. PVG [8] presents a unified representation model that simultaneously incorporates both dynamic and static components without relying on priors. To achieve realistic geometry and efficient rendering, 2DGS [22] collapses 3D Gaussians onto 2D planes, while hybrid approaches [41, 48] combine different Gaussians to better capture region-specific features. In summary, current urban NVS methods primarily focus on effectively handling dynamic elements and enhancing geometry representation, while the challenge of extrapolated view synthesis remains largely underexplored.
+
+Autonomous Driving Simulators. Current simulators focus on three key challenges: parameter initialization [16, 42], traffic simulation [28, 51, 63], and sensor simulation [1, 13, 18, 27, 56, 62]. Sensor simulation is crucial for generating realistic sensory data that AVs depend on for perception and decision-making. Early sensor simulators [13, 40, 50] provide simulated environments that are valuable for research but lack visual realism. Recent studies have focused on data-driven simulators that extract data from real-world driving logs, creating more realistic and adaptable environments. These methods can be classified into two categories: generation-based and reconstruction-based approaches. The former rely on inputs such as text, video, and other data sources for simulation, supported by world models or prior knowledge [18, 27, 62]. Reconstruction-based simulations leverage real-world data
+
+to ensure both visual fidelity and geometric consistency [47, 49, 56]. UniSim [56] is a pioneering example of this approach, utilizing NeRF-based scene representation to create dynamic scenes with geometric information that are both editable and controllable. Extrapolated view synthesis is essential for these simulators, as it enables the generation of realistic and consistent views from diverse angles.
+
+Autonomous Driving Datasets. High-quality datasets play a vital role in advancing autonomous driving research. The KITTI dataset [19], released in 2012, marked a major milestone, significantly accelerating advances in AVs [17, 33, 43]. Since then, many influential autonomous vehicle datasets have been developed to tackle challenges like adverse weather conditions [37], multimodal fusion [3, 4], repeated driving [4, 12], collaborative driving [29, 30, 52], and motion prediction [5, 14, 46], etc. We leverage publicly available datasets with multi-traversal, multi-agent, and multi-camera recordings, enabling a comprehensive and robust evaluation of extrapolated urban view synthesis.
+
+# 3. The EUVS Benchmark
+
+# 3.1. Dataset Curation
+
+We leverage three publicly available, community-verified autonomous driving datasets—nuPlan [4], Argoverse 2 [46], and MARS [30]—to enhance adoption and foster trust through their established reliability. nuPlan [4] provides 1,200 hours of driving data from four cities, serving as the first large-scale planning benchmark. Argoverse 2 [46] supports multimodal perception and forecasting with 1,000 annotated 3D scenarios, 20,000 unlabeled lidar sequences, and 250,000 motion forecasting cases. MARS [30] enables collaborative driving research with multi-agent and multitraversal scenarios. The original datasets were not designed for evaluating extrapolated view synthesis, which requires our significant labor in data processing— $300+$  hours of manual traversal selection and  $800+$  hours of computing to run COLMAP. By integrating these datasets, our benchmark enables the evaluation of view synthesis across diverse and realistic urban environments under varying conditions. Figure 3 illustrates the distribution of the integrated datasets.
+
+# 3.2. Evaluation Framework
+
+To systematically assess model performance in extrapolated urban view synthesis, our evaluation framework incorporates three evaluation settings and three data configurations. Data configurations include multi-traversal, multi-agent, and multi-camera, while evaluation settings are categorized into (1) translation only, (2) rotation only, and (3) translation + rotation, as illustrated in Figure 4.
+
+Setting 1. The translation-only experimental setup involves scenarios where the vehicle's position shifts without any change in orientation. This scenario is commonly observed
+
+![](images/1709a7854bc488c0ae02b1c9a19f4299eefca5241f7ba846a7195561fb2aa78d.jpg)  
+Figure 2. Dataset visualization. Our dataset features diverse scenes across various locations in different cities, sourced from multiple datasets. Typical driving scenarios include maneuvers such as lane changes, cross intersections, and T-junctions. Top: Each column displays images captured at the same location by different agents or traversals. Bottom: Each image displays the COLMAP points at a specific location, along with the corresponding camera poses.
+
+![](images/686306d5c9869386ddea58a0a3dd01fc160eb04be8c4e3c8449e63501b05a228.jpg)  
+Figure 3. Dataset distribution. Our dataset comprises 90,810 frames distributed over 104 cases, capturing a diverse array of multi-traversal paths, multi-agent interactions, and multi-camera perspectives across varying evaluation settings.
+
+in lane changes. We use traversals from different lanes in multi-traversal data, focusing on the three front cameras. The data is sourced from nuPlan [4] and Argoverse 2 [46].
+
+Setting 2. The second setting, rotation only, evaluates models on views with significant orientation changes. In vision-centric autonomous vehicles, this corresponds to transitions between cameras capturing different directions. We leverage multi-camera data from nuPlan [4], training on three forward-facing and three rear-facing cameras, while evaluating on two side-facing cameras.
+
+Setting 3. The third setting, combining translation and rotation, includes both positional shifts and orientation changes, posing the greatest challenge for NVS. To address this, we utilize multi-traversal driving data collected from the same location but across different traversal routes. For example, the training and test sets may include routes that approach an intersection from different directions. Typical route combinations feature scenarios such as intersections,
+
+T-junctions, and Y-junctions, as shown in Figure 2, ensuring diversity and comprehensive evaluation. The data for this setting is from MARS [30] and Argoverse 2 [46].
+
+# 3.3. Algorithm Overview
+
+Vanilla 3D Gaussian Splatting. 3D Gaussian Splatting (3DGS) [25] leverage 3D Gaussians to explicitly represent the scene, which achieves high quality while offering real-time rendering by avoiding unnecessary computation in the empty space. Building on this, 3DGM [31] leverages multitraversal consensus to differentiate transient and permanent elements, enabling joint 2D segmentation and 3D mapping without using any human supervision.
+
+Planar-based and Geometry Refined Gaussian Splat-ting. GaussianPro [11] builds on 3DGS [25] by introducing multi-frame geometric optimization, which guides the densi-sification of 3D Gaussians, enhancing scene consistency in complex geometries. It further refines geometry by encour
+
+![](images/dce74e08eb5f1a159d2d3546b7f157deb1bfd9ffda30b71b6febb0bc60b72ed1.jpg)  
+(a) Evaluation Setting 1: Translation Only
+
+![](images/dcd886910944c08c09424ea1e29b545ff39f8ff761dbbd9bbe7bd98c2d7a4e29.jpg)
+
+![](images/cb960acf25f7e663d00c9736e853be8325d6acbf1a823ac3560a89ba1df9b371.jpg)  
+(b) Evaluation Setting 2: Rotation Only  
+(c) Evaluation Setting 3: Translation + Rotation  
+Figure 4. Qualitative and quantitative results across three evaluation settings. The performance drop from interpolation to extrapolation is significant in both qualitative and quantitative comparison. Different testing settings have distinct scenario characteristics, enabling the evaluation of a method's capabilities from various aspects, thus systematically assessing the overall performance of reconstruction algorithms, including geometric accuracy, hallucination ability, view consistency, and depth precision, etc.
+
+aging Gaussian primitives to adopt flat structures. Similarly, 2DGS [22] projects the 3D volume into a set of 2D oriented planar Gaussian disks, enabling high-fidelity surface reconstruction. PGSR [7] introduces an unbiased depth rendering method and integrates single-view geometric, multiview photometric, and geometric regularization techniques to improve global geometry accuracy.
+
+Gaussian Splatting with Diffusion Priors. VEGS [23] introduces a novel view generalization approach that harnesses pre-extracted surface normals to align 3D Gaussians while generating augmented camera views guided by diffusion priors. These diffusion priors serve a dual purpose: providing denoising loss guidance and supervising the training of augmented cameras. This process effectively mitigates floating artifacts and fragmented geometries, resulting in more accurate and coherent 3D representations.
+
+Feature-Enhanced Gaussian Splatting. Feature 3DGS [65] extends 3D Gaussian Splatting with a Parallel N-dimensional Gaussian Rasterizer, allowing simultaneous rendering of radiance fields and high-dimensional semantic features. By embedding semantic features directly into 3D
+
+Gaussians, the approach enhances optimization, enabling better correspondence with scene semantics and achieving more detailed and accurate spatial representations.
+
+NeRF-based Method. Instant-NGP [35] uses a multiresolution hash encoding to map spatial coordinates into compact latent representations via hash tables. It efficiently encodes high-frequency details by combining trainable feature vectors with interpolation, enabling adaptive and scalable input encodings. Zip-NeRF [2] leverages multisampling with isotropic Gaussians for scale-aware features and introduces a smooth anti-aliasing loss to address z-aliasing. In addition, it incorporates a novel distance normalization technique to better manage close and distant objects, achieving high-quality rendering and fast training.
+
+# 4. Experiment
+
+# 4.1. Experiment Setup
+
+Implementation Details. All 3DGS-based methods are initialized only from sparse points obtained by COLMAP [39] and exclude lidar points. We employ Grounded-SAM-2
+
+Table 1. Quantitative rendering results across three evaluation settings. In. denotes interpolation, while Ex. represents extrapolation. Different baselines excel in different settings, reflecting the comprehensiveness and completeness of the evaluation protocol.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Method</td><td colspan="3">PSNR↑</td><td colspan="3">SSIM↑</td><td colspan="3">LPIPS↓</td><td colspan="3">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td><td>In.</td><td>Ex.</td><td>Drop</td></tr><tr><td rowspan="9">Setting 1</td><td>3DGS [25]</td><td>21.36</td><td>16.37</td><td>23.4%</td><td>0.8275</td><td>0.7203</td><td>13.0%</td><td>0.2041</td><td>0.2599</td><td>27.3%</td><td>0.6828</td><td>0.6039</td><td>11.6%</td></tr><tr><td>3DGM [31]</td><td>20.96</td><td>16.35</td><td>22.0%</td><td>0.8293</td><td>0.7248</td><td>12.6%</td><td>0.2003</td><td>0.2542</td><td>26.9%</td><td>0.6802</td><td>0.6087</td><td>10.5%</td></tr><tr><td>GSPro [11]</td><td>21.51</td><td>16.39</td><td>23.8%</td><td>0.8310</td><td>0.7189</td><td>13.5%</td><td>0.1804</td><td>0.2450</td><td>35.8%</td><td>0.7081</td><td>0.6130</td><td>13.4%</td></tr><tr><td>VEGS [23]</td><td>21.26</td><td>15.88</td><td>25.3%</td><td>0.8107</td><td>0.7047</td><td>13.1%</td><td>0.2498</td><td>0.3062</td><td>22.6%</td><td>0.6323</td><td>0.5521</td><td>12.7%</td></tr><tr><td>PGSR [7]</td><td>20.57</td><td>16.32</td><td>20.7%</td><td>0.8104</td><td>0.7102</td><td>12.4%</td><td>0.2262</td><td>0.2733</td><td>20.8%</td><td>0.6515</td><td>0.5848</td><td>10.2%</td></tr><tr><td>2DGS [22]</td><td>20.87</td><td>16.30</td><td>21.9%</td><td>0.8076</td><td>0.7103</td><td>12.0%</td><td>0.2438</td><td>0.2890</td><td>18.5%</td><td>0.6256</td><td>0.5644</td><td>9.8%</td></tr><tr><td>Feature 3DGS [65]</td><td>21.02</td><td>16.01</td><td>23.8%</td><td>0.8096</td><td>0.7243</td><td>10.5%</td><td>0.1876</td><td>0.2575</td><td>37.3%</td><td>0.6958</td><td>0.6122</td><td>12.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>19.68</td><td>14.06</td><td>28.6%</td><td>0.7856</td><td>0.6917</td><td>12.0%</td><td>0.2711</td><td>0.3418</td><td>26.1%</td><td>0.6318</td><td>0.5542</td><td>12.3%</td></tr><tr><td>Instant-NGP [35]</td><td>18.77</td><td>12.65</td><td>32.6%</td><td>0.7631</td><td>0.6252</td><td>18.1%</td><td>0.4874</td><td>0.5938</td><td>21.8%</td><td>0.5465</td><td>0.4837</td><td>11.5%</td></tr><tr><td></td><td>AVERAGE</td><td>20.67</td><td>15.59</td><td>24.6%</td><td>0.8083</td><td>0.7046</td><td>12.8%</td><td>0.2501</td><td>0.3134</td><td>25.3%</td><td>0.6505</td><td>0.5774</td><td>11.2%</td></tr><tr><td rowspan="9">Setting 2</td><td>3DGS [25]</td><td>25.75</td><td>19.53</td><td>24.2%</td><td>0.8766</td><td>0.7511</td><td>14.3%</td><td>0.1536</td><td>0.2668</td><td>73.7%</td><td>0.7327</td><td>0.6319</td><td>13.8%</td></tr><tr><td>3DGM [31]</td><td>25.75</td><td>18.78</td><td>27.1%</td><td>0.8786</td><td>0.7464</td><td>15.0%</td><td>0.1556</td><td>0.2813</td><td>80.8%</td><td>0.7278</td><td>0.6344</td><td>12.8%</td></tr><tr><td>GSPro [11]</td><td>26.42</td><td>19.39</td><td>26.6%</td><td>0.8821</td><td>0.7470</td><td>15.3%</td><td>0.1329</td><td>0.2246</td><td>69.0%</td><td>0.7523</td><td>0.6487</td><td>13.8%</td></tr><tr><td>VEGS [23]</td><td>24.54</td><td>23.33</td><td>4.9%</td><td>0.8366</td><td>0.7949</td><td>5.0%</td><td>0.2301</td><td>0.2811</td><td>22.2%</td><td>0.6595</td><td>0.6133</td><td>7.0%</td></tr><tr><td>PGSR [7]</td><td>24.53</td><td>18.38</td><td>25.1%</td><td>0.8612</td><td>0.7119</td><td>17.3%</td><td>0.1555</td><td>0.2532</td><td>62.8%</td><td>0.7200</td><td>0.5817</td><td>19.2%</td></tr><tr><td>2DGS [22]</td><td>25.15</td><td>18.83</td><td>25.1%</td><td>0.8578</td><td>0.7204</td><td>16.0%</td><td>0.1756</td><td>0.2917</td><td>66.1%</td><td>0.6898</td><td>0.5785</td><td>16.1%</td></tr><tr><td>Feature 3DGS [65]</td><td>24.91</td><td>19.59</td><td>21.4%</td><td>0.8800</td><td>0.7864</td><td>10.6%</td><td>0.1377</td><td>0.2278</td><td>65.4%</td><td>0.7427</td><td>0.6464</td><td>13.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>29.06</td><td>17.36</td><td>40.3%</td><td>0.8660</td><td>0.6715</td><td>22.5%</td><td>0.2078</td><td>0.3582</td><td>72.4%</td><td>0.7479</td><td>0.5843</td><td>21.9%</td></tr><tr><td>Instant-NGP [35]</td><td>25.61</td><td>17.15</td><td>33.0%</td><td>0.8596</td><td>0.7212</td><td>16.1%</td><td>0.3340</td><td>0.5171</td><td>54.8%</td><td>0.7254</td><td>0.6182</td><td>14.8%</td></tr><tr><td></td><td>AVERAGE</td><td>25.75</td><td>19.15</td><td>25.6%</td><td>0.8665</td><td>0.7390</td><td>14.7%</td><td>0.1870</td><td>0.3002</td><td>62.5%</td><td>0.7220</td><td>0.6153</td><td>14.8%</td></tr><tr><td rowspan="9">Setting 3</td><td>3DGS [25]</td><td>21.22</td><td>14.99</td><td>29.4%</td><td>0.8550</td><td>0.7169</td><td>16.1%</td><td>0.2252</td><td>0.4050</td><td>79.8%</td><td>0.7002</td><td>0.4774</td><td>31.8%</td></tr><tr><td>3DGM [31]</td><td>20.62</td><td>14.60</td><td>29.2%</td><td>0.8543</td><td>0.7233</td><td>15.3%</td><td>0.2254</td><td>0.4049</td><td>79.6%</td><td>0.6874</td><td>0.4672</td><td>32.0%</td></tr><tr><td>GSPro [11]</td><td>21.58</td><td>14.82</td><td>31.3%</td><td>0.8634</td><td>0.6996</td><td>19.0%</td><td>0.2010</td><td>0.3877</td><td>92.9%</td><td>0.7093</td><td>0.4541</td><td>36.0%</td></tr><tr><td>VEGS [23]</td><td>21.13</td><td>14.25</td><td>32.6%</td><td>0.8266</td><td>0.6475</td><td>21.7%</td><td>0.2359</td><td>0.4422</td><td>87.5%</td><td>0.6785</td><td>0.4442</td><td>34.5%</td></tr><tr><td>PGSR [7]</td><td>19.60</td><td>14.17</td><td>27.7%</td><td>0.8238</td><td>0.6984</td><td>15.2%</td><td>0.2934</td><td>0.4363</td><td>48.7%</td><td>0.5867</td><td>0.3787</td><td>35.5%</td></tr><tr><td>2DGS [22]</td><td>17.35</td><td>11.36</td><td>34.5%</td><td>0.7568</td><td>0.5447</td><td>28.0%</td><td>0.4296</td><td>0.5459</td><td>27.1%</td><td>0.3552</td><td>0.2327</td><td>34.5%</td></tr><tr><td>Feature 3DGS [65]</td><td>21.88</td><td>14.33</td><td>34.5%</td><td>0.8643</td><td>0.6386</td><td>26.1%</td><td>0.1400</td><td>0.3816</td><td>172.6%</td><td>0.7411</td><td>0.4669</td><td>37.0%</td></tr><tr><td>Zip-NeRF [2]</td><td>20.61</td><td>14.42</td><td>30.0%</td><td>0.8383</td><td>0.6565</td><td>21.7%</td><td>0.2197</td><td>0.4546</td><td>106.9%</td><td>0.7108</td><td>0.3645</td><td>48.7%</td></tr><tr><td>Instant-NGP [35]</td><td>19.63</td><td>14.39</td><td>26.7%</td><td>0.8179</td><td>0.7104</td><td>13.1%</td><td>0.4956</td><td>0.6592</td><td>33.0%</td><td>0.6083</td><td>0.4157</td><td>31.7%</td></tr><tr><td></td><td>AVERAGE</td><td>20.40</td><td>14.15</td><td>30.6%</td><td>0.8334</td><td>0.6707</td><td>19.5%</td><td>0.2740</td><td>0.4575</td><td>70.0%</td><td>0.6419</td><td>0.4113</td><td>35.9%</td></tr></table>
+
+Table 2. Quantitative comparison of depth evaluation in extrapolated views in Setting 1. 3DGM [31] demonstrates superior performance on most evaluation metrics, while VEGS [23] and GSPro [11] excel in SqRel and Delta1, respectively.  
+
+<table><tr><td>Baseline</td><td>AbsRel ↓</td><td>RMSE ↓</td><td>SqRel ↓</td><td>Delta1 ↑</td><td>Delta2 ↑</td><td>Delta3 ↑</td></tr><tr><td>3DGS [25]</td><td>0.361</td><td>14.44</td><td>10.41</td><td>0.649</td><td>0.824</td><td>0.895</td></tr><tr><td>3DGM [31]</td><td>0.301</td><td>13.93</td><td>8.906</td><td>0.651</td><td>0.846</td><td>0.915</td></tr><tr><td>PGSR [7]</td><td>0.366</td><td>17.57</td><td>21.50</td><td>0.759</td><td>0.834</td><td>0.883</td></tr><tr><td>GSPro [11]</td><td>0.355</td><td>19.66</td><td>32.01</td><td>0.643</td><td>0.839</td><td>0.909</td></tr><tr><td>VEGS [23]</td><td>0.368</td><td>15.00</td><td>8.398</td><td>0.441</td><td>0.691</td><td>0.827</td></tr></table>
+
+[38] to mask out pixels corresponding to potentially movable objects during both training and evaluation and also exclude them from the initialization of 3DGS.
+
+Evaluation Metrics. We use three widely-used metrics to evaluate visual quality: peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and learned perceptual image patch similarity (LPIPS) [61]. We also employ DINOv2 [36] feature cosine similarity to evaluate image quality in latent space. For geometry evaluation, we use depth metrics, including RMSE and  $\delta_{1.25}$ . Additionally, we incorporate the Fréchet Inception Distance (FID) [21] to
+
+Table 3. Perceptual quality metric of VEGS [23]. Our benchmark also incorporates the Fréchet Inception Distance (FID) to evaluate the inpainting ability of models with generative priors.  
+
+<table><tr><td></td><td>Setting 1</td><td>Setting 2</td><td>Setting 3</td><td>AVERAGE</td></tr><tr><td>FID (In.) ↓</td><td>46.3</td><td>33.5</td><td>46.1</td><td>42.0</td></tr><tr><td>FID (Ex.) ↓</td><td>87.4</td><td>67.2</td><td>132.4</td><td>95.7</td></tr><tr><td>FID (Drop)</td><td>89%</td><td>101%</td><td>187%</td><td>126.7%</td></tr></table>
+
+evaluate the inpainting ability of models with strong priors.
+
+# 4.2. Experimental Results
+
+Table 1 presents the quantitative results across Settings 1-3, while Figure 5 illustrates the qualitative outcomes on the extrapolated test set. Table 3 and Table 2 present the perceptual quality and depth metrics. The results indicate that, while the metrics perform relatively well in the interpolated test set, there is a significant drop in performance in the extrapolated test set across all baselines.
+
+Setting 1: Translation-only. In Setting 1, training views fully cover test views with moderate translational changes. (1) Results show a consistent drop in performance from
+
+![](images/5481253f8bc9af45aa50f2778f2efc58a4a90a023e48c8b55a1490a87f41c2d2.jpg)  
+Setting 1: Translation Only
+
+![](images/544945f12614aa72971e9dcd893b56c88f38ebbcc03e182571dfcb3fd272fe91.jpg)  
+Setting 2: Rotation Only
+
+![](images/a281b5f540c7d598c32ec069ca3181a039727fc9a85a60f86c9fbaf2d2c6fcb8.jpg)  
+Setting 3: Rotation + Translation  
+Figure 5. Qualitative comparison of extrapolated view synthesis across different settings. For each setting, results from different methods are compared against the ground truth. Red boxes highlight areas where methods are limited in capturing fine details, such as road surfaces, sky regions, or object boundaries, demonstrating the challenges faced by each approach under varying movement complexities.
+
+interpolation to extrapolation across all metrics, highlighting the challenge of generalization to views with variations. Relative drops vary by metric: PSNR falls  $23 - 25\%$  (e.g., GSPro [11]:  $21.51 \rightarrow 16.39$ ), with SSIM and LPIPS showing similar declines. (2) On the extrapolative test set, methods perform comparably: GSPro tops PSNR (16.39) and minimizes LPIPS (0.2450), while 3DGM [31] leads in SSIM (0.7248). Both yield similar feature cosine similarity; VEGS [23] and PGSR [7] lag slightly. Results suggest that although GSPro marginally outperforms others, differences are small, underscoring the need for improved solutions.
+
+Setting 2: Rotation-only. In Setting 2, training views provide extensive coverage of the surrounding scene. However, most methods show poor generalization, with PSNR dropping by  $22.75\%$ . Rotation changes are particularly challenging in textured regions (e.g., trees and intricate details), often resulting in blurring, while regions perpendicular to the vehicle remain difficult to capture. Additionally, distant areas pose reconstruction challenges, frequently leading to missing buildings and sky blackouts. Among the evaluated baselines, VEGS [23] and GSPro [11] stand out as the best-performing baselines in this setting: VEGS utilizes its diffusion prior for inpainting and refining missing regions, while GSPro's robust geometry handling improves generalization.
+
+Setting 3: Translation + Rotation. In Setting 3, the view changes are the largest. (1) All methods exhibit notable performance drops from interpolation to extrapolation across metrics. For instance, 3DGS [25] experiences a PSNR
+
+drop of  $29.4\%$  ( $21.22 \rightarrow 14.99$ ), while GSPro [11] undergoes a similar drop of  $31.3\%$  ( $21.58 \rightarrow 14.82$ ). (2) Feature 3DGS [65] and 3DGM [31] stand out as leading methods, excelling in LPIPS (0.3816) and SSIM (0.7233), respectively. However, overall performance remains limited, with PSNR consistently falling below 15, highlighting significant room for improvement in generating high-fidelity outputs for extrapolated views.
+
+# 5. Discussions
+
+Lighting Inconsistency Handling. Lighting inconsistencies are a widespread challenge in multi-traversal datasets due to varying illumination and weather conditions. To address this, we have taken specific measures. (1) Importantly, our multi-traversal dataset is manually curated to ensure that the lighting across images appears consistent to the eye. This step helps reduce the impact of extreme lighting changes and ensures a fairer evaluation of our method under controlled conditions. (2) One potential approach is to incorporate an appearance embedding for each image. We experiment with the Gaussian in the Wild (GS-W) baseline [59]. GS-W replaces traditional spherical harmonic-based color modeling with a method that separates intrinsic properties of each Gaussian point from dynamic appearance features of each image. This approach captures the stable, inherent appearance of objects while accommodating dynamic factors like highlights and shadows. Despite these efforts, our results, especially in Setting 3, still exhibit
+
+![](images/da6c60a73c394fcedf097463a5914d3d68971797e22304e6938efca9efb646be.jpg)  
+(a) Mitigating lighting inconsistency by camera embedding.
+
+![](images/9739511aa7f4910e80e89a9e7eb4c373e6276bbd22fcc5af6056f54a9bad3e71.jpg)  
+(b) Qualitative dynamic scenes rendering comparison.  
+Figure 6. Qualitative results of dynamic baseline and lighting handling. We mitigate the lighting inconsistency issue by carefully selecting traversals under similar lighting conditions, and it can be further alleviated by introducing camera embeddings. We provide the quantitative evaluation of dynamic scene reconstruction methods in Setting 2.
+
+Table 4. Quantitative performance of GS-W [59] in different settings. After learning the lighting features, the interpolated and extrapolated test metrics show significant improvement compared to other baselines. However, there is still a considerable drop from interpolation to extrapolation.  
+
+<table><tr><td rowspan="2">Setting</td><td colspan="2">PSNR ↑</td><td colspan="2">SSIM ↑</td><td colspan="2">LPIPS ↓</td><td colspan="2">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td></tr><tr><td>Setting 1</td><td>28.15</td><td>20.22</td><td>0.89</td><td>0.78</td><td>0.15</td><td>0.23</td><td>0.71</td><td>0.64</td></tr><tr><td>Setting 2</td><td>30.10</td><td>21.21</td><td>0.91</td><td>0.82</td><td>0.13</td><td>0.20</td><td>0.76</td><td>0.67</td></tr><tr><td>Setting 3</td><td>28.62</td><td>19.36</td><td>0.87</td><td>0.73</td><td>0.15</td><td>0.31</td><td>0.74</td><td>0.50</td></tr></table>
+
+a significant performance drop, as shown in Table 4 and Figure 6a, underscoring the limitations of Gaussian-based models in handling extrapolated, unseen scenarios.
+
+Dynamic Scenes. In addition to the static scene reconstruction methods that we evaluated in Table 1, some dynamic scene reconstruction techniques have recently emerged. We conduct evaluation for Setting 2 to assess these approaches, e.g., OmniRe [10]. It organizes rigid-deformable nodes and background nodes to capture dynamic scene structures and employs SMPL [32] for non-rigid object modeling. As illustrated in Figure 6b, the rendering results reveal a significant performance gap between the training and extrapolated test cameras. In the extrapolated test views, objects such as trees and stakes lose texture and geometric details, resulting in noticeably blurry outputs, whereas the training views maintain high fidelity. As shown in Table 5, the reconstruction metrics indicate an average drop of  $25\%$  when transitioning from interpolated to extrapolated settings. The results highlight the challenges of extrapolated view synthesis in dynamic scenes and the need for further research.
+
+# 6. Conclusions, Limitations and Future Work
+
+Conclusions. We introduce the first benchmark enabling quantitative evaluation of extrapolated view synthesis, advancing photorealistic simulation for self-driving
+
+Table 5. Quantitative performance of OmniRe [10] in Setting 2. The experiment uses a single traversal with dynamic objects, showing a noticeable drop from interpolation to extrapolation.  
+
+<table><tr><td rowspan="2">Setting</td><td colspan="2">PSNR ↑</td><td colspan="2">SSIM ↑</td><td colspan="2">LPIPS ↓</td><td colspan="2">Feat Cos Sim ↑</td></tr><tr><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td><td>In.</td><td>Ex.</td></tr><tr><td>Setting 2</td><td>19.78</td><td>15.32</td><td>0.65</td><td>0.45</td><td>0.38</td><td>0.53</td><td>0.73</td><td>0.58</td></tr></table>
+
+and robotics. Our benchmark integrates real-world multi-traversal, multi-agent, and multi-camera data, categorizes scenes into different evaluation settings, and evaluates state-of-the-art NVS models. Experimental results reveal that while some methods address specific challenges, current models demonstrate limited generalization, with significant overfitting to training views and suboptimal performance in extrapolated view synthesis. To support further research, we will release the dataset and benchmark, addressing the long-standing data scarcity and providing evaluation protocols. We believe the EUVS benchmark will catalyze meaningful advancements in self-driving and robotics innovation.
+
+Limitations and Future Work. Our benchmark does have limitations. First, although we provide the ground truth to enable quantitative evaluation for static scenes in all settings and the foreground objects evaluation in Setting 2, we lack the foreground evaluation in Settings 1 and 3. Future work will aim to expand our work to include the dynamic object evaluation in Settings 1 and 3 using multi-agent data. Secondly, although we carefully manually selected and ensured that the test trajectory viewpoints are well covered by training trajectories, a more in-depth evaluation of how observed and unseen regions differ is left for future work.
+
+Acknowledgment. This work was supported in part through NSF grants 2238968 and 2121391, and the NYU IT High Performance Computing resources, services, and staff expertise. Yiming Li is supported by NVIDIA Graduate Fellowship (2024-2025).
+
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+# F-Bench: Rethinking Human Preference Evaluation Metrics for Benchmarking Face Generation, Customization, and Restoration
+
+Lu Liu $^{1,*}$ , Huiyu Duan $^{1,*}$ , Qiang Hu $^{1,\dagger}$ , Liu Yang $^{1}$ , Chunlei Cai $^{2}$
+
+Tianxiao Ye $^{2}$ , Huayu Liu $^{1}$ , Xiaoyun Zhang $^{1}$ , Guangtao Zhai $^{1}$
+
+<sup>1</sup>Shanghai Jiao Tong University, Shanghai, China <sup>2</sup>Bilibili Inc., Shanghai, China
+
+![](images/be54ea568985a727a2cc4028c6a24db27d8ed7043d43028000e0e447b132f563.jpg)  
+Figure 1. Data construction pipeline of  $F$ -bench and content overview of FaceQ database. From left to right, (a) Diverse input source data for face generation, customization, and restoration. (b)  $F$ -Bench benchmarks 29 face generative models, including 14 face generation models, 6 face customization models, and 9 face restoration models. (c) Multi-dimensional subjective preference evaluation in  $F$ -Bench. (d) 3D scatter plots of MOS distributions across FaceQ three subsets.
+
+![](images/50a31b7cb83ff8691ad34b7636a1481484922af6f46b1659ee084656b72f3aeb.jpg)
+
+![](images/cf85e2bc4cae21c3c7775c8426f5183047677a9fc1bbce0840f052dde717a00a.jpg)
+
+# Abstract
+
+Recent artificial intelligence (AI) generative models have demonstrated remarkable capabilities in image production, and have been widely applied to face image generation, customization, and restoration. However, many AI-generated faces (AIGFs) still suffer from issues such as unique distortions, unrealistic details, and unexpected identity shifts, underscoring the need for a comprehensive quality evaluation method for AIGFs. To this end, we introduce FaceQ, the first comprehensive AI-generated Face image database with fine-grained Quality annotations aligned with human preferences, which consists of 12K images and 491K ratings across multiple dimensions. Using the FaceQ database, we establish F-Bench, a benchmark for comparing and evaluating face generation, customization, and restoration models, highlighting strengths and weaknesses across various prompts and evaluation dimensions. Additionally, we assess the performance of existing image quality assessment (IQA) methods on FaceQ, and further propose a large multimodal model (LMM) based Face quality Evaluator (F
+
+Eval) to accurately assess the multi-dimensional quality of generated faces in a one-for-all manner. Extensive experimental results demonstrate the state-of-the-art performance of our F-Eval. The project page is: https://media-sjtu.github.io/F-Bench/.
+
+# 1. Introduction
+
+Generative models, including VAE [47], GAN [26], and diffusion models [33, 74, 80], have made remarkable progress in recent years, and have been extended to the fields of text-to-image generation [3], text-driven image editing [44], image restoration [99], etc, leading to high-quality artificial intelligence generated images (AIGIs). As an important aspect of AIGIs, many studies have also investigated face generation [100], face customization [57, 108], and face restoration [62, 87], producing creative, high-quality face images. Despite these advances, many AI-generated faces (AIGFs) still suffer from perceptual deficiencies.
+
+Many natural face image quality assessment databases have been established in the literature [48, 51, 59, 86]. However, natural images are mainly degraded by distor
+
+Table 1. Comparison between FaceQ and existing AIGC quality assessment databases (top) as well as natural face quality assessment databases (bottom). FaceQ is the first large-scale AI-generated, customized and restored face quality assessment database.  
+
+<table><tr><td>Database</td><td>Domain</td><td>Source</td><td>Images</td><td>Scores</td><td>Dimensions</td></tr><tr><td>AGIQA-3K (TCSVT2024) [51]</td><td>General</td><td>AI-generated</td><td>2,982</td><td>MOS</td><td>Perception, Alignment</td></tr><tr><td>AIGCIQA (CVPR2024) [86]</td><td>General</td><td>AI-generated</td><td>2,400</td><td>MOS</td><td>Quality, Authenticity, Correspondence</td></tr><tr><td>RichHF-18K (CVPR2024) [59]</td><td>General</td><td>AI-generated</td><td>17,760</td><td>MOS</td><td>Plausibility, Aesthetics, Text-image Alignment, Overall</td></tr><tr><td>PIQ23 (CVPR2023) [13]</td><td>Face</td><td>Real</td><td>5,116</td><td>Pair</td><td>Overall, Details, Exposure</td></tr><tr><td>FaceQ</td><td>Face</td><td>AI-generated, customized and restored</td><td>12,255</td><td>MOS</td><td>Quality, Authenticity, ID Fidelity, Correspondence</td></tr></table>
+
+tions such as noise, blur, compression [23, 66, 110], etc., while AIGIs generally suffer from unique distortions including unrealistic structures and text-image inconsistencies [59, 86], etc. Recently, many studies have investigated human preferences for AIGIs [39, 50, 59, 86, 103]. However, these general AIGI quality assessment works may not be well aligned with human preferences on AIGFs, since the perceptual quality of AIGFs can be significantly affected by small deviations in facial attributes,(e.g., eye size, skin texture, identity shifts), while the number of AIGFs in these AIGI databases is limited. Moreover, current AIGI quality assessment works mainly focus on the image generation, while human preferences for face customization have rarely been considered, where identity fidelity is significant.
+
+The above limitation highlights the necessity of establishing a comprehensive quality evaluator for AIGFs. To this end, we propose FaceQ, the first AI-generated Face image Quality assessment database with three popular tasks. Specifically, FaceQ contains  $12\mathrm{K}+$  images obtained from 29 generative models across three tasks: 1) face generation, 2) face customization, and 3) face restoration, as shown in Fig.1. Based on the generated images, we collect  $491\mathrm{K}+$  quality ratings from multiple dimensions including quality, authenticity, identity (ID) fidelity, and text-image correspondence, respectively, finally forming  $32\mathrm{K}+$  mean opinion scores (MOSs). Using FaceQ, we establish a human preference benchmark, i.e., F-Bench, for face generation, customization, and restoration models, and thoroughly analyze the generation performance across different evaluation perspectives, models, and categories. In addition, we also compare the correlation of existing image quality assessment (IQA), face quality assessment (FQA), AIGI quality assessment, and preference evaluation metrics with human preferences.
+
+Furthermore, we present F-Eval, the first generated Face image quality Evaluation method designed to perform comprehensive multi-dimensional quality evaluation for generated, customized, and restorted faces in a one-for-all manner. Specifically, F-Eval leverages large multimodal models (LMMs) [11] and adopts instruction tuning [63] for preference-related vision-language adaption. We also apply low-rank adaptation (LoRA) [35] techniques for more efficient feature refining. Extensive experimental results demonstrate that F-Eval outperforms existing quality assessment methods in terms of multiple dimensions relevant to human preference for all three tasks. The main contribu
+
+tions of our work are highlighted as follows:
+
+- We construct FaceQ, the first generated face quality assessment database consisting  $491\mathrm{K}+$  human preference ratings from quality, authenticity, ID fidelity, correspondence dimensions, on  $12\mathrm{K}+$  generative face images across three tasks.  
+- We establish F-Bench, a comprehensive human preference benchmark for 29 face generation, customization, and restoration methods. It also extensively evaluates the alignment of 26 existing quality assessment methods with human preferences.  
+- We present F-Eval, a LMM-based quality assessment model to predict multi-dimensional human preference on generated faces. Extensive experiments demonstrate the state-of-art QA performance of the proposed F-Eval.
+
+# 2. Related Work
+
+Face Generation & Customization & Restoration. (1) For face generation models, earlier works such as GANs [26, 43, 85] have demonstrated significant influences. Recently, diffusion models [73, 74, 77] have achieved rapid developments in text-to-image generation. These models can be categorized into pixel-space diffusion models [1, 72, 73, 76], and latent space diffusion models [17, 58, 71, 74]. (2) For face customization, this is a recently defined task that aims to create images of a specific person with the input of an identity reference image and prompts [98]. It can be divided into two categories including conventional test-time optimization [24, 49, 75] and tuning-free customization methods utilizing pre-trained diffusion models [20, 30, 57, 91, 101, 108]. (3) For face restoration, which aims to restore high-quality face images from their low-quality counterparts. Some traditional restoration methods utilize geometric priors [16, 19, 46] or reference priors [54, 55] while in recent years, exploring generative priors such as GAN priors [15, 28, 94, 107, 113] and diffusion priors [36, 37, 62, 84, 87, 97, 109] has become a prevalent trend. Despite these improvements, the generated, customized, and restored images may suffer from various quality issues, highlighting the necessity of evaluators.
+
+Face Image Quality Assessment Database. Existing face image quality assessment (FIQA) can be divided into Biometric FIQA [12, 31, 60, 69] and Generic FIQA [13, 18, 82, 92]. BFIQA methods are most developed to evaluate the biometric utility for face recognition. GFIQA meth
+
+![](images/0ca6f16b7c42b7cffbe0d97807f01593ad18168ac065d62cf16b2ebdca062ecf.jpg)  
+Figure 2. Rating comparisons of eight dimensions. Each column presents a pair of intuitive examples of each dimension, with red indicating the better rating and blue indicating the worse one. From left to right, the subsets are face generation, face customization, and face restoration subsets. The last row displays the corresponding prompts, reference image-prompt pairs, and the GT-LQ image pairs.
+
+![](images/15cf956e90dd11acd6ae04bce2981f7b38875f0c25c21bc20e03bb64418aa45d.jpg)
+
+![](images/959bcd90fe7fba8303ac06245c48e7d7a9e96871c01f3bfb428c7c084619b239.jpg)
+
+ods [82] focus on perceptual degradation in face restoration task. Both of these databases consist of natural face images, which has distinctly different nature with generated faces.
+
+AIGC Quality Assessment Database. In recent years, plenty of researchers have raised interest in assessing AI-generated images(AIGIs) quality assessment [23, 40, 48, 51, 86, 104] by building various databases as shown in Tab 1. All of these existing database contain various categories of general AIGI images, leaving a notable gap in datasets dedicated to AI-generated face images.
+
+# 3. FaceQ Database Construction
+
+In this section, we introduce the proposed generative face quality assessment database FaceQ. The database includes 12,255 images and 491,130 human opinion ratings. Our FaceQ demonstrates the merits of comprehensive generated visual content and multi-dimensional labeling, which can significantly facilitate the advancement of AIGC research.
+
+# 3.1. Data Collection
+
+# 3.1.1. FaceQ-Gen Subset Collection
+
+Prompt Sources. The prompts in FaceQ-Gen subset are sourced from MS-COCO [61] [57] and GPT-4o [10]. These face-centric prompts can be categorized into nine types: General, Accessories, Clothes, Action, View, Expression, Background, Style, and Facial Attributes.
+
+Models Collection. We collect 14 representative face generation models, including Deep Floyd [1], Stable Diffusion V1.5 [74], Stable Diffusion V2.1 [74], SD-XL [71], Realistic Vision [8], Stable Cascade [70], ProtoVision V6.6 [7], SD3 [9], Playground V2.5 [52], Kolors [6], PixArt-alpha [17], Hunyuan [58], and Flux-dev [3]. Negative prompts and safe sensors are enabled. In total, FaceQ-Gen includes 4,032 generated face images.
+
+# 3.1.2. FaceQ-Cus Subset Collection
+
+Identity and Prompt Sources. Face customization relies on a reference identity image and a guiding prompt. The reference images in FaceQ-Cus are partially self-collected,
+
+with the rest sourced from [57]. The prompts are selected and filtered from the FaceQ-Gen prompt list.
+
+Models Collection. We collect six representative face customization methods, including ELITE [98], FastComposer [101], IP-Adapter-FaceID [4], InstantID [91], IP-Adapter-Face-ID-Plus [5], and PhotoMaker V2 [57]. Here, we use single reference image as input. In total, FaceQ-Cus includes 4,200 generated face images.
+
+# 3.1.3. FaceQ-Res Subset Collection
+
+Low Quality Images Source. (1) Synthetic: We construct two degraded pipelines following previous works [15, 93, 95, 97] to simulate real-world degradations on both indomain data from VFHQ [90], CelebRef [56] and out-of-domain self-collected high-quality Asian face images (2) Real-world: Real-world low-quality images are sourced from various public datasets, including AgeAB [68], CelebChild [28], Wider [105], LFW [38] and MegaFace [45], ensuring the degradation diversity.
+
+Models Collection and Face Image Restoration. We evaluate both diffusion-prior-based methods such as DiffBIR [62], DifFace [109], StableSR [87], and GAN or Transformer-based methods GFPGAN [94], GPEN [107], CodeFormer [113], VQFR [28] and Face-SPARNet [15]. Each method is benchmarked on both the  $F$ -Res synthetic dataset and the real-world dataset. In total, FaceQ-Res include 4023 restored images, with 2007 images in the real-world case and 2016 images in the synthetic case.
+
+# 3.2. Human Preference Dimension Design
+
+The evaluation dimensions of generated faces need specific design to adequately reflect human preference, given the complexity of perceptual factors involved. To the end, we decompose "quality" into four core dimensions: Quality, Authenticity, ID Fidelity, and Correspondence.
+
+Quality. This dimension evaluates the overall perceptual quality of the image, considering factors such as color accuracy, blur, noise, and artifacts. It is used in all tasks.
+
+Authenticity. This dimension evaluates how closely the
+
+![](images/906cf53f1707bfcabc0ffea135230ee9f39b5e4307d42b8189ee2f896f3f2245.jpg)  
+(a) Face generation MOS distribution
+
+![](images/f75d4c146079fe3a3a587bb40ab780de22b24212ea513086b7e2ba41df47cde3.jpg)  
+(b) Face customization MOS distribution
+
+![](images/e6fc96cb02e178976b89dc1fedc2b07e1fc527d99f6a9e0dbe615ac2b0e0470d.jpg)  
+(c) Face restoration MOS distribution
+
+![](images/3c50297297cdc84bc438869a8f6c868263c2dfd6249d458e8a5464371dc5356b.jpg)  
+(d) Hunyuan-DiT  
+Figure 3. Mean Opinion Score (MOS) distribution histograms and kernel density curves. (a)-(c) MOS distributions for three subsets. (d)-(h) Model-wise MOS distributions. MOS Distributions of other methods are provided in the supplementary material.
+
+![](images/5c5a432204711046296b8eb590eb28e6cfa3397c63fa6bd83fcdec4b96b1c1c7.jpg)  
+(e) SD3
+
+![](images/79d7ab75f175a10401291e5733ca09c3a9a45d4049bcae52a7f8d3669e2ca469.jpg)  
+(f) InstantID
+
+![](images/96e20e2700d895b48c3bae974748669a32f3565913b33186b0a6b646c5450d6c.jpg)  
+(g) VQFR (real world)
+
+![](images/5549685e6ba630acb1c517d5728a32ae0ca6ceee01efa7ff46dfa9400665b798.jpg)  
+(h) StableSR (synthetic)
+
+generated image resembles a natural, real-life photograph, with particular emphasis on realistic skin texture, facial details, and wrinkles. It is used in face generation task.
+
+ID Fidelity. This dimension evaluates how well the identity of the reference image is preserved in the customized or restored image in face customization and restoration tasks.
+
+Correspondence. This dimension evaluates text-to-image alignment in face generation and customization tasks.
+
+# 3.3. Subjective Experiment
+
+Main Assessment. To ensure a comprehensive, fair, and reliable subjective assessment, 180 participants with normal or corrected-to-normal eyesight are recruited for the experiment. They first take expert-led tutorials before the main assessment. In the main assessment, participants are asked to rate the image by dragging a sliding window from 0 to 5 with a two-digit decimal from different dimensions. All images are displayed on 27-inch 4K Dell monitors, randomly presented, at their original resolution under standard lighting conditions. The experiment follows the ITU-R BT.500-14 guidelines [78] for subjective evaluations.
+
+Subjective Score Processing. To eliminate the inter-annotator variability, outlier detection based on Kurtosis is conducted with a rejection rate of  $3\%$  [78]. As a result, each image is rated by at least 15 subjects. These valid ratings are converted and scaled into Z-scores ranging from [0, 100] with the following formulas:
+
+$$
+z _ {i j} = \frac {r _ {i j} - \mu_ {i}}{\sigma_ {i}}, \quad z _ {i j} ^ {\prime} = \frac {1 0 0 (z _ {i j} + 3)}{6}, \tag {1}
+$$
+
+$$
+\mu_ {i} = \frac {1}{M _ {i}} \sum_ {j = 1} ^ {M _ {i}} r _ {i j}, \sigma_ {i} = \sqrt {\frac {1}{M _ {i} - 1} \sum_ {j = 1} ^ {M _ {i}} (r _ {i j} - \mu_ {i}) ^ {2}}, \tag {2}
+$$
+
+Here,  $r_{ij}$  represents the original ratings provided by the  $i$ -th evaluator for the  $j$ -th image,  $M_i$  denotes the total number of images that were assessed by the  $i$ -th participant in this group. Finally, the mean opinion score (MOS) of the image  $j$  ( $MOS_j$ ) is computed by averaging the rescaled
+
+z-scores as follows:
+
+$$
+M O S _ {j} = \frac {1}{N _ {j}} \sum_ {i = 1} ^ {N _ {j}} z _ {i j} ^ {\prime} \tag {3}
+$$
+
+where  $N_{j}$  denotes the number of valid subjects for image  $j$ , and  $z_{ij}^{\prime}$  denotes rescaled z-scores.
+
+# 4. F-Bench: Benchmarking Current Generative Face Models
+
+In this section, we establish a human preference benchmark F-Bench for today's state-of-the-art face generation, customization, and restoration methods, from quality, authenticity, ID fidelity, and correspondence dimensions. This benchmark analyzes the strengths and weaknesses, providing new insights and potential directions for future work.
+
+# 4.1. Perspective Analysis
+
+Fig.3 demonstrate the MOS distribution across eight dimensions in the three subsets, highlighting distinct variations between dimensions. (1) In the face generation task, the Correspondence score is the highest among the three dimensions, indicating that existing generative models perform well in aligning with prompts. The distribution of Authenticity is skewed towards lower scores, suggesting that current face generation models still fall short in generating photorealistic face images that satisfy human preferences. (2) In face customization, models perform the worst in the Quality dimension overall, demonstrating the difficulty of injecting identity information without compromising image quality. Identity Fidelity shows a bimodal distribution, reflecting the dichotomous nature of human judgment regarding whether the generated face accurately represents the same identity. (3) In face restoration, models perform better in Quality than in Identity Fidelity.
+
+# 4.2. Model-wise Comparison
+
+Face Generation. Fig.4a presents the average MOS scores across three dimensions: Quality, Authenticity, and Correspondence. Correspondence scores show a steady increase
+
+![](images/303eb0332611bac5a2f83daa16a9a9abd49abc0fce780e81bf45e786228ec912.jpg)  
+Figure 4. Average MOS score comparison across all models and dimensions. (a) Face generation. (b) Face customization. (c) Face restoration. The models are arranged in a clockwise order by release date.
+
+![](images/f59aec7a75dddcb25645866c238883c65a864408f00f39ecea66cc85f857374e.jpg)
+
+![](images/23104c2b45121fa81dc3d3fde8bf89c52a2708806106f4cf5126a2ed3de561b8.jpg)
+
+![](images/58c75820987283522713a3ba1b67a33e0791394c6a0c2832d19922b94416984a.jpg)  
+Figure 5. Violin plots of quality, authenticity and correspondence scores in FaceQ-Gen subset across nine prompt categories.
+
+over time, indicating consistent improvement in text comprehension. Quality scores generally rise with the release year, although Hunyuan [58] and Dreamlike [2] exhibit deviations. Hunyuan [58] oversmoothes the facial details and performs worse compared to its contemporaries, while Dreamlike [2] performs the opposite. Authenticity scores exhibit the greatest variation among models, suggesting that current face generation models place insufficient emphasis on authenticity. Except for Realistic Vision [8], SD3 [9], Flux-dev [3], and Dreamlike [2], most models lag in authenticity relative to quality, highlighting a common phenomenon of high-quality but less realistic outputs in generative models. Fig.3d,e give some examples of MOS distributions of different methods, revealing a reasonable fine-grained performance difference.
+
+Face Customization. Fig.4b is the performance radar chart for face customization models. IP-Adapter-FaceID-Plus[5] achieves the best performance across all dimensions, followed by PhotoMaker [57]. This highlights their great robustness in identity encoders. ELITE [98] scores the lowest in all dimensions. IP-Adapter-FaceID [4] produces high-quality images but lacks accuracy in Identity Fidelity. This may be because the base model [71] introduces many AI artifacts, which affect both Identity Fidelity and Quality. InstantID [91] and FastComposer [101] score well in Identity Fidelity but underperform significantly in Quality and Correspondence, indicating strong identity preservation but limited text-driven editing capabilities. Fig.3h illustrate the model-wise MOS distributions, revealing similar trends to those observed in the radar chart.
+
+Face Restoration. Fig.4c displays the average performance comparison of nine face restoration models. DR2 [97] exhibits the weakest performance in both Quality and Identity fidelity. This may be due to the degradation removal process of DR2 [97], which results in the loss of fine de
+
+tails and excessive smoothing. In contrast, StableSR [89] and CodeFormer [113] achieve the best overall performance among the nine face restoration models, successfully preserving both intricate details and accurate identity representations. When comparing the performance on real-world and synthetic data, most methods struggle to achieve satisfactory results on complex real-world degradations, except for SAPRNet [15] and DiffBIR [62]. StableSR [89] and GFPGAN [94] show strong robustness, performing consistently well on both real-world and synthetic data.
+
+# 4.3. Class-wise Comparison
+
+For the face generation task, we analyze the Mean Opinion Score (MOS) distributions of Quality, Authenticity, and Correspondence across nine prompt categories, as shown in Fig.5. The violin plots highlight distinct performance patterns across these categories. The Action, Expression, and Facial Attributes categories exhibit lower MOS values in all three dimensions, with notable variability. In the Action category, limited visibility of the face due to body movements affects the generation of fine facial details, resulting in reduced scores, especially in Quality and Correspondence. The Expression category poses challenges in maintaining spatial relationships and physical constraints, leading to distortion and artifacts in expressions with exaggerated facial movements, such as laughing or crying, thereby impacting both Quality and Authenticity. For Facial Attributes, generating images with precise attributes (e.g., specific eye color, hair style) is challenging, particularly when multiple attributes are specified, which lowers the scores. In contrast, the General and Background categories achieve the highest MOS scores across all dimensions, as simpler or less specific prompts are easier for the model to interpret accurately. The Clothes and Accessories categories also perform well, indicating that the model handles clothes and accessory prompts effectively. Overall, prompts with specific or
+
+![](images/ea49b49f9d03c0009d83adb59ba0355c21572a7476d5ebc10ade03953940f09e.jpg)  
+Figure 6. The overall framework of F-Eval. F-Eval can evaluate quality, authenticity, correspondence, and identity fidelity in a one-for-all framework. It can process both single and paired images, along with prompts, to produce quality scores. It consists of three encoders, including a vision encoder, a face encoder, and a text tokenizer to process multi-modal inputs. These features are projected into the same space by trained projectors. A pre-trained large language model is utilized to fuse the features while fine-tuned with four LoRA experts. Specific LoRA will be activated by dimension ID, which is classified by a trainable router.
+
+![](images/eabc3a39c23181b6f185bfa475841063d2fa90b82c807841ba30c66e7609deb8.jpg)
+
+complex attribute requirements tend to result in lower MOS scores, while general or simple prompts yield consistently high scores across dimensions. This can be attributed to the absence of high-quality fine-grained text-face pair datasets during the training of generative models.
+
+# 5. F-Eval Method
+
+In this section, we introduce our one-for-all generated face quality assessment method, F-Eval, towards predicting quality scores from multiple dimensions for three tasks using one model.
+
+# 5.1. Overall Architecture
+
+The overall architecture of F-Eval is depicted in Fig. 6. As shown on the left, F-Eval can assess four dimensions: quality, authenticity, text-image correspondence, and identity fidelity, with multimodal inputs, i.e.text prompts, image and optional reference image, to output quality-related answers. On the right, the input image(s) can originate from all three tasks. F-Eval employs a vision encoder and a face encoder to extract visual features, with projectors projecting both into a unified language space. User prompts are encoded into textual embeddings through a tokenizer. These multimodal features are concatenated and fed into a pre-trained large language model for the final output.
+
+# 5.2. Model Design
+
+Vision Encoding. For input image(s), F-Eval adopt a vision encoder to extract global features and a face encoder captures face features related to facial structure and identity. Specifically, the vision encoder, Qwen-VL-2.5-ViT [11], is tuned on FaceQ to adjust different dimensions. Face encoder is Arcface [22], which is frozen. Two two-layer multi-layer perception projectors then map the features.
+
+Feature Fusion via the LLM. For input prompts, it is tokenized into text tokens and then concatenated with visual tokens. Here, Qwen-VL2.5-7B [11] is employed as the pretrained LLM backbone to combine visual tokens and text tokens to perform multi-modal learning.. Finally, the output features of the LLM are decoded with a text decoder and then projected to the prompt-corresponded quality space.
+
+# 5.3. Multi-Expert LoRA Tuning
+
+Instruction Tuning. Previous IQA methods are often designed for specific dimensions [106, 112], addressing only one aspect of the problem or requiring retraining of model weights for different dimensions. Leveraging the generalization ability of LLMs, instruction tuning allows for the integration of different dimensions within a unified framework. Therefore, we construct diverse instruction data for the four facial quality evaluation dimensions in the FaceQ dataset and fine-tune F-Eval by adjusting the visual encoder, projector, and LLM parameters to adapt it to the specific task. As a result, F-Eval is capable of evaluating facial quality using unified weights.
+
+Mixture of LoRA Experts (MoLE). Tuning a holistic quality model for different dimensions using a single LoRA expert introduces inherent interference between dimensions. Hence, F-Eval integrates four LoRA experts for four dimensions when tuning vision encoder and LLM, constituting MoLE modules. A router is trained to classify input prompts into the four dimensions and output the corresponding dimension ID  $k$ . Specifically, for a frozen linear layer  $h = Wx$  with input  $x \in \mathbb{R}^{d_i}$  and weight matrix  $W \in \mathbb{R}^{d_o \times d_i}$ , a LoRA expert is trained to learn a low-rank decomposed update:
+
+$$
+h = W x + \Delta W x = W x + \frac {\alpha}{r} B A x, \tag {4}
+$$
+
+Table 2. Performance comparison on FaceQ-Gen and FaceQ-Cus subsets.  $\spadesuit$ ,  $\clubsuit$ ,  $\diamond$ , and  $\heartsuit$  denote traditional IQA models, face IQA models, classical deep learning-based IQA models, and AIGC IQA models respectively. * indicates fine-tuned results.  
+
+<table><tr><td>Task</td><td colspan="9">Face Generation</td><td colspan="8">Face Customization</td><td></td></tr><tr><td>Dimension</td><td colspan="3">Quality</td><td colspan="3">Authenticity</td><td colspan="3">Correspondence</td><td colspan="3">Quality</td><td colspan="3">ID Fidelity</td><td colspan="2">Correspondence</td><td></td></tr><tr><td>Model</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td></tr><tr><td>◆NIQE [67]</td><td>0.1726</td><td>0.1142</td><td>0.2553</td><td>0.0869</td><td>0.0571</td><td>0.1346</td><td>0.0752</td><td>0.0507</td><td>0.1098</td><td>0.1365</td><td>0.0899</td><td>0.1436</td><td>0.1490</td><td>0.0991</td><td>0.1310</td><td>0.1186</td><td>0.0784</td><td>0.1245</td></tr><tr><td>◆ILNIQE [111]</td><td>0.1981</td><td>0.1319</td><td>0.3159</td><td>0.0675</td><td>0.0445</td><td>0.1505</td><td>0.0889</td><td>0.0591</td><td>0.1665</td><td>0.2032</td><td>0.1327</td><td>0.2479</td><td>0.2192</td><td>0.1452</td><td>0.2778</td><td>0.1878</td><td>0.1251</td><td>0.2275</td></tr><tr><td>◆HOSA [102]</td><td>0.2537</td><td>0.1708</td><td>0.2972</td><td>0.1103</td><td>0.0728</td><td>0.1446</td><td>0.122</td><td>0.0814</td><td>0.1495</td><td>0.1019</td><td>0.0688</td><td>0.0597</td><td>0.0753</td><td>0.0506</td><td>0.0552</td><td>0.1036</td><td>0.0696</td><td>0.0748</td></tr><tr><td>◆BPRI-PSS [64]</td><td>0.2362</td><td>0.1595</td><td>0.2413</td><td>0.1700</td><td>0.1142</td><td>0.1772</td><td>0.1673</td><td>0.1121</td><td>0.1647</td><td>0.0238</td><td>0.0166</td><td>0.0314</td><td>0.1425</td><td>0.0972</td><td>0.1758</td><td>0.1100</td><td>0.0729</td><td>0.1067</td></tr><tr><td>◆FISBLIM [27]</td><td>0.0901</td><td>0.0595</td><td>0.0433</td><td>0.0028</td><td>0.0003</td><td>0.0175</td><td>0.1000</td><td>0.0665</td><td>0.0196</td><td>0.1614</td><td>0.1024</td><td>0.1690</td><td>0.0256</td><td>0.0173</td><td>0.0126</td><td>0.0852</td><td>0.0559</td><td>0.0854</td></tr><tr><td>◆ArcFace[22]</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>0.3099</td><td>0.2094</td><td>0.3605</td><td>0.5062</td><td>0.3439</td><td>0.5572</td><td>0.1837</td><td>0.1243</td><td>0.2244</td></tr><tr><td>◆SER-FIQ[83]</td><td>0.1552</td><td>0.1034</td><td>0.1561</td><td>0.0470</td><td>0.0314</td><td>0.0575</td><td>0.1130</td><td>0.075</td><td>0.1110</td><td>-0.1241</td><td>-0.080</td><td>-0.1241</td><td>-0.0109</td><td>-0.0078</td><td>0.0042</td><td>-0.1680</td><td>-0.1121</td><td>-0.1911</td></tr><tr><td>◆DSL-FIQA[18]</td><td>0.5606</td><td>0.3927</td><td>0.5945</td><td>0.3156</td><td>0.2096</td><td>0.3960</td><td>0.3706</td><td>0.2514</td><td>0.4355</td><td>0.3615</td><td>0.2450</td><td>0.3651</td><td>0.2429</td><td>0.1652</td><td>0.2519</td><td>0.1040</td><td>0.0703</td><td>0.0974</td></tr><tr><td>◆IFQA[41]</td><td>0.2313</td><td>0.1549</td><td>0.3261</td><td>0.1597</td><td>0.1062</td><td>0.2097</td><td>0.1597</td><td>0.1077</td><td>0.2260</td><td>0.2401</td><td>0.1614</td><td>0.2220</td><td>0.1503</td><td>0.0973</td><td>0.1739</td><td>0.3731</td><td>0.2546</td><td>0.3941</td></tr><tr><td>◆CNNIAQ*[42]</td><td>0.4219</td><td>0.2895</td><td>0.3510</td><td>0.3037</td><td>0.2054</td><td>0.2973</td><td>0.2824</td><td>0.1931</td><td>0.2595</td><td>0.6244</td><td>0.4376</td><td>0.6620</td><td>0.6511</td><td>0.4441</td><td>0.6381</td><td>0.3765</td><td>0.2545</td><td>0.3264</td></tr><tr><td>◇VGG16*[79]</td><td>0.5846</td><td>0.4141</td><td>0.6006</td><td>0.5010</td><td>0.3508</td><td>0.5181</td><td>0.4349</td><td>0.2994</td><td>0.4723</td><td>0.7217</td><td>0.5324</td><td>0.7857</td><td>0.6735</td><td>0.4717</td><td>0.6636</td><td>0.5635</td><td>0.3932</td><td>0.5589</td></tr><tr><td>◇VGG19*[79]</td><td>0.5728</td><td>0.4043</td><td>0.5644</td><td>0.4681</td><td>0.3248</td><td>0.4479</td><td>0.4171</td><td>0.2873</td><td>0.4754</td><td>0.7952</td><td>0.6031</td><td>0.8096</td><td>0.7544</td><td>0.5417</td><td>0.7555</td><td>0.6585</td><td>0.4742</td><td>0.6465</td></tr><tr><td>◇ResNet18*[29]</td><td>0.6150</td><td>0.4417</td><td>0.6660</td><td>0.4600</td><td>0.3160</td><td>0.4604</td><td>0.4829</td><td>0.3360</td><td>0.4628</td><td>0.7966</td><td>0.6013</td><td>0.8006</td><td>0.7473</td><td>0.5335</td><td>0.7656</td><td>0.6308</td><td>0.4488</td><td>0.6191</td></tr><tr><td>◇ResNet34*[29]</td><td>0.6092</td><td>0.4354</td><td>0.6537</td><td>0.5564</td><td>0.3949</td><td>0.5401</td><td>0.4410</td><td>0.3065</td><td>0.5207</td><td>0.8141</td><td>0.6211</td><td>0.8151</td><td>0.7969</td><td>0.5878</td><td>0.8157</td><td>0.5708</td><td>0.4000</td><td>0.5810</td></tr><tr><td>◇HyperIAQ*[81]</td><td>0.6333</td><td>0.4545</td><td>0.6591</td><td>0.6106</td><td>0.4406</td><td>0.6042</td><td>0.4235</td><td>0.2912</td><td>0.4240</td><td>0.8524</td><td>0.6631</td><td>0.8205</td><td>0.8419</td><td>0.6463</td><td>0.8588</td><td>0.6628</td><td>0.4757</td><td>0.6454</td></tr><tr><td>◇TRES*[25]</td><td>0.7766</td><td>0.5867</td><td>0.8047</td><td>0.6458</td><td>0.4703</td><td>0.6579</td><td>0.5708</td><td>0.4038</td><td>0.6270</td><td>0.8883</td><td>0.7083</td><td>0.8951</td><td>0.8330</td><td>0.6409</td><td>0.8658</td><td>0.7393</td><td>0.5497</td><td>0.7400</td></tr><tr><td>◆MANIAQ*[106]</td><td>0.7871</td><td>0.5951</td><td>0.8150</td><td>0.7308</td><td>0.5436</td><td>0.7794</td><td>0.6278</td><td>0.4443</td><td>0.7066</td><td>0.8970</td><td>0.7185</td><td>0.8952</td><td>0.8590</td><td>0.6654</td><td>0.8796</td><td>0.7849</td><td>0.5941</td><td>0.7822</td></tr><tr><td>◇PromptIAQ*[14]</td><td>0.7823</td><td>0.5907</td><td>0.8245</td><td>0.7232</td><td>0.5327</td><td>0.7558</td><td>0.6514</td><td>0.4698</td><td>0.7065</td><td>0.9071</td><td>0.7315</td><td>0.8821</td><td>0.8693</td><td>0.6792</td><td>0.8876</td><td>0.8348</td><td>0.6342</td><td>0.8281</td></tr><tr><td>♥CLIPScore[32]</td><td>0.0967</td><td>0.0642</td><td>0.1315</td><td>0.0640</td><td>0.0408</td><td>0.0817</td><td>0.2396</td><td>0.1591</td><td>0.2733</td><td>0.3126</td><td>0.2106</td><td>0.3185</td><td>0.1816</td><td>0.1218</td><td>0.1811</td><td>0.7008</td><td>0.5098</td><td>0.6986</td></tr><tr><td>♥BLIPScore[53]</td><td>0.1306</td><td>0.0872</td><td>0.1929</td><td>0.0935</td><td>0.0613</td><td>0.1569</td><td>0.2051</td><td>0.1364</td><td>0.2963</td><td>0.3073</td><td>0.2063</td><td>0.3136</td><td>0.1213</td><td>0.0796</td><td>0.1266</td><td>0.6707</td><td>0.4797</td><td>0.6123</td></tr><tr><td>♥ImageReward [103]</td><td>0.3849</td><td>0.2631</td><td>0.4358</td><td>0.2606</td><td>0.1736</td><td>0.3181</td><td>0.5155</td><td>0.3542</td><td>0.5871</td><td>0.3232</td><td>0.2166</td><td>0.3196</td><td>0.1905</td><td>0.1270</td><td>0.1839</td><td>0.7714</td><td>0.5673</td><td>0.7740</td></tr><tr><td>♥MINTIAQ[88]</td><td>0.7002</td><td>0.5160</td><td>0.8047</td><td>0.6217</td><td>0.4450</td><td>0.6826</td><td>0.5491</td><td>0.3891</td><td>0.6584</td><td>0.5378</td><td>0.3775</td><td>0.5574</td><td>0.4088</td><td>0.2816</td><td>0.4041</td><td>0.2886</td><td>0.1932</td><td>0.2959</td></tr><tr><td>♥MINTIAQ*[88]</td><td>0.8312</td><td>0.6474</td><td>0.8974</td><td>0.8177</td><td>0.6306</td><td>0.8511</td><td>0.7908</td><td>0.5991</td><td>0.8667</td><td>0.8904</td><td>0.7092</td><td>0.8816</td><td>0.8524</td><td>0.6697</td><td>0.8755</td><td>0.8391</td><td>0.6413</td><td>0.8318</td></tr><tr><td>F-Eval (Ours)</td><td>0.8486</td><td>0.6670</td><td>0.9085</td><td>0.8312</td><td>0.6585</td><td>0.8578</td><td>0.8471</td><td>0.6637</td><td>0.9106</td><td>0.9462</td><td>0.7961</td><td>0.9461</td><td>0.9188</td><td>0.7640</td><td>0.9322</td><td>0.9460</td><td>0.7959</td><td>0.9457</td></tr></table>
+
+where  $A\in \mathbb{R}^{r\times d_i}$  and  $B\in \mathbb{R}^{d_o\times r}$  are the low-rank matrices,  $r\ll \min (d_o,d_i)$  is the rank, and  $\alpha$  is scaling factor. For prompt of certain dimension, the corresponding expert is activated based on the dimension ID  $k$ , which can be formulated as:
+
+$$
+E _ {k} (x) = \frac {\alpha_ {k}}{r _ {k}} B _ {k} A _ {k} x, \tag {5}
+$$
+
+where  $E_{k}(\cdot)$  is the k-th LoRA expert.
+
+# 6. Experiments
+
+# 6.1. Implementation Details
+
+The LLM used in F-Eval is Qwen-2.5VL [11], with an input token channel dimension of 3584. The vision encoder, face encoder, and LLM are all frozen during training. The ranks of LoRA experts are 16,32,16,16, respectively. The LoRA alphas are set equal to LoRA ranks. LoRA dropout is set as 0.05. The model is trained on 2 NVIDIA GeForce RTX 3090 GPUs with flash-attn [21] enabled. We use AdamW Optimizer to train the network for 10 epochs with a batch size of 4 and learning rate  $1e^{-4}$ .
+
+# 6.2. Comparison with existing QA Models
+
+We conduct comprehensive experiments on the proposed FaceQ database to evaluate the effectiveness of both current quality assessment methods and our proposed methods, as shown in Tab.2, Tab.3, and Tab.4. The evaluation metrics are Spearman rank-order correlation coefficient (SRCC), Kendall rank order correlation coefficient (KRCC), and Pearson linear correlation coefficient (PLCC), which assess the correlation between predicted scores by the QA
+
+methods and the MOS scores provided by humans. Higher metrics indicated better alignment with human preferences. The comparison QA models falls into four categories: 1) Traditional IQA Models. NR-IQA models include NIQE [67], ILNIQE [111], HOSA [102], BPRI-PSS [64], FISBLIM [27]. FR-IQA models include LPIPS [112], SSIM [96] and PSNR [34]. 2) Classical Deep learning-based IQA Models. This category includes CNNIQA [42], VGG16 [79], VGG19 [79], ResNet18 [29], ResNet34 [29], Hyper-IQA [81], TReS [25], MANIQA [106], PromptIQA[14]. All models are retrained on FaceQ with an 80:20 training/testing split. 3) AIGC IQA Models. This category includes pre-trained vision-language models, including CLIP-Score [32], BLIPScore [53], zero-shot metric ImageReward [103], and the AIGC-specific QA model MINTIQA [88]. 4) Face IQA Models. This category includes SER-FIQ [83], DSL-FIQA [18], ArcFace [22], IFQA[41].
+
+# 6.3. Performance Analysis
+
+Traditional IQA Models. Traditional IQA methods, including both NR-IQA and FR-IQA models, generally perform poorly across all tasks and dimensions, with low SRCC, KRCC, and PLCC scores.
+
+Classical Deep Learning-based IQA Models. After being trained on our dataset, deep learning-based IQA models, such as MANIQA [106] and HyperIQA [81], significantly outperform traditional models in terms of quality and authenticity. However, these methods face challenges in text understanding, leading to unsatisfactory correlations.
+
+AIGC IQA Models. CLIPScore [32] BLIPScore [53], and
+
+Table 3. Performance comparison on FaceQ-Res synthetic subset.  $\spadesuit$ ,  $\heartsuit$ ,  $\clubsuit$ , and  $\diamond$  denote traditional NR-IQA models, FR-IQA models, face IQA models, and classical deep learning-based IQA models respectively. * indicates fine-tuned results.  
+
+<table><tr><td rowspan="2">Dimension Model</td><td colspan="3">Quality</td><td colspan="3">ID Fidelity</td></tr><tr><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td></tr><tr><td>▲BMPRI[65]</td><td>0.2161</td><td>0.1428</td><td>0.1862</td><td>0.1113</td><td>0.0739</td><td>0.1069</td></tr><tr><td>▲NIQE[67]</td><td>0.1798</td><td>0.1213</td><td>0.1642</td><td>0.2193</td><td>0.1480</td><td>0.2118</td></tr><tr><td>▲ILNIQE[111]</td><td>0.2505</td><td>0.1727</td><td>0.3180</td><td>0.2696</td><td>0.1857</td><td>0.3321</td></tr><tr><td>▲HOSA[102]</td><td>0.3758</td><td>0.2522</td><td>0.3748</td><td>0.3418</td><td>0.3455</td><td>0.2301</td></tr><tr><td>▲BPII-LSSn [64]</td><td>0.1398</td><td>0.0957</td><td>0.0999</td><td>0.1244</td><td>0.0837</td><td>0.0973</td></tr><tr><td>▲BPII [64]</td><td>0.1637</td><td>0.1065</td><td>0.1480</td><td>0.0195</td><td>0.0121</td><td>0.0281</td></tr><tr><td>▲FISBLIM [27]</td><td>0.1589</td><td>0.1089</td><td>0.2038</td><td>0.1054</td><td>0.0709</td><td>0.1715</td></tr><tr><td>\( \diamondsuit \)LPIPS[112]</td><td>0.3909</td><td>0.2658</td><td>0.4643</td><td>0.4372</td><td>0.3018</td><td>0.4870</td></tr><tr><td>\( \diamondsuit \)SSIM[96]</td><td>0.1017</td><td>0.0675</td><td>0.0488</td><td>0.0933</td><td>0.0601</td><td>0.0504</td></tr><tr><td>\( \diamondsuit \)PSNR [34]</td><td>0.0198</td><td>0.0113</td><td>0.0536</td><td>0.0986</td><td>0.0662</td><td>0.1212</td></tr><tr><td>\( \diamondsuit \)ArcFace[22]</td><td>0.3466</td><td>0.2327</td><td>0.3774</td><td>0.5728</td><td>0.4030</td><td>0.5762</td></tr><tr><td>\( \diamondsuit \)SER-FIQ [25]</td><td>0.3813</td><td>0.2584</td><td>0.3746</td><td>0.3951</td><td>0.2641</td><td>0.3707</td></tr><tr><td>\( \diamondsuit \)DSL-FIQA [18]</td><td>0.6387</td><td>0.4508</td><td>0.6528</td><td>0.4882</td><td>0.3360</td><td>0.5379</td></tr><tr><td>\( \diamondsuit \)IFQA [41]</td><td>0.2273</td><td>0.1527</td><td>0.3348</td><td>0.3214</td><td>0.2185</td><td>0.3874</td></tr><tr><td>\( \diamondsuit \)CNNIA* [42]</td><td>0.4661</td><td>0.3197</td><td>0.3836</td><td>0.4678</td><td>0.3216</td><td>0.4288</td></tr><tr><td>\( \diamondsuit \)ResNet18* [29]</td><td>0.7254</td><td>0.5295</td><td>0.6982</td><td>0.6662</td><td>0.4802</td><td>0.6527</td></tr><tr><td>\( \diamondsuit \)ResNet34* [29]</td><td>0.6693</td><td>0.4916</td><td>0.6550</td><td>0.5905</td><td>0.4170</td><td>0.6084</td></tr><tr><td>\( \diamondsuit \)VGG16* [79]</td><td>0.7487</td><td>0.5513</td><td>0.7101</td><td>0.6177</td><td>0.4413</td><td>0.6381</td></tr><tr><td>\( \diamondsuit \)VGG19* [79]</td><td>0.6994</td><td>0.5126</td><td>0.6722</td><td>0.6038</td><td>0.4278</td><td>0.5999</td></tr><tr><td>\( \diamondsuit \)HyperIA* [81]</td><td>0.8269</td><td>0.6323</td><td>0.8228</td><td>0.7615</td><td>0.5585</td><td>0.7471</td></tr><tr><td>\( \diamondsuit \)MANIA* [106]</td><td>0.8287</td><td>0.6403</td><td>0.8778</td><td>0.7704</td><td>0.5660</td><td>0.7619</td></tr><tr><td>\( \diamondsuit \)TReS* [25]</td><td>0.8656</td><td>0.6830</td><td>0.8622</td><td>0.7951</td><td>0.5879</td><td>0.7829</td></tr><tr><td>\( \diamondsuit \)PromptIA* [14]</td><td>0.8519</td><td>0.6661</td><td>0.8733</td><td>0.8220</td><td>0.6275</td><td>0.8254</td></tr><tr><td>F-Eval (Ours)</td><td>0.8692</td><td>0.6855</td><td>0.9009</td><td>0.8507</td><td>0.6731</td><td>0.8726</td></tr></table>
+
+Table 4. Performance comparison on FaceQ-Res real-world subset.  $\spadesuit$ ,  $\clubsuit$ , and  $\diamond$  denote traditional IQA models, face IQA models, and classical deep learning-based IQA models respectively. * indicates fine-tuned results.  
+
+<table><tr><td rowspan="2">Dimension Model</td><td colspan="3">Quality</td><td colspan="3">ID Fidelity</td></tr><tr><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td><td>SRCC↑</td><td>KRCC↑</td><td>PLCC↑</td></tr><tr><td>▲BMPRII[65]</td><td>0.1582</td><td>0.1093</td><td>0.2799</td><td>0.0149</td><td>0.0108</td><td>0.1386</td></tr><tr><td>▲NIQE[67]</td><td>0.1783</td><td>0.1186</td><td>0.1962</td><td>0.1245</td><td>0.0810</td><td>0.1701</td></tr><tr><td>▲ILNIQE[111]</td><td>0.2230</td><td>0.1610</td><td>0.2291</td><td>0.1964</td><td>0.1362</td><td>0.2340</td></tr><tr><td>▲HOSA[102]</td><td>0.3927</td><td>0.4277</td><td>0.2654</td><td>0.3328</td><td>0.2234</td><td>0.3813</td></tr><tr><td>▲BPRI-LSSn [64]</td><td>0.2715</td><td>0.1840</td><td>0.3022</td><td>0.2059</td><td>0.1380</td><td>0.2475</td></tr><tr><td>▲BPRI [64]</td><td>0.1920</td><td>0.1313</td><td>0.2200</td><td>0.0846</td><td>0.0570</td><td>0.1136</td></tr><tr><td>▲FISBLIM [27]</td><td>0.2512</td><td>0.1705</td><td>0.2725</td><td>0.2341</td><td>0.1581</td><td>0.2699</td></tr><tr><td>▲ArcFace[22]</td><td>0.2371</td><td>0.1565</td><td>0.4183</td><td>0.4956</td><td>0.3470</td><td>0.6330</td></tr><tr><td>▲SER-FIQ [25]</td><td>-0.0482</td><td>-0.0299</td><td>0.1023</td><td>0.0421</td><td>0.0299</td><td>0.1584</td></tr><tr><td>▲DSL-FIQA [18]</td><td>0.6509</td><td>0.4641</td><td>0.6494</td><td>0.4840</td><td>0.3362</td><td>0.5118</td></tr><tr><td>▲IFQA [41]</td><td>0.0251</td><td>0.0210</td><td>0.1221</td><td>0.0893</td><td>0.0603</td><td>0.2086</td></tr><tr><td>◇CNNIQA* [42]</td><td>0.3650</td><td>0.2506</td><td>0.4705</td><td>0.3252</td><td>0.2197</td><td>0.3112</td></tr><tr><td>◇VGG16* [79]</td><td>0.4996</td><td>0.3439</td><td>0.4269</td><td>0.4117</td><td>0.2859</td><td>0.4622</td></tr><tr><td>◇VGG19* [79]</td><td>0.5871</td><td>0.4181</td><td>0.5133</td><td>0.3054</td><td>0.2044</td><td>0.3594</td></tr><tr><td>◇ResNet18* [29]</td><td>0.5977</td><td>0.4221</td><td>0.5722</td><td>0.5554</td><td>0.3909</td><td>0.6161</td></tr><tr><td>◇ResNet34* [29]</td><td>0.6259</td><td>0.4475</td><td>0.6168</td><td>0.5036</td><td>0.3539</td><td>0.6136</td></tr><tr><td>◇HyperiQA* [81]</td><td>0.7926</td><td>0.5965</td><td>0.7926</td><td>0.7783</td><td>0.5845</td><td>0.8163</td></tr><tr><td>◇MANIQA* [106]</td><td>0.8356</td><td>0.6482</td><td>0.8467</td><td>0.7597</td><td>0.5655</td><td>0.8081</td></tr><tr><td>◇TReS* [25]</td><td>0.8287</td><td>0.6391</td><td>0.8501</td><td>0.7287</td><td>0.5441</td><td>0.8009</td></tr><tr><td>◇PromptIQA* [14]</td><td>0.8115</td><td>0.6186</td><td>0.8645</td><td>0.7398</td><td>0.5526</td><td>0.8297</td></tr><tr><td>F-Eval(Ours)</td><td>0.8448</td><td>0.6577</td><td>0.8705</td><td>0.7957</td><td>0.6057</td><td>0.8366</td></tr></table>
+
+ImageReward [103] exhibit weak correlations with human preference, likely due to their focus on high-level semantics rather than low-level details crucial for image quality assessment. MINTIQA [88] achieves best performance among current AIGC IQA methods, but its performance is still unsatisfactory, particularly on the customization task. Fine-tuning on our dataset leads to significant improvements, highlighting the great potential of FaceQ.
+
+Face IQA Models. ArcFace similarity [22] demonstrates its ability to extract identity-related features. However, it lacks perceptual sensitivity for image quality, leading to poor performance in quality assessment. DSL-FIQA [18], as the latest method, achieves the best performance in predicting quality scores among face IQA methods, but it is
+
+still far from satisfactory. SER-FIQ fails to align with human perception across most dimensions and tasks. Experiments confirm that these natural face evaluation algorithms struggle to assess the complex characteristics of AIGFs, highlighting the need for an effective AIGF evaluator.
+
+F-Eval (Ours). Our method achieves optimal performance across all tasks and dimensions, with the most significant gain in the customization task, as existing methods rarely focus human preferences in face customization. Among the four dimensions, the improvements in correspondence and ID fidelity stand out, thanks to dual-stream vision encoding and the powerful LLM backbone for text understanding and modality fusion. The MoLE technique allows the model to learn distinct features for each dimension.
+
+# 6.4. Ablation Study
+
+We conducted the ablation study to validate the utility of the core components of F-Eval in Tab. 5.
+
+Effectiveness of Vision Encoding. 1) The effectiveness of the face encoder is demonstrated by comparing the second and last rows. Without the face encoder, a significant performance drop is observed, indicating that the extracted features help the LLM interpret face images. 2) Removing the projector leads to a dramatic performance drop.
+
+Effectiveness of MoLE. We conducted three sets of LoRA adaptation experiments: fine-tuning a single LoRA for all dimensions and tasks, fine-tuning three LoRA experts for three tasks, and fine-tuning four LoRA experts for four dimensions. The results show that fine-tuning multiple dimensions with a single LoRA leads to performance deterioration, which further confirms the independence of the characteristics across different dimensions.
+
+Table 5. Ablation study of the proposed F-Eval method. Here only present SRCC due to space limitations.  
+
+<table><tr><td colspan="6">Feature &amp; Strategy</td><td colspan="3">Face Generation</td><td colspan="3">Face Customization</td><td colspan="3">Face Restoration syn</td><td colspan="3">Face Restoration rw</td><td></td></tr><tr><td>Vision</td><td>Projector</td><td>Face</td><td>Single LoRA</td><td>Task LoRA</td><td>Dim. LoRA</td><td>Quality</td><td>Authen.</td><td>Corres.</td><td>Quality</td><td>ID.</td><td>Corres.</td><td>Quality</td><td>ID.</td><td>Corres.</td><td>Quality</td><td>ID.</td><td>Quality</td><td>ID.</td></tr><tr><td>✓</td><td></td><td>✓</td><td></td><td></td><td>✓</td><td>0.808</td><td>0.750</td><td>0.846</td><td>0.924</td><td>0.843</td><td>0.927</td><td>0.777</td><td>0.776</td><td>0.776</td><td>0.707</td><td>0.748</td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td></td><td>✓</td><td>0.815</td><td>0.752</td><td>0.835</td><td>0.924</td><td>0.855</td><td>0.921</td><td>0.812</td><td>0.783</td><td>0.716</td><td>0.603</td><td></td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>0.793</td><td>0.776</td><td>0.819</td><td>0.941</td><td>0.885</td><td>0.942</td><td>0.838</td><td>0.823</td><td>0.802</td><td>0.671</td><td></td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>0.823</td><td>0.780</td><td>0.838</td><td>0.942</td><td>0.873</td><td>0.942</td><td>0.824</td><td>0.826</td><td>0.754</td><td>0.638</td><td></td><td></td><td></td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>0.849</td><td>0.831</td><td>0.847</td><td>0.946</td><td>0.919</td><td>0.946</td><td>0.869</td><td>0.851</td><td>0.845</td><td>0.796</td><td></td><td></td><td></td></tr></table>
+
+# 7. Conclusion
+
+In this work, we conduct a pioneering generative face image quality assessment study. Specifically, we introduce FaceQ, the first generated face quality assessment database comprising 12,255 face images and 491,130 human preference ratings. Then, we establish F-Bench, a benchmark for evaluating the capabilities of existing face generation, customization, and restoration models, while also reveals the limitations of current Image Quality Assessment (IQA) and Face Quality Assessment (FQA) methods. Furthermore, we propose an evaluation model F-Eval to accurately predict human preferences on generated face images, which demonstrates state-of-the-art performance. We believe this work will contribute to advancing generative models and help overcome current limitations in AIGC community.
+
+# Acknowledgment
+
+This work is supported by the National Natural Science Foundation of China under Grants 62271308, 62401365, 62225112, 62132006, U24A20220, STCSM under Grants 24ZR1432000, 24511106902, 24511106900, 22511105700, 22DZ2229005, 111 plan under Grant Number BP0719010, China Postdoctoral Science Foundation under Grants BX20250411, 2025M773473, and State Key Laboratory of UHD Video and Audio Production and Presentation.
+
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+        "text": "FALCON: Resolving Visual Redundancy and Fragmentation in High-resolution Multimodal Large Language Models via Visual Registers",
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+        "text": "Renshan Zhang $^{1}$ , Rui Shao $^{1\\dagger}$ , Gongwei Chen $^{1}$ , Miao Zhang $^{1}$ , Kaiwen Zhou $^{2}$ , Weili Guan $^{1}$ , Liqiang Nie $^{1\\dagger}$ $^{1}$ Harbin Institute of Technology, Shenzhen  $^{2}$ Huawei Noah's Ark Lab",
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+        "text": "zhangrenshan@stu.hit.edu.cn shaorui@hit.edu.cn",
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+        "text": "Abstract",
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+        "text": "The incorporation of high-resolution visual input equips multimodal large language models (MLLMs) with enhanced visual perception capabilities for real-world tasks. However, most existing high-resolution MLLMs rely on a cropping-based approach to process images, which leads to fragmented visual encoding and a sharp increase in redundant tokens. To tackle these issues, we propose the FALCON model. FALCON introduces a novel visual register technique to simultaneously: 1) Eliminate redundant tokens at the stage of visual encoding. To directly address the visual redundancy present in the output of vision encoder, we propose a Register-based Representation Compacting (ReCompact) mechanism. This mechanism introduces a set of learnable visual registers designed to adaptively aggregate essential information while discarding redundancy. It enables the encoder to produce a more compact visual representation with a minimal number of output tokens, thus eliminating the need for an additional compression module. 2) Ensure continuity in visual encoding. To address the potential encoding errors caused by fragmented visual inputs, we develop a Register Interactive Attention (ReAtten) module. This module facilitates effective and efficient information exchange across sub-images by enabling interactions between visual registers. It ensures the continuity of visual semantics throughout the encoding. We conduct comprehensive experiments with FALCON on high-resolution benchmarks across a wide range of scenarios. FALCON demonstrates superior performance with a remarkable 9-fold reduction in visual tokens.",
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+        "text": "1. Introduction",
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+        "text": "Recently, multimodal large language models (MLLMs) [2, 9, 30, 32, 59, 60] have made significant advancements in",
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+        "type": "image",
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+        "image_caption": [
+            "Figure 1. Comparison between existing high-resolution MLLMs and FALCON. FALCON eliminates visual redundancy and ensures the continuity of high-resolution encoding through the use of ReCompact and ReAtten mechanisms."
+        ],
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+        "text": "performing various vision-language tasks [45, 46, 61], facilitating more natural human-machine interactions. Early MLLMs [9, 32, 59] typically processed images at a fixed low resolution, such as  $224 \\times 224$ . This limited their capabilities in many real-world applications that require high-resolution input. To equip MLLMs with high-resolution visual perception, recent efforts [15, 17, 33, 58, 67] have introduced a cropping-based high-resolution processing method. Specifically, As shown in Fig. 1(b), this approach crops high-resolution images into multiple non-overlapping sub-images that match the pre-trained resolution of the encoder. Each sub-image is processed independently by the vision encoder. Then the resulting visual features are concatenated and fed into the large language model (LLM).",
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+        "type": "text",
+        "text": "Although effective, cropping-based methods still face issues of: 1) Visual Redundancy. The number of visual to-",
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+        "page_idx": 0
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+    {
+        "type": "header",
+        "text": "This ICCV 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": "†Corresponding authors",
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+    {
+        "type": "page_number",
+        "text": "23530",
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+    {
+        "type": "text",
+        "text": "kens grows dramatically with increasing resolution. While this enriches the visual details, it also leads to an increase in redundant tokens. These redundant tokens significantly increase the computational burden on LLM and interfere with the processing of visual information [65]. To address these issues, as illustrated in Fig. 1(b), existing methods typically rely on additional compression techniques. Representative approaches include combining learnable queries with cross-attention [1, 28, 60] or simply employing pooling layers [48, 55]. However, these methods either demand substantial training resources or fail to fully address redundancy. 2) Visual Fragmentation. Cropping an image into multiple non-overlapping sub-images may disrupt visual semantics and potentially lead to encoding errors. As shown in Fig. 1(a), in an OCR task, the word \"pineapple\" may be incorrectly segmented into \"pine\" and \"apple\", causing the LLM to misinterpret the word. Similarly, fragmentation can also hinder the identification of objects. For example, the \"rubin vase\" pattern illustrated in Fig. 1(a) depicts both a vase and two faces simultaneously. However, the fragmentation could lead to the vase being unrecognizable.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address these issues, as shown in Fig. 1(c), we propose the FALCON model. FALCON introduces a novel visual register technique to simultaneously: 1) Eliminate redundant tokens during visual encoding. To eliminate redundancy directly at the stage of visual encoding, we propose a novel Register-based Representation Compacting (ReCompact) mechanism. This mechanism introduces a set of learnable visual registers as additional inputs to the vision encoder. The registers are designed to adaptively aggregate essential information from image tokens and discard redundant content. Then the outputs corresponding to the visual registers are considered as a non-redundant visual representation, serving as the compact input for the LLM instead of a large number of image tokens. This mechanism enables the vision encoder to convey comprehensive visual information in a compact representation using minimal tokens, thus removing the need for an additional compression module. 2) Ensure continuity in visual encoding. To avoid the potential encoding errors caused by fragmented visual inputs, we develop a novel Register Interactive Attention (ReAtten) module. This module leverages the compact and comprehensive representation produced by visual registers to facilitate information exchange across sub-images. It gathers visual registers from different sub-images and employs a specialized cross-ViT attention module to enable interactions among them. Such interaction enables thorough information exchange across the entire image, thus ensuring visual continuity throughout the encoding process. Additionally, the compactness of the visual registers further enhances the efficiency of these interactions. Consequently, this module provides LLMs with a reliable foundation to accurately interpret visual content and reduce hallucinations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Note that the widely used Abstractor-like modules [28, 33, 58, 60], including QFormer [9], ReSampler [1], follow a similar approach by using query tokens to extract information from image tokens after visual encoding. The key difference is that the visual register mechanism directly adopts the pretrained ViT to aggregate information into a set of specified register tokens. This design is based on the observation that a well-pretrained ViT can naturally gather global information into some specific tokens through self-attention [10]. It offers the visual register mechanism several strengths in terms of: 1) Training Efficiency. The substantial number of randomly initialized parameters in Abstractor-like modules requires extensive data for pretraining. For instance, QFormer [22], Abstractor [60], and Resampler [1] use large corpora of 129M, 400M, and 1.4B samples, respectively. In contrast, by leveraging well-pretrained ViT parameters, the visual register mechanism requires only 3.5M samples for pretraining. The ablation results in Fig. 4 further demonstrate this advantages. 2) Addressing Visual Fragmentation. By leveraging the compact and comprehensive representation produced by visual registers, the proposed ReAtten module can effectively facilitate information exchange across sub-images. This is an important function that is notably lacking in Abstractor-like modules. Combined with ReCompact, it enables the visual register mechanism to simultaneously address the issues of visual redundancy and fragmentation. The ablation results in Tab. 5 validate the effectiveness of ReAtten.",
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+        "text": "We summarize our main contributions as follows:",
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+    {
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+        "list_items": [
+            "- To address the issue of visual redundancy directly at the encoding phase, we introduce the Register-based Representation Compacting (ReCompact) mechanism. This mechanism enables vision encoder to capture rich visual information using only a minimal number of tokens, effectively eliminating redundancy and obviating the need for additional compression modules.",
+            "- To address the issue of visual fragmentation caused by image cropping, we propose the register interactive attention (ReAtten) module. This module ensures the semantic continuity of high-resolution visual encoding in an efficient and effective manner.",
+            "- We introduce FALCON, a model that leverages the proposed visual register technique. Comprehensive evaluations on high-resolution visual understanding benchmarks highlight the superiority of FALCON. Notably, FALCON achieves exceptional results with a remarkable reduction in visual tokens by  $9 \\times$ ."
+        ],
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+        "type": "text",
+        "text": "2. Related Work",
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+    {
+        "type": "text",
+        "text": "2.1. Multimodal Large Language Models",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Research on MLLMs [1, 2, 30, 47, 59, 60] has made significant strides in recent years. By incorporating image in",
+        "bbox": [
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+        "text": "23531",
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+        "page_idx": 1
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+        "img_path": "images/2f27ac45349ad0f7f21ad2a796584b3c4076140f766605856e347b5f07931124.jpg",
+        "image_caption": [
+            "Figure 2. Overall framework of the proposed FALCON. The model introduces a set of learnable visual registers, which are fed into the ViT along with the image tokens from each sub-image. During the visual encoding, the ReCompact mechanism enables information from the image tokens to be aggregated into the visual registers, while the proposed ReAtten facilitates information exchange among the visual registers across different sub-images. Ultimately, these visual registers provide a compact visual representation as input to the LLM."
+        ],
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "puts into pretrained LLMs [8, 51, 52], MLLMs demonstrate strong capabilities across various vision-language tasks. Typically, these models use a pretrained vision encoder [43, 62] to transform input images into a set of visual tokens. These tokens are then projected into the input space of the LLM through a projection module (e.g., MLP [30, 32], QFormer [9] and Abstractor [60]) and processed alongside text inputs. Building on the progress of MLLMs, recent studies have shifted from designing specialized methods for certain tasks [44-46] to employing MLLMs as generalist agents, capable of handling diverse practical tasks such as document analysis [15, 57, 64], online video assistant [24], retrieval-augmented generation [40], game agents [27, 29], robot manipulation [18, 21, 39], and GUI agent [3, 5, 54]. Despite these advances, MLLMs still struggle with the fixed low resolution of pretrained image encoders, which can limit their effectiveness in handling high-resolution images.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. High-resolution MLLMs",
+        "text_level": 1,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To address the limitation of MLLMs in handling only low-resolution visual inputs, early studies attempted to either directly incorporate vision encoders that were pre-trained on higher-resolution images [36, 38], or to improve the resolution of pre-trained encoders through additional training [1, 60]. While achieving some progress, they still remain restricted by the fixed resolutions. To accommodate the varying resolutions and aspect ratios, cropping-based techniques have been widely adopted in recent works [15, 17, 33, 58, 67]. However, these approaches still face challenges related to visual redundancy and fragmentation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To mitigate the issue of redundancy, existing models typically require an additional compression module. For example, Abstractor-like modules utilizing learnable queries combined with cross-attention are widely adopted [1, 28, 33, 58, 60]. These modules typically require pretraining on massive amounts of data, which diminishes their practical efficacy. In contrast, some approaches use pooling",
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+        "type": "text",
+        "text": "layers [48, 55] or convolutional layers [15, 36]. Though resource-efficient, they often fail to address the issue of redundancy. In this work, we present an initial exploration to directly eliminate redundancy during the visual encoding phase, thereby removing the need for additional compression. To address the issue of fragmentation, several concurrent studies also make preliminary investigation. TextMonkey [33] uses Shifted Window Attention [35] to exchange information between sub-images. But the exchange is still limited to local regions. MiniMonkey [16] proposed a Complementary Image Pyramid strategy to generate complementary cropping schemes. However, this strategy inevitably encodes the same visual content multiple times, further exacerbating visual redundancy. In this work, we propose the ReAtten module to facilitate continuous visual encoding through the interaction among visual registers.",
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+    {
+        "type": "text",
+        "text": "3. FALCON",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The overall framework of FALCON is illustrated in Fig. 2. The method begins with shape-adaptive cropping [58], where the image is cropped into multiple non-overlapping sub-images, each matching the resolution of the pre-trained vision encoder. Additionally, a resized version of the full image is used to supplement global layout information. To directly eliminate redundancy during visual encoding, we propose Register-based Representation Compacting (Re-Compact) mechanism. This mechanism introduces a set of learnable visual registers, which are paired with image tokens from each sub-image and fed into the vision encoder to capture rich visual information. To ensure the continuity of visual semantics throughout the encoding, a novel Register Interactive Attention (ReAtten) module is integrated into the Vision Transformer (ViT) [11] to facilitate information exchange between sub-images via the visual registers. Finally, the compact visual representations produced by the visual registers are processed through a simple MLP module before being fed into the LLM for further analysis.",
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+    {
+        "type": "page_number",
+        "text": "23532",
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+    {
+        "type": "text",
+        "text": "3.1. Mitigating Visual Redundancy via ReCompact",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Existing MLLMs typically use a ViT-based vision encoder, such as CLIP [43]. For an input image of size  $H \\times W$ , it is patched into multiple  $P \\times P$  patches. Each patch is treated as an individual image token, resulting in  $N = \\frac{H}{P} \\times \\frac{W}{P}$  tokens, denoted as  $I = \\{i_1, \\dots, i_N\\}$ . In most current MLLMs, output features corresponding to all image tokens are usually preserved in their entirety. However, when high-resolution images are included, the number of image tokens increases dramatically, placing a substantial burden on the computational resources of LLMs. Consequently, most high-resolution MLLMs necessitate an additional compression module, which can be resource-inefficient. Previous research has shown that most image tokens contain only localized information from their surrounding areas [10]. It suggests that a significant portion of these tokens may be redundant, particularly those originating from background regions. This observation motivates us to directly eliminate redundancy in the output of the vision encoder, thereby reducing the number of visual tokens and avoiding the need for an additional compression module.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To achieve this, we propose a novel Register-based Representation Compacting (ReCompact) mechanism. This mechanism employs a set of visual registers to aggregate essential information from image tokens, resulting in a more compact visual representation. Specifically, as shown in Fig. 2, we introduce a set of learnable visual registers, denoted by  $R = \\{r_1,\\dots ,r_M\\}$ , where  $M$  represents the number of visual registers, and  $M\\ll N$ . Given a single input image, the image tokens are concatenated with visual registers to create a new input for ViT, represented as  $V = \\mathrm{Concat}(I,R) = \\{i_1,\\dots ,i_N,r_1,\\dots ,r_M\\}$ . During visual encoding, the self-attention mechanism in ViT enables the visual register to adaptively aggregate important information from image tokens while discarding redundant content. Denote  $X_{k,l}\\in \\mathcal{R}^{(N + M)\\times D}$  as the input hidden states of the  $k$ -th sub-image at the  $l$ -th layer, where  $D$  is the dimensionality. The self-attention is formulated as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {X} _ {k, l} = \\operatorname {S e l f - A t t e n} \\left(X _ {k, l}\\right) = \\operatorname {S o f t m a x} \\left(\\frac {X _ {k , l} X _ {k , l} ^ {T}}{\\sqrt {D _ {\\text {k e y}}}}\\right) X _ {k, l} \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Notably, we do not apply any attention masks for specific constraints. Our experiments show that pretraining on a modest amount of data is sufficient to effectively adapt the pretrained ViT to the proposed ReCompact, enabling it to aggregate essential information within the visual registers. After visual encoding, The output features corresponding to the visual registers, denoted as  $F = \\{f_{1},\\dots ,f_{M}\\}$ , are then used as the visual representation of the image and fed into the LLM for various vision-language tasks.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To further adapt the ReCompact mechanism for cropping-based high-resolution image perception, we share",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "the same set of visual registers as input for different sub-images. The input for the  $k$ -th sub-image is formulated as  $V_{k} = \\mathrm{Concat}(I_{k},R)$ , where  $k = 1,2,\\dots ,N_{c}$  and  $N_{c}$  denotes the total number of sub-images. After encoding, the outputs of the visual registers for all sub-images are concatenated, yielding  $F_{hr} = \\mathrm{Concat}(F_1,F_2,\\dots ,F_{N_c})$  which serves as the input to the LLM. The ReCompact mechanism enables the vision encoder to represent rich visual information using only a minimal number of  $M$  tokens per sub-image, which significantly reduces the visual redundancy and eliminates the need for additional compression.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Ensuring Visual Continuity via ReAtten",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "When using the cropping-based high-resolution image encoding method, each sub-image is independently encoded by the vision encoder. This process can disrupt semantic coherence and result in the misrepresentation of visual concepts. To preserve the continuity of visual semantics, it is crucial to enable information exchange between sub-images during encoding. A naive approach would be to directly concatenate the image features from all sub-images and apply self-attention. However, the quadratic computational complexity makes this approach impractical. In Sec. 3.1, we introduced the ReCompact mechanism, where the visual registers effectively aggregate rich visual information while discarding redundancy during visual encoding, allowing them to serve as compact yet comprehensive image representations. Consequently, interactions between visual registers can naturally facilitate sufficient information exchange across different sub-images in an efficient manner.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To enable information exchange between visual registers across different sub-images, we introduce a novel Register Interactive Attention (ReAtten) module. As shown in Fig. 2, the ReAtten module is integrated into each of the  $L$  layers of the ViT. After the self-attention process in Eq. (1), we acquire  $\\hat{X}_{k,l} = \\{\\hat{X}_{k,l}^{I},\\hat{X}_{k,l}^{R}\\}$ , where  $\\hat{X}^I\\in \\mathcal{R}^{N\\times D}$  and  $\\hat{X}^R\\in \\mathcal{R}^{M\\times D}$  represent the hidden states corresponding to image tokens and visual registers, respectively. The states of the visual registers from different sub-images are concatenated to form  $\\hat{X}_l^R = \\mathrm{Concat}\\left(\\{\\hat{X}_{k,l}^R\\}_{k = 1}^{N_c}\\right)\\in$ $\\mathcal{R}^{M\\cdot N_c\\times D}$ . Then these concatenated registers are processed via ReAtten to enable information exchange across subimages, which can be formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\overline {{X}} _ {l} ^ {R} = \\mathrm {R e A t t e n} (\\hat {X} _ {l} ^ {R}) = \\hat {X} _ {l} ^ {R} + \\mathrm {C r o s s - V i T - A t t e n} (\\hat {X} _ {l} ^ {R}) (2)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where Cross-ViT-Atten is implemented as a self-attention layer. Once the information exchange is completed, the registers and image tokens from a same sub-image are concatenated and then passed into the feedforward network (FFN) for transformation, yielding the output of the  $l$ -th layer:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nX _ {k, l + 1} = \\operatorname {F F N} \\left(\\operatorname {C o n c a t} \\left(\\hat {X} _ {k, l} ^ {I}, \\bar {X} _ {k, l} ^ {R}\\right)\\right) \\tag {3}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "23533",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/7fea22fdc3cc3b493e312b32f4a98ebdb9f316bfc9d08bbff01a1afa4a45a549.jpg",
+        "image_caption": [
+            "Figure 3. The progressive training pipeline. **Stage 0:** Align the frozen vision and language backbones by training only the MLP and registers. **Stage 1:** Tune all parameters with caption and OCR data on low-resolution for coarse alignment. **Stage 2:** Integrate high-resolution input along with fine-grained captions and OCR to achieve refined alignment. **Stage 3:** Froze ViT and introduce ReAtten module for high-resolution instruction tuning."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "By integrating ReAtten into each layer of the ViT model, FALCON enables effective information exchange between cropped sub-images through visual registers, thereby ensuring semantic continuity of the high-resolution image throughout the visual encoding process.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Learning Expressive Visual Representation via Progressive Training Pipeline",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To empower the ReCompact mechanism with the capability to capture rich visual patterns and to enable smoother initialization of the ReAtten module under high-resolution conditions, we develop a specialized progressive training pipeline. As illustrated in Fig. 3, this pipeline progressively transitions from low to high resolution across four stages.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Stage 0: Static Alignment on Low-resolution. Since both the visual registers and MLP projector are randomly initialized, in stage 0, we aim to achieve a initial alignment between the pretrained vision encoder and the LLM. To facilitate this, we begin by using low-resolution images as inputs, which are directly resized to match the resolution of the vision encoder. We then statically pretrain the model by keeping both the vision encoder and LLM frozen, tuning only the visual registers and MLP using image caption data.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Stage 1: Coarse Alignment on Low-resolution. To better adapt the pre-trained vision encoder to our newly introduced ReCompact mechanism, in stage 1, we unfreeze all model parameters to enable a more thorough tuning. To facilitate the visual registers to progressively learn capturing visual information from coarse to fine granularity, we con",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "tinue to use low-resolution inputs and employ high-quality, extended captions rich in visual content, along with full-text OCR data for training. This design allows the registers to acquire holistic scene understanding ability.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Stage 2: Refined Alignment on High-resolution. To further enhance the capacity of the visual register to capture fine-grained visual details, in stage 2, we transition the model to process high-resolution image for refined alignment. Additionally, we employ datasets that includes a series of fine-grained captions and OCR tasks, such as regional captions and text location. This facilitates the visual registers to capture comprehensive fine-grained details.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Stage 3: Instruction Tuning on High-resolution. To adapt the well-aligned visual register for a wide range of real-world tasks, in stage 3, we perform instruction tuning with a mixture of datasets covering various tasks, such as VQA, document understanding, and science reasoning. Additionally, the proposed ReAtten module is integrated to address visual fragmentation caused by cropping-based high-resolution image encoding. Since the vision encoder with ReCompact is well-aligned, the vision encoder is kept frozen and other parameters including ReAtten are trainable during instruction tuning. Notably, to facilitate a smoother initialization for the newly introduced ReAtten modules, we initialize parameters of each ReAtten module with the ViT self-attention parameters at the corresponding depth. This design enables ReAtten to effectively leverage pre-trained parameters, avoiding the need for extensive fine-tuning.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We implement FALCON with SigLIP-L/16-384px [62] as the vision encoder and Llama-3.1-8B-Instruct [12] as the LLM backbone. A two-layer MLP module with GeLU [13] activation is served as the vision-language projection layer. The number of visual registers is set to 64, achieving remarkable visual token compression rates of  $9 \\times$ . The maximum number of sub-images is set to 16.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.1. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate FALCON using the recently proposed MMERealWorld [66] benchmark, a comprehensive and largescale benchmark specifically designed to assess the high-resolution understanding capabilities of MLLMs. MMERealWorld comprises 13,366 high-resolution images with an average resolution of  $2,000 \\times 1,500$  pixels, spanning five domains: OCR in the wild, Remote Sensing, Diagrams and Tables, Monitoring, and Autonomous Driving. This benchmark is well-suited for evaluating the practical high-resolution understanding capabilities of MLLMs.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Tab. 1, FALCON significantly outperform other advanced MLLMs in both perception and reasoning tasks. FALCON achieves state-of-the-art performance with only 64 tokens per sub-image, resulting in a remarkable vi",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "23534",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Evaluation on MME-RealWorld Benchmark. \"OCR\", \"RS\", \"DT\", \"MO\", and \"AD\" stand for OCR in the Wild, Remote Sensing, Diagram and Table, Monitoring, and Autonomous Driving, respectively. \"Avg\" denotes the weighted average accuracy across all samples, while \"Avg-C\" denotes the weighted average accuracy across different domains. \"Sizev\" indicates the image resolution supported by the model, where  $\\times n$  signifies a cropping-based high-resolution processing approach with up to  $n$  sub-images. \"Tokenc\" denotes the number of visual tokens after compression. † For models utilizing hybrid vision encoders, \"Sizev\" represents the setting of encoder with the highest resolution. We gray out the models that are either closed-source or have at least twice the number of visual tokens compared to ours. Among these, the lighter gray denotes scores below ours. The underline indicates that the second performance is achieved. Notably, FALCON achieves state-of-the-art performance with just 64 tokens per sub-image, surpassing most models that have large amount of visual tokens and many advanced closed-source commercial models.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/16635d14cdbcc4f4fe268638884ac70a1a1f19331fea4bda213dfe27f740dd5a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Type</td><td>Method</td><td>\\( Size^v \\)</td><td>\\( Token^c \\)</td><td colspan=\"6\">Perception</td><td colspan=\"5\">Reasoning</td><td></td><td></td></tr><tr><td></td><td colspan=\"3\">Task Split</td><td>OCR</td><td>RS</td><td>DT</td><td>MO</td><td>AD</td><td>Avg</td><td>Avg-C</td><td>OCR</td><td>DT</td><td>MO</td><td>AD</td><td>Avg</td><td>Avg-C</td></tr><tr><td rowspan=\"10\">Visual Tokens\\(\\nabla 1024\\)</td><td>MiniGPT-v2 [4]</td><td>\\( 448^2 \\)</td><td>256</td><td>39.0</td><td>23.3</td><td>20.4</td><td>19.3</td><td>26.0</td><td>26.9</td><td>25.6</td><td>30.0</td><td>20.4</td><td>16.9</td><td>23.7</td><td>23.0</td><td>22.7</td></tr><tr><td>Qwen-VL-Chat [1]</td><td>\\( 448^2 \\)</td><td>256</td><td>32.4</td><td>15.1</td><td>15.6</td><td>22.1</td><td>15.1</td><td>20.8</td><td>20.1</td><td>28.6</td><td>13.6</td><td>16.5</td><td>24.6</td><td>22.0</td><td>20.8</td></tr><tr><td>LLaVA1.5-13B [30]</td><td>\\( 336^2 \\)</td><td>576</td><td>44.1</td><td>23.3</td><td>20.2</td><td>20.5</td><td>26.1</td><td>28.4</td><td>26.8</td><td>30.2</td><td>20.8</td><td>27.5</td><td>24.8</td><td>25.5</td><td>25.8</td></tr><tr><td>ShareGPT4V-13B [6]</td><td>\\( 336^2 \\)</td><td>576</td><td>44.6</td><td>23.1</td><td>20.2</td><td>19.3</td><td>26.1</td><td>28.4</td><td>26.6</td><td>26.0</td><td>20.8</td><td>27.3</td><td>24.6</td><td>24.6</td><td>24.7</td></tr><tr><td>TextMonkey [33]</td><td>\\( 448^2 \\times 4 \\)</td><td>256 × 4</td><td>37.3</td><td>11.7</td><td>5.9</td><td>16.1</td><td>14.3</td><td>18.2</td><td>17.1</td><td>30.4</td><td>2.2</td><td>4.4</td><td>20.0</td><td>16.0</td><td>14.3</td></tr><tr><td>Mini-Gemini-7B-HD† [26]</td><td>\\( 336^2 \\times 4 \\)</td><td>576</td><td>42.0</td><td>31.3</td><td>22.3</td><td>34.2</td><td>24.8</td><td>31.1</td><td>30.9</td><td>35.4</td><td>24.6</td><td>25.9</td><td>23.3</td><td>26.1</td><td>27.3</td></tr><tr><td>DeepSeek-VL† [36]</td><td>\\( 1024^2 \\)</td><td>576</td><td>49.6</td><td>25.5</td><td>23.4</td><td>27.0</td><td>33.4</td><td>33.1</td><td>31.8</td><td>45.2</td><td>23.8</td><td>16.7</td><td>27.3</td><td>28.0</td><td>28.3</td></tr><tr><td>MiniCPM-V 2.5 [56]</td><td>\\( 448^2 \\times 9 \\)</td><td>96 × 9</td><td>66.8</td><td>27.7</td><td>52.8</td><td>38.7</td><td>34.2</td><td>47.4</td><td>44.0</td><td>44.0</td><td>31.8</td><td>37.0</td><td>31.0</td><td>34.5</td><td>36.0</td></tr><tr><td>Monkey [28]</td><td>\\( 448^2 \\times 4 \\)</td><td>256 × 4</td><td>54.6</td><td>25.0</td><td>32.5</td><td>28.0</td><td>29.7</td><td>36.3</td><td>34.0</td><td>27.2</td><td>20.8</td><td>27.3</td><td>33.0</td><td>28.8</td><td>27.1</td></tr><tr><td>FALCON</td><td>\\( 384^2 \\times 16 \\)</td><td>64 × 16</td><td>66.4</td><td>49.6</td><td>47.2</td><td>40.4</td><td>36.5</td><td>50.3</td><td>48.0</td><td>55.4</td><td>39.2</td><td>44.4</td><td>34.5</td><td>40.7</td><td>43.4</td></tr><tr><td rowspan=\"6\">Visual Tokens\\(\\nabla 2048\\)</td><td>LLaVA-Next-Qwen72B [31]</td><td>\\( 336^2 \\times 4 \\)</td><td>576 × 4</td><td>37.1</td><td>29.1</td><td>27.7</td><td>29.4</td><td>18.0</td><td>29.0</td><td>28.3</td><td>17.2</td><td>34.2</td><td>27.3</td><td>29.7</td><td>27.9</td><td>27.1</td></tr><tr><td>LLaVA-Next-liama3 [31]</td><td>\\( 336^2 \\times 4 \\)</td><td>576 × 4</td><td>47.9</td><td>25.4</td><td>26.6</td><td>19.5</td><td>18.7</td><td>30.1</td><td>27.6</td><td>55.2</td><td>23.4</td><td>21.1</td><td>30.7</td><td>32.1</td><td>32.6</td></tr><tr><td>mPLUG-DocOwl 1.5 [15]</td><td>\\( 448^2 \\times 9 \\)</td><td>256 × 9</td><td>51.2</td><td>23.7</td><td>29.3</td><td>25.0</td><td>28.3</td><td>33.7</td><td>31.5</td><td>42.6</td><td>19.8</td><td>20.5</td><td>26.0</td><td>26.9</td><td>27.2</td></tr><tr><td>CogVLM2-liama3-Chat [14]</td><td>\\( 1344^2 \\)</td><td>2304</td><td>70.0</td><td>28.8</td><td>47.5</td><td>33.7</td><td>30.2</td><td>45.8</td><td>42.0</td><td>54.0</td><td>32.8</td><td>41.2</td><td>31.2</td><td>37.3</td><td>39.8</td></tr><tr><td>IXC2.5 [63]</td><td>\\( 560^2 \\times 24 \\)</td><td>400 × 24</td><td>69.3</td><td>36.1</td><td>63.9</td><td>39.5</td><td>33.6</td><td>52.5</td><td>48.5</td><td>53.4</td><td>41.0</td><td>17.7</td><td>30.0</td><td>33.9</td><td>35.5</td></tr><tr><td>LLaVA-OneVision [20]</td><td>\\( 384^2 \\times 9 \\)</td><td>729 × 9</td><td>78.7</td><td>53.5</td><td>60.7</td><td>40.3</td><td>45.8</td><td>59.6</td><td>55.8</td><td>61.8</td><td>40.0</td><td>40.8</td><td>34.1</td><td>41.2</td><td>44.2</td></tr><tr><td rowspan=\"4\">Closed-source</td><td>GPT-4o-mini</td><td>-</td><td>-</td><td>62.5</td><td>6.7</td><td>44.2</td><td>26.5</td><td>24.2</td><td>37.1</td><td>32.8</td><td>47.0</td><td>39.8</td><td>25.8</td><td>26.8</td><td>32.5</td><td>34.9</td></tr><tr><td>Gemini-1.5-pro [50]</td><td>-</td><td>-</td><td>67.6</td><td>14.0</td><td>39.9</td><td>31.1</td><td>26.6</td><td>39.6</td><td>35.9</td><td>52.7</td><td>33.2</td><td>28.3</td><td>19.2</td><td>29.2</td><td>33.4</td></tr><tr><td>GPT-4o</td><td>-</td><td>-</td><td>77.7</td><td>28.9</td><td>46.7</td><td>33.9</td><td>22.4</td><td>46.4</td><td>41.9</td><td>61.4</td><td>44.8</td><td>36.5</td><td>26.4</td><td>37.6</td><td>42.3</td></tr><tr><td>Claude 3.5 Sonnet</td><td>-</td><td>-</td><td>72.5</td><td>25.7</td><td>67.4</td><td>32.2</td><td>40.8</td><td>52.9</td><td>47.7</td><td>61.9</td><td>61.2</td><td>41.8</td><td>31.9</td><td>44.1</td><td>49.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "sual compression rate of 9 times. In addition, FALCON also outperforms most models that have twice as many visual tokens. Specifically, FALCON outperforms CogVLM2-llama3-Chat [14] in average scores on both perception and reasoning task, which uses 2304 tokens per-image. It also surpasses IXC2.5 [63] in average scores on the reasoning tasks, which has a maximum token counts of 9600. Notably, FALCON achieves higher average scores in both perception and reasoning tasks compared to three advanced commercial models, GPT-4o, GPT-4o-mini and Gemini1.5-pro [50], with it notably outperforming all commercial models in the sub-tasks of remote sensing and monitoring. These results demonstrate that the ReCompact and ReAtten technique proposed by FALCON effectively eliminate visual redundancy and ensure visual continuity, allowing comprehensive and detailed visual information to be conveyed with a highly compact visual representation.",
+        "bbox": [
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+            573,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To further assess FALCON's capabilities in high-resolution understanding, we conduct evaluations on more high-resolution benchmarks: V* [53], DocVQA [42], TextVQA [49] and ChartQA [41]. V* focuses on evaluating",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "models' capabilities for fine-grained attribute recognition and spatial reasoning. DocVQA challenges models to comprehend text-dense document images. ChartQA evaluates models' proficiency in interpreting various types of chart, while TextVQA assesses the ability to recognize small text in real-world scenes. As shown in Tab. 2, FALCON demonstrates superior performance across all these benchmarks.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the performance of FALCON across a broader range of domains, we further conduct experiments with diverse popular benchmarks. As shown in Tab. 4, POPE [25], ScienceQA [37], MMBench [34] and SEED-Bench [19] are selected to assess models' capabilities in hallucination, scientific reasoning, and comprehensive ability. FALCON achieves SOTA performance across all these benchmarks. The results demonstrate that FALCON exhibits superior capabilities across a wide range of tasks.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We perform extensive ablation studies to validate the effectiveness of the proposed ReCompact and ReAtten.",
+        "bbox": [
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+            853,
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+            883
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Ablation on Training Data. To eliminate the influx",
+        "bbox": [
+            531,
+            885,
+            903,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "23535",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d317d5be1748869dd71a6b23903c1097fcf424c80a45494cda3caca2b06ef27f.jpg",
+        "table_caption": [
+            "Table 2. Evaluations on diverse high-resolution Benchmarks. \"V*  ${}_{Avg}$  \" represents the weighted average score for the two subtasks in the  ${V}^{ * }$  benchmark. † denotes OCR inputs are utilized."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>V*Avg</td><td>DocVQA</td><td>TextVQA</td><td>ChartQA</td></tr><tr><td colspan=\"5\">Low-resolution MLLMs</td></tr><tr><td>Qwen-VL [1]</td><td>-</td><td>65.1</td><td>63.8</td><td>59.0</td></tr><tr><td>InstructBLIP [9]</td><td>34.0</td><td>4.5</td><td>50.7</td><td>10.9</td></tr><tr><td>LLaVA-v1.5-7B [30]</td><td>48.7</td><td>8.5</td><td>58.2†</td><td>17.8</td></tr><tr><td>mPLUG-Owl2 [60]</td><td>-</td><td>17.9</td><td>58.2†</td><td>22.8</td></tr><tr><td colspan=\"5\">High-resolution MLLMs</td></tr><tr><td>UReader [58]</td><td>-</td><td>65.4</td><td>57.6</td><td>59.3</td></tr><tr><td>Monkey [28]</td><td>-</td><td>66.5</td><td>65.8</td><td>59.0</td></tr><tr><td>LlvaF-FlexAttn [23]</td><td>54.4</td><td>-</td><td>48.9</td><td>-</td></tr><tr><td>S2-Wrapper-7B [48]</td><td>55.5</td><td>-</td><td>61.0</td><td>-</td></tr><tr><td>LlvaNxt-Vicuna7B [31]</td><td>61.8</td><td>-</td><td>64.9</td><td>54.3</td></tr><tr><td>SliME-7B [67]</td><td>-</td><td>-</td><td>64.4</td><td>33.9</td></tr><tr><td>FALCON</td><td>64.4</td><td>74.4</td><td>66.5</td><td>68.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablation results on training data. We train FALCON with two-stage pipeline and exactly the same dataset as LLaVAv1.5 [30]. The results confirm the superiority of the proposed method when the influence of training data is excluded.",
+        "bbox": [
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+            398
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/033cda0170d90fa03b901d164de4d812f479bd3f65f7a6d76335bf8e0d8b24d8.jpg",
+        "image_caption": [
+            "Figure 4. Comparison of different compression methods. We report the sum of the \"Avg-C\" scores for the perception and reasoning tasks in MME-RealWorld. The superior performance demonstrates that ReCompact effectively eliminates redundancy and produces a more expressive and compact visual representation."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
+            411,
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+            573
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ence of training data and demonstrate the advantages of the proposed method, we utilize exactly the same dataset as LLaVA-v1.5 [30] and employ a two-stage pipeline for training. As shown in Tab. 3, the proposed method exhibits significant performance advantages across multiple benchmarks when trained on the same dataset.",
+        "bbox": [
+            89,
+            657,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of ReCompact mechanism. To verify the advantages of the proposed ReCompact mechanism in reducing visual redundancy and compressing visual representations during the visual encoding, we compare the Re-Compact with other commonly used compression methods. This includes pooling [48, 55], Pixel Shuffle [7] and Abstractor [60], where the Abstractor serves as a representative module that combines query tokens with cross-attention.",
+        "bbox": [
+            89,
+            750,
+            482,
+            869
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 4, ReCompact demonstrates superior performance compared to other compression methods.",
+        "bbox": [
+            89,
+            869,
+            483,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/1150b29a95b08510f57717b0145b9822dac0fba53380b848ac9d6d1e3113870e.jpg",
+        "table_caption": [
+            "Table 4. Evaluation on benchmarks across diverse domains. The POPE, SQA, MMBench and SEED-Bench are used to assess hallucination, scientific reasoning, and overall abilities, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>SQA</td><td>POPE</td><td>MMB</td><td>SEED-Img</td></tr><tr><td colspan=\"5\">Low-Resolution MLLMs</td></tr><tr><td>Qwen-VL [1]</td><td>67.1</td><td>-</td><td>41.6</td><td>62.3</td></tr><tr><td>InstructBLIP [9]</td><td>63.1</td><td>78.9</td><td>38.4</td><td>58.8</td></tr><tr><td>LlaVA-v1.5-7B [30]</td><td>66.8</td><td>85.9</td><td>62.8</td><td>65.8</td></tr><tr><td>mPLUG-Owl2 [60]</td><td>68.7</td><td>85.8</td><td>63.5</td><td>64.5</td></tr><tr><td colspan=\"5\">High-Resolution MLLMs</td></tr><tr><td>Monkey [28]</td><td>69.4</td><td>83.7</td><td>57.4</td><td>64.3</td></tr><tr><td>LlaVA-FlexAttn [23]</td><td>-</td><td>85.9</td><td>65.7</td><td>-</td></tr><tr><td>S2-Wrapper-7B [48]</td><td>-</td><td>-</td><td>66.2</td><td>67.9</td></tr><tr><td>LLaVA-Next-Vicuna7B [31]</td><td>70.1</td><td>86.5</td><td>66.5</td><td>69.6</td></tr><tr><td>SliME-7B [67]</td><td>76.8</td><td>85.4</td><td>63.1</td><td>67.0</td></tr><tr><td>FALCON</td><td>88.8</td><td>88.0</td><td>76.1</td><td>73.3</td></tr></table>",
+        "bbox": [
+            521,
+            142,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/de7f372c5cc25c3bf236cf9c0af8cca376b8630b98794d3b553b18055604e759.jpg",
+        "table_caption": [
+            "Table 5. Comparison of different methods for maintaining visual continuity. The \"Baseline\" model refers to a condition where no specific methods are applied to preserve visual continuity. We report the \"Avg-C\" score for MME-RealWorld. The results show that the ReAtten module more effectively addresses the issue of visual fragmentation compared to other methods, thereby improving overall performance and reducing hallucinations."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">V*AVg</td><td colspan=\"2\">MME-RealWorld</td><td rowspan=\"2\">POPE</td></tr><tr><td>Perception</td><td>Reasoning</td></tr><tr><td>Baseline</td><td>51.3</td><td>38.2</td><td>35.6</td><td>85.7</td></tr><tr><td>CIP [16]</td><td>50.3</td><td>38.4</td><td>37.2</td><td>86.3</td></tr><tr><td>W-Atten [33]</td><td>60.2</td><td>41.0</td><td>38.1</td><td>86.4</td></tr><tr><td>ReAtten</td><td>61.3</td><td>42.1</td><td>39.0</td><td>87.3</td></tr></table>",
+        "bbox": [
+            544,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "These results indicate that ReCompact effectively eliminates visual redundancy and produces a more expressive compact visual representation. In contrast, we argue that the pooling layer and Pixel Shuffle merely reduces the number of tokens by merging adjacent ones, failing to eliminate redundancy that interferes with the LLM's understanding of visual content. Additionally, although Abstractor uses more parameters, its performance is generally lower than that of pooling and ReCompact. This result suggests that even millions of samples may be insufficient for fully training Abstractor, which diminishes their practical efficacy.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effectiveness of ReAtten Module. To validate the advantage of the proposed ReAtten Module, we compare ReAtten with other contemporary methods, including the Shifted Window Attention (W-Attn) [35] adopted by TextMonkey [33] and the Complementary Image Pyramid (CIP) introduced by MiniMonkey [16].",
+        "bbox": [
+            511,
+            702,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As shown in Tab. 5, the model incorporating ReAtten achieves significant improvements over the baseline across all benchmarks and demonstrates superiority compared to other methods. These results indicate that the ReAtten module effectively enhances the ability of the model in high-resolution perception and mitigates hallucinations by addressing the issue of visual fragmentation. In contrast, we",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "23536",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/69a61bdb051446db242affaf1ca3d6af18de2936a64fc459257188dc0fac5037.jpg",
+        "image_caption": [
+            "(a) Input Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            109,
+            333,
+            233
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ceb0250439bd1470cb952aa6838c3da9139588af5237a80a9f74e4373251c0c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/bd66f1083bbf9ca89b53d071f4a99d6ba15b6ea2d41b3298cad141cc222eef11.jpg",
+        "image_caption": [
+            "(b) Register-to-1"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            344,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5059284c6bb109e87b39beafc78b52016928dfabae1f0d576551336ded1848a6.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/95f15239a632e544a78a17d734546edff477e66bf722bd4973c44a87b7dcafed.jpg",
+        "image_caption": [
+            "Image Attention"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            467,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d67645d774671878f7e1abc1423fa5dc384083272d41db0887c544e8031ffb02.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/1253deae450cc82ae011ce0b29a5cf61ef43fe4fbaff73bfe804d96497da7381.jpg",
+        "image_caption": [
+            "(c) Ablation on ReAtten"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            599,
+            170,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "w/ ReAtten",
+        "bbox": [
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+        "type": "text",
+        "text": "w/o ReAtten",
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+        "img_path": "images/813b26bb016597ba79d2f958654b8d68b721c43981cec7fa7c93c4039fc1a5c1.jpg",
+        "image_caption": [
+            "Figure 5. Visualization of the register-to-image attention map. We randomly select visual registers and extract the attention scores that each register assigns to image tokens. These scores are then visualized as heatmaps overlaid on the input image. The results in (b) show that each visual register focuses on specific parts of the image, capturing rich visual patterns. Meanwhile, registers pay minimal attention to background areas, effectively avoiding the inclusion of redundancy. We also conduct qualitative ablation studies of the ReAtten module. As shown in (c), in the ViT model without ReAtten, the attention patterns across different sub-images appear extremely fragmented. In contrast, the ViT model with ReAtten shows continuous attention patterns, indicating effective information interaction between sub-images.",
+            "Figure 6. Ablation on different visual register counts. Increasing the number of visual registers generally enhances accuracy across both benchmarks. However, the improvement rate noticeably tapers off when the register count exceeds 64. Based on this observation, to better balance the efficiency and performance, we select register counts of 64 for FALCON."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "argue that the information exchange in W-Atten is limited to a local window, which hinders sufficient information exchange among all sub-images. Meanwhile, CIP introduces further redundancy by repeatedly encoding the same visual content, which can even lead to a decline in performance.",
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+        "type": "text",
+        "text": "Ablation on the Number of Visual Registers. To investigate how visual register count affects model performance, we conduct experiments with visual register counts set to 36, 64, and 144. These counts correspond to visual token compression rates of  $16 \\times$ ,  $9 \\times$ , and  $4 \\times$ , respectively. As shown in Fig. 6, increasing the number of visual registers generally enhances model's high-resolution comprehension capabilities and reduces hallucinations. However, when the register count exceeds 64, the improvement gains start tapering off noticeably. Meanwhile, increasing visual registers demands more computational resources. Compared to the baseline model with 36 registers, models configured with 64 and 144 registers require 1.15 and 2.41 times more training time, respectively. Base on these observations, to achieve a better balance between efficiency and performance, we select 64 as the register counts for FALCON.",
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+    {
+        "type": "text",
+        "text": "4.3. Qualitative Analysis",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "To qualitatively analyze the proposed visual register technique, we visualize the register-to-image attention maps within ViT. Specifically, for a given visual register, we extract the attention scores it assigns to image tokens in each sub-image and concatenate them to construct a complete heatmap. As shown in Fig. 5(b), each visual register focuses on relatively distinct areas of the image, highlighting that it captures a diverse range of visual details. Moreover, the visual registers tend to avoid background areas, indicating their effectiveness in identifying and discarding visual redundancy. These properties enable visual registers to effectively produce a comprehensive and non-redundant visual representation. Additionally, to qualitatively evaluate the effectiveness of the ReAtten module, we visualize the attention maps within ViT models with and without ReAtten. As shown in Fig. 5(c), in the ViT model without ReAtten, the attention patterns across different sub-images appear highly fragmented. In contrast, the ViT model with ReAtten exhibits continuous attention patterns, indicating effective information exchange between sub-images.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "To address visual redundancy and fragmentation in high-resolution MLLMs, we propose FALCON. FALCON employs an innovative visual register technique that simultaneously addresses both challenges. This technique uses a Re-Compact mechanism to adaptively aggregate essential visual information through visual registers, creating a compact, non-redundant representation. Additionally, a ReAtten module is introduced to further enhances visual continuity by enabling information exchange among sub-images via visual registers. Extensive experiments demonstrate FALCON's superiority in high-resolution understanding.",
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+        "text": "23537",
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+    {
+        "type": "text",
+        "text": "6. Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This study is supported by National Natural Science Foundation of China (Grant No. 62306090, No. U24A20328), Natural Science Foundation of Guangdong Province of China (Grant No. 2024A1515010147), Shenzhen Science and Technology Program (KQTD20240729102207002), Natural Science Foundation of Beijing, China (Grant No. L254018), Jiangsu Science and Technology Major Program (Grant No. BG2024041) and China Postdoctoral Science Foundation (Grant No. 2024M764192).",
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+        "type": "text",
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+            "[67] Yi-Fan Zhang, Qingsong Wen, Chaoyou Fu, Xue Wang, Zhang Zhang, Liang Wang, and Rong Jin. Beyond llava-hd: Diving into high-resolution large multimodal models. arXiv preprint arXiv:2406.08487, 2024. 1, 3, 7"
+        ],
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2025/FALCON_ Resolving Visual Redundancy and Fragmentation in High-resolution Multimodal Large Language Models via Visual Registers/3c258128-6a38-46a9-bf2a-aabe422e5840_origin.pdf

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2025/FALCON_ Resolving Visual Redundancy and Fragmentation in High-resolution Multimodal Large Language Models via Visual Registers/full.md

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+# FALCON: Resolving Visual Redundancy and Fragmentation in High-resolution Multimodal Large Language Models via Visual Registers
+
+Renshan Zhang $^{1}$ , Rui Shao $^{1\dagger}$ , Gongwei Chen $^{1}$ , Miao Zhang $^{1}$ , Kaiwen Zhou $^{2}$ , Weili Guan $^{1}$ , Liqiang Nie $^{1\dagger}$ $^{1}$ Harbin Institute of Technology, Shenzhen  $^{2}$ Huawei Noah's Ark Lab
+
+zhangrenshan@stu.hit.edu.cn shaorui@hit.edu.cn
+
+chengongwei@hit.edu.cn nieliqiang@gmail.com
+
+https://github.com/JiuTian-VL/FALCON
+
+# Abstract
+
+The incorporation of high-resolution visual input equips multimodal large language models (MLLMs) with enhanced visual perception capabilities for real-world tasks. However, most existing high-resolution MLLMs rely on a cropping-based approach to process images, which leads to fragmented visual encoding and a sharp increase in redundant tokens. To tackle these issues, we propose the FALCON model. FALCON introduces a novel visual register technique to simultaneously: 1) Eliminate redundant tokens at the stage of visual encoding. To directly address the visual redundancy present in the output of vision encoder, we propose a Register-based Representation Compacting (ReCompact) mechanism. This mechanism introduces a set of learnable visual registers designed to adaptively aggregate essential information while discarding redundancy. It enables the encoder to produce a more compact visual representation with a minimal number of output tokens, thus eliminating the need for an additional compression module. 2) Ensure continuity in visual encoding. To address the potential encoding errors caused by fragmented visual inputs, we develop a Register Interactive Attention (ReAtten) module. This module facilitates effective and efficient information exchange across sub-images by enabling interactions between visual registers. It ensures the continuity of visual semantics throughout the encoding. We conduct comprehensive experiments with FALCON on high-resolution benchmarks across a wide range of scenarios. FALCON demonstrates superior performance with a remarkable 9-fold reduction in visual tokens.
+
+# 1. Introduction
+
+Recently, multimodal large language models (MLLMs) [2, 9, 30, 32, 59, 60] have made significant advancements in
+
+![](images/d729d5f337aba80dea70000a3b80a55cd315708e8941f483cec9704ffe13e941.jpg)  
+Figure 1. Comparison between existing high-resolution MLLMs and FALCON. FALCON eliminates visual redundancy and ensures the continuity of high-resolution encoding through the use of ReCompact and ReAtten mechanisms.
+
+performing various vision-language tasks [45, 46, 61], facilitating more natural human-machine interactions. Early MLLMs [9, 32, 59] typically processed images at a fixed low resolution, such as  $224 \times 224$ . This limited their capabilities in many real-world applications that require high-resolution input. To equip MLLMs with high-resolution visual perception, recent efforts [15, 17, 33, 58, 67] have introduced a cropping-based high-resolution processing method. Specifically, As shown in Fig. 1(b), this approach crops high-resolution images into multiple non-overlapping sub-images that match the pre-trained resolution of the encoder. Each sub-image is processed independently by the vision encoder. Then the resulting visual features are concatenated and fed into the large language model (LLM).
+
+Although effective, cropping-based methods still face issues of: 1) Visual Redundancy. The number of visual to-
+
+kens grows dramatically with increasing resolution. While this enriches the visual details, it also leads to an increase in redundant tokens. These redundant tokens significantly increase the computational burden on LLM and interfere with the processing of visual information [65]. To address these issues, as illustrated in Fig. 1(b), existing methods typically rely on additional compression techniques. Representative approaches include combining learnable queries with cross-attention [1, 28, 60] or simply employing pooling layers [48, 55]. However, these methods either demand substantial training resources or fail to fully address redundancy. 2) Visual Fragmentation. Cropping an image into multiple non-overlapping sub-images may disrupt visual semantics and potentially lead to encoding errors. As shown in Fig. 1(a), in an OCR task, the word "pineapple" may be incorrectly segmented into "pine" and "apple", causing the LLM to misinterpret the word. Similarly, fragmentation can also hinder the identification of objects. For example, the "rubin vase" pattern illustrated in Fig. 1(a) depicts both a vase and two faces simultaneously. However, the fragmentation could lead to the vase being unrecognizable.
+
+To address these issues, as shown in Fig. 1(c), we propose the FALCON model. FALCON introduces a novel visual register technique to simultaneously: 1) Eliminate redundant tokens during visual encoding. To eliminate redundancy directly at the stage of visual encoding, we propose a novel Register-based Representation Compacting (ReCompact) mechanism. This mechanism introduces a set of learnable visual registers as additional inputs to the vision encoder. The registers are designed to adaptively aggregate essential information from image tokens and discard redundant content. Then the outputs corresponding to the visual registers are considered as a non-redundant visual representation, serving as the compact input for the LLM instead of a large number of image tokens. This mechanism enables the vision encoder to convey comprehensive visual information in a compact representation using minimal tokens, thus removing the need for an additional compression module. 2) Ensure continuity in visual encoding. To avoid the potential encoding errors caused by fragmented visual inputs, we develop a novel Register Interactive Attention (ReAtten) module. This module leverages the compact and comprehensive representation produced by visual registers to facilitate information exchange across sub-images. It gathers visual registers from different sub-images and employs a specialized cross-ViT attention module to enable interactions among them. Such interaction enables thorough information exchange across the entire image, thus ensuring visual continuity throughout the encoding process. Additionally, the compactness of the visual registers further enhances the efficiency of these interactions. Consequently, this module provides LLMs with a reliable foundation to accurately interpret visual content and reduce hallucinations.
+
+Note that the widely used Abstractor-like modules [28, 33, 58, 60], including QFormer [9], ReSampler [1], follow a similar approach by using query tokens to extract information from image tokens after visual encoding. The key difference is that the visual register mechanism directly adopts the pretrained ViT to aggregate information into a set of specified register tokens. This design is based on the observation that a well-pretrained ViT can naturally gather global information into some specific tokens through self-attention [10]. It offers the visual register mechanism several strengths in terms of: 1) Training Efficiency. The substantial number of randomly initialized parameters in Abstractor-like modules requires extensive data for pretraining. For instance, QFormer [22], Abstractor [60], and Resampler [1] use large corpora of 129M, 400M, and 1.4B samples, respectively. In contrast, by leveraging well-pretrained ViT parameters, the visual register mechanism requires only 3.5M samples for pretraining. The ablation results in Fig. 4 further demonstrate this advantages. 2) Addressing Visual Fragmentation. By leveraging the compact and comprehensive representation produced by visual registers, the proposed ReAtten module can effectively facilitate information exchange across sub-images. This is an important function that is notably lacking in Abstractor-like modules. Combined with ReCompact, it enables the visual register mechanism to simultaneously address the issues of visual redundancy and fragmentation. The ablation results in Tab. 5 validate the effectiveness of ReAtten.
+
+We summarize our main contributions as follows:
+
+- To address the issue of visual redundancy directly at the encoding phase, we introduce the Register-based Representation Compacting (ReCompact) mechanism. This mechanism enables vision encoder to capture rich visual information using only a minimal number of tokens, effectively eliminating redundancy and obviating the need for additional compression modules.  
+- To address the issue of visual fragmentation caused by image cropping, we propose the register interactive attention (ReAtten) module. This module ensures the semantic continuity of high-resolution visual encoding in an efficient and effective manner.  
+- We introduce FALCON, a model that leverages the proposed visual register technique. Comprehensive evaluations on high-resolution visual understanding benchmarks highlight the superiority of FALCON. Notably, FALCON achieves exceptional results with a remarkable reduction in visual tokens by  $9 \times$ .
+
+# 2. Related Work
+
+# 2.1. Multimodal Large Language Models
+
+Research on MLLMs [1, 2, 30, 47, 59, 60] has made significant strides in recent years. By incorporating image in
+
+![](images/2f27ac45349ad0f7f21ad2a796584b3c4076140f766605856e347b5f07931124.jpg)  
+Figure 2. Overall framework of the proposed FALCON. The model introduces a set of learnable visual registers, which are fed into the ViT along with the image tokens from each sub-image. During the visual encoding, the ReCompact mechanism enables information from the image tokens to be aggregated into the visual registers, while the proposed ReAtten facilitates information exchange among the visual registers across different sub-images. Ultimately, these visual registers provide a compact visual representation as input to the LLM.
+
+puts into pretrained LLMs [8, 51, 52], MLLMs demonstrate strong capabilities across various vision-language tasks. Typically, these models use a pretrained vision encoder [43, 62] to transform input images into a set of visual tokens. These tokens are then projected into the input space of the LLM through a projection module (e.g., MLP [30, 32], QFormer [9] and Abstractor [60]) and processed alongside text inputs. Building on the progress of MLLMs, recent studies have shifted from designing specialized methods for certain tasks [44-46] to employing MLLMs as generalist agents, capable of handling diverse practical tasks such as document analysis [15, 57, 64], online video assistant [24], retrieval-augmented generation [40], game agents [27, 29], robot manipulation [18, 21, 39], and GUI agent [3, 5, 54]. Despite these advances, MLLMs still struggle with the fixed low resolution of pretrained image encoders, which can limit their effectiveness in handling high-resolution images.
+
+# 2.2. High-resolution MLLMs
+
+To address the limitation of MLLMs in handling only low-resolution visual inputs, early studies attempted to either directly incorporate vision encoders that were pre-trained on higher-resolution images [36, 38], or to improve the resolution of pre-trained encoders through additional training [1, 60]. While achieving some progress, they still remain restricted by the fixed resolutions. To accommodate the varying resolutions and aspect ratios, cropping-based techniques have been widely adopted in recent works [15, 17, 33, 58, 67]. However, these approaches still face challenges related to visual redundancy and fragmentation.
+
+To mitigate the issue of redundancy, existing models typically require an additional compression module. For example, Abstractor-like modules utilizing learnable queries combined with cross-attention are widely adopted [1, 28, 33, 58, 60]. These modules typically require pretraining on massive amounts of data, which diminishes their practical efficacy. In contrast, some approaches use pooling
+
+layers [48, 55] or convolutional layers [15, 36]. Though resource-efficient, they often fail to address the issue of redundancy. In this work, we present an initial exploration to directly eliminate redundancy during the visual encoding phase, thereby removing the need for additional compression. To address the issue of fragmentation, several concurrent studies also make preliminary investigation. TextMonkey [33] uses Shifted Window Attention [35] to exchange information between sub-images. But the exchange is still limited to local regions. MiniMonkey [16] proposed a Complementary Image Pyramid strategy to generate complementary cropping schemes. However, this strategy inevitably encodes the same visual content multiple times, further exacerbating visual redundancy. In this work, we propose the ReAtten module to facilitate continuous visual encoding through the interaction among visual registers.
+
+# 3. FALCON
+
+The overall framework of FALCON is illustrated in Fig. 2. The method begins with shape-adaptive cropping [58], where the image is cropped into multiple non-overlapping sub-images, each matching the resolution of the pre-trained vision encoder. Additionally, a resized version of the full image is used to supplement global layout information. To directly eliminate redundancy during visual encoding, we propose Register-based Representation Compacting (Re-Compact) mechanism. This mechanism introduces a set of learnable visual registers, which are paired with image tokens from each sub-image and fed into the vision encoder to capture rich visual information. To ensure the continuity of visual semantics throughout the encoding, a novel Register Interactive Attention (ReAtten) module is integrated into the Vision Transformer (ViT) [11] to facilitate information exchange between sub-images via the visual registers. Finally, the compact visual representations produced by the visual registers are processed through a simple MLP module before being fed into the LLM for further analysis.
+
+# 3.1. Mitigating Visual Redundancy via ReCompact
+
+Existing MLLMs typically use a ViT-based vision encoder, such as CLIP [43]. For an input image of size  $H \times W$ , it is patched into multiple  $P \times P$  patches. Each patch is treated as an individual image token, resulting in  $N = \frac{H}{P} \times \frac{W}{P}$  tokens, denoted as  $I = \{i_1, \dots, i_N\}$ . In most current MLLMs, output features corresponding to all image tokens are usually preserved in their entirety. However, when high-resolution images are included, the number of image tokens increases dramatically, placing a substantial burden on the computational resources of LLMs. Consequently, most high-resolution MLLMs necessitate an additional compression module, which can be resource-inefficient. Previous research has shown that most image tokens contain only localized information from their surrounding areas [10]. It suggests that a significant portion of these tokens may be redundant, particularly those originating from background regions. This observation motivates us to directly eliminate redundancy in the output of the vision encoder, thereby reducing the number of visual tokens and avoiding the need for an additional compression module.
+
+To achieve this, we propose a novel Register-based Representation Compacting (ReCompact) mechanism. This mechanism employs a set of visual registers to aggregate essential information from image tokens, resulting in a more compact visual representation. Specifically, as shown in Fig. 2, we introduce a set of learnable visual registers, denoted by  $R = \{r_1,\dots ,r_M\}$ , where  $M$  represents the number of visual registers, and  $M\ll N$ . Given a single input image, the image tokens are concatenated with visual registers to create a new input for ViT, represented as  $V = \mathrm{Concat}(I,R) = \{i_1,\dots ,i_N,r_1,\dots ,r_M\}$ . During visual encoding, the self-attention mechanism in ViT enables the visual register to adaptively aggregate important information from image tokens while discarding redundant content. Denote  $X_{k,l}\in \mathcal{R}^{(N + M)\times D}$  as the input hidden states of the  $k$ -th sub-image at the  $l$ -th layer, where  $D$  is the dimensionality. The self-attention is formulated as:
+
+$$
+\hat {X} _ {k, l} = \operatorname {S e l f - A t t e n} \left(X _ {k, l}\right) = \operatorname {S o f t m a x} \left(\frac {X _ {k , l} X _ {k , l} ^ {T}}{\sqrt {D _ {\text {k e y}}}}\right) X _ {k, l} \tag {1}
+$$
+
+Notably, we do not apply any attention masks for specific constraints. Our experiments show that pretraining on a modest amount of data is sufficient to effectively adapt the pretrained ViT to the proposed ReCompact, enabling it to aggregate essential information within the visual registers. After visual encoding, The output features corresponding to the visual registers, denoted as  $F = \{f_{1},\dots ,f_{M}\}$ , are then used as the visual representation of the image and fed into the LLM for various vision-language tasks.
+
+To further adapt the ReCompact mechanism for cropping-based high-resolution image perception, we share
+
+the same set of visual registers as input for different sub-images. The input for the  $k$ -th sub-image is formulated as  $V_{k} = \mathrm{Concat}(I_{k},R)$ , where  $k = 1,2,\dots ,N_{c}$  and  $N_{c}$  denotes the total number of sub-images. After encoding, the outputs of the visual registers for all sub-images are concatenated, yielding  $F_{hr} = \mathrm{Concat}(F_1,F_2,\dots ,F_{N_c})$  which serves as the input to the LLM. The ReCompact mechanism enables the vision encoder to represent rich visual information using only a minimal number of  $M$  tokens per sub-image, which significantly reduces the visual redundancy and eliminates the need for additional compression.
+
+# 3.2. Ensuring Visual Continuity via ReAtten
+
+When using the cropping-based high-resolution image encoding method, each sub-image is independently encoded by the vision encoder. This process can disrupt semantic coherence and result in the misrepresentation of visual concepts. To preserve the continuity of visual semantics, it is crucial to enable information exchange between sub-images during encoding. A naive approach would be to directly concatenate the image features from all sub-images and apply self-attention. However, the quadratic computational complexity makes this approach impractical. In Sec. 3.1, we introduced the ReCompact mechanism, where the visual registers effectively aggregate rich visual information while discarding redundancy during visual encoding, allowing them to serve as compact yet comprehensive image representations. Consequently, interactions between visual registers can naturally facilitate sufficient information exchange across different sub-images in an efficient manner.
+
+To enable information exchange between visual registers across different sub-images, we introduce a novel Register Interactive Attention (ReAtten) module. As shown in Fig. 2, the ReAtten module is integrated into each of the  $L$  layers of the ViT. After the self-attention process in Eq. (1), we acquire  $\hat{X}_{k,l} = \{\hat{X}_{k,l}^{I},\hat{X}_{k,l}^{R}\}$ , where  $\hat{X}^I\in \mathcal{R}^{N\times D}$  and  $\hat{X}^R\in \mathcal{R}^{M\times D}$  represent the hidden states corresponding to image tokens and visual registers, respectively. The states of the visual registers from different sub-images are concatenated to form  $\hat{X}_l^R = \mathrm{Concat}\left(\{\hat{X}_{k,l}^R\}_{k = 1}^{N_c}\right)\in$ $\mathcal{R}^{M\cdot N_c\times D}$ . Then these concatenated registers are processed via ReAtten to enable information exchange across subimages, which can be formulated as:
+
+$$
+\overline {{X}} _ {l} ^ {R} = \mathrm {R e A t t e n} (\hat {X} _ {l} ^ {R}) = \hat {X} _ {l} ^ {R} + \mathrm {C r o s s - V i T - A t t e n} (\hat {X} _ {l} ^ {R}) (2)
+$$
+
+where Cross-ViT-Atten is implemented as a self-attention layer. Once the information exchange is completed, the registers and image tokens from a same sub-image are concatenated and then passed into the feedforward network (FFN) for transformation, yielding the output of the  $l$ -th layer:
+
+$$
+X _ {k, l + 1} = \operatorname {F F N} \left(\operatorname {C o n c a t} \left(\hat {X} _ {k, l} ^ {I}, \bar {X} _ {k, l} ^ {R}\right)\right) \tag {3}
+$$
+
+![](images/7fea22fdc3cc3b493e312b32f4a98ebdb9f316bfc9d08bbff01a1afa4a45a549.jpg)  
+Figure 3. The progressive training pipeline. **Stage 0:** Align the frozen vision and language backbones by training only the MLP and registers. **Stage 1:** Tune all parameters with caption and OCR data on low-resolution for coarse alignment. **Stage 2:** Integrate high-resolution input along with fine-grained captions and OCR to achieve refined alignment. **Stage 3:** Froze ViT and introduce ReAtten module for high-resolution instruction tuning.
+
+By integrating ReAtten into each layer of the ViT model, FALCON enables effective information exchange between cropped sub-images through visual registers, thereby ensuring semantic continuity of the high-resolution image throughout the visual encoding process.
+
+# 3.3. Learning Expressive Visual Representation via Progressive Training Pipeline
+
+To empower the ReCompact mechanism with the capability to capture rich visual patterns and to enable smoother initialization of the ReAtten module under high-resolution conditions, we develop a specialized progressive training pipeline. As illustrated in Fig. 3, this pipeline progressively transitions from low to high resolution across four stages.
+
+Stage 0: Static Alignment on Low-resolution. Since both the visual registers and MLP projector are randomly initialized, in stage 0, we aim to achieve a initial alignment between the pretrained vision encoder and the LLM. To facilitate this, we begin by using low-resolution images as inputs, which are directly resized to match the resolution of the vision encoder. We then statically pretrain the model by keeping both the vision encoder and LLM frozen, tuning only the visual registers and MLP using image caption data.
+
+Stage 1: Coarse Alignment on Low-resolution. To better adapt the pre-trained vision encoder to our newly introduced ReCompact mechanism, in stage 1, we unfreeze all model parameters to enable a more thorough tuning. To facilitate the visual registers to progressively learn capturing visual information from coarse to fine granularity, we con
+
+tinue to use low-resolution inputs and employ high-quality, extended captions rich in visual content, along with full-text OCR data for training. This design allows the registers to acquire holistic scene understanding ability.
+
+Stage 2: Refined Alignment on High-resolution. To further enhance the capacity of the visual register to capture fine-grained visual details, in stage 2, we transition the model to process high-resolution image for refined alignment. Additionally, we employ datasets that includes a series of fine-grained captions and OCR tasks, such as regional captions and text location. This facilitates the visual registers to capture comprehensive fine-grained details.
+
+Stage 3: Instruction Tuning on High-resolution. To adapt the well-aligned visual register for a wide range of real-world tasks, in stage 3, we perform instruction tuning with a mixture of datasets covering various tasks, such as VQA, document understanding, and science reasoning. Additionally, the proposed ReAtten module is integrated to address visual fragmentation caused by cropping-based high-resolution image encoding. Since the vision encoder with ReCompact is well-aligned, the vision encoder is kept frozen and other parameters including ReAtten are trainable during instruction tuning. Notably, to facilitate a smoother initialization for the newly introduced ReAtten modules, we initialize parameters of each ReAtten module with the ViT self-attention parameters at the corresponding depth. This design enables ReAtten to effectively leverage pre-trained parameters, avoiding the need for extensive fine-tuning.
+
+# 4. Experiments
+
+We implement FALCON with SigLIP-L/16-384px [62] as the vision encoder and Llama-3.1-8B-Instruct [12] as the LLM backbone. A two-layer MLP module with GeLU [13] activation is served as the vision-language projection layer. The number of visual registers is set to 64, achieving remarkable visual token compression rates of  $9 \times$ . The maximum number of sub-images is set to 16.
+
+# 4.1. Experimental Results
+
+We evaluate FALCON using the recently proposed MMERealWorld [66] benchmark, a comprehensive and largescale benchmark specifically designed to assess the high-resolution understanding capabilities of MLLMs. MMERealWorld comprises 13,366 high-resolution images with an average resolution of  $2,000 \times 1,500$  pixels, spanning five domains: OCR in the wild, Remote Sensing, Diagrams and Tables, Monitoring, and Autonomous Driving. This benchmark is well-suited for evaluating the practical high-resolution understanding capabilities of MLLMs.
+
+As shown in Tab. 1, FALCON significantly outperform other advanced MLLMs in both perception and reasoning tasks. FALCON achieves state-of-the-art performance with only 64 tokens per sub-image, resulting in a remarkable vi
+
+Table 1. Evaluation on MME-RealWorld Benchmark. "OCR", "RS", "DT", "MO", and "AD" stand for OCR in the Wild, Remote Sensing, Diagram and Table, Monitoring, and Autonomous Driving, respectively. "Avg" denotes the weighted average accuracy across all samples, while "Avg-C" denotes the weighted average accuracy across different domains. "Sizev" indicates the image resolution supported by the model, where  $\times n$  signifies a cropping-based high-resolution processing approach with up to  $n$  sub-images. "Tokenc" denotes the number of visual tokens after compression. † For models utilizing hybrid vision encoders, "Sizev" represents the setting of encoder with the highest resolution. We gray out the models that are either closed-source or have at least twice the number of visual tokens compared to ours. Among these, the lighter gray denotes scores below ours. The underline indicates that the second performance is achieved. Notably, FALCON achieves state-of-the-art performance with just 64 tokens per sub-image, surpassing most models that have large amount of visual tokens and many advanced closed-source commercial models.
+
+<table><tr><td>Type</td><td>Method</td><td>\( Size^v \)</td><td>\( Token^c \)</td><td colspan="6">Perception</td><td colspan="5">Reasoning</td><td></td><td></td></tr><tr><td></td><td colspan="3">Task Split</td><td>OCR</td><td>RS</td><td>DT</td><td>MO</td><td>AD</td><td>Avg</td><td>Avg-C</td><td>OCR</td><td>DT</td><td>MO</td><td>AD</td><td>Avg</td><td>Avg-C</td></tr><tr><td rowspan="10">Visual Tokens\(\nabla 1024\)</td><td>MiniGPT-v2 [4]</td><td>\( 448^2 \)</td><td>256</td><td>39.0</td><td>23.3</td><td>20.4</td><td>19.3</td><td>26.0</td><td>26.9</td><td>25.6</td><td>30.0</td><td>20.4</td><td>16.9</td><td>23.7</td><td>23.0</td><td>22.7</td></tr><tr><td>Qwen-VL-Chat [1]</td><td>\( 448^2 \)</td><td>256</td><td>32.4</td><td>15.1</td><td>15.6</td><td>22.1</td><td>15.1</td><td>20.8</td><td>20.1</td><td>28.6</td><td>13.6</td><td>16.5</td><td>24.6</td><td>22.0</td><td>20.8</td></tr><tr><td>LLaVA1.5-13B [30]</td><td>\( 336^2 \)</td><td>576</td><td>44.1</td><td>23.3</td><td>20.2</td><td>20.5</td><td>26.1</td><td>28.4</td><td>26.8</td><td>30.2</td><td>20.8</td><td>27.5</td><td>24.8</td><td>25.5</td><td>25.8</td></tr><tr><td>ShareGPT4V-13B [6]</td><td>\( 336^2 \)</td><td>576</td><td>44.6</td><td>23.1</td><td>20.2</td><td>19.3</td><td>26.1</td><td>28.4</td><td>26.6</td><td>26.0</td><td>20.8</td><td>27.3</td><td>24.6</td><td>24.6</td><td>24.7</td></tr><tr><td>TextMonkey [33]</td><td>\( 448^2 \times 4 \)</td><td>256 × 4</td><td>37.3</td><td>11.7</td><td>5.9</td><td>16.1</td><td>14.3</td><td>18.2</td><td>17.1</td><td>30.4</td><td>2.2</td><td>4.4</td><td>20.0</td><td>16.0</td><td>14.3</td></tr><tr><td>Mini-Gemini-7B-HD† [26]</td><td>\( 336^2 \times 4 \)</td><td>576</td><td>42.0</td><td>31.3</td><td>22.3</td><td>34.2</td><td>24.8</td><td>31.1</td><td>30.9</td><td>35.4</td><td>24.6</td><td>25.9</td><td>23.3</td><td>26.1</td><td>27.3</td></tr><tr><td>DeepSeek-VL† [36]</td><td>\( 1024^2 \)</td><td>576</td><td>49.6</td><td>25.5</td><td>23.4</td><td>27.0</td><td>33.4</td><td>33.1</td><td>31.8</td><td>45.2</td><td>23.8</td><td>16.7</td><td>27.3</td><td>28.0</td><td>28.3</td></tr><tr><td>MiniCPM-V 2.5 [56]</td><td>\( 448^2 \times 9 \)</td><td>96 × 9</td><td>66.8</td><td>27.7</td><td>52.8</td><td>38.7</td><td>34.2</td><td>47.4</td><td>44.0</td><td>44.0</td><td>31.8</td><td>37.0</td><td>31.0</td><td>34.5</td><td>36.0</td></tr><tr><td>Monkey [28]</td><td>\( 448^2 \times 4 \)</td><td>256 × 4</td><td>54.6</td><td>25.0</td><td>32.5</td><td>28.0</td><td>29.7</td><td>36.3</td><td>34.0</td><td>27.2</td><td>20.8</td><td>27.3</td><td>33.0</td><td>28.8</td><td>27.1</td></tr><tr><td>FALCON</td><td>\( 384^2 \times 16 \)</td><td>64 × 16</td><td>66.4</td><td>49.6</td><td>47.2</td><td>40.4</td><td>36.5</td><td>50.3</td><td>48.0</td><td>55.4</td><td>39.2</td><td>44.4</td><td>34.5</td><td>40.7</td><td>43.4</td></tr><tr><td rowspan="6">Visual Tokens\(\nabla 2048\)</td><td>LLaVA-Next-Qwen72B [31]</td><td>\( 336^2 \times 4 \)</td><td>576 × 4</td><td>37.1</td><td>29.1</td><td>27.7</td><td>29.4</td><td>18.0</td><td>29.0</td><td>28.3</td><td>17.2</td><td>34.2</td><td>27.3</td><td>29.7</td><td>27.9</td><td>27.1</td></tr><tr><td>LLaVA-Next-liama3 [31]</td><td>\( 336^2 \times 4 \)</td><td>576 × 4</td><td>47.9</td><td>25.4</td><td>26.6</td><td>19.5</td><td>18.7</td><td>30.1</td><td>27.6</td><td>55.2</td><td>23.4</td><td>21.1</td><td>30.7</td><td>32.1</td><td>32.6</td></tr><tr><td>mPLUG-DocOwl 1.5 [15]</td><td>\( 448^2 \times 9 \)</td><td>256 × 9</td><td>51.2</td><td>23.7</td><td>29.3</td><td>25.0</td><td>28.3</td><td>33.7</td><td>31.5</td><td>42.6</td><td>19.8</td><td>20.5</td><td>26.0</td><td>26.9</td><td>27.2</td></tr><tr><td>CogVLM2-liama3-Chat [14]</td><td>\( 1344^2 \)</td><td>2304</td><td>70.0</td><td>28.8</td><td>47.5</td><td>33.7</td><td>30.2</td><td>45.8</td><td>42.0</td><td>54.0</td><td>32.8</td><td>41.2</td><td>31.2</td><td>37.3</td><td>39.8</td></tr><tr><td>IXC2.5 [63]</td><td>\( 560^2 \times 24 \)</td><td>400 × 24</td><td>69.3</td><td>36.1</td><td>63.9</td><td>39.5</td><td>33.6</td><td>52.5</td><td>48.5</td><td>53.4</td><td>41.0</td><td>17.7</td><td>30.0</td><td>33.9</td><td>35.5</td></tr><tr><td>LLaVA-OneVision [20]</td><td>\( 384^2 \times 9 \)</td><td>729 × 9</td><td>78.7</td><td>53.5</td><td>60.7</td><td>40.3</td><td>45.8</td><td>59.6</td><td>55.8</td><td>61.8</td><td>40.0</td><td>40.8</td><td>34.1</td><td>41.2</td><td>44.2</td></tr><tr><td rowspan="4">Closed-source</td><td>GPT-4o-mini</td><td>-</td><td>-</td><td>62.5</td><td>6.7</td><td>44.2</td><td>26.5</td><td>24.2</td><td>37.1</td><td>32.8</td><td>47.0</td><td>39.8</td><td>25.8</td><td>26.8</td><td>32.5</td><td>34.9</td></tr><tr><td>Gemini-1.5-pro [50]</td><td>-</td><td>-</td><td>67.6</td><td>14.0</td><td>39.9</td><td>31.1</td><td>26.6</td><td>39.6</td><td>35.9</td><td>52.7</td><td>33.2</td><td>28.3</td><td>19.2</td><td>29.2</td><td>33.4</td></tr><tr><td>GPT-4o</td><td>-</td><td>-</td><td>77.7</td><td>28.9</td><td>46.7</td><td>33.9</td><td>22.4</td><td>46.4</td><td>41.9</td><td>61.4</td><td>44.8</td><td>36.5</td><td>26.4</td><td>37.6</td><td>42.3</td></tr><tr><td>Claude 3.5 Sonnet</td><td>-</td><td>-</td><td>72.5</td><td>25.7</td><td>67.4</td><td>32.2</td><td>40.8</td><td>52.9</td><td>47.7</td><td>61.9</td><td>61.2</td><td>41.8</td><td>31.9</td><td>44.1</td><td>49.2</td></tr></table>
+
+sual compression rate of 9 times. In addition, FALCON also outperforms most models that have twice as many visual tokens. Specifically, FALCON outperforms CogVLM2-llama3-Chat [14] in average scores on both perception and reasoning task, which uses 2304 tokens per-image. It also surpasses IXC2.5 [63] in average scores on the reasoning tasks, which has a maximum token counts of 9600. Notably, FALCON achieves higher average scores in both perception and reasoning tasks compared to three advanced commercial models, GPT-4o, GPT-4o-mini and Gemini1.5-pro [50], with it notably outperforming all commercial models in the sub-tasks of remote sensing and monitoring. These results demonstrate that the ReCompact and ReAtten technique proposed by FALCON effectively eliminate visual redundancy and ensure visual continuity, allowing comprehensive and detailed visual information to be conveyed with a highly compact visual representation.
+
+To further assess FALCON's capabilities in high-resolution understanding, we conduct evaluations on more high-resolution benchmarks: V* [53], DocVQA [42], TextVQA [49] and ChartQA [41]. V* focuses on evaluating
+
+models' capabilities for fine-grained attribute recognition and spatial reasoning. DocVQA challenges models to comprehend text-dense document images. ChartQA evaluates models' proficiency in interpreting various types of chart, while TextVQA assesses the ability to recognize small text in real-world scenes. As shown in Tab. 2, FALCON demonstrates superior performance across all these benchmarks.
+
+To evaluate the performance of FALCON across a broader range of domains, we further conduct experiments with diverse popular benchmarks. As shown in Tab. 4, POPE [25], ScienceQA [37], MMBench [34] and SEED-Bench [19] are selected to assess models' capabilities in hallucination, scientific reasoning, and comprehensive ability. FALCON achieves SOTA performance across all these benchmarks. The results demonstrate that FALCON exhibits superior capabilities across a wide range of tasks.
+
+# 4.2. Ablation Study
+
+We perform extensive ablation studies to validate the effectiveness of the proposed ReCompact and ReAtten.
+
+Ablation on Training Data. To eliminate the influx
+
+Table 2. Evaluations on diverse high-resolution Benchmarks. "V*  ${}_{Avg}$  " represents the weighted average score for the two subtasks in the  ${V}^{ * }$  benchmark. † denotes OCR inputs are utilized.  
+
+<table><tr><td>Model</td><td>V*Avg</td><td>DocVQA</td><td>TextVQA</td><td>ChartQA</td></tr><tr><td colspan="5">Low-resolution MLLMs</td></tr><tr><td>Qwen-VL [1]</td><td>-</td><td>65.1</td><td>63.8</td><td>59.0</td></tr><tr><td>InstructBLIP [9]</td><td>34.0</td><td>4.5</td><td>50.7</td><td>10.9</td></tr><tr><td>LLaVA-v1.5-7B [30]</td><td>48.7</td><td>8.5</td><td>58.2†</td><td>17.8</td></tr><tr><td>mPLUG-Owl2 [60]</td><td>-</td><td>17.9</td><td>58.2†</td><td>22.8</td></tr><tr><td colspan="5">High-resolution MLLMs</td></tr><tr><td>UReader [58]</td><td>-</td><td>65.4</td><td>57.6</td><td>59.3</td></tr><tr><td>Monkey [28]</td><td>-</td><td>66.5</td><td>65.8</td><td>59.0</td></tr><tr><td>LlvaF-FlexAttn [23]</td><td>54.4</td><td>-</td><td>48.9</td><td>-</td></tr><tr><td>S2-Wrapper-7B [48]</td><td>55.5</td><td>-</td><td>61.0</td><td>-</td></tr><tr><td>LlvaNxt-Vicuna7B [31]</td><td>61.8</td><td>-</td><td>64.9</td><td>54.3</td></tr><tr><td>SliME-7B [67]</td><td>-</td><td>-</td><td>64.4</td><td>33.9</td></tr><tr><td>FALCON</td><td>64.4</td><td>74.4</td><td>66.5</td><td>68.8</td></tr></table>
+
+Table 3. Ablation results on training data. We train FALCON with two-stage pipeline and exactly the same dataset as LLaVAv1.5 [30]. The results confirm the superiority of the proposed method when the influence of training data is excluded.
+
+![](images/033cda0170d90fa03b901d164de4d812f479bd3f65f7a6d76335bf8e0d8b24d8.jpg)  
+Figure 4. Comparison of different compression methods. We report the sum of the "Avg-C" scores for the perception and reasoning tasks in MME-RealWorld. The superior performance demonstrates that ReCompact effectively eliminates redundancy and produces a more expressive and compact visual representation.
+
+ence of training data and demonstrate the advantages of the proposed method, we utilize exactly the same dataset as LLaVA-v1.5 [30] and employ a two-stage pipeline for training. As shown in Tab. 3, the proposed method exhibits significant performance advantages across multiple benchmarks when trained on the same dataset.
+
+Effectiveness of ReCompact mechanism. To verify the advantages of the proposed ReCompact mechanism in reducing visual redundancy and compressing visual representations during the visual encoding, we compare the Re-Compact with other commonly used compression methods. This includes pooling [48, 55], Pixel Shuffle [7] and Abstractor [60], where the Abstractor serves as a representative module that combines query tokens with cross-attention.
+
+As shown in Fig. 4, ReCompact demonstrates superior performance compared to other compression methods.
+
+Table 4. Evaluation on benchmarks across diverse domains. The POPE, SQA, MMBench and SEED-Bench are used to assess hallucination, scientific reasoning, and overall abilities, respectively.  
+
+<table><tr><td>Model</td><td>SQA</td><td>POPE</td><td>MMB</td><td>SEED-Img</td></tr><tr><td colspan="5">Low-Resolution MLLMs</td></tr><tr><td>Qwen-VL [1]</td><td>67.1</td><td>-</td><td>41.6</td><td>62.3</td></tr><tr><td>InstructBLIP [9]</td><td>63.1</td><td>78.9</td><td>38.4</td><td>58.8</td></tr><tr><td>LlaVA-v1.5-7B [30]</td><td>66.8</td><td>85.9</td><td>62.8</td><td>65.8</td></tr><tr><td>mPLUG-Owl2 [60]</td><td>68.7</td><td>85.8</td><td>63.5</td><td>64.5</td></tr><tr><td colspan="5">High-Resolution MLLMs</td></tr><tr><td>Monkey [28]</td><td>69.4</td><td>83.7</td><td>57.4</td><td>64.3</td></tr><tr><td>LlaVA-FlexAttn [23]</td><td>-</td><td>85.9</td><td>65.7</td><td>-</td></tr><tr><td>S2-Wrapper-7B [48]</td><td>-</td><td>-</td><td>66.2</td><td>67.9</td></tr><tr><td>LLaVA-Next-Vicuna7B [31]</td><td>70.1</td><td>86.5</td><td>66.5</td><td>69.6</td></tr><tr><td>SliME-7B [67]</td><td>76.8</td><td>85.4</td><td>63.1</td><td>67.0</td></tr><tr><td>FALCON</td><td>88.8</td><td>88.0</td><td>76.1</td><td>73.3</td></tr></table>
+
+Table 5. Comparison of different methods for maintaining visual continuity. The "Baseline" model refers to a condition where no specific methods are applied to preserve visual continuity. We report the "Avg-C" score for MME-RealWorld. The results show that the ReAtten module more effectively addresses the issue of visual fragmentation compared to other methods, thereby improving overall performance and reducing hallucinations.  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">V*AVg</td><td colspan="2">MME-RealWorld</td><td rowspan="2">POPE</td></tr><tr><td>Perception</td><td>Reasoning</td></tr><tr><td>Baseline</td><td>51.3</td><td>38.2</td><td>35.6</td><td>85.7</td></tr><tr><td>CIP [16]</td><td>50.3</td><td>38.4</td><td>37.2</td><td>86.3</td></tr><tr><td>W-Atten [33]</td><td>60.2</td><td>41.0</td><td>38.1</td><td>86.4</td></tr><tr><td>ReAtten</td><td>61.3</td><td>42.1</td><td>39.0</td><td>87.3</td></tr></table>
+
+These results indicate that ReCompact effectively eliminates visual redundancy and produces a more expressive compact visual representation. In contrast, we argue that the pooling layer and Pixel Shuffle merely reduces the number of tokens by merging adjacent ones, failing to eliminate redundancy that interferes with the LLM's understanding of visual content. Additionally, although Abstractor uses more parameters, its performance is generally lower than that of pooling and ReCompact. This result suggests that even millions of samples may be insufficient for fully training Abstractor, which diminishes their practical efficacy.
+
+Effectiveness of ReAtten Module. To validate the advantage of the proposed ReAtten Module, we compare ReAtten with other contemporary methods, including the Shifted Window Attention (W-Attn) [35] adopted by TextMonkey [33] and the Complementary Image Pyramid (CIP) introduced by MiniMonkey [16].
+
+As shown in Tab. 5, the model incorporating ReAtten achieves significant improvements over the baseline across all benchmarks and demonstrates superiority compared to other methods. These results indicate that the ReAtten module effectively enhances the ability of the model in high-resolution perception and mitigates hallucinations by addressing the issue of visual fragmentation. In contrast, we
+
+![](images/69a61bdb051446db242affaf1ca3d6af18de2936a64fc459257188dc0fac5037.jpg)  
+(a) Input Image
+
+![](images/8ceb0250439bd1470cb952aa6838c3da9139588af5237a80a9f74e4373251c0c.jpg)
+
+![](images/bd66f1083bbf9ca89b53d071f4a99d6ba15b6ea2d41b3298cad141cc222eef11.jpg)  
+(b) Register-to-1
+
+![](images/5059284c6bb109e87b39beafc78b52016928dfabae1f0d576551336ded1848a6.jpg)
+
+![](images/95f15239a632e544a78a17d734546edff477e66bf722bd4973c44a87b7dcafed.jpg)  
+Image Attention
+
+![](images/d67645d774671878f7e1abc1423fa5dc384083272d41db0887c544e8031ffb02.jpg)
+
+![](images/1253deae450cc82ae011ce0b29a5cf61ef43fe4fbaff73bfe804d96497da7381.jpg)  
+(c) Ablation on ReAtten
+
+w/ ReAtten
+
+w/o ReAtten
+
+![](images/813b26bb016597ba79d2f958654b8d68b721c43981cec7fa7c93c4039fc1a5c1.jpg)  
+Figure 5. Visualization of the register-to-image attention map. We randomly select visual registers and extract the attention scores that each register assigns to image tokens. These scores are then visualized as heatmaps overlaid on the input image. The results in (b) show that each visual register focuses on specific parts of the image, capturing rich visual patterns. Meanwhile, registers pay minimal attention to background areas, effectively avoiding the inclusion of redundancy. We also conduct qualitative ablation studies of the ReAtten module. As shown in (c), in the ViT model without ReAtten, the attention patterns across different sub-images appear extremely fragmented. In contrast, the ViT model with ReAtten shows continuous attention patterns, indicating effective information interaction between sub-images.  
+Figure 6. Ablation on different visual register counts. Increasing the number of visual registers generally enhances accuracy across both benchmarks. However, the improvement rate noticeably tapers off when the register count exceeds 64. Based on this observation, to better balance the efficiency and performance, we select register counts of 64 for FALCON.
+
+argue that the information exchange in W-Atten is limited to a local window, which hinders sufficient information exchange among all sub-images. Meanwhile, CIP introduces further redundancy by repeatedly encoding the same visual content, which can even lead to a decline in performance.
+
+Ablation on the Number of Visual Registers. To investigate how visual register count affects model performance, we conduct experiments with visual register counts set to 36, 64, and 144. These counts correspond to visual token compression rates of  $16 \times$ ,  $9 \times$ , and  $4 \times$ , respectively. As shown in Fig. 6, increasing the number of visual registers generally enhances model's high-resolution comprehension capabilities and reduces hallucinations. However, when the register count exceeds 64, the improvement gains start tapering off noticeably. Meanwhile, increasing visual registers demands more computational resources. Compared to the baseline model with 36 registers, models configured with 64 and 144 registers require 1.15 and 2.41 times more training time, respectively. Base on these observations, to achieve a better balance between efficiency and performance, we select 64 as the register counts for FALCON.
+
+# 4.3. Qualitative Analysis
+
+To qualitatively analyze the proposed visual register technique, we visualize the register-to-image attention maps within ViT. Specifically, for a given visual register, we extract the attention scores it assigns to image tokens in each sub-image and concatenate them to construct a complete heatmap. As shown in Fig. 5(b), each visual register focuses on relatively distinct areas of the image, highlighting that it captures a diverse range of visual details. Moreover, the visual registers tend to avoid background areas, indicating their effectiveness in identifying and discarding visual redundancy. These properties enable visual registers to effectively produce a comprehensive and non-redundant visual representation. Additionally, to qualitatively evaluate the effectiveness of the ReAtten module, we visualize the attention maps within ViT models with and without ReAtten. As shown in Fig. 5(c), in the ViT model without ReAtten, the attention patterns across different sub-images appear highly fragmented. In contrast, the ViT model with ReAtten exhibits continuous attention patterns, indicating effective information exchange between sub-images.
+
+# 5. Conclusion
+
+To address visual redundancy and fragmentation in high-resolution MLLMs, we propose FALCON. FALCON employs an innovative visual register technique that simultaneously addresses both challenges. This technique uses a Re-Compact mechanism to adaptively aggregate essential visual information through visual registers, creating a compact, non-redundant representation. Additionally, a ReAtten module is introduced to further enhances visual continuity by enabling information exchange among sub-images via visual registers. Extensive experiments demonstrate FALCON's superiority in high-resolution understanding.
+
+# 6. Acknowledgement
+
+This study is supported by National Natural Science Foundation of China (Grant No. 62306090, No. U24A20328), Natural Science Foundation of Guangdong Province of China (Grant No. 2024A1515010147), Shenzhen Science and Technology Program (KQTD20240729102207002), Natural Science Foundation of Beijing, China (Grant No. L254018), Jiangsu Science and Technology Major Program (Grant No. BG2024041) and China Postdoctoral Science Foundation (Grant No. 2024M764192).
+
+# References
+
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+        "text": "FA: Forced Prompt Learning of Vision-Language Models for Out-of-Distribution Detection",
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+        "text": "Xinhua Lu $^{1,2,4}$ , Runhe Lai $^{1,2,4}$ , Yanqi Wu $^{1,2,4}$ , Kanghao Chen $^{3\\dagger}$ , Wei-Shi Zheng $^{1,2,4}$ , Ruixuan Wang $^{1,2,4\\dagger}$ $^{1}$ Sun Yat-sen University  $^{2}$ Peng Cheng Laboratory  \n $^{3}$ Hong Kong University of Science and Technology (Guangzhou)  \n $^{4}$ Key Laboratory of Machine Intelligence and Advanced Computing",
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+        "text": "{luxh55, lairh5, wuyq268}@mail2.sysu.edu.cn, kchen879@connect.hkust-gz.edu.cn, wszheng@ieee.org, wangruix5@mail.sysu.edu.cn",
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+        "text": "Abstract",
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+        "text": "Pre-trained vision-language models (VLMs) have advanced out-of-distribution (OOD) detection recently. However, existing CLIP-based methods often focus on learning OOD-related knowledge to improve OOD detection, showing limited generalization or reliance on external largescale auxiliary datasets. In this study, instead of delving into the intricate OOD-related knowledge, we propose an innovative CLIP-based framework based on Forced prompt leArning (FA), designed to make full use of the InDistribution (ID) knowledge and ultimately boost the effectiveness of OOD detection. Our key insight is to learn a prompt (i.e. forced prompt) that contains more diversified and richer descriptions of the ID classes beyond the textual semantics of class labels. Specifically, it promotes better discernment for ID images, by forcing more notable semantic similarity between ID images and the learnable forced prompt. Moreover, we introduce a forced coefficient, encouraging the forced prompt to learn more comprehensive and nuanced descriptions of the ID classes. In this way, FA is capable of achieving notable improvements in OOD detection, even when trained without any external auxiliary datasets, while maintaining an identical number of trainable parameters as CoOp. Extensive empirical evaluations confirm our method consistently outperforms current state-of-the-art methods. Code is available at https://github.com/0xFIFA/FA.",
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+        "text": "1. Introduction",
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+        "text": "AI models often encounter Out-of-Distribution (OOD) samples [14, 25, 28, 38], which differ from the distribution of the training data, when deployed in real-world applications.",
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+        "image_caption": [
+            "Figure 1. Comparison of CLIP-based OOD detection methods. Existing methods focus on OOD-related knowledge to learn a complex ID/OOD decision boundary as shown in the orange area in (b). In contrast, our FA aims to fully exploit ID knowledge by forcing the model to learn richer descriptions of the ID classes beyond the textual semantics of class labels. These richer descriptions of the ID classes compared to the reference text allow better discernment of ID/OOD samples (orange vs. blue area in (a))."
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+        "text": "Detecting OOD data is vital for the reliability of AI systems. This problem becomes harder in fields like intelligent diagnosis, where only a small amount of labeled data is available, motivating the problem of few-shot OOD detection.",
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+        "text": "To tackle the OOD detection problem, previous single-modal post-hoc methods [14, 16, 24, 27, 41] achieve notable success based on a model pre-trained on the ID dataset. However, they come with limitations, such as requiring substantial computational resources and annotation costs for training, which hinder the performance of few-shot OOD detection. With the development of large pre-trained vision-language models (VLMs) like CLIP [37], few-shot OOD detection has achieved remarkable performance. Most of the CLIP-based OOD detection methods [30, 32] focus on",
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+        "text": "CVF",
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+        "text": "This ICCV 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": "† Corresponding author.",
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+    {
+        "type": "page_number",
+        "text": "1152",
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+    {
+        "type": "text",
+        "text": "leveraging the powerful generalization capability of CLIP to improve OOD detection.",
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+    {
+        "type": "text",
+        "text": "Recent CLIP-based OOD detection methods [1, 11, 23, 33, 34, 46, 48] aim to learn OOD-related knowledge to improve OOD detection performance. For example, recent CLIP-based works [11, 46] improve OOD detection by relying on training on external large-scale auxiliary datasets, which entails significant resource overhead. To eliminate dependence on external datasets, existing methods [1, 33, 48] learn OOD-related knowledge from exposed outliers based only on ID training data, such as background regions in ID training images. However, these OOD features extracted from specific regions are difficult to match with infinite OOD data encountered in practice. Moreover, some methods [23, 34] aim to learn negative prompts semantically opposite to the ID class labels, while these limited negative prompts are often insufficient to capture the distinctions between the diverse and numerous OOD data and the ID data. Overall, improving OOD detection by learning OOD-related knowledge shows inherent limitations or requires significant computational resources as well as labor costs. Inspired by the method [44] for open-set recognition, which demonstrates that enhancing closed-set accuracy can typically improve open-set recognition capabilities, we are motivated to explore ways to improve the identification of ID images, thereby enhancing OOD detection performance.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, rather than focusing on the intricate OOD-related knowledge, we propose a novel CLIP-based framework based on Forced prompt leArning (FA), which aims to fully exploit the ID knowledge and ultimately improve OOD detection. Our key insight is to learn a prompt that contains richer knowledge beyond the textual semantics of class labels. It facilitates advanced discernment for ID images, by forcing higher semantic similarity between ID images and the learnable prompt (i.e. forced prompt), which provides more diversified and richer descriptions of the ID classes. In this way, FA can achieve significant improvements in OOD detection performance, even when trained without any additional external data, while maintaining the same number of learnable parameters as CoOp [54].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we introduce a novel forced prompt along with the original prompt, both of which are initialized identically. FA preserves the generalization capability of the VLMs (i.e. CLIP) by freezing the original prompt and optimizing a trainable copy (i.e. forced prompt). In particular, the forced prompt treats the original prompt as a reference, while forcing the text features associated with the forced prompt to be more salient compared to those associated with the original prompt. In this way, it effectively improves the OOD performance even without sacrificing the ID classification capability of the model. Additionally, we introduce a forced coefficient, encouraging the forced",
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+    {
+        "type": "text",
+        "text": "prompt to learn more comprehensive connotations. Experimentally, FA achieves superior few-shot OOD detection performance across diverse OOD benchmarks. Compared to current SOTA methods [48] that focus on learning OOD-related knowledge, our method significantly reduces the average FPR95 score from  $31.62\\%$  to  $27.81\\%$  and improves the average AUROC from  $92.01\\%$  to  $93.26\\%$  even in 1-shot OOD detection on ImageNet-1k. The main contributions are summarized as follows:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- We propose a simple yet effective framework, which fully exploits the ID knowledge to improve OOD detection without focusing on intricate OOD-related knowledge.",
+            "- We present a Forced prompt leArning (FA) strategy to exploit richer knowledge beyond the textual semantics of class labels.",
+            "- We evaluate our method on diverse OOD benchmarks, showing that our model consistently outperforms current state-of-the-art methods."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Prompt Learning. In recent years, pre-trained vision-language models (VLMs) such as CLIP [37] have demonstrated powerful few-shot learning capabilities in both visual and textual domains. However, the design of the prompt greatly affects the performance of VLMs for downstream tasks, which may require manually crafting numerous prompts. Inspired by prompt learning studies in natural language processing (NLP) [26], CoOp [54] uses a set of learnable context vectors to transfer CLIP for specific downstream tasks, becoming a pioneering method for subsequent studies [4, 33, 53]. Currently, prompt learning is widely used in OOD detection mainly to represent various OOD-related knowledge. In this work, we learn the forced prompt, which contains richer descriptions of the ID classes to improve OOD detection.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Out-of-Distribution Detection. Conventional methods explore OOD detection for single-modal models. One line of studies designs score functions to differentiate ID and OOD data based on output from the pre-trained models, such as logit output [14, 16, 24, 27] or outputs from the penultimate layer [22, 41, 42, 50]. These methods are called post-hoc methods. Another line of studies [9, 10, 18, 31, 39, 43, 55] adopts various training strategies to learn a reliable decision boundary between ID and OOD data.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, the development of OOD detectors based on VLMs, especially CLIP, has received much attention as VLMs have demonstrated their remarkable generalization capability in both visual and textual domains. Some studies leverage real outlier information from external auxiliary OOD datasets [11, 46] or extensive corpora [5, 20] to promote OOD detection. However, this is impractical in real-world scenarios, where outliers are infinite and agnostic.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "1153",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/d6c07d7693e54a2e5e7e9bf056c4470e042bca80776d2e49bb596b306ede69d4.jpg",
+        "image_caption": [
+            "Figure 2. Overview of the proposed FA framework. Our framework includes the learnable forced prompt and the frozen original prompt, both of which are initialized identically by a manual template \"a photo of a [class-c]\". The learnable forced prompt treats the frozen original prompt as a reference, forcing its text features to become more salient compared to those generated by the original prompt. The richer and more diversified description of ID classes learned by FA can ultimately improve OOD detection."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To eliminate the dependence on external data, recent methods [1, 23, 32, 33, 48] were developed under the assumption that only ID data are available. As a representative zero-shot method that only uses available ID labels, MCM [30] employs softmax scaling to align visual features with ID text concepts for OOD detection. GL-MCM [32] further introduces a local maximum concept matching(L-MCM) score to improve the separability of the local information. Compared with zero-shot methods, which may undergo a domain gap with ID downstream data, prompt learning methods achieve better OOD detection performance with access to few-shot ID samples. For prompt learning OOD detection methods, LoCoOp [33] and SCT [48] keep the textual embeddings of ID classes away from ID-irrelevant local region embeddings in the multi-modal embedding space by their proposed entropy maximization strategy, which ensures that OOD embeddings can be dissimilar to any textual embedding of ID classes. To detect challenging OOD samples to improve OOD detection, ID-like [1] explores the vicinity of ID samples to construct OOD samples correlated to the ID and refines the additional \"ID-like\" text embeddings to fine-grained differences. In addition, NegPrompt [23] and LSN [34] introduce the negative connotations of ID categories which can be represented by additional negative prompts, enabling more accurate detection of OOD samples. Overall, various OOD-related knowledge is commonly adopted to address the model's overconfidence in current research. In this work, we focus on leveraging ID knowledge to improve OOD detection, instead of exploring complex OOD-related knowledge.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Prompt Learning with CLIP. CLIP contains an image encoder  $f(\\cdot)$  and a text encoder  $g(\\cdot)$ , designed to extract features from images and text descriptions respectively. Generally, for an ID dataset which contains  $C$  categories, the hand-crafted prompt  $\\hat{\\mathbf{u}}_c$  \"a photo of a [class-c]\" is designed to match images, where class-c represents the class name. Formally, these prompts are individually encoded in  $\\hat{\\mathbf{t}}_c = g(\\hat{\\mathbf{u}}_c) \\in \\mathbb{R}^{d \\times 1}$ ,  $c = 1, \\dots, C$ . Given an image  $\\mathbf{x}$ , it can be encoded in  $\\mathbf{z} = f(\\mathbf{x}) \\in \\mathbb{R}^{d \\times 1}$ . Because image features and corresponding text features are aligned on the multimodal embedding space, the cosine similarity  $\\cos(\\mathbf{z}, \\hat{\\mathbf{t}}_c)$  of  $\\mathbf{z}$  and  $\\hat{\\mathbf{t}}_c$  can represent the matching degree between the image  $\\mathbf{x}$  and text description  $\\hat{\\mathbf{u}}_c$ . Therefore, if the text feature  $\\mathbf{t}_c$  of class  $c$  has the highest similarity to  $\\mathbf{z}$ , the image  $\\mathbf{x}$  will be considered to be class  $c$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To effectively transfer CLIP to downstream image recognition tasks, CoOp [54] sets a portion of tokens in the text prompt as continuous learnable parameters. Concretely, CoOp initializes the text prompts as  $\\mathbf{u}_c = [\\mathbf{v}_1,\\dots ,\\mathbf{v}_L,\\mathbf{w}_c],c\\in \\{1,\\dots ,C\\}$ , where  $L$  is the length of the prompt's tokens,  $\\mathbf{v}_i$  ( $i\\in \\{1,\\ldots ,L\\}$ ) is the learnable vector with the same dimension as the word embedding and  $\\mathbf{w}_c$  is the word embedding for the class name of class  $c$ . The text prompt  $\\mathbf{u}_c$  is encoded into features  $\\mathbf{t}_c = g(\\mathbf{u}_c)$ . Together with the image feature  $\\mathbf{z}$ , the probability for the image  $\\mathbf{x}$  to be classified into class  $c$  is defined as",
+        "bbox": [
+            511,
+            659,
+            908,
+            825
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (y = c \\mid \\mathbf {x}) = \\frac {e ^ {\\cos (\\mathbf {z} , \\mathbf {t} _ {c}) / \\tau}}{\\sum_ {j = 1} ^ {C} e ^ {\\cos (\\mathbf {z} , \\mathbf {t} _ {j}) / \\tau}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            835,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  is a fixed temperature scaling hyper-parameter.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "1154",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overall, the prompt's tokens can be trained to align with training data by minimizing the cross-entropy loss with the prediction probability from Eq. (1).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "OOD Detection. In the OOD detection task, the model is expected to determine whether a test image belongs to one of the learned ID classes. Therefore, OOD detection can be seen as a binary classification problem to distinguish ID images from OOD images in a test set  $\\mathcal{D}_{test}$  as follows",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nD (\\mathbf {x}) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} S (\\mathbf {x}) \\geq \\mu \\\\ 0, & \\text {i f} S (\\mathbf {x}) <   \\mu \\end{array} , \\right. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            199,
+            223,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{x} \\in \\mathcal{D}_{test}$ , 1 and 0 respectively indicate that  $\\mathbf{x}$  is classified as the ID class and the OOD class by the OOD detector  $D(\\cdot)$ ,  $S(\\cdot)$  is certain score function, and  $\\mu$  is a predefined threshold constant.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Methodology",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Overview",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this study, we propose a novel CLIP-based framework based on Forced prompt leArning (FA), designed to fully exploit the ID knowledge from few-shot ID samples by forcing the prompt to learn richer knowledge beyond the textual semantics of class labels. As shown in Fig. 2, we introduce a forced prompt along with the original prompt, both of which are initialized with the same semantics. By freezing the original prompt and optimizing a trainable copy, ID images will show higher semantic similarity to the forced prompt compared to the original prompt. Moreover, to encourage descriptions of ID classes learned by the forced prompt to become more detailed and comprehensive, we also introduce a forced coefficient. During testing, the model is capable of effectively distinguishing between ID data and OOD data, benefiting from the diversified descriptions of the ID classes provided by the forced prompt.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Forced prompt learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Merely the semantic information conveyed by class names is insufficient to comprehensively encompass the discriminative information of each class. In order to explore richer semantic descriptions of the ID classes beyond the textual semantics of class labels, a novel forced prompt along with the original prompt is proposed. To implement the above objective, we introduce a simple yet effective training strategy using the forced cross-entropy (FCE) loss based on the forced prompt as follows",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {F C E} = \\mathbb {E} _ {\\left(\\mathbf {x}, y _ {c}\\right) \\sim \\mathcal {D} _ {t r a i n} ^ {I D}} \\left[ - \\log \\frac {e ^ {s _ {c} ^ {f} / \\tau}}{\\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {f} / \\tau} + \\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {o} / \\tau}} \\right], \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            811,
+            480,
+            867
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the ID training dataset  $\\mathcal{D}_{train}^{ID}$  consists of ID image-label pairs  $(\\mathbf{x},y_{c})$ ,  $s_j^f = \\cos (\\mathbf{z},\\mathbf{t}_j^f)$  and  $s_j^o = \\cos (\\mathbf{z},\\mathbf{t}_j^o)$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "represent the similarity between the image feature and the prompt feature corresponding to the forced prompt and the original prompt, respectively.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Based on this loss function, the ID image features will be forced to show higher cosine similarity to the learnable forced prompt compared to the original text prompt. This is because the cosine similarity between the ID image features and the original text prompt is already high before any further prompt learning. Consequently, the forced prompt is forced to uncover richer discriminative information of ID classes, so that the text features of the forced prompt achieve a higher cosine similarity with the image features compared to those of the original prompt. Benefiting from this information specific to the ID classes, the cosine similarity between the image features of an OOD image and the text features of both prompts may exhibit less distinction compared to those of the ID data. Therefore, even when trained without any reliance on external auxiliary datasets, the detector will have a notable capability to distinguish ID data from OOD data.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However, this naive FCE loss may not work effectively because of its inherent limitations. Concretely, employing random initialization for both prompts fails to fully leverage the semantic information provided by CLIP's prior knowledge, resulting in limited performance. To solve this limitation, we propose to initialize the forced prompt using the manual template (i.e. \"a photo of a [class-c]\") identified to the original prompt. In this way, both prompts with manual initialization will have clear semantic information compared to random initialization, thereby improving the model's generalization capability. Specifically, the class labels are utilized in both prompts by concatenating with the prompt embedding to provide foundational semantic information related to the category names, based on CLIP's prior knowledge. In particular, for the forced prompt, we adopt the shared learnable vector across all classes rather than the independent learnable vector for each class. This choice is inspired by CoOp [54], which demonstrates that using an independent learnable vector mostly underperforms the shared learnable vector in challenging low-data scenarios since the former has more parameters and requires more data for training. Formally, we utilize the embeddings of the manual template to initialize the prompt's embeddings of both prompts, formulated as  $\\mathbf{u}_c = [\\mathbf{v}_1,\\dots ,\\mathbf{v}_L,\\mathbf{w}_c], c\\in$ $\\{1,\\dots ,C\\}$ , which will be fed to the text encoder to obtain prompt feature  $\\mathbf{t}_c$  (see Section 3). Here,  $L$  is the length of the token (e.g., for the \"a photo of a\",  $L = 4$ ). Then we freeze the original prompt and the class label part of both the prompts to preserve the generalization capability of CLIP, while only making the forced prompt learnable. Note that our method effectively improves OOD detection performance while maintaining consistency with CoOp in the number of learnable parameters without leveraging ad",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "1155",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ditional learnable prompts, unlike existing work [1, 23, 34].",
+        "bbox": [
+            89,
+            90,
+            480,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Although the above prompt design achieves moderate performance, relying solely on a single original prompt as a reference is somewhat insufficient to develop a comprehensive capability, particularly with the limitations of ID data (e.g., few-shot OOD). To encourage the forced prompt to capture more comprehensive and nuanced descriptions of the ID classes, we introduce a forced coefficient  $K$  ( $K \\geq 0, K \\in \\mathbb{N}$ ), which indicates the intensity with which the model is compelled to learn from the data. Formally, we first derive the original text features  $\\{\\mathbf{t}_1^o, \\dots, \\mathbf{t}_C^o\\}$  from the original prompt and the image features  $\\mathbf{z}$  from the corresponding image. Then, we compute the cosine similarity between the original text features and the image features for  $K$  iterations, which will be used in the subsequent computation of the cross-entropy loss function. Notably, when  $K = 0$ , no original prompt is used, and the model operates equivalently to CoOp. Based on the forced coefficient, we refine Eq. (3) as follows",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {F C E - K} = \\mathbb {E} _ {\\left(\\mathbf {x}, y _ {c}\\right) \\sim \\mathcal {D} _ {t r a i n} ^ {I D}} \\left[ - \\log \\frac {e ^ {s _ {c} ^ {f} / \\tau}}{\\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {f} / \\tau} + K \\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {o} / \\tau}} \\right]. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            391,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Based on this function, the cosine similarity between the ID image features and the text features of the forced prompt must become more salient as the coefficient  $K$  increases.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Model inference",
+        "text_level": 1,
+        "bbox": [
+            89,
+            502,
+            251,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During model inference, for the downstream classification task, we adopt the same strategy as CLIP, depending solely on the forced prompt [1]. For the OOD detection task, our method can be flexibly combined with different score functions, such as the MCM [30] score and the GL-MCM [32] score. The MCM score is defined as the maximum similarity between the global image features  $\\mathbf{z}^g$  (i.e.  $\\mathbf{z}$ ) and all text features  $\\mathbf{t}_c^a$  (i.e. the concatenation of text features  $\\mathbf{t}_c^f$  and  $\\mathbf{t}_c^o$ ) after applying softmax with temperature  $\\tau_0$ , i.e.,",
+        "bbox": [
+            89,
+            525,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {\\mathrm {M C M}} (\\mathbf {x}) = \\max  _ {c} \\frac {e ^ {\\cos \\left(\\mathbf {z} ^ {g} , \\mathbf {t} _ {c} ^ {a}\\right) / \\tau_ {0}}}{\\sum_ {j = 1} ^ {C} e ^ {\\cos \\left(\\mathbf {z} ^ {g} , \\mathbf {t} _ {j} ^ {f}\\right) / \\tau_ {0}} + K e ^ {\\cos \\left(\\mathbf {z} ^ {g} , \\mathbf {t} _ {j} ^ {o}\\right) / \\tau_ {0}}}, \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "while the GL-MCM score simultaneously considers both global and local features, which can be expressed as",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {\\mathrm {G L - M C M}} (\\mathbf {x}) = S _ {\\mathrm {M C M}} (\\mathbf {x}) + S _ {\\mathrm {L - M C M}} (\\mathbf {x}), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            770,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {\\mathrm {L - M C M}} (\\mathbf {x}) = \\max  _ {i, c} \\frac {e ^ {\\cos \\left(\\mathbf {z} _ {i} ^ {l} , \\mathbf {t} _ {c} ^ {a}\\right) / \\tau_ {0}}}{\\sum_ {j = 1} ^ {C} e ^ {\\cos \\left(\\mathbf {z} _ {i} ^ {l} , \\mathbf {t} _ {j} ^ {f}\\right) / \\tau_ {0}} + K e ^ {\\cos \\left(\\mathbf {z} _ {i} ^ {l} , \\mathbf {t} _ {j} ^ {o}\\right) / \\tau_ {0}}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            96,
+            800,
+            480,
+            854
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{z}_i^l (i\\in \\{1,\\dots ,N\\})$  represents  $N$  extracted local features generated by CLIP's image encoder [32, 33]. We set  $\\tau_0 = 1$  during model inference.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+            90,
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+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental details",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We use a popular benchmark for conventional OOD detection [19, 30, 32, 33], where ImageNet-1k [7] serves as the ID dataset, and the OOD datasets are iNaturalist [17], SUN [47], Places [52], and Texture [6]. Moreover, inspired by existing studies [1, 2], we use datasets like OpenImage-O [45], NINCO [2], and ImageNet-O [15], which are cleaner and more realistic, to simulate the more challenging OOD detection. Besides, we also utilize other widely adopted datasets for few-shot settings as ID datasets [49, 51, 54], which include StanfordCars [21], UCF101 [40], Caltech101 [12], Flowers102 [35], EuroSAT [13], FGVCAircraft [29], OxfordPets [36], and Food101 [3], considering factors such as image resolution and the number of classes.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Setup. Following previous studies [33], we use the ViTB/16 [8] as the backbone model. For our model, when using ImageNet-1k as the ID dataset, the epochs are respectively set to 30 and 50 for the 1-shot and 16-shot settings, while for other ID datasets, we set the epoch to 200 following CoOp [54]. The value of forced coefficient  $K$  is uniformly set to 3, which will be further discussed in the sensitivity study. Other hyperparameters are as follows: learning rate  $= 2\\mathrm{e} - 3$ , batch size  $= 160$ , SGD (momentum  $= 0.9$ , weight decay  $= 5\\mathrm{e} - 4$ ) as the optimizer with a cosine scheduler,  $\\tau = 1$  in Eq. (3) and Eq. (4). All experiments on our model can be conducted on a single Nvidia A30 GPU. The average experiment results (including our reproductions) over four runs are reported for comparison.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Comparison Methods. To validate the effectiveness of our FA fairly, we mainly compare it with CLIP-based OOD detection methods that do not use real outliers (e.g. OOD labels). For previous post-hoc methods, including MSP [14], ODIN [24], Energy [27], ReAct [41], and MaxLogit [16], we adapt these methods with the CLIP image encoder as the CLIP-based post-hoc methods. For zero-shot methods, we select MCM [30], GL-MCM [32] and CLIPN [46] as baselines. For prompt learning methods, we adopt CoOp [54], LoCoOp [33], IDLike [1], and SCT [48] as baselines.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Metrics. For evaluation, we adopt the following metrics: (1) The False Positive Rate at  $95\\%$  True Positive Rate for in-distribution samples (FPR95); (2) The Area Under the Receiver Operating Characteristic Curve (AUROC); (3) In-distribution data classification Top-1 accuracy (ID ACC).",
+        "bbox": [
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+            714,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.2. Main results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Conventional OOD Detection. Table 1 summarizes our comparison results on the ImageNet-1k benchmarks, which show that our FA achieves state-of-the-art OOD detection performance among other CLIP-based methods under different few-shot settings (More details under the 4-shot set",
+        "bbox": [
+            511,
+            824,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1156",
+        "bbox": [
+            483,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/df04df2d128cd259127b9519eb43a98675da97ff4d11497a8e58d74958be8209.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">iNaturalist</td><td colspan=\"2\">SUN</td><td colspan=\"2\">Places</td><td colspan=\"2\">Textures</td><td colspan=\"2\">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td colspan=\"11\">Zero-shot methods</td></tr><tr><td>MCM</td><td>31.95</td><td>94.16</td><td>37.22</td><td>92.55</td><td>42.98</td><td>90.10</td><td>58.35</td><td>85.83</td><td>42.63</td><td>90.66</td></tr><tr><td>GL-MCM</td><td>15.09</td><td>96.72</td><td>29.08</td><td>93.41</td><td>37.07</td><td>90.37</td><td>58.94</td><td>83.11</td><td>35.04</td><td>90.90</td></tr><tr><td>CLIPN</td><td>19.17</td><td>96.17</td><td>26.43</td><td>94.02</td><td>32.26</td><td>92.62</td><td>41.23</td><td>90.12</td><td>30.21</td><td>93.19</td></tr><tr><td colspan=\"11\">CLIP-based post-hoc methods</td></tr><tr><td>\\( MSP^† \\)</td><td>74.57</td><td>77.74</td><td>76.95</td><td>73.97</td><td>79.72</td><td>72.18</td><td>73.66</td><td>74.84</td><td>76.22</td><td>74.68</td></tr><tr><td>\\( ODIN^† \\)</td><td>98.93</td><td>57.73</td><td>88.72</td><td>78.42</td><td>87.80</td><td>76.88</td><td>85.47</td><td>71.49</td><td>90.23</td><td>71.13</td></tr><tr><td>\\( Energy^† \\)</td><td>64.98</td><td>87.18</td><td>46.42</td><td>91.17</td><td>57.40</td><td>87.33</td><td>50.39</td><td>88.22</td><td>54.80</td><td>88.48</td></tr><tr><td>\\( ReAct^† \\)</td><td>65.57</td><td>86.87</td><td>46.17</td><td>91.04</td><td>56.85</td><td>87.42</td><td>49.88</td><td>88.13</td><td>54.62</td><td>88.37</td></tr><tr><td>\\( MaxLogit^† \\)</td><td>60.88</td><td>88.03</td><td>44.83</td><td>91.16</td><td>55.54</td><td>87.45</td><td>48.72</td><td>88.63</td><td>52.49</td><td>88.82</td></tr><tr><td colspan=\"11\">Prompt learning based methods</td></tr><tr><td>\\( CoOp_{MCM} \\)</td><td>41.14±9.39</td><td>91.47±2.12</td><td>39.06±4.17</td><td>91.68±0.83</td><td>45.38±4.88</td><td>89.16±1.28</td><td>51.37±3.09</td><td>87.82±1.12</td><td>44.24±1.39</td><td>90.03±0.32</td></tr><tr><td>\\( CoOp_{GL} \\)</td><td>23.30±6.37</td><td>94.59±1.51</td><td>32.08±3.87</td><td>92.21±0.95</td><td>39.22±4.55</td><td>89.59±1.58</td><td>55.78±3.46</td><td>83.26±1.38</td><td>37.59±0.34</td><td>89.91±0.31</td></tr><tr><td>\\( LoCoOp_{MCM} \\)</td><td>36.64±4.87</td><td>92.78±0.93</td><td>31.86±3.79</td><td>93.50±0.92</td><td>38.81±3.37</td><td>90.70±0.97</td><td>48.11±2.31</td><td>89.43±0.68</td><td>38.85±2.67</td><td>91.59±0.58</td></tr><tr><td>\\( LoCoOp_{GL} \\)</td><td>21.97±2.91</td><td>95.39±0.59</td><td>24.95±2.37</td><td>94.42±0.59</td><td>34.14±2.66</td><td>91.14±0.69</td><td>49.04±2.77</td><td>87.73±0.96</td><td>32.53±2.19</td><td>92.17±0.47</td></tr><tr><td>IDLike</td><td>17.73±1.91</td><td>96.68±0.31</td><td>48.17±1.39</td><td>89.53±0.58</td><td>50.43±6.58</td><td>88.27±2.27</td><td>29.12±7.64</td><td>93.25±2.16</td><td>36.36±3.86</td><td>91.93±1.18</td></tr><tr><td>\\( LSN^† \\)</td><td>59.28±7.02</td><td>87.20±3.15</td><td>40.15±0.82</td><td>91.47±0.14</td><td>46.11±1.86</td><td>88.74±0.57</td><td>60.34±0.14</td><td>83.92±0.42</td><td>51.47±1.53</td><td>87.84±0.58</td></tr><tr><td>\\( NegPrompt^† \\)</td><td>65.03±8.69</td><td>84.56±2.52</td><td>44.39±1.66</td><td>89.63±0.66</td><td>51.31±6.21</td><td>86.55±2.19</td><td>87.60±1.61</td><td>63.76±3.02</td><td>62.08±3.71</td><td>81.13±1.78</td></tr><tr><td>\\( SCT_{MCM} \\)</td><td>41.93±12.17</td><td>91.77±2.40</td><td>30.39±2.17</td><td>93.76±0.39</td><td>38.73±2.54</td><td>90.78±0.34</td><td>46.78±3.51</td><td>88.96±1.16</td><td>39.46±3.39</td><td>91.32±0.90</td></tr><tr><td>\\( SCT_{GL} \\)</td><td>20.57±10.2</td><td>95.63±1.89</td><td>24.56±3.03</td><td>94.39±0.53</td><td>33.27±2.96</td><td>91.27±0.57</td><td>48.12±2.97</td><td>86.76±0.89</td><td>31.62±3.19</td><td>92.01±0.77</td></tr><tr><td>\\( FA_{MCM}(Ours) \\)</td><td>25.50±2.72</td><td>94.72±0.27</td><td>36.24±3.15</td><td>92.40±0.95</td><td>35.38±2.75</td><td>91.99±0.68</td><td>28.34±0.87</td><td>93.95±0.19</td><td>31.37±1.07</td><td>93.25±0.32</td></tr><tr><td>\\( FA_{GL}(Ours) \\)</td><td>14.12±1.32</td><td>96.76±0.10</td><td>29.99±1.57</td><td>92.95±0.66</td><td>32.48±1.48</td><td>91.83±0.49</td><td>34.66±1.21</td><td>91.50±0.36</td><td>27.81±0.44</td><td>93.26±0.27</td></tr><tr><td colspan=\"11\">Prompt learning based methods</td></tr><tr><td>\\( CoOp_{MCM} \\)</td><td>30.26±1.98</td><td>93.43±0.81</td><td>34.69±0.43</td><td>92.59±0.14</td><td>41.91±0.71</td><td>90.11±0.23</td><td>44.68±2.11</td><td>89.95±0.48</td><td>37.89±0.71</td><td>91.52±0.29</td></tr><tr><td>\\( CoOp_{GL} \\)</td><td>15.96±1.67</td><td>96.11±0.55</td><td>27.26±1.99</td><td>93.29±0.46</td><td>35.36±2.08</td><td>90.58±0.64</td><td>48.63±2.11</td><td>86.11±0.59</td><td>31.81±1.27</td><td>91.51±0.39</td></tr><tr><td>\\( LoCoOp_{MCM} \\)</td><td>27.35±3.19</td><td>94.12±0.80</td><td>30.93±1.19</td><td>93.75±0.26</td><td>38.26±1.53</td><td>91.12±0.27</td><td>41.36±2.56</td><td>90.99±0.53</td><td>34.47±0.73</td><td>92.49±0.14</td></tr><tr><td>\\( LoCoOp_{GL} \\)</td><td>18.46±1.38</td><td>95.85±0.63</td><td>22.43±0.96</td><td>95.15±0.22</td><td>31.53±1.52</td><td>92.15±0.22</td><td>43.35±3.12</td><td>89.38±0.78</td><td>28.94±1.29</td><td>93.13±0.17</td></tr><tr><td>IDLike</td><td>19.23±10.5</td><td>96.70±1.58</td><td>54.15±2.88</td><td>87.64±1.19</td><td>56.63±0.07</td><td>85.86±0.44</td><td>34.69±6.41</td><td>91.90±2.31</td><td>41.18±1.73</td><td>90.53±0.01</td></tr><tr><td>\\( LSN^† \\)</td><td>36.17±4.81</td><td>92.66±1.16</td><td>34.27±0.44</td><td>93.53±0.20</td><td>41.47±0.85</td><td>90.52±0.37</td><td>46.43±0.60</td><td>89.38±0.24</td><td>39.58±0.73</td><td>91.53±0.09</td></tr><tr><td>\\( NegPrompt^† \\)</td><td>37.79±0.11</td><td>90.49±0.01</td><td>32.11±3.77</td><td>92.25±1.00</td><td>35.52±0.41</td><td>91.16±0.03</td><td>43.93±9.09</td><td>88.38±3.31</td><td>37.34±1.41</td><td>90.57±0.59</td></tr><tr><td>\\( SCT_{MCM} \\)</td><td>29.41±2.19</td><td>93.76±0.55</td><td>27.28±2.80</td><td>94.22±0.40</td><td>36.35±2.13</td><td>91.16±0.33</td><td>42.25±1.89</td><td>90.52±0.48</td><td>33.82±1.78</td><td>92.42±0.35</td></tr><tr><td>\\( SCT_{GL} \\)</td><td>15.19±2.16</td><td>96.71±0.44</td><td>20.00±0.61</td><td>95.57±0.11</td><td>29.71±0.85</td><td>92.37±0.12</td><td>44.17±0.82</td><td>88.59±0.39</td><td>27.27±0.44</td><td>93.31±0.17</td></tr><tr><td>\\( FA_{MCM}(Ours) \\)</td><td>25.79±1.48</td><td>94.29±0.35</td><td>33.54±1.17</td><td>93.02±0.19</td><td>33.77±1.64</td><td>92.64±0.42</td><td>23.17±1.31</td><td>95.14±0.26</td><td>29.07±1.11</td><td>93.77±0.19</td></tr><tr><td>\\( FA_{GL}(Ours) \\)</td><td>14.49±1.27</td><td>96.48±0.29</td><td>27.65±1.08</td><td>93.46±0.18</td><td>31.09±1.38</td><td>92.44±0.34</td><td>29.50±0.89</td><td>92.93±0.18</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/455dd344dd79e267e82084b1808e48db370c8956b7fe646176768df80503b981.jpg",
+        "table_caption": [
+            "Table 1. Comparison results on ImageNet-1k OOD benchmarks. All results using the same backbone ViT-B/16. The results marked with  $\\dagger$  are taken from [48]; the others are our reproductions. The prompt learning based methods are run under four trials, reporting the mean and standard deviation of the performance. The subscripts  ${}_{\\mathrm{{MCM}}}$  and  ${}_{\\mathrm{{GL}}}$  indicate the use of the MCM score and the GL-MCM score. The best and second-best results are indicated in bold and underline.  $\\uparrow$  indicates larger values are better;  $\\downarrow$  indicates smaller values are better. All values are percentages."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>1-shot</td><td>4-shot</td><td>16-shot</td></tr><tr><td>CoOp</td><td>67.44±0.50</td><td>69.71±0.07</td><td>70.99±0.14</td></tr><tr><td>LoCoOp</td><td>67.40±0.64</td><td>69.55±0.10</td><td>71.53±0.17</td></tr><tr><td>IDLike</td><td>68.17±0.57</td><td>68.91±0.14</td><td>69.46±0.02</td></tr><tr><td>SCT</td><td>68.63±0.13</td><td>69.93±0.22</td><td>71.78±0.05</td></tr><tr><td>FA(Ours)</td><td>68.67±0.39</td><td>69.96±0.04</td><td>71.02±0.09</td></tr></table>",
+        "bbox": [
+            117,
+            670,
+            455,
+            779
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Comparison results in ID Top-1 accuracy on ImageNet-1k under different few-shot settings. Other notations are the same as Tab. 1.",
+        "bbox": [
+            89,
+            784,
+            482,
+            825
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ting are provided in the Appendix A). Specifically, in the 16-shot setting, FA with GL-MCM score  $\\left(\\mathrm{FA}_{\\mathrm{GL}}\\right)$  outperforms the best baseline  $\\mathrm{SCT}_{\\mathrm{GL}}$  (average FPR95 of  $25.68\\%$  vs.  $27.27\\%$ , and average AUROC of  $93.82\\%$  vs.  $93.31\\%$ ).",
+        "bbox": [
+            89,
+            839,
+            483,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Additionally, in the 1-shot setting,  $\\mathrm{FA}_{\\mathrm{GL}}$  surpasses  $\\mathrm{SCT}_{\\mathrm{GL}}$  by a large margin, showing improvements of at least  $1.25\\%$  and  $3.81\\%$  on average AUROC and FPR95. More importantly, even the average score of  $\\mathrm{FA}_{\\mathrm{MCM}}$  has exceeded  $\\mathrm{SCT}_{\\mathrm{GL}}$  in the 1-shot setting. Moreover, our FA effectively improves the OOD performance without sacrificing the ID classification capability of the model, as shown in Tab. 2.",
+        "bbox": [
+            511,
+            672,
+            906,
+            779
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In particular, we can also observe that our method performs not well on the SUN dataset, as shown in Tab. 1. This is related to the presence of a significant number of samples belonging to ID category in these datasets, as demonstrated by recent studies [1]. In other words, the SUN dataset in the popular OOD benchmark requires more thorough cleaning to be effectively used as an OOD dataset.",
+        "bbox": [
+            511,
+            779,
+            908,
+            883
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Challenging OOD Detection. Recent studies [1, 2] have",
+        "bbox": [
+            511,
+            883,
+            906,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "1157",
+        "bbox": [
+            483,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/686b772dca172fa9cee16de40529ad055d9d0de180ebf534e139582902000e4e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">OpenImage-O</td><td colspan=\"2\">NINCO</td><td colspan=\"2\">ImageNet-O</td><td colspan=\"2\">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>CoOpMCM</td><td>37.95±0.59</td><td>91.99±0.22</td><td>78.00±0.23</td><td>73.00±0.59</td><td>70.14±0.86</td><td>81.34±0.83</td><td>62.03±0.38</td><td>82.11±0.48</td></tr><tr><td>CoOpGL</td><td>32.23±1.00</td><td>92.22±0.25</td><td>72.04±0.81</td><td>75.35±0.88</td><td>67.35±1.19</td><td>78.44±0.94</td><td>57.21±0.96</td><td>81.99±0.58</td></tr><tr><td>LoCoOpMCM</td><td>37.03±0.94</td><td>92.24±0.21</td><td>77.96±0.63</td><td>72.78±0.79</td><td>70.96±0.75</td><td>81.25±0.39</td><td>61.98±0.55</td><td>82.09±0.35</td></tr><tr><td>LoCoOpGL</td><td>33.87±1.23</td><td>92.53±0.07</td><td>75.16±0.92</td><td>72.97±0.39</td><td>68.06±1.92</td><td>81.19±0.25</td><td>59.03±1.27</td><td>82.23±0.17</td></tr><tr><td>IDLike</td><td>54.43±2.35</td><td>87.89±0.45</td><td>78.93±1.79</td><td>69.32±0.42</td><td>84.08±1.45</td><td>67.45±0.86</td><td>72.48±0.89</td><td>74.89±0.28</td></tr><tr><td>SCTMCM</td><td>37.28±1.16</td><td>92.04±0.33</td><td>78.51±0.86</td><td>71.09±1.19</td><td>71.45±0.54</td><td>81.29±0.15</td><td>62.41±0.73</td><td>81.48±0.52</td></tr><tr><td>SCTGL</td><td>32.24±0.34</td><td>92.75±0.17</td><td>74.15±0.53</td><td>73.14±0.94</td><td>68.35±0.62</td><td>80.84±0.45</td><td>58.25±0.39</td><td>82.24±0.44</td></tr><tr><td>FAmCM(Ours)</td><td>37.93±1.65</td><td>91.84±0.45</td><td>70.44±1.24</td><td>77.77±0.94</td><td>63.84±1.36</td><td>82.71±0.30</td><td>57.40±1.34</td><td>84.08±0.47</td></tr><tr><td>FAGL(Ours)</td><td>32.10±0.89</td><td>92.39±0.28</td><td>65.61±1.32</td><td>79.01±0.71</td><td>63.13±0.98</td><td>80.39±0.21</td><td>53.61±0.89</td><td>83.93±0.31</td></tr></table>",
+        "bbox": [
+            91,
+            88,
+            906,
+            237
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c89bb2e0ccfc86f226a8bd042677dedbc56597f4d2e5952389cc4f3c7082576e.jpg",
+        "table_caption": [
+            "Table 3. Challenging OOD detection results on cleaner OOD datasets in the 16-shot setting. We use the same notation as Tab. 1."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">ID Dataset</td><td rowspan=\"2\">Method</td><td colspan=\"2\">iNaturalist</td><td colspan=\"2\">SUN</td><td colspan=\"2\">Places</td><td colspan=\"2\">Textures</td><td colspan=\"2\">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td rowspan=\"7\">UCF101</td><td>CoOpMCM</td><td>14.40±6.61</td><td>97.41±1.36</td><td>37.09±3.94</td><td>93.14±0.48</td><td>40.07±2.77</td><td>91.89±0.65</td><td>33.24±4.21</td><td>93.19±1.22</td><td>31.21±3.58</td><td>93.91±0.45</td></tr><tr><td>CoOpGL</td><td>9.65±6.35</td><td>98.18±0.98</td><td>28.54±5.07</td><td>94.51±0.92</td><td>32.94±1.74</td><td>93.28±0.32</td><td>35.96±2.65</td><td>91.83±1.42</td><td>26.77±3.22</td><td>94.45±0.42</td></tr><tr><td>LoCoOpMCM</td><td>2.38±0.98</td><td>99.21±0.22</td><td>19.73±4.24</td><td>96.11±0.78</td><td>22.57±3.01</td><td>94.96±0.77</td><td>15.89±3.12</td><td>96.12±0.67</td><td>15.14±1.91</td><td>96.60±0.33</td></tr><tr><td>LoCoOpGL</td><td>1.13±0.22</td><td>99.65±0.09</td><td>17.93±4.09</td><td>96.51±0.89</td><td>22.34±4.58</td><td>95.03±1.06</td><td>18.17±3.01</td><td>95.25±0.71</td><td>14.89±2.49</td><td>96.61±0.58</td></tr><tr><td>IDLike</td><td>66.63±27.6</td><td>89.75±5.52</td><td>87.88±6.56</td><td>78.04±6.14</td><td>84.47±12.1</td><td>76.04±8.53</td><td>49.07±11.2</td><td>91.19±2.74</td><td>72.01±14.0</td><td>83.76±5.64</td></tr><tr><td>SCTMCM</td><td>1.51±0.51</td><td>99.44±0.10</td><td>24.17±5.54</td><td>95.21±0.88</td><td>26.62±4.41</td><td>93.75±0.81</td><td>15.34±3.84</td><td>95.98±0.64</td><td>16.91±3.20</td><td>96.09±0.48</td></tr><tr><td>SCTGL</td><td>0.79±0.27</td><td>99.75±0.04</td><td>18.69±2.41</td><td>95.86±0.56</td><td>23.77±2.47</td><td>93.98±0.47</td><td>17.44±2.62</td><td>94.52±0.54</td><td>15.17±1.56</td><td>96.03±0.25</td></tr><tr><td rowspan=\"2\"></td><td>FAmCM(Ours)</td><td>0.12±0.11</td><td>99.94±0.01</td><td>3.06±1.33</td><td>99.34±0.23</td><td>4.68±1.00</td><td>99.08±0.26</td><td>2.68±0.51</td><td>99.31±0.43</td><td>2.63±0.58</td><td>99.42±0.22</td></tr><tr><td>FAGL(Ours)</td><td>0.13±0.02</td><td>99.94±0.02</td><td>4.98±1.02</td><td>99.01±0.22</td><td>7.46±0.86</td><td>98.44±0.27</td><td>5.67±0.83</td><td>98.75±0.19</td><td>4.56±0.47</td><td>99.03±0.13</td></tr><tr><td rowspan=\"7\">EuroSAT</td><td>CoOpMCM</td><td>99.14±0.73</td><td>31.95±9.17</td><td>98.29±0.49</td><td>44.36±4.19</td><td>97.28±0.85</td><td>47.51±4.63</td><td>86.69±4.37</td><td>69.17±3.15</td><td>95.35±1.03</td><td>48.25±3.09</td></tr><tr><td>CoOpGL</td><td>92.45±4.26</td><td>57.59±10.4</td><td>90.97±3.49</td><td>61.89±4.83</td><td>88.69±3.85</td><td>64.00±4.92</td><td>62.37±1.93</td><td>83.58±2.31</td><td>83.62±1.18</td><td>66.77±2.83</td></tr><tr><td>LoCoOpMCM</td><td>96.51±3.33</td><td>53.49±8.06</td><td>93.52±5.68</td><td>55.59±9.19</td><td>92.88±4.05</td><td>57.89±5.19</td><td>76.45±7.48</td><td>78.59±2.66</td><td>89.84±4.29</td><td>61.39±3.90</td></tr><tr><td>LoCoOpGL</td><td>86.13±12.2</td><td>72.68±7.97</td><td>87.81±6.37</td><td>68.58±6.40</td><td>85.93±4.15</td><td>69.90±3.40</td><td>54.89±4.67</td><td>87.00±1.01</td><td>78.69±4.65</td><td>74.54±3.59</td></tr><tr><td>IDLike</td><td>98.02±2.13</td><td>73.32±5.83</td><td>95.74±2.84</td><td>65.19±6.86</td><td>94.79±3.67</td><td>69.44±5.06</td><td>63.34±9.10</td><td>86.68±2.98</td><td>87.97±4.21</td><td>73.66±5.04</td></tr><tr><td>SCTMCM</td><td>99.79±0.22</td><td>32.90±6.73</td><td>98.36±0.84</td><td>44.30±3.41</td><td>97.77±0.86</td><td>48.08±1.64</td><td>83.98±6.92</td><td>73.25±3.58</td><td>94.97±2.19</td><td>49.63±2.39</td></tr><tr><td>SCTGL</td><td>96.57±5.41</td><td>58.21±5.31</td><td>92.41±4.55</td><td>61.54±3.47</td><td>90.49±5.02</td><td>63.33±2.71</td><td>55.29±14.7</td><td>85.48±3.68</td><td>83.69±7.02</td><td>67.14±2.20</td></tr><tr><td rowspan=\"2\"></td><td>FAmCM(Ours)</td><td>85.24±6.88</td><td>78.62±3.18</td><td>36.24±10.8</td><td>92.13±2.44</td><td>28.17±10.2</td><td>94.05±1.68</td><td>10.36±3.97</td><td>97.71±0.69</td><td>39.99±7.79</td><td>90.63±1.91</td></tr><tr><td>FAGL(Ours)</td><td>77.82±7.28</td><td>86.88±2.15</td><td>56.10±8.03</td><td>88.43±2.26</td><td>49.87±7.69</td><td>89.07±1.49</td><td>8.99±2.51</td><td>97.74±0.36</td><td>48.19±6.23</td><td>90.53±1.42</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Representative OOD detection results with various ID datasets in the 16-shot setting. We use the same notation as Tab. 1.",
+        "bbox": [
+            112,
+            551,
+            880,
+            566
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/076c5ec2f75ee8cd53e39c8b2940dcccfd6dbd0bae3b8b4fc0d38aacd046cb8c.jpg",
+        "image_caption": [
+            "Figure 3. A portion of OOD detection average performance using other ID datasets under the 16-shot setting. We report the mean and standard deviation of the AUROC for our FA (blue) and CoOp (orange) using the MCM score. More details can be found in the Appendix B."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            593,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "shown that some of the used OOD datasets contain more or less images of objects that belong to ID classes in ImageNet-1k [7]. Hence, probing the true performance of OOD detectors for ImageNet-1k demands OOD datasets that are both challenging and genuinely OOD. As shown in Tab. 3, to fully substantiate the effectiveness of our",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FA, we leverage 3 additional cleaner and more challenging OOD datasets, including OpenImage-O [45], NINCO [2], and ImageNet-O [15], inspired by [2]. Notably, both our  $\\mathrm{FA}_{\\mathrm{MCM}}$  and  $\\mathrm{FA}_{\\mathrm{GL}}$  consistently outperform current SOTA methods in terms of average FPR95 and AUROC under different few-shot settings (More details under the 1-shot and 4-shot settings are provided in the Appendix A).",
+        "bbox": [
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+            593,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Various ID Datasets. Considering factors like dataset variety, image resolution, and the number of classes [30], we also leverage 8 additional widely used datasets for few-shot setting as ID datasets for comparison [30, 34, 54]. Overall, despite our model is simple, it achieves superior average OOD performance on these ID datasets compared to other methods. We selected representative results using UCF101 [40] and EuroSAT [13] as ID datasets in the 16-shot setting, as shown in Tab. 4. Since using the other datasets (i.e. Food101 [3], StandfordCars [21], Caltech101 [12], FGVCAircraft [29], Flowers102 [35], and OxfordPets [36]) as ID datasets for OOD detection presents relatively lower difficulty as shown in Fig. 3, we leave more",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1158",
+        "bbox": [
+            483,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3179384cf6c5f32757ff2ec23c1096e85edf7724d0bee176cc0262fa0bb2070b.jpg",
+        "image_caption": [
+            "(a) Conventional OOD benchmark"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            112,
+            88,
+            281,
+            190
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/473ae12adfd35b414a654564acef41ba335a1dae659dd6e9bbf391ca6c4e51ab.jpg",
+        "image_caption": [
+            "(b)Challenging OOD benchmark",
+            "Figure 4. Sensitivity study of hyperparameter  $K$ . We report the average FPR95 (Blue) and AUROC (Orange) of our  $\\mathrm{FA}_{\\mathrm{GL}}$  on different OOD benchmarks using ImageNet-1k as the ID dataset under 16-shot setting. Dashed lines represent the performance of the best baseline (i.e.  $\\mathrm{SCT}_{\\mathrm{GL}}$ )."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            290,
+            88,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "experimental details in Appendix B.",
+        "bbox": [
+            89,
+            287,
+            331,
+            303
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In particular, for the ID dataset EuroSAT,  $\\mathrm{FA}_{\\mathrm{MCM}}$  surpasses the best-competing method  $\\mathrm{LoCoOp_{GL}}$  by  $16.09\\%$  in average AUROC and  $38.7\\%$  in average FPR95, underscoring its effectiveness and versatility even when the ID dataset is of low resolution (64x64 pixels).",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3. Ablation study",
+        "text_level": 1,
+        "bbox": [
+            89,
+            390,
+            240,
+            406
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Influence of the  $\\mathcal{L}_{FCE-K}$ . As shown in Tab. 5, we trained the model  $\\mathrm{FA}_{CE}$  and  $\\mathrm{FA}_{FCE-K}$  using the standard cross-entropy loss  $\\mathcal{L}_{CE}$  and our  $\\mathcal{L}_{FCE-K}$ , respectively. Our  $\\mathrm{FA}_{FCE-K}$  significantly outperforms  $\\mathrm{FA}_{CE}$  under the same inference setting, which demonstrate the effectiveness of our  $\\mathcal{L}_{FCE-K}$ .",
+        "bbox": [
+            89,
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+            503
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Initialization of the forced and original prompt. As shown in Tab. 6, we perform experiments comparing different initialization scenarios for both prompts. Manual initialization uses the embeddings of \"a photo of a [class-c]\" to initialize the prompt's embeddings, while the random initialization setting is based on CoOp [54]. The results show that employing consistent manual initialization for both prompts enables the forced prompt to effectively learn more specific descriptions of the ID classes.",
+        "bbox": [
+            89,
+            503,
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+            638
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Influence of the shared learnable vector. We also explore the influence of the shared learnable vector and the independent learnable vector for the forced prompts. As shown in Tab. 7, we can observe that using the shared learnable vector performs well in the few-shot setting since the independent learnable vector for each class has more parameters and requires more training data [54].",
+        "bbox": [
+            89,
+            640,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4. Sensitivity study",
+        "text_level": 1,
+        "bbox": [
+            89,
+            757,
+            253,
+            773
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As shown in Fig. 4, we explore the influence of the hyperparameter  $K$ . Overall, with  $K$  ranging from 1 to 6, the results indicate that our proposed framework is insensitive to the choice of  $K$ . Concretely, our method is stable and outperforms the best baseline  $\\mathrm{SCT}_{\\mathrm{GL}}$  in average AUROC and FPR95 on both conventional and challenging OOD detection benchmarks. Specially, as  $K$  increases, the average AUROC shows an upward trend and then tends to be sta",
+        "bbox": [
+            89,
+            779,
+            482,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ble (see Fig. 4 (a)), showing a bottleneck in capturing more comprehensive semantic representations of the ID classes.",
+        "bbox": [
+            511,
+            90,
+            903,
+            122
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/0d2ab2d3dc31e25d8dcba5b51277f58ee42c764870cb61853ec9ae9292522cbb.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"2\">MCM</td><td colspan=\"2\">GL-MCM</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>FAce</td><td>41.43±3.11</td><td>91.01±0.67</td><td>34.29±1.94</td><td>90.99±0.56</td></tr><tr><td>FAFCE-K</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>",
+        "bbox": [
+            521,
+            136,
+            898,
+            204
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/3a5bbe0446b33e23b45d99fc3a7d3742084c89f429d48ecaf48249aafdb4719f.jpg",
+        "table_caption": [
+            "Table 5. Influence of the  $\\mathcal{L}_{FCE-K}$ . MCM and GL-MCM refer to the score functions used during model inference."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Forced-M-Init</td><td rowspan=\"2\">Original-M-Init</td><td colspan=\"2\">FA MCM</td><td colspan=\"2\">FA GL</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>-</td><td>-</td><td>40.71±4.00</td><td>91.28±0.82</td><td>34.88±2.92</td><td>92.12±0.76</td></tr><tr><td>✓</td><td>-</td><td>40.81±2.25</td><td>91.25±0.64</td><td>36.03±2.84</td><td>91.62±1.01</td></tr><tr><td>-</td><td>✓</td><td>31.35±1.34</td><td>93.35±0.34</td><td>26.39±1.02</td><td>93.64±0.19</td></tr><tr><td>✓</td><td>✓</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>",
+        "bbox": [
+            521,
+            257,
+            898,
+            354
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c2c3d01904873d81b6eba1a93aff2071de38602fb85df39b9cc6d5be0849582c.jpg",
+        "table_caption": [
+            "Table 6. Ablation study of different initialization scenarios for the forced and original prompts. \"M-Init\" represents manual initialization.  $\\checkmark$  represents using manual initialization; - represents using random initialization."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Shared- Vector</td><td rowspan=\"2\">M-Init</td><td colspan=\"2\">FA MCM</td><td colspan=\"2\">FA GL</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>-</td><td>-</td><td>44.02±2.24</td><td>90.17±0.42</td><td>46.29±1.33</td><td>88.24±0.41</td></tr><tr><td>✓</td><td>-</td><td>40.71±4.00</td><td>91.28±0.82</td><td>34.88±2.92</td><td>92.12±0.76</td></tr><tr><td>-</td><td>✓</td><td>34.69±0.62</td><td>92.57±0.12</td><td>29.27±0.55</td><td>92.82±0.80</td></tr><tr><td>✓</td><td>✓</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>",
+        "bbox": [
+            521,
+            435,
+            898,
+            534
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 7. Ablation study of the shared learnable vector.  $\\sqrt{}$  - for \"Shared-vector\" represents using the shared / independent learnable vector for the forced prompt;  $\\sqrt{}$  - for \"M-Init\" represents using manual / random initialization for the forced prompt.",
+        "bbox": [
+            511,
+            540,
+            905,
+            597
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            513,
+            617,
+            633,
+            633
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this study, we propose a novel CLIP-based framework for OOD detection based on Forced prompt leArning (FA), which focuses on fully exploiting the ID knowledge to effectively improve OOD detection without exploring complex OOD-related knowledge. We introduce a learnable forced prompt in addition to the frozen original prompt, both of which are using the same manual initialization. The forced prompt treats the original prompt as a reference, forcing itself to learn more diversified semantic descriptions of the ID classes rather than being limited to the textual semantics of class labels. We also introduce a forced coefficient to facilitate the forced prompt in learning more nuanced descriptions of the ID classes. Comprehensive experimental evaluations demonstrate that our method consistently surpasses current state-of-the-art methods on diverse benchmarks. We expect that our study can bring new insight on VLMs-based OOD detection methods and inspire more future research.",
+        "bbox": [
+            511,
+            643,
+            906,
+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "1159",
+        "bbox": [
+            483,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7. Acknowledgments",
+        "text_level": 1,
+        "bbox": [
+            91,
+            90,
+            269,
+            107
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work is supported in part by the National Natural Science Foundation of China (grant No. 62071502), the Major Key Project of PCL (grant No. PCL2023A09), and Guangdong Excellent Youth Team Program (grant No. 2023B1515040025).",
+        "bbox": [
+            89,
+            114,
+            483,
+            190
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            203,
+            187,
+            218
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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2025/FA_ Forced Prompt Learning of Vision-Language Models for Out-of-Distribution Detection/8ae5a438-b943-4e71-b751-475d9f24c3b7_origin.pdf

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2025/FA_ Forced Prompt Learning of Vision-Language Models for Out-of-Distribution Detection/full.md

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+# FA: Forced Prompt Learning of Vision-Language Models for Out-of-Distribution Detection
+
+Xinhua Lu $^{1,2,4}$ , Runhe Lai $^{1,2,4}$ , Yanqi Wu $^{1,2,4}$ , Kanghao Chen $^{3\dagger}$ , Wei-Shi Zheng $^{1,2,4}$ , Ruixuan Wang $^{1,2,4\dagger}$ $^{1}$ Sun Yat-sen University  $^{2}$ Peng Cheng Laboratory  
+ $^{3}$ Hong Kong University of Science and Technology (Guangzhou)  
+ $^{4}$ Key Laboratory of Machine Intelligence and Advanced Computing
+
+{luxh55, lairh5, wuyq268}@mail2.sysu.edu.cn, kchen879@connect.hkust-gz.edu.cn, wszheng@ieee.org, wangruix5@mail.sysu.edu.cn
+
+# Abstract
+
+Pre-trained vision-language models (VLMs) have advanced out-of-distribution (OOD) detection recently. However, existing CLIP-based methods often focus on learning OOD-related knowledge to improve OOD detection, showing limited generalization or reliance on external largescale auxiliary datasets. In this study, instead of delving into the intricate OOD-related knowledge, we propose an innovative CLIP-based framework based on Forced prompt leArning (FA), designed to make full use of the InDistribution (ID) knowledge and ultimately boost the effectiveness of OOD detection. Our key insight is to learn a prompt (i.e. forced prompt) that contains more diversified and richer descriptions of the ID classes beyond the textual semantics of class labels. Specifically, it promotes better discernment for ID images, by forcing more notable semantic similarity between ID images and the learnable forced prompt. Moreover, we introduce a forced coefficient, encouraging the forced prompt to learn more comprehensive and nuanced descriptions of the ID classes. In this way, FA is capable of achieving notable improvements in OOD detection, even when trained without any external auxiliary datasets, while maintaining an identical number of trainable parameters as CoOp. Extensive empirical evaluations confirm our method consistently outperforms current state-of-the-art methods. Code is available at https://github.com/0xFIFA/FA.
+
+# 1. Introduction
+
+AI models often encounter Out-of-Distribution (OOD) samples [14, 25, 28, 38], which differ from the distribution of the training data, when deployed in real-world applications.
+
+![](images/d9ad327290586f4d05943d5523b636a0b2470f791793f567897944331faba407.jpg)  
+Figure 1. Comparison of CLIP-based OOD detection methods. Existing methods focus on OOD-related knowledge to learn a complex ID/OOD decision boundary as shown in the orange area in (b). In contrast, our FA aims to fully exploit ID knowledge by forcing the model to learn richer descriptions of the ID classes beyond the textual semantics of class labels. These richer descriptions of the ID classes compared to the reference text allow better discernment of ID/OOD samples (orange vs. blue area in (a)).
+
+Detecting OOD data is vital for the reliability of AI systems. This problem becomes harder in fields like intelligent diagnosis, where only a small amount of labeled data is available, motivating the problem of few-shot OOD detection.
+
+To tackle the OOD detection problem, previous single-modal post-hoc methods [14, 16, 24, 27, 41] achieve notable success based on a model pre-trained on the ID dataset. However, they come with limitations, such as requiring substantial computational resources and annotation costs for training, which hinder the performance of few-shot OOD detection. With the development of large pre-trained vision-language models (VLMs) like CLIP [37], few-shot OOD detection has achieved remarkable performance. Most of the CLIP-based OOD detection methods [30, 32] focus on
+
+leveraging the powerful generalization capability of CLIP to improve OOD detection.
+
+Recent CLIP-based OOD detection methods [1, 11, 23, 33, 34, 46, 48] aim to learn OOD-related knowledge to improve OOD detection performance. For example, recent CLIP-based works [11, 46] improve OOD detection by relying on training on external large-scale auxiliary datasets, which entails significant resource overhead. To eliminate dependence on external datasets, existing methods [1, 33, 48] learn OOD-related knowledge from exposed outliers based only on ID training data, such as background regions in ID training images. However, these OOD features extracted from specific regions are difficult to match with infinite OOD data encountered in practice. Moreover, some methods [23, 34] aim to learn negative prompts semantically opposite to the ID class labels, while these limited negative prompts are often insufficient to capture the distinctions between the diverse and numerous OOD data and the ID data. Overall, improving OOD detection by learning OOD-related knowledge shows inherent limitations or requires significant computational resources as well as labor costs. Inspired by the method [44] for open-set recognition, which demonstrates that enhancing closed-set accuracy can typically improve open-set recognition capabilities, we are motivated to explore ways to improve the identification of ID images, thereby enhancing OOD detection performance.
+
+In this paper, rather than focusing on the intricate OOD-related knowledge, we propose a novel CLIP-based framework based on Forced prompt leArning (FA), which aims to fully exploit the ID knowledge and ultimately improve OOD detection. Our key insight is to learn a prompt that contains richer knowledge beyond the textual semantics of class labels. It facilitates advanced discernment for ID images, by forcing higher semantic similarity between ID images and the learnable prompt (i.e. forced prompt), which provides more diversified and richer descriptions of the ID classes. In this way, FA can achieve significant improvements in OOD detection performance, even when trained without any additional external data, while maintaining the same number of learnable parameters as CoOp [54].
+
+Specifically, we introduce a novel forced prompt along with the original prompt, both of which are initialized identically. FA preserves the generalization capability of the VLMs (i.e. CLIP) by freezing the original prompt and optimizing a trainable copy (i.e. forced prompt). In particular, the forced prompt treats the original prompt as a reference, while forcing the text features associated with the forced prompt to be more salient compared to those associated with the original prompt. In this way, it effectively improves the OOD performance even without sacrificing the ID classification capability of the model. Additionally, we introduce a forced coefficient, encouraging the forced
+
+prompt to learn more comprehensive connotations. Experimentally, FA achieves superior few-shot OOD detection performance across diverse OOD benchmarks. Compared to current SOTA methods [48] that focus on learning OOD-related knowledge, our method significantly reduces the average FPR95 score from  $31.62\%$  to  $27.81\%$  and improves the average AUROC from  $92.01\%$  to  $93.26\%$  even in 1-shot OOD detection on ImageNet-1k. The main contributions are summarized as follows:
+
+- We propose a simple yet effective framework, which fully exploits the ID knowledge to improve OOD detection without focusing on intricate OOD-related knowledge.  
+- We present a Forced prompt leArning (FA) strategy to exploit richer knowledge beyond the textual semantics of class labels.  
+- We evaluate our method on diverse OOD benchmarks, showing that our model consistently outperforms current state-of-the-art methods.
+
+# 2. Related work
+
+Prompt Learning. In recent years, pre-trained vision-language models (VLMs) such as CLIP [37] have demonstrated powerful few-shot learning capabilities in both visual and textual domains. However, the design of the prompt greatly affects the performance of VLMs for downstream tasks, which may require manually crafting numerous prompts. Inspired by prompt learning studies in natural language processing (NLP) [26], CoOp [54] uses a set of learnable context vectors to transfer CLIP for specific downstream tasks, becoming a pioneering method for subsequent studies [4, 33, 53]. Currently, prompt learning is widely used in OOD detection mainly to represent various OOD-related knowledge. In this work, we learn the forced prompt, which contains richer descriptions of the ID classes to improve OOD detection.
+
+Out-of-Distribution Detection. Conventional methods explore OOD detection for single-modal models. One line of studies designs score functions to differentiate ID and OOD data based on output from the pre-trained models, such as logit output [14, 16, 24, 27] or outputs from the penultimate layer [22, 41, 42, 50]. These methods are called post-hoc methods. Another line of studies [9, 10, 18, 31, 39, 43, 55] adopts various training strategies to learn a reliable decision boundary between ID and OOD data.
+
+Recently, the development of OOD detectors based on VLMs, especially CLIP, has received much attention as VLMs have demonstrated their remarkable generalization capability in both visual and textual domains. Some studies leverage real outlier information from external auxiliary OOD datasets [11, 46] or extensive corpora [5, 20] to promote OOD detection. However, this is impractical in real-world scenarios, where outliers are infinite and agnostic.
+
+![](images/d6c07d7693e54a2e5e7e9bf056c4470e042bca80776d2e49bb596b306ede69d4.jpg)  
+Figure 2. Overview of the proposed FA framework. Our framework includes the learnable forced prompt and the frozen original prompt, both of which are initialized identically by a manual template "a photo of a [class-c]". The learnable forced prompt treats the frozen original prompt as a reference, forcing its text features to become more salient compared to those generated by the original prompt. The richer and more diversified description of ID classes learned by FA can ultimately improve OOD detection.
+
+To eliminate the dependence on external data, recent methods [1, 23, 32, 33, 48] were developed under the assumption that only ID data are available. As a representative zero-shot method that only uses available ID labels, MCM [30] employs softmax scaling to align visual features with ID text concepts for OOD detection. GL-MCM [32] further introduces a local maximum concept matching(L-MCM) score to improve the separability of the local information. Compared with zero-shot methods, which may undergo a domain gap with ID downstream data, prompt learning methods achieve better OOD detection performance with access to few-shot ID samples. For prompt learning OOD detection methods, LoCoOp [33] and SCT [48] keep the textual embeddings of ID classes away from ID-irrelevant local region embeddings in the multi-modal embedding space by their proposed entropy maximization strategy, which ensures that OOD embeddings can be dissimilar to any textual embedding of ID classes. To detect challenging OOD samples to improve OOD detection, ID-like [1] explores the vicinity of ID samples to construct OOD samples correlated to the ID and refines the additional "ID-like" text embeddings to fine-grained differences. In addition, NegPrompt [23] and LSN [34] introduce the negative connotations of ID categories which can be represented by additional negative prompts, enabling more accurate detection of OOD samples. Overall, various OOD-related knowledge is commonly adopted to address the model's overconfidence in current research. In this work, we focus on leveraging ID knowledge to improve OOD detection, instead of exploring complex OOD-related knowledge.
+
+# 3. Preliminaries
+
+Prompt Learning with CLIP. CLIP contains an image encoder  $f(\cdot)$  and a text encoder  $g(\cdot)$ , designed to extract features from images and text descriptions respectively. Generally, for an ID dataset which contains  $C$  categories, the hand-crafted prompt  $\hat{\mathbf{u}}_c$  "a photo of a [class-c]" is designed to match images, where class-c represents the class name. Formally, these prompts are individually encoded in  $\hat{\mathbf{t}}_c = g(\hat{\mathbf{u}}_c) \in \mathbb{R}^{d \times 1}$ ,  $c = 1, \dots, C$ . Given an image  $\mathbf{x}$ , it can be encoded in  $\mathbf{z} = f(\mathbf{x}) \in \mathbb{R}^{d \times 1}$ . Because image features and corresponding text features are aligned on the multimodal embedding space, the cosine similarity  $\cos(\mathbf{z}, \hat{\mathbf{t}}_c)$  of  $\mathbf{z}$  and  $\hat{\mathbf{t}}_c$  can represent the matching degree between the image  $\mathbf{x}$  and text description  $\hat{\mathbf{u}}_c$ . Therefore, if the text feature  $\mathbf{t}_c$  of class  $c$  has the highest similarity to  $\mathbf{z}$ , the image  $\mathbf{x}$  will be considered to be class  $c$ .
+
+To effectively transfer CLIP to downstream image recognition tasks, CoOp [54] sets a portion of tokens in the text prompt as continuous learnable parameters. Concretely, CoOp initializes the text prompts as  $\mathbf{u}_c = [\mathbf{v}_1,\dots ,\mathbf{v}_L,\mathbf{w}_c],c\in \{1,\dots ,C\}$ , where  $L$  is the length of the prompt's tokens,  $\mathbf{v}_i$  ( $i\in \{1,\ldots ,L\}$ ) is the learnable vector with the same dimension as the word embedding and  $\mathbf{w}_c$  is the word embedding for the class name of class  $c$ . The text prompt  $\mathbf{u}_c$  is encoded into features  $\mathbf{t}_c = g(\mathbf{u}_c)$ . Together with the image feature  $\mathbf{z}$ , the probability for the image  $\mathbf{x}$  to be classified into class  $c$  is defined as
+
+$$
+p (y = c \mid \mathbf {x}) = \frac {e ^ {\cos (\mathbf {z} , \mathbf {t} _ {c}) / \tau}}{\sum_ {j = 1} ^ {C} e ^ {\cos (\mathbf {z} , \mathbf {t} _ {j}) / \tau}}, \tag {1}
+$$
+
+where  $\tau$  is a fixed temperature scaling hyper-parameter.
+
+Overall, the prompt's tokens can be trained to align with training data by minimizing the cross-entropy loss with the prediction probability from Eq. (1).
+
+OOD Detection. In the OOD detection task, the model is expected to determine whether a test image belongs to one of the learned ID classes. Therefore, OOD detection can be seen as a binary classification problem to distinguish ID images from OOD images in a test set  $\mathcal{D}_{test}$  as follows
+
+$$
+D (\mathbf {x}) = \left\{ \begin{array}{l l} 1, & \text {i f} S (\mathbf {x}) \geq \mu \\ 0, & \text {i f} S (\mathbf {x}) <   \mu \end{array} , \right. \tag {2}
+$$
+
+where  $\mathbf{x} \in \mathcal{D}_{test}$ , 1 and 0 respectively indicate that  $\mathbf{x}$  is classified as the ID class and the OOD class by the OOD detector  $D(\cdot)$ ,  $S(\cdot)$  is certain score function, and  $\mu$  is a predefined threshold constant.
+
+# 4. Methodology
+
+# 4.1. Overview
+
+In this study, we propose a novel CLIP-based framework based on Forced prompt leArning (FA), designed to fully exploit the ID knowledge from few-shot ID samples by forcing the prompt to learn richer knowledge beyond the textual semantics of class labels. As shown in Fig. 2, we introduce a forced prompt along with the original prompt, both of which are initialized with the same semantics. By freezing the original prompt and optimizing a trainable copy, ID images will show higher semantic similarity to the forced prompt compared to the original prompt. Moreover, to encourage descriptions of ID classes learned by the forced prompt to become more detailed and comprehensive, we also introduce a forced coefficient. During testing, the model is capable of effectively distinguishing between ID data and OOD data, benefiting from the diversified descriptions of the ID classes provided by the forced prompt.
+
+# 4.2. Forced prompt learning
+
+Merely the semantic information conveyed by class names is insufficient to comprehensively encompass the discriminative information of each class. In order to explore richer semantic descriptions of the ID classes beyond the textual semantics of class labels, a novel forced prompt along with the original prompt is proposed. To implement the above objective, we introduce a simple yet effective training strategy using the forced cross-entropy (FCE) loss based on the forced prompt as follows
+
+$$
+\mathcal {L} _ {F C E} = \mathbb {E} _ {\left(\mathbf {x}, y _ {c}\right) \sim \mathcal {D} _ {t r a i n} ^ {I D}} \left[ - \log \frac {e ^ {s _ {c} ^ {f} / \tau}}{\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {f} / \tau} + \sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {o} / \tau}} \right], \tag {3}
+$$
+
+where the ID training dataset  $\mathcal{D}_{train}^{ID}$  consists of ID image-label pairs  $(\mathbf{x},y_{c})$ ,  $s_j^f = \cos (\mathbf{z},\mathbf{t}_j^f)$  and  $s_j^o = \cos (\mathbf{z},\mathbf{t}_j^o)$
+
+represent the similarity between the image feature and the prompt feature corresponding to the forced prompt and the original prompt, respectively.
+
+Based on this loss function, the ID image features will be forced to show higher cosine similarity to the learnable forced prompt compared to the original text prompt. This is because the cosine similarity between the ID image features and the original text prompt is already high before any further prompt learning. Consequently, the forced prompt is forced to uncover richer discriminative information of ID classes, so that the text features of the forced prompt achieve a higher cosine similarity with the image features compared to those of the original prompt. Benefiting from this information specific to the ID classes, the cosine similarity between the image features of an OOD image and the text features of both prompts may exhibit less distinction compared to those of the ID data. Therefore, even when trained without any reliance on external auxiliary datasets, the detector will have a notable capability to distinguish ID data from OOD data.
+
+However, this naive FCE loss may not work effectively because of its inherent limitations. Concretely, employing random initialization for both prompts fails to fully leverage the semantic information provided by CLIP's prior knowledge, resulting in limited performance. To solve this limitation, we propose to initialize the forced prompt using the manual template (i.e. "a photo of a [class-c]") identified to the original prompt. In this way, both prompts with manual initialization will have clear semantic information compared to random initialization, thereby improving the model's generalization capability. Specifically, the class labels are utilized in both prompts by concatenating with the prompt embedding to provide foundational semantic information related to the category names, based on CLIP's prior knowledge. In particular, for the forced prompt, we adopt the shared learnable vector across all classes rather than the independent learnable vector for each class. This choice is inspired by CoOp [54], which demonstrates that using an independent learnable vector mostly underperforms the shared learnable vector in challenging low-data scenarios since the former has more parameters and requires more data for training. Formally, we utilize the embeddings of the manual template to initialize the prompt's embeddings of both prompts, formulated as  $\mathbf{u}_c = [\mathbf{v}_1,\dots ,\mathbf{v}_L,\mathbf{w}_c], c\in$ $\{1,\dots ,C\}$ , which will be fed to the text encoder to obtain prompt feature  $\mathbf{t}_c$  (see Section 3). Here,  $L$  is the length of the token (e.g., for the "a photo of a",  $L = 4$ ). Then we freeze the original prompt and the class label part of both the prompts to preserve the generalization capability of CLIP, while only making the forced prompt learnable. Note that our method effectively improves OOD detection performance while maintaining consistency with CoOp in the number of learnable parameters without leveraging ad
+
+ditional learnable prompts, unlike existing work [1, 23, 34].
+
+Although the above prompt design achieves moderate performance, relying solely on a single original prompt as a reference is somewhat insufficient to develop a comprehensive capability, particularly with the limitations of ID data (e.g., few-shot OOD). To encourage the forced prompt to capture more comprehensive and nuanced descriptions of the ID classes, we introduce a forced coefficient  $K$  ( $K \geq 0, K \in \mathbb{N}$ ), which indicates the intensity with which the model is compelled to learn from the data. Formally, we first derive the original text features  $\{\mathbf{t}_1^o, \dots, \mathbf{t}_C^o\}$  from the original prompt and the image features  $\mathbf{z}$  from the corresponding image. Then, we compute the cosine similarity between the original text features and the image features for  $K$  iterations, which will be used in the subsequent computation of the cross-entropy loss function. Notably, when  $K = 0$ , no original prompt is used, and the model operates equivalently to CoOp. Based on the forced coefficient, we refine Eq. (3) as follows
+
+$$
+\mathcal {L} _ {F C E - K} = \mathbb {E} _ {\left(\mathbf {x}, y _ {c}\right) \sim \mathcal {D} _ {t r a i n} ^ {I D}} \left[ - \log \frac {e ^ {s _ {c} ^ {f} / \tau}}{\sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {f} / \tau} + K \sum_ {j = 1} ^ {C} e ^ {s _ {j} ^ {o} / \tau}} \right]. \tag {4}
+$$
+
+Based on this function, the cosine similarity between the ID image features and the text features of the forced prompt must become more salient as the coefficient  $K$  increases.
+
+# 4.3. Model inference
+
+During model inference, for the downstream classification task, we adopt the same strategy as CLIP, depending solely on the forced prompt [1]. For the OOD detection task, our method can be flexibly combined with different score functions, such as the MCM [30] score and the GL-MCM [32] score. The MCM score is defined as the maximum similarity between the global image features  $\mathbf{z}^g$  (i.e.  $\mathbf{z}$ ) and all text features  $\mathbf{t}_c^a$  (i.e. the concatenation of text features  $\mathbf{t}_c^f$  and  $\mathbf{t}_c^o$ ) after applying softmax with temperature  $\tau_0$ , i.e.,
+
+$$
+S _ {\mathrm {M C M}} (\mathbf {x}) = \max  _ {c} \frac {e ^ {\cos \left(\mathbf {z} ^ {g} , \mathbf {t} _ {c} ^ {a}\right) / \tau_ {0}}}{\sum_ {j = 1} ^ {C} e ^ {\cos \left(\mathbf {z} ^ {g} , \mathbf {t} _ {j} ^ {f}\right) / \tau_ {0}} + K e ^ {\cos \left(\mathbf {z} ^ {g} , \mathbf {t} _ {j} ^ {o}\right) / \tau_ {0}}}, \tag {5}
+$$
+
+while the GL-MCM score simultaneously considers both global and local features, which can be expressed as
+
+$$
+S _ {\mathrm {G L - M C M}} (\mathbf {x}) = S _ {\mathrm {M C M}} (\mathbf {x}) + S _ {\mathrm {L - M C M}} (\mathbf {x}), \tag {6}
+$$
+
+$$
+S _ {\mathrm {L - M C M}} (\mathbf {x}) = \max  _ {i, c} \frac {e ^ {\cos \left(\mathbf {z} _ {i} ^ {l} , \mathbf {t} _ {c} ^ {a}\right) / \tau_ {0}}}{\sum_ {j = 1} ^ {C} e ^ {\cos \left(\mathbf {z} _ {i} ^ {l} , \mathbf {t} _ {j} ^ {f}\right) / \tau_ {0}} + K e ^ {\cos \left(\mathbf {z} _ {i} ^ {l} , \mathbf {t} _ {j} ^ {o}\right) / \tau_ {0}}}, \tag {7}
+$$
+
+where  $\mathbf{z}_i^l (i\in \{1,\dots ,N\})$  represents  $N$  extracted local features generated by CLIP's image encoder [32, 33]. We set  $\tau_0 = 1$  during model inference.
+
+# 5. Experiments
+
+# 5.1. Experimental details
+
+Datasets. We use a popular benchmark for conventional OOD detection [19, 30, 32, 33], where ImageNet-1k [7] serves as the ID dataset, and the OOD datasets are iNaturalist [17], SUN [47], Places [52], and Texture [6]. Moreover, inspired by existing studies [1, 2], we use datasets like OpenImage-O [45], NINCO [2], and ImageNet-O [15], which are cleaner and more realistic, to simulate the more challenging OOD detection. Besides, we also utilize other widely adopted datasets for few-shot settings as ID datasets [49, 51, 54], which include StanfordCars [21], UCF101 [40], Caltech101 [12], Flowers102 [35], EuroSAT [13], FGVCAircraft [29], OxfordPets [36], and Food101 [3], considering factors such as image resolution and the number of classes.
+
+Setup. Following previous studies [33], we use the ViTB/16 [8] as the backbone model. For our model, when using ImageNet-1k as the ID dataset, the epochs are respectively set to 30 and 50 for the 1-shot and 16-shot settings, while for other ID datasets, we set the epoch to 200 following CoOp [54]. The value of forced coefficient  $K$  is uniformly set to 3, which will be further discussed in the sensitivity study. Other hyperparameters are as follows: learning rate  $= 2\mathrm{e} - 3$ , batch size  $= 160$ , SGD (momentum  $= 0.9$ , weight decay  $= 5\mathrm{e} - 4$ ) as the optimizer with a cosine scheduler,  $\tau = 1$  in Eq. (3) and Eq. (4). All experiments on our model can be conducted on a single Nvidia A30 GPU. The average experiment results (including our reproductions) over four runs are reported for comparison.
+
+Comparison Methods. To validate the effectiveness of our FA fairly, we mainly compare it with CLIP-based OOD detection methods that do not use real outliers (e.g. OOD labels). For previous post-hoc methods, including MSP [14], ODIN [24], Energy [27], ReAct [41], and MaxLogit [16], we adapt these methods with the CLIP image encoder as the CLIP-based post-hoc methods. For zero-shot methods, we select MCM [30], GL-MCM [32] and CLIPN [46] as baselines. For prompt learning methods, we adopt CoOp [54], LoCoOp [33], IDLike [1], and SCT [48] as baselines.
+
+Metrics. For evaluation, we adopt the following metrics: (1) The False Positive Rate at  $95\%$  True Positive Rate for in-distribution samples (FPR95); (2) The Area Under the Receiver Operating Characteristic Curve (AUROC); (3) In-distribution data classification Top-1 accuracy (ID ACC).
+
+# 5.2. Main results
+
+Conventional OOD Detection. Table 1 summarizes our comparison results on the ImageNet-1k benchmarks, which show that our FA achieves state-of-the-art OOD detection performance among other CLIP-based methods under different few-shot settings (More details under the 4-shot set
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">iNaturalist</td><td colspan="2">SUN</td><td colspan="2">Places</td><td colspan="2">Textures</td><td colspan="2">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td colspan="11">Zero-shot methods</td></tr><tr><td>MCM</td><td>31.95</td><td>94.16</td><td>37.22</td><td>92.55</td><td>42.98</td><td>90.10</td><td>58.35</td><td>85.83</td><td>42.63</td><td>90.66</td></tr><tr><td>GL-MCM</td><td>15.09</td><td>96.72</td><td>29.08</td><td>93.41</td><td>37.07</td><td>90.37</td><td>58.94</td><td>83.11</td><td>35.04</td><td>90.90</td></tr><tr><td>CLIPN</td><td>19.17</td><td>96.17</td><td>26.43</td><td>94.02</td><td>32.26</td><td>92.62</td><td>41.23</td><td>90.12</td><td>30.21</td><td>93.19</td></tr><tr><td colspan="11">CLIP-based post-hoc methods</td></tr><tr><td>\( MSP^† \)</td><td>74.57</td><td>77.74</td><td>76.95</td><td>73.97</td><td>79.72</td><td>72.18</td><td>73.66</td><td>74.84</td><td>76.22</td><td>74.68</td></tr><tr><td>\( ODIN^† \)</td><td>98.93</td><td>57.73</td><td>88.72</td><td>78.42</td><td>87.80</td><td>76.88</td><td>85.47</td><td>71.49</td><td>90.23</td><td>71.13</td></tr><tr><td>\( Energy^† \)</td><td>64.98</td><td>87.18</td><td>46.42</td><td>91.17</td><td>57.40</td><td>87.33</td><td>50.39</td><td>88.22</td><td>54.80</td><td>88.48</td></tr><tr><td>\( ReAct^† \)</td><td>65.57</td><td>86.87</td><td>46.17</td><td>91.04</td><td>56.85</td><td>87.42</td><td>49.88</td><td>88.13</td><td>54.62</td><td>88.37</td></tr><tr><td>\( MaxLogit^† \)</td><td>60.88</td><td>88.03</td><td>44.83</td><td>91.16</td><td>55.54</td><td>87.45</td><td>48.72</td><td>88.63</td><td>52.49</td><td>88.82</td></tr><tr><td colspan="11">Prompt learning based methods</td></tr><tr><td>\( CoOp_{MCM} \)</td><td>41.14±9.39</td><td>91.47±2.12</td><td>39.06±4.17</td><td>91.68±0.83</td><td>45.38±4.88</td><td>89.16±1.28</td><td>51.37±3.09</td><td>87.82±1.12</td><td>44.24±1.39</td><td>90.03±0.32</td></tr><tr><td>\( CoOp_{GL} \)</td><td>23.30±6.37</td><td>94.59±1.51</td><td>32.08±3.87</td><td>92.21±0.95</td><td>39.22±4.55</td><td>89.59±1.58</td><td>55.78±3.46</td><td>83.26±1.38</td><td>37.59±0.34</td><td>89.91±0.31</td></tr><tr><td>\( LoCoOp_{MCM} \)</td><td>36.64±4.87</td><td>92.78±0.93</td><td>31.86±3.79</td><td>93.50±0.92</td><td>38.81±3.37</td><td>90.70±0.97</td><td>48.11±2.31</td><td>89.43±0.68</td><td>38.85±2.67</td><td>91.59±0.58</td></tr><tr><td>\( LoCoOp_{GL} \)</td><td>21.97±2.91</td><td>95.39±0.59</td><td>24.95±2.37</td><td>94.42±0.59</td><td>34.14±2.66</td><td>91.14±0.69</td><td>49.04±2.77</td><td>87.73±0.96</td><td>32.53±2.19</td><td>92.17±0.47</td></tr><tr><td>IDLike</td><td>17.73±1.91</td><td>96.68±0.31</td><td>48.17±1.39</td><td>89.53±0.58</td><td>50.43±6.58</td><td>88.27±2.27</td><td>29.12±7.64</td><td>93.25±2.16</td><td>36.36±3.86</td><td>91.93±1.18</td></tr><tr><td>\( LSN^† \)</td><td>59.28±7.02</td><td>87.20±3.15</td><td>40.15±0.82</td><td>91.47±0.14</td><td>46.11±1.86</td><td>88.74±0.57</td><td>60.34±0.14</td><td>83.92±0.42</td><td>51.47±1.53</td><td>87.84±0.58</td></tr><tr><td>\( NegPrompt^† \)</td><td>65.03±8.69</td><td>84.56±2.52</td><td>44.39±1.66</td><td>89.63±0.66</td><td>51.31±6.21</td><td>86.55±2.19</td><td>87.60±1.61</td><td>63.76±3.02</td><td>62.08±3.71</td><td>81.13±1.78</td></tr><tr><td>\( SCT_{MCM} \)</td><td>41.93±12.17</td><td>91.77±2.40</td><td>30.39±2.17</td><td>93.76±0.39</td><td>38.73±2.54</td><td>90.78±0.34</td><td>46.78±3.51</td><td>88.96±1.16</td><td>39.46±3.39</td><td>91.32±0.90</td></tr><tr><td>\( SCT_{GL} \)</td><td>20.57±10.2</td><td>95.63±1.89</td><td>24.56±3.03</td><td>94.39±0.53</td><td>33.27±2.96</td><td>91.27±0.57</td><td>48.12±2.97</td><td>86.76±0.89</td><td>31.62±3.19</td><td>92.01±0.77</td></tr><tr><td>\( FA_{MCM}(Ours) \)</td><td>25.50±2.72</td><td>94.72±0.27</td><td>36.24±3.15</td><td>92.40±0.95</td><td>35.38±2.75</td><td>91.99±0.68</td><td>28.34±0.87</td><td>93.95±0.19</td><td>31.37±1.07</td><td>93.25±0.32</td></tr><tr><td>\( FA_{GL}(Ours) \)</td><td>14.12±1.32</td><td>96.76±0.10</td><td>29.99±1.57</td><td>92.95±0.66</td><td>32.48±1.48</td><td>91.83±0.49</td><td>34.66±1.21</td><td>91.50±0.36</td><td>27.81±0.44</td><td>93.26±0.27</td></tr><tr><td colspan="11">Prompt learning based methods</td></tr><tr><td>\( CoOp_{MCM} \)</td><td>30.26±1.98</td><td>93.43±0.81</td><td>34.69±0.43</td><td>92.59±0.14</td><td>41.91±0.71</td><td>90.11±0.23</td><td>44.68±2.11</td><td>89.95±0.48</td><td>37.89±0.71</td><td>91.52±0.29</td></tr><tr><td>\( CoOp_{GL} \)</td><td>15.96±1.67</td><td>96.11±0.55</td><td>27.26±1.99</td><td>93.29±0.46</td><td>35.36±2.08</td><td>90.58±0.64</td><td>48.63±2.11</td><td>86.11±0.59</td><td>31.81±1.27</td><td>91.51±0.39</td></tr><tr><td>\( LoCoOp_{MCM} \)</td><td>27.35±3.19</td><td>94.12±0.80</td><td>30.93±1.19</td><td>93.75±0.26</td><td>38.26±1.53</td><td>91.12±0.27</td><td>41.36±2.56</td><td>90.99±0.53</td><td>34.47±0.73</td><td>92.49±0.14</td></tr><tr><td>\( LoCoOp_{GL} \)</td><td>18.46±1.38</td><td>95.85±0.63</td><td>22.43±0.96</td><td>95.15±0.22</td><td>31.53±1.52</td><td>92.15±0.22</td><td>43.35±3.12</td><td>89.38±0.78</td><td>28.94±1.29</td><td>93.13±0.17</td></tr><tr><td>IDLike</td><td>19.23±10.5</td><td>96.70±1.58</td><td>54.15±2.88</td><td>87.64±1.19</td><td>56.63±0.07</td><td>85.86±0.44</td><td>34.69±6.41</td><td>91.90±2.31</td><td>41.18±1.73</td><td>90.53±0.01</td></tr><tr><td>\( LSN^† \)</td><td>36.17±4.81</td><td>92.66±1.16</td><td>34.27±0.44</td><td>93.53±0.20</td><td>41.47±0.85</td><td>90.52±0.37</td><td>46.43±0.60</td><td>89.38±0.24</td><td>39.58±0.73</td><td>91.53±0.09</td></tr><tr><td>\( NegPrompt^† \)</td><td>37.79±0.11</td><td>90.49±0.01</td><td>32.11±3.77</td><td>92.25±1.00</td><td>35.52±0.41</td><td>91.16±0.03</td><td>43.93±9.09</td><td>88.38±3.31</td><td>37.34±1.41</td><td>90.57±0.59</td></tr><tr><td>\( SCT_{MCM} \)</td><td>29.41±2.19</td><td>93.76±0.55</td><td>27.28±2.80</td><td>94.22±0.40</td><td>36.35±2.13</td><td>91.16±0.33</td><td>42.25±1.89</td><td>90.52±0.48</td><td>33.82±1.78</td><td>92.42±0.35</td></tr><tr><td>\( SCT_{GL} \)</td><td>15.19±2.16</td><td>96.71±0.44</td><td>20.00±0.61</td><td>95.57±0.11</td><td>29.71±0.85</td><td>92.37±0.12</td><td>44.17±0.82</td><td>88.59±0.39</td><td>27.27±0.44</td><td>93.31±0.17</td></tr><tr><td>\( FA_{MCM}(Ours) \)</td><td>25.79±1.48</td><td>94.29±0.35</td><td>33.54±1.17</td><td>93.02±0.19</td><td>33.77±1.64</td><td>92.64±0.42</td><td>23.17±1.31</td><td>95.14±0.26</td><td>29.07±1.11</td><td>93.77±0.19</td></tr><tr><td>\( FA_{GL}(Ours) \)</td><td>14.49±1.27</td><td>96.48±0.29</td><td>27.65±1.08</td><td>93.46±0.18</td><td>31.09±1.38</td><td>92.44±0.34</td><td>29.50±0.89</td><td>92.93±0.18</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>
+
+Table 1. Comparison results on ImageNet-1k OOD benchmarks. All results using the same backbone ViT-B/16. The results marked with  $\dagger$  are taken from [48]; the others are our reproductions. The prompt learning based methods are run under four trials, reporting the mean and standard deviation of the performance. The subscripts  ${}_{\mathrm{{MCM}}}$  and  ${}_{\mathrm{{GL}}}$  indicate the use of the MCM score and the GL-MCM score. The best and second-best results are indicated in bold and underline.  $\uparrow$  indicates larger values are better;  $\downarrow$  indicates smaller values are better. All values are percentages.  
+
+<table><tr><td>Method</td><td>1-shot</td><td>4-shot</td><td>16-shot</td></tr><tr><td>CoOp</td><td>67.44±0.50</td><td>69.71±0.07</td><td>70.99±0.14</td></tr><tr><td>LoCoOp</td><td>67.40±0.64</td><td>69.55±0.10</td><td>71.53±0.17</td></tr><tr><td>IDLike</td><td>68.17±0.57</td><td>68.91±0.14</td><td>69.46±0.02</td></tr><tr><td>SCT</td><td>68.63±0.13</td><td>69.93±0.22</td><td>71.78±0.05</td></tr><tr><td>FA(Ours)</td><td>68.67±0.39</td><td>69.96±0.04</td><td>71.02±0.09</td></tr></table>
+
+Table 2. Comparison results in ID Top-1 accuracy on ImageNet-1k under different few-shot settings. Other notations are the same as Tab. 1.
+
+ting are provided in the Appendix A). Specifically, in the 16-shot setting, FA with GL-MCM score  $\left(\mathrm{FA}_{\mathrm{GL}}\right)$  outperforms the best baseline  $\mathrm{SCT}_{\mathrm{GL}}$  (average FPR95 of  $25.68\%$  vs.  $27.27\%$ , and average AUROC of  $93.82\%$  vs.  $93.31\%$ ).
+
+Additionally, in the 1-shot setting,  $\mathrm{FA}_{\mathrm{GL}}$  surpasses  $\mathrm{SCT}_{\mathrm{GL}}$  by a large margin, showing improvements of at least  $1.25\%$  and  $3.81\%$  on average AUROC and FPR95. More importantly, even the average score of  $\mathrm{FA}_{\mathrm{MCM}}$  has exceeded  $\mathrm{SCT}_{\mathrm{GL}}$  in the 1-shot setting. Moreover, our FA effectively improves the OOD performance without sacrificing the ID classification capability of the model, as shown in Tab. 2.
+
+In particular, we can also observe that our method performs not well on the SUN dataset, as shown in Tab. 1. This is related to the presence of a significant number of samples belonging to ID category in these datasets, as demonstrated by recent studies [1]. In other words, the SUN dataset in the popular OOD benchmark requires more thorough cleaning to be effectively used as an OOD dataset.
+
+Challenging OOD Detection. Recent studies [1, 2] have
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">OpenImage-O</td><td colspan="2">NINCO</td><td colspan="2">ImageNet-O</td><td colspan="2">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>CoOpMCM</td><td>37.95±0.59</td><td>91.99±0.22</td><td>78.00±0.23</td><td>73.00±0.59</td><td>70.14±0.86</td><td>81.34±0.83</td><td>62.03±0.38</td><td>82.11±0.48</td></tr><tr><td>CoOpGL</td><td>32.23±1.00</td><td>92.22±0.25</td><td>72.04±0.81</td><td>75.35±0.88</td><td>67.35±1.19</td><td>78.44±0.94</td><td>57.21±0.96</td><td>81.99±0.58</td></tr><tr><td>LoCoOpMCM</td><td>37.03±0.94</td><td>92.24±0.21</td><td>77.96±0.63</td><td>72.78±0.79</td><td>70.96±0.75</td><td>81.25±0.39</td><td>61.98±0.55</td><td>82.09±0.35</td></tr><tr><td>LoCoOpGL</td><td>33.87±1.23</td><td>92.53±0.07</td><td>75.16±0.92</td><td>72.97±0.39</td><td>68.06±1.92</td><td>81.19±0.25</td><td>59.03±1.27</td><td>82.23±0.17</td></tr><tr><td>IDLike</td><td>54.43±2.35</td><td>87.89±0.45</td><td>78.93±1.79</td><td>69.32±0.42</td><td>84.08±1.45</td><td>67.45±0.86</td><td>72.48±0.89</td><td>74.89±0.28</td></tr><tr><td>SCTMCM</td><td>37.28±1.16</td><td>92.04±0.33</td><td>78.51±0.86</td><td>71.09±1.19</td><td>71.45±0.54</td><td>81.29±0.15</td><td>62.41±0.73</td><td>81.48±0.52</td></tr><tr><td>SCTGL</td><td>32.24±0.34</td><td>92.75±0.17</td><td>74.15±0.53</td><td>73.14±0.94</td><td>68.35±0.62</td><td>80.84±0.45</td><td>58.25±0.39</td><td>82.24±0.44</td></tr><tr><td>FAmCM(Ours)</td><td>37.93±1.65</td><td>91.84±0.45</td><td>70.44±1.24</td><td>77.77±0.94</td><td>63.84±1.36</td><td>82.71±0.30</td><td>57.40±1.34</td><td>84.08±0.47</td></tr><tr><td>FAGL(Ours)</td><td>32.10±0.89</td><td>92.39±0.28</td><td>65.61±1.32</td><td>79.01±0.71</td><td>63.13±0.98</td><td>80.39±0.21</td><td>53.61±0.89</td><td>83.93±0.31</td></tr></table>
+
+Table 3. Challenging OOD detection results on cleaner OOD datasets in the 16-shot setting. We use the same notation as Tab. 1.  
+
+<table><tr><td rowspan="2">ID Dataset</td><td rowspan="2">Method</td><td colspan="2">iNaturalist</td><td colspan="2">SUN</td><td colspan="2">Places</td><td colspan="2">Textures</td><td colspan="2">Average</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td rowspan="7">UCF101</td><td>CoOpMCM</td><td>14.40±6.61</td><td>97.41±1.36</td><td>37.09±3.94</td><td>93.14±0.48</td><td>40.07±2.77</td><td>91.89±0.65</td><td>33.24±4.21</td><td>93.19±1.22</td><td>31.21±3.58</td><td>93.91±0.45</td></tr><tr><td>CoOpGL</td><td>9.65±6.35</td><td>98.18±0.98</td><td>28.54±5.07</td><td>94.51±0.92</td><td>32.94±1.74</td><td>93.28±0.32</td><td>35.96±2.65</td><td>91.83±1.42</td><td>26.77±3.22</td><td>94.45±0.42</td></tr><tr><td>LoCoOpMCM</td><td>2.38±0.98</td><td>99.21±0.22</td><td>19.73±4.24</td><td>96.11±0.78</td><td>22.57±3.01</td><td>94.96±0.77</td><td>15.89±3.12</td><td>96.12±0.67</td><td>15.14±1.91</td><td>96.60±0.33</td></tr><tr><td>LoCoOpGL</td><td>1.13±0.22</td><td>99.65±0.09</td><td>17.93±4.09</td><td>96.51±0.89</td><td>22.34±4.58</td><td>95.03±1.06</td><td>18.17±3.01</td><td>95.25±0.71</td><td>14.89±2.49</td><td>96.61±0.58</td></tr><tr><td>IDLike</td><td>66.63±27.6</td><td>89.75±5.52</td><td>87.88±6.56</td><td>78.04±6.14</td><td>84.47±12.1</td><td>76.04±8.53</td><td>49.07±11.2</td><td>91.19±2.74</td><td>72.01±14.0</td><td>83.76±5.64</td></tr><tr><td>SCTMCM</td><td>1.51±0.51</td><td>99.44±0.10</td><td>24.17±5.54</td><td>95.21±0.88</td><td>26.62±4.41</td><td>93.75±0.81</td><td>15.34±3.84</td><td>95.98±0.64</td><td>16.91±3.20</td><td>96.09±0.48</td></tr><tr><td>SCTGL</td><td>0.79±0.27</td><td>99.75±0.04</td><td>18.69±2.41</td><td>95.86±0.56</td><td>23.77±2.47</td><td>93.98±0.47</td><td>17.44±2.62</td><td>94.52±0.54</td><td>15.17±1.56</td><td>96.03±0.25</td></tr><tr><td rowspan="2"></td><td>FAmCM(Ours)</td><td>0.12±0.11</td><td>99.94±0.01</td><td>3.06±1.33</td><td>99.34±0.23</td><td>4.68±1.00</td><td>99.08±0.26</td><td>2.68±0.51</td><td>99.31±0.43</td><td>2.63±0.58</td><td>99.42±0.22</td></tr><tr><td>FAGL(Ours)</td><td>0.13±0.02</td><td>99.94±0.02</td><td>4.98±1.02</td><td>99.01±0.22</td><td>7.46±0.86</td><td>98.44±0.27</td><td>5.67±0.83</td><td>98.75±0.19</td><td>4.56±0.47</td><td>99.03±0.13</td></tr><tr><td rowspan="7">EuroSAT</td><td>CoOpMCM</td><td>99.14±0.73</td><td>31.95±9.17</td><td>98.29±0.49</td><td>44.36±4.19</td><td>97.28±0.85</td><td>47.51±4.63</td><td>86.69±4.37</td><td>69.17±3.15</td><td>95.35±1.03</td><td>48.25±3.09</td></tr><tr><td>CoOpGL</td><td>92.45±4.26</td><td>57.59±10.4</td><td>90.97±3.49</td><td>61.89±4.83</td><td>88.69±3.85</td><td>64.00±4.92</td><td>62.37±1.93</td><td>83.58±2.31</td><td>83.62±1.18</td><td>66.77±2.83</td></tr><tr><td>LoCoOpMCM</td><td>96.51±3.33</td><td>53.49±8.06</td><td>93.52±5.68</td><td>55.59±9.19</td><td>92.88±4.05</td><td>57.89±5.19</td><td>76.45±7.48</td><td>78.59±2.66</td><td>89.84±4.29</td><td>61.39±3.90</td></tr><tr><td>LoCoOpGL</td><td>86.13±12.2</td><td>72.68±7.97</td><td>87.81±6.37</td><td>68.58±6.40</td><td>85.93±4.15</td><td>69.90±3.40</td><td>54.89±4.67</td><td>87.00±1.01</td><td>78.69±4.65</td><td>74.54±3.59</td></tr><tr><td>IDLike</td><td>98.02±2.13</td><td>73.32±5.83</td><td>95.74±2.84</td><td>65.19±6.86</td><td>94.79±3.67</td><td>69.44±5.06</td><td>63.34±9.10</td><td>86.68±2.98</td><td>87.97±4.21</td><td>73.66±5.04</td></tr><tr><td>SCTMCM</td><td>99.79±0.22</td><td>32.90±6.73</td><td>98.36±0.84</td><td>44.30±3.41</td><td>97.77±0.86</td><td>48.08±1.64</td><td>83.98±6.92</td><td>73.25±3.58</td><td>94.97±2.19</td><td>49.63±2.39</td></tr><tr><td>SCTGL</td><td>96.57±5.41</td><td>58.21±5.31</td><td>92.41±4.55</td><td>61.54±3.47</td><td>90.49±5.02</td><td>63.33±2.71</td><td>55.29±14.7</td><td>85.48±3.68</td><td>83.69±7.02</td><td>67.14±2.20</td></tr><tr><td rowspan="2"></td><td>FAmCM(Ours)</td><td>85.24±6.88</td><td>78.62±3.18</td><td>36.24±10.8</td><td>92.13±2.44</td><td>28.17±10.2</td><td>94.05±1.68</td><td>10.36±3.97</td><td>97.71±0.69</td><td>39.99±7.79</td><td>90.63±1.91</td></tr><tr><td>FAGL(Ours)</td><td>77.82±7.28</td><td>86.88±2.15</td><td>56.10±8.03</td><td>88.43±2.26</td><td>49.87±7.69</td><td>89.07±1.49</td><td>8.99±2.51</td><td>97.74±0.36</td><td>48.19±6.23</td><td>90.53±1.42</td></tr></table>
+
+Table 4. Representative OOD detection results with various ID datasets in the 16-shot setting. We use the same notation as Tab. 1.
+
+![](images/076c5ec2f75ee8cd53e39c8b2940dcccfd6dbd0bae3b8b4fc0d38aacd046cb8c.jpg)  
+Figure 3. A portion of OOD detection average performance using other ID datasets under the 16-shot setting. We report the mean and standard deviation of the AUROC for our FA (blue) and CoOp (orange) using the MCM score. More details can be found in the Appendix B.
+
+shown that some of the used OOD datasets contain more or less images of objects that belong to ID classes in ImageNet-1k [7]. Hence, probing the true performance of OOD detectors for ImageNet-1k demands OOD datasets that are both challenging and genuinely OOD. As shown in Tab. 3, to fully substantiate the effectiveness of our
+
+FA, we leverage 3 additional cleaner and more challenging OOD datasets, including OpenImage-O [45], NINCO [2], and ImageNet-O [15], inspired by [2]. Notably, both our  $\mathrm{FA}_{\mathrm{MCM}}$  and  $\mathrm{FA}_{\mathrm{GL}}$  consistently outperform current SOTA methods in terms of average FPR95 and AUROC under different few-shot settings (More details under the 1-shot and 4-shot settings are provided in the Appendix A).
+
+Various ID Datasets. Considering factors like dataset variety, image resolution, and the number of classes [30], we also leverage 8 additional widely used datasets for few-shot setting as ID datasets for comparison [30, 34, 54]. Overall, despite our model is simple, it achieves superior average OOD performance on these ID datasets compared to other methods. We selected representative results using UCF101 [40] and EuroSAT [13] as ID datasets in the 16-shot setting, as shown in Tab. 4. Since using the other datasets (i.e. Food101 [3], StandfordCars [21], Caltech101 [12], FGVCAircraft [29], Flowers102 [35], and OxfordPets [36]) as ID datasets for OOD detection presents relatively lower difficulty as shown in Fig. 3, we leave more
+
+![](images/3179384cf6c5f32757ff2ec23c1096e85edf7724d0bee176cc0262fa0bb2070b.jpg)  
+(a) Conventional OOD benchmark
+
+![](images/473ae12adfd35b414a654564acef41ba335a1dae659dd6e9bbf391ca6c4e51ab.jpg)  
+(b)Challenging OOD benchmark  
+Figure 4. Sensitivity study of hyperparameter  $K$ . We report the average FPR95 (Blue) and AUROC (Orange) of our  $\mathrm{FA}_{\mathrm{GL}}$  on different OOD benchmarks using ImageNet-1k as the ID dataset under 16-shot setting. Dashed lines represent the performance of the best baseline (i.e.  $\mathrm{SCT}_{\mathrm{GL}}$ ).
+
+experimental details in Appendix B.
+
+In particular, for the ID dataset EuroSAT,  $\mathrm{FA}_{\mathrm{MCM}}$  surpasses the best-competing method  $\mathrm{LoCoOp_{GL}}$  by  $16.09\%$  in average AUROC and  $38.7\%$  in average FPR95, underscoring its effectiveness and versatility even when the ID dataset is of low resolution (64x64 pixels).
+
+# 5.3. Ablation study
+
+Influence of the  $\mathcal{L}_{FCE-K}$ . As shown in Tab. 5, we trained the model  $\mathrm{FA}_{CE}$  and  $\mathrm{FA}_{FCE-K}$  using the standard cross-entropy loss  $\mathcal{L}_{CE}$  and our  $\mathcal{L}_{FCE-K}$ , respectively. Our  $\mathrm{FA}_{FCE-K}$  significantly outperforms  $\mathrm{FA}_{CE}$  under the same inference setting, which demonstrate the effectiveness of our  $\mathcal{L}_{FCE-K}$ .
+
+Initialization of the forced and original prompt. As shown in Tab. 6, we perform experiments comparing different initialization scenarios for both prompts. Manual initialization uses the embeddings of "a photo of a [class-c]" to initialize the prompt's embeddings, while the random initialization setting is based on CoOp [54]. The results show that employing consistent manual initialization for both prompts enables the forced prompt to effectively learn more specific descriptions of the ID classes.
+
+Influence of the shared learnable vector. We also explore the influence of the shared learnable vector and the independent learnable vector for the forced prompts. As shown in Tab. 7, we can observe that using the shared learnable vector performs well in the few-shot setting since the independent learnable vector for each class has more parameters and requires more training data [54].
+
+# 5.4. Sensitivity study
+
+As shown in Fig. 4, we explore the influence of the hyperparameter  $K$ . Overall, with  $K$  ranging from 1 to 6, the results indicate that our proposed framework is insensitive to the choice of  $K$ . Concretely, our method is stable and outperforms the best baseline  $\mathrm{SCT}_{\mathrm{GL}}$  in average AUROC and FPR95 on both conventional and challenging OOD detection benchmarks. Specially, as  $K$  increases, the average AUROC shows an upward trend and then tends to be sta
+
+ble (see Fig. 4 (a)), showing a bottleneck in capturing more comprehensive semantic representations of the ID classes.
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">MCM</td><td colspan="2">GL-MCM</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>FAce</td><td>41.43±3.11</td><td>91.01±0.67</td><td>34.29±1.94</td><td>90.99±0.56</td></tr><tr><td>FAFCE-K</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>
+
+Table 5. Influence of the  $\mathcal{L}_{FCE-K}$ . MCM and GL-MCM refer to the score functions used during model inference.  
+
+<table><tr><td rowspan="2">Forced-M-Init</td><td rowspan="2">Original-M-Init</td><td colspan="2">FA MCM</td><td colspan="2">FA GL</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>-</td><td>-</td><td>40.71±4.00</td><td>91.28±0.82</td><td>34.88±2.92</td><td>92.12±0.76</td></tr><tr><td>✓</td><td>-</td><td>40.81±2.25</td><td>91.25±0.64</td><td>36.03±2.84</td><td>91.62±1.01</td></tr><tr><td>-</td><td>✓</td><td>31.35±1.34</td><td>93.35±0.34</td><td>26.39±1.02</td><td>93.64±0.19</td></tr><tr><td>✓</td><td>✓</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>
+
+Table 6. Ablation study of different initialization scenarios for the forced and original prompts. "M-Init" represents manual initialization.  $\checkmark$  represents using manual initialization; - represents using random initialization.  
+
+<table><tr><td rowspan="2">Shared- Vector</td><td rowspan="2">M-Init</td><td colspan="2">FA MCM</td><td colspan="2">FA GL</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>-</td><td>-</td><td>44.02±2.24</td><td>90.17±0.42</td><td>46.29±1.33</td><td>88.24±0.41</td></tr><tr><td>✓</td><td>-</td><td>40.71±4.00</td><td>91.28±0.82</td><td>34.88±2.92</td><td>92.12±0.76</td></tr><tr><td>-</td><td>✓</td><td>34.69±0.62</td><td>92.57±0.12</td><td>29.27±0.55</td><td>92.82±0.80</td></tr><tr><td>✓</td><td>✓</td><td>29.07±1.11</td><td>93.77±0.19</td><td>25.68±0.58</td><td>93.82±0.11</td></tr></table>
+
+Table 7. Ablation study of the shared learnable vector.  $\sqrt{}$  - for "Shared-vector" represents using the shared / independent learnable vector for the forced prompt;  $\sqrt{}$  - for "M-Init" represents using manual / random initialization for the forced prompt.
+
+# 6. Conclusion
+
+In this study, we propose a novel CLIP-based framework for OOD detection based on Forced prompt leArning (FA), which focuses on fully exploiting the ID knowledge to effectively improve OOD detection without exploring complex OOD-related knowledge. We introduce a learnable forced prompt in addition to the frozen original prompt, both of which are using the same manual initialization. The forced prompt treats the original prompt as a reference, forcing itself to learn more diversified semantic descriptions of the ID classes rather than being limited to the textual semantics of class labels. We also introduce a forced coefficient to facilitate the forced prompt in learning more nuanced descriptions of the ID classes. Comprehensive experimental evaluations demonstrate that our method consistently surpasses current state-of-the-art methods on diverse benchmarks. We expect that our study can bring new insight on VLMs-based OOD detection methods and inspire more future research.
+
+# 7. Acknowledgments
+
+This work is supported in part by the National Natural Science Foundation of China (grant No. 62071502), the Major Key Project of PCL (grant No. PCL2023A09), and Guangdong Excellent Youth Team Program (grant No. 2023B1515040025).
+
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+        "text": "FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging",
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+        "text": "Xin You $^{1,2,3}$  Runze Yang $^{1}$  Chuyan Zhang $^{1}$  Zhongliang Jiang $^{2}$  Jie Yang $^{1,*}$  Nassir Navab $^{2,*}$",
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+        "text": "$^{1}$  Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China",
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+        "text": "$^{2}$  Computer Aided Medical Procedures, Technical University of Munich, Munich, Germany",
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+        "text": "3 Munich Center for Machine Learning, Munich, Germany",
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+        "text": "xin.you@tum.de, nassir.navab@tum.de",
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+        "text": "Abstract",
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+        "text": "The temporal interpolation task for 4D medical imaging, plays a crucial role in clinical practice of respiratory motion modeling. Following the simplified linear-motion hypothesis, existing approaches adopt optical flow-based models to interpolate intermediate frames. However, realistic respiratory motions should be nonlinear and quasi-periodic with specific frequencies. Intuited by this property, we resolve the temporal interpolation task from the frequency perspective, and propose a Fourier Basis-guided Diffusion model, termed FB-Diff. Specifically, due to the regular motion discipline of respiration, physiological motion priors are introduced to describe general characteristics of temporal data distributions. Then a Fourier motion operator is elaborately devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space of Variational Autoencoder. Well-learned Fourier bases can better simulate respiratory motions with motion patterns of specific frequencies. Conditioned on starting and ending frames, the diffusion model further leverages well-learned Fourier bases via the basis interaction operator, which promotes the temporal interpolation task in a generative manner. Extensive results demonstrate that FB-Diff achieves state-of-the-art (SOTA) perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Codes are available here.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "4D medical images, which depict 3D volumes with temporal variations, are essential in clinical practice for capturing dynamic changes and monitoring the progression of diseases over time [12, 25, 49, 52]. A significant application is the temporal modeling for breathing-induced motions of",
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+    {
+        "type": "text",
+        "text": "cardiac or pulmonary anatomical structures. That task aims to enrich motion visualizations by generating intermediate frames under the condition of starting and ending frames, which is consistent with the concept of Video Frame Interpolation (VFI) in natural scenarios.",
+        "bbox": [
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+        "text": "VFI has been thoroughly investigated through systematic studies in recent years [10, 24, 31, 37, 39, 41, 58, 61, 62]. However, due to unique properties and constraints of medical imaging, it remains a challenge to directly implement these frameworks into 4D medical video interpolation with maintaining equally promising performance. Specifically, the quality of ground truth intermediate frames in medical imaging is often compromised due to factors such as imaging noise, unstable breathing, causing unexpected artifacts [17, 25, 43, 49]. Thus, the lower image quality compared to videos in the natural domain, will degrade the interpolation performance of VFI models. Besides, potential patients' movement might induce an additional disturbance to the temporal modeling [5, 38].",
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+    {
+        "type": "text",
+        "text": "Furthermore, there exists a discrepancy on the type of motions between natural and medical scenes. The former focuses on the object movement and illumination intensity change. While in the medical domain, motions can be depicted as subtle anatomical variance with quasi-periodic motion discipline [51, 56]. Thus, a specific motion prior of anatomies is effective to boost the temporal interpolation, especially for the medical data with limited resources from a small pool of individuals.",
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+        "text": "On account of these challenges, we present the following question: \"How can we devise a specialist VFI model tailored for 4D temporal medical volumes?\" Existing methods [2, 13, 29, 30, 51] on medical VFI face a major shortcoming: the linear motion hypothesis in a breathing period is required for the regression of intermediate frames as revealed in Fig.1(a). However, respiratory motions should be a nonlinear oscillatory process that cannot be simply mod-",
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+        "text": "This ICCV 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": "28010",
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+        "image_caption": [
+            "(b) Nonlinear & quasi-periodic motion  $\\Longrightarrow$  Our model",
+            "Figure 1. Temporal Interpolation for respiratory motions. (a) Simplified linear-motion hypothesis: interpolating intermediate frames by regressing optical flows with linear variations. (b) Nonlinear & quasi-periodic motions: leveraging diffusion models conditioned on Fourier motion bases, which represent various motion patterns indicating nonlinear and locally inconsistent anatomical variations."
+        ],
+        "image_footnote": [],
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+        "type": "text",
+        "text": "eled with a linear equation [32, 51]. Also, these methods fail to recognize that respiratory motions in heart or lung, are indeed a quasi-periodic motion process with specific frequencies by extending the timeline. Intuited by this, we resolve the respiratory motion simulation from a frequency perspective. In Fig.1(b), each medical volume in the temporal domain can be viewed as a specific value in the periodic curve. That periodic curve can be decomposed as a group of sine and cosine bases with multiple frequencies [46]. Comparatively, there exists a group of Fourier bases, which are capable of reconstructing original temporal sequences. Here Fourier bases with different frequencies refer to various motion patterns, which indicate nonlinear and locally anisotropic variations of anatomical structures. In our work, Fourier bases are acquired by the Fast Fourier Transform (FFT) on the temporal domain.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, 4D data distributions of the respiratory process depict a regular motion discipline, with temporal variations from inhaling to exhaling, or from diastole to systole. Motivated by that observation, physiology motion priors are introduced to encode generic characteristics of the respiratory process. Then a Fourier Motion Operator  $O_{FM}$  is elaborately devised to yield enhanced motion bases by incorporating physiology motion priors and case-specific spectral information in the feature space. Specifically, A Variational Autoencoder (VAE) is introduced to map the video space into the feature space. Physiology motion priors are defined as learnable frequency embeddings, which can be updated by pretraining a Variational Autoen",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "coder (VAE) on given temporal data. And case-specific frequency information can be extracted by FFT in the temporal domain. Well-learned physiology motion priors can enrich Fourier bases with generic properties of respiratory motions. Then enhanced Fourier motion bases can better simulate the quasi-periodic respiratory process with motion patterns of specific frequencies. On the grounds that diffusion models show promising performance in generating realistic videos [15, 16, 35, 48], a Markov chain process is learned to transform Gaussian noise into target videos by the proposed Fourier Bases-guided Diffusion, termed FB-Diff. Since only starting and ending frames are available during inference, they serve as conditional prompts for intermediate frame interpolation. Meanwhile, we devise the basis interaction operator to inject enhanced Fourier bases into the conditional diffusion model. Then, FB-Diff can well address the temporal interpolation task in a generative manner.",
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+        "type": "text",
+        "text": "Our proposed method has achieved state-of-the-art (SOTA) interpolation performance compared with other methods for 4D medical imaging, particularly on the mid-most frames. For quantitative results, more comprehensive evaluation metrics are adopted in this work, including traditional reconstruction metrics and feature-level perceptual metrics. FB-Diff not only presents promising reconstruction metrics but also superior perceptual results. Qualitative visualizations reveal better temporal consistency by FB-Diff compared with other linear-motion-based methods. Our main contributions are summarized as follows:",
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+        "image_caption": [
+            "Figure 2. The pipeline of FB-Diff. (a) The Fourier motion operator is proposed to extract Fourier bases in a feature space of VAE. Bases consist of learnable generic motion priors and case-specific frequency information. (b) Fourier bases are first adapted to the masked video domain under the guidance of well-learned motion priors and pretrained VAE weights. Domain-adapted bases serve as the conditional input to boost the video synthesis by diffusion models."
+        ],
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+        "list_items": [
+            "- We propose a diffusion model termed FB-Diff for the temporal interpolation of 4D medical imaging. FB-Diff leverages Fourier motion bases, which indicate motion patterns with specific frequencies to resolve the respiratory modeling with nonlinear and quasi-periodic motions.",
+            "- We introduce the Fourier motion operator  $O_{FM}$  to extract Fourier bases, containing physiology motion priors and case-specific frequency representations.",
+            "- We devise the basis interaction operator to inject Fourier bases into the diffusion model. Fourier bases can boost the video synthesis for temporal interpolation.",
+            "- Extensive results demonstrate that FB-Diff reveals SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics."
+        ],
+        "bbox": [
+            89,
+            589,
+            482,
+            800
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            89,
+            814,
+            232,
+            830
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Video Frame Interpolation. Popular VFI techniques are mainly classified into motion-free and motion-based approaches, depending on whether optical flows are incorporated or not. Motion-based: These approaches warp",
+        "bbox": [
+            89,
+            839,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "input frames forward or backward based on optical flows acquired by either off-the-shelf networks [11, 23, 44, 45, 50] or custom-designed flow estimators [20, 21, 27, 31, 33, 58]. Warped intermediate frames are then refined by delicately designed networks [3, 26] to enhance visual quality. Recently, Transformer-based motion estimators are proposed to raise the upper limit of VFI performance [36, 41, 58] Motion-Free: Motion-free methods rely on implicit spatiotemporal modeling [8, 9, 19, 28] to generate the intermediate frame. However, due to a limited quality of 4D medical videos and quasi-periodic motion priors, existing VFI frameworks are not feasible. That is why we aim to propose a specialist VFI model for 4D medical sequences.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4D Medical VFI. Existing methods on this topic mainly leverage volumetric motions for 4D temporal interpolation. Specifically, SVIN [13] estimates forward and backward deformation fields, which will yield precise intermediate frames by linearly combining bidirectional information. MPVF [51] resolves various magnitudes of motions by proposing a multi-pyramid voxel flows model that takes",
+        "bbox": [
+            511,
+            794,
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+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "28012",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "multi-scale voxel flows into account. DDM [29] can learn spatial deformation information between the source and target volumes and provide a latent code for generating intermediate frames along a geodesic path. UVI-Net [30] utilizes the flow calculation model with the time-domain cycle-consistency constraint and linear motion hypothesis, to realize motion modeling in an unsupervised style. However, the linear hypothesis for motions will induce temporal inconsistency and spatial distortion.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Diffusion-based Video Interpolation. Denoising diffusion probabilistic models [15, 16, 35] reveal promising performance in generating realistic images or videos. Some methods maximize the potential of diffusion models to resolve video interpolation tasks. Essentially, these approaches implicitly learn the temporal motions from the starting frame to the ending frame [1, 7, 24]. LDMVFI [10] proposes a latent diffusion model, which approaches the VFI problem from a generative perspective by formulating it as a conditional synthesis issue. However, these diffusion models do not leverage effective conditional guidance, which is crucial for medical VFI with intrinsic motion priors. Thus, we introduce Fourier bases to enhance the conditional synthesis.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Fourier Motion Bases",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since respiratory motions for heart or lung exhibit a quasi-periodic characteristic, we intend to resolve this task from a frequency perspective. Specifically, the respiration can be viewed as an oscillatory process with certain frequencies. Thus, we draw an analogy between 2D time-varying curves and 4D temporal medical volumes. Curves can be decomposed into a group of harmonic oscillators with various frequencies [46]. Similarly, temporal volumes can be restored via a stack of extracted Fourier bases, which are embodied with various motion patterns of anatomical deformation. The whole process can be formulated as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {B} _ {k} = \\sum_ {n = 0} ^ {N - 1} V _ {n} e ^ {- i 2 \\pi k \\frac {n}{N}}, k = 0, 1, \\dots , N - 1, \\tag {1}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\nV _ {n} = \\frac {1}{T} \\sum_ {k = 0} ^ {N - 1} \\mathcal {B} _ {k} e ^ {i 2 \\pi n \\frac {k}{N}}, n = 0, 1, \\dots , N - 1, \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathcal{B}_k$  means the  $k_{th}$  Fourier basis in the frequency domain,  $V_{n}$  refers to the  $n_{th}$  medical volume, and  $N$  is the frame number. These Fourier bases describe locally anisotropic anatomical variations with different motion intensities, promoting the performance of the temporal interpolation model  $\\mathcal{I}$ . Thus, the goal of our work is to deduce 4D medical videos  $V$  conditioned on two prompting frames  $V_{0}, V_{N-1}$  and Fourier motion bases  $\\mathcal{B}$ :",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {I} ^ {*} = \\underset {\\mathcal {I}} {\\arg \\min } \\| \\boldsymbol {V} - \\mathcal {I} \\left(V _ {0}, V _ {N - 1}; \\mathcal {B}\\right) \\| _ {\\mathcal {D}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "image",
+        "img_path": "images/3a5fb39ec16e2282dd96e4173cb949fd02dec76d57657897bdfbad4585e8955a.jpg",
+        "image_caption": [
+            "Figure 3. The details of Fourier motion operator. Fourier bases are decomposed as physiology motion priors and case-specific Fourier features, corresponding to phase and magnitude components."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "$\\mathcal{I}^*$  refers to the optimal solution in the interpolation model set, and  $\\mathcal{D}$  represents the distance-based normed space. We systematically organize the following sections along Fourier bases. Section 3.2 introduces the design of the Fourier Motion Operator, which constructs Fourier bases with physiology motion priors and case-specific frequency information. Section 3.3 adapts Fourier bases to the to-be-interpolated video domain with well-learned physiology motion priors. Section 3.4 provides details of the diffusion model conditioned on Fourier bases.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Fourier Motion Operator",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To explicitly extract the Fourier bases with various motion patterns for the respiration process, we introduce the Fourier Operator  $O_{\\mathcal{F}}$  as a neural operator. As stated in Eq.(2),  $O_{\\mathcal{F}}$  will operate in the temporal domain, not the spatial domain. Since the common Fourier operator  $O_{\\mathcal{F}}$  only mines case-specific frequency representations, general physiology characteristics inside respiratory data are ignored. Inspired by that notion, we devise the Fourier motion operator  $O_{FM}$  as a neural operator in the feature space. To map the image space into feature space, we introduce a Variational Autoencoder (VAE) as revealed in Fig.2(a). Due to no built-in 4D convolutional operator, we replace it with 3D spatial convolution and 1D temporal convolution as [34, 59] did. The spatial layer in Fig.2(a) consists of spatial convolution, GELU, and group normalization operations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The Fourier motion operator  $O_{FM}$  is devised to acquire spectral characteristics with both physiology motion priors and case-specific representations in the feature space. Firstly, physiology motion priors are introduced as learnable frequency embeddings, which are updated by backward gradients of restoring given temporal data via VAE. Well-trained frequency embeddings  $\\theta$  can represent the generic discipline of the regular respiration process [54], with  $\\theta_{k}$  referring to the  $k_{th}$  element  $(k = 0,1,\\dots,N - 1)$ . Then Fourier bases  $\\mathcal{B}$  are made up of physiology motion priors  $\\theta$  and case-specific features  $F$ , which arise from the output of",
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+    {
+        "type": "page_number",
+        "text": "28013",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "spatial and temporal layers. As depicted by Fig.3,  $\\mathcal{B}$  with a complex type is yielded in the following style:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {B} = \\underbrace {\\mathcal {M} (\\left\\| O _ {\\mathcal {F}} (F) \\right\\| _ {2})} _ {\\text {C a s e - S p e c i f i c}} \\cdot \\underbrace {e ^ {i U (\\tau (\\theta))}} _ {\\text {G e n e r a l}}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$\\tau$  means the channel transform,  $U$  refers to the upsampling which unifies the resolution of  $\\theta$  and  $\\pmb{F}$ . These operations transform general motion priors into the phase part of Fourier bases, which determines the motion variation standing for the whole dataset distribution. Then  $\\| \\cdot \\| _2$  means the  $L_{2}$  norm,  $\\mathcal{M}$  is the convolutional mapping operation. They will output motion bases' magnitude information, which selectively highlights regions in spectral maps relevant to case-specific information.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Meanwhile, feature maps  $F$  are further enriched with more fine-grained frequency details. The specific mechanism can be described with Eq.(5):",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\boldsymbol {F}} = \\boldsymbol {F} + \\sigma \\mathcal {O} _ {\\mathcal {F}} ^ {- 1} (\\mathcal {B}), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "here  $O_{\\mathcal{F}}^{-1}$  and  $\\sigma$  refer to the inverse Fourier transform and Sigmoid operators, which will boost deep features  $\\hat{F}$  with enriched details, including shape and texture information.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. Frame Inpainting-based Basis Synthesis",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Due to the fact that only starting and ending frames can be acquired during inference, a significant step is to adapt Fourier bases to the masked video domain. Motivated by the fact that strong correlations exist between Fourier motion bases and inpainted temporal sequences, we plan to jointly optimize these two variables. To accomplish that goal, we repurpose well-calibrated physiology motion priors from VAE, which prove to be effective in providing the motion guidance for intermediate frame inpainting. Also, pretrained weights of VAE encode implicit temporal dependencies between frames, enhancing the reconstruction of masked video sequences via the finetuned VAE noted as  $\\mathcal{G}$ . A mathematical formulation is defined as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {V}, \\hat {\\mathcal {B}} = \\mathcal {G} (\\hat {\\boldsymbol {\\theta}}, V _ {\\boldsymbol {M}}) = \\mathcal {G} (\\hat {\\boldsymbol {\\theta}}, V _ {0},.., \\mathbf {0},.., V _ {N - 1}), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\hat{\\theta}$  and  $V_{M}$  correspond to well-trained general motions and zero-masked videos,  $\\hat{V}$  and  $\\hat{B}$  refer to inpainted videos and domain-adapted Fourier bases.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The interaction between temporal video representations and  $\\hat{\\mathcal{B}}$  is implemented via the Fourier motion operator as shown in Fig.2(b). For the joint optimization process, video sequences will contribute temporal variations, enhancing the synthesis of adapted Fourier bases. Conversely, Fourier bases for zero-masked inputs inherently generate a spectral map that emphasizes regions with motion in the temporal axis. This activated map aids in temporal frame inpainting by exerting attention on regions with different magnitudes.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/e46e1aa2636d3a69e2489f0e0819f6dad5bd9bb3792fe805fd5471e932837caa.jpg",
+        "image_caption": [
+            "Figure 4. The architecture of basis interaction operator. Fourier motion bases selectively enhance video representations by measuring the motion intensity of different regions. Then those enhanced temporal representations can enrich denoised embeddings from the diffusion model."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Basis-guided 4D Conditional Diffusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "VAE in Fig.2(a) is not only devised for universal motion priors, but also for the latent diffusion model (LDM), which shows better compatibility for extra conditional inputs. Besides, LDM synthesizes latent embeddings occupying less GPU memory compared to 4D temporal volumes. And the VAE decoder is leveraged to reconstruct interpolated video sequences with synthesized latent embeddings.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the specific diffusion process, the whole video sequence  $V$  is first encoded as a latent embedding  $z_0 = \\mathcal{G}_e(V)$ . Then the latent code  $z_0$  is perturbed as:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, 1), \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\overline{\\alpha}_t = \\prod_{i=1}^t (1 - \\beta_t)$  with  $\\beta_t$  is the noise coefficient at time step  $t$ , and  $t$  is uniformly sampled from the timestep index set  $[1,2,\\dots,T]$ . This process can be regarded as a Markov chain, which incrementally adds Gaussian noise to the latent code  $z_0$ . The denoising model  $d$  receives  $z_t$  as input and is optimized under conditional guidance to learn the latent space distribution with the objective function:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\epsilon} = E _ {z _ {t}, \\epsilon \\sim \\mathcal {N} (0, 1)} \\| \\epsilon - \\epsilon_ {d} \\left(z _ {t}, t; \\hat {\\mathcal {B}}, \\mathcal {G} _ {e} \\left(\\boldsymbol {V} _ {\\boldsymbol {M}}\\right), \\hat {\\boldsymbol {V}}\\right) \\| ^ {2}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "here  $\\epsilon_d$  is the regressed noise, adapted Fourier bases  $\\hat{\\mathcal{B}}$  and inpainted coarse videos  $\\hat{V}$  are incorporated as the conditional guidance. Moreover, feature maps of starting and ending frames by the VAE encoder  $\\mathcal{G}_e$  serve as a strong prompt for the 4D video synthesis. Then during the training process of FB-Diff, the total loss  $\\mathcal{L}$  consists of the denoising loss  $\\mathcal{L}_{\\epsilon}$  and the  $L_{2}$ -norm reconstruction loss  $\\mathcal{L}_r(\\hat{V},V)$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To inject Fourier motion bases into LDM and harness coarsely inpainted results, we design the Basis Interaction Operator (BIO) as shown in Fig.4. Specifically, inpainted videos are mapped into video feature representations via spatial & temporal layers and the downsampling operation. Fourier motion bases with various motion patterns, selectively enhance video representations by measuring the motion intensity of different regions. Those enhanced temporal representations can enrich denoised embeddings from",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "28014",
+        "bbox": [
+            478,
+            944,
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+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/cad301eea28cf45b15abfeb328188c97382b503a0137fcc1c8a0ba6185357e99.jpg",
+        "table_caption": [
+            "Table 1. Baseline comparison with flow-based and diffusion-based models. (Bold: the best, Underlined: the second best. Δ values represent the relative difference between our model and UVI-Net, and red and blue numbers stand for better and worse results)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"4\">ACDC Cardiac</td><td colspan=\"4\">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>31.43±0.421</td><td>1.563±0.206</td><td>26.3</td><td>93.6</td><td>30.49±0.304</td><td>2.650±0.245</td><td>38.5</td><td>125.6</td></tr><tr><td>Voxelmorph [2]</td><td>30.77±0.502</td><td>1.969±0.197</td><td>29.4</td><td>102.1</td><td>29.90±0.373</td><td>2.815±0.260</td><td>43.2</td><td>149.0</td></tr><tr><td>Transmorph [6]</td><td>29.81±0.532</td><td>2.136±0.255</td><td>31.5</td><td>109.5</td><td>29.04±0.403</td><td>2.946±0.291</td><td>40.5</td><td>143.5</td></tr><tr><td>MPVF [51]</td><td>31.53±0.410</td><td>1.594±0.201</td><td>24.8</td><td>91.3</td><td>30.76±0.265</td><td>2.418±0.246</td><td>39.4</td><td>120.3</td></tr><tr><td>UVI-Net [30]</td><td>32.16±0.402</td><td>1.662±0.245</td><td>23.0</td><td>94.2</td><td>31.57±0.311</td><td>2.211±0.216</td><td>37.8</td><td>121.7</td></tr><tr><td>IFRNet [31]</td><td>30.58±0.408</td><td>1.752±0.249</td><td>27.8</td><td>97.5</td><td>30.05±0.280</td><td>2.316±0.273</td><td>39.7</td><td>124.0</td></tr><tr><td>LDMVFI [10]</td><td>27.11±0.460</td><td>2.943±0.410</td><td>28.8</td><td>99.2</td><td>26.31±0.453</td><td>3.659±0.341</td><td>42.1</td><td>142.7</td></tr><tr><td>LDDM [7]</td><td>24.53±0.481</td><td>2.634±0.308</td><td>33.4</td><td>105.7</td><td>25.19±0.273</td><td>2.914±0.287</td><td>48.7</td><td>146.3</td></tr><tr><td>Conditional Diff [16]</td><td>26.59±0.545</td><td>2.460±0.357</td><td>30.1</td><td>95.7</td><td>25.95±0.391</td><td>3.294±0.375</td><td>45.0</td><td>133.0</td></tr><tr><td>DDM [29]</td><td>29.79±0.504</td><td>2.089±0.352</td><td>27.4</td><td>110.3</td><td>29.67±0.420</td><td>2.705±0.330</td><td>40.8</td><td>165.5</td></tr><tr><td>FB-Diff</td><td>30.95±0.386</td><td>1.452±0.205</td><td>21.5</td><td>88.9</td><td>30.18±0.287</td><td>2.066±0.215</td><td>37.7</td><td>113.6</td></tr><tr><td>Δ value</td><td>1.21 ↓</td><td>0.210 ↓</td><td>1.5 ↓</td><td>5.3 ↓</td><td>1.39 ↓</td><td>0.145 ↓</td><td>0.1 ↓</td><td>8.1 ↓</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the diffusion model, promoting a promising synthesis of highlighted regions. Thus, BIO can boost well-interpolated videos with spatial and temporal consistency.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+            429,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Dataset. To evaluate the interpolation performance of our framework, we conduct experiments on public ACDC cardiac [4] and 4D-Lung datasets [22]. For ACDC with the MRI modality, volume sequences between the end-diastolic and end-systolic phases are extracted as valid 4D data. Of all the 150 4D sequences, cases with identity 1-100, 101-120, and 121-150 serve as the training, validation, and testing sets. Besides, all MRI volumes are cropped to  $128 \\times 128 \\times 32$ , and the frame number ranges from 6 to 16 [53, 57]. For 4D-Lung CT images, the end-inspiratory and end-expiratory scans are set as the initial and final images. We collect 125 4D videos from [22], with the resolution equal to  $6 \\times 128 \\times 128 \\times 128$ . They are split as  $80 / 15 / 30$  cases for training, validation, and inference. We uniform the frame number as 16 with zero paddings.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "**Evaluations.** We select quantitative evaluation metrics including Peak Signal-to-Noise Ratio (PSNR) [18], Learned Perceptual Image Patch Similarity (LPIPS) [55, 60], Fréchet Inception Distance (FID) [14], and Fréchet Video Distance (FVD) [47]. Compared to PSNR, which is the traditional pixel-wise reconstruction metric, LPIPS and FVD evaluate perceptual quality from the perspective of human vision [10, 24, 61], which is more feasible and favored in clinical practice. Specifically, LPIPS reveals important perceptual similarity like human vision. FID and FVD evaluate the dataset distribution bias between realistic and synthesized data, including spatial and temporal consistency.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training Details. The VAE maps the image space into",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the downsampled latent space with a ratio of  $1/8$ . And the proposed conditional diffusion model is implemented with a lightweight UNet. All models are trained using the AdamW optimizer with the linear warm-up strategy. The batch size, diffusion step  $T$ , and training epoch are equal to 2, 1000, and 500. Experiments are implemented based on Pytorch and 2 NVIDIA RTX 4090 GPUs. More details about the network and training settings are described in the Appendix.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparisons with SOTA baselines",
+        "text_level": 1,
+        "bbox": [
+            511,
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Quantitative Comparison. We comprehensively conduct experiments on ACDC cardiac and 4D Lung datasets. Quantitative results are illustrated in Tab.1. Our model achieves the best performance across the benchmark on perceptual evaluation metrics from the perspective of human vision [10, 61], which are clinically favored compared with the pixel-centric reconstruction metric [7]. Specifically, FB-Diff outperforms UVI-Net [30] with  $0.210 \\downarrow$  LPIPS and  $5.3 \\downarrow$  FVD values on ACDC. Also, our model maintains quite satisfactory PSNR values of  $30.95\\mathrm{dB}$  and  $30.18\\mathrm{dB}$  on ACDC and 4D Lung. Although diffusion models are not sensitive to pixel-wise intensities [15], the conditional guidance of Fourier bases and coarsely inpainted videos is effective to boost the interpolation performance of diffusion models. Tab.1 reveals that FB-Diff significantly surpasses existing diffusion models on all metrics.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, the interpolation process becomes most challenging for the midmost frames since they are positioned farthest from the two reference frames [24]. And our model can better resolve this issue due to stronger temporal representations based on quasi-periodic motion modeling. Thus, a quantitative evaluation of central frames is necessary. As shown in Tab.2, FB-Diff demonstrates greater performance advantages, with  $4.3\\downarrow$  FID and  $8.2\\downarrow$  FVD values compared with UVI-Net. Additionally, FB-Diff acquires a competi",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "28015",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8da4c198ac582ec7f985250dd8520efe4944f7261aca5a0b3ecc632bc930d0c8.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative comparison of the midmost frame interpolation between different models. VM: Voxelmorph."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            137,
+            89,
+            867,
+            349
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/da4ed1f522b999eaef26e04949fe27039f74ff39048bbe97f6a0fa1e5ba4dbe0.jpg",
+        "table_caption": [
+            "Table 2. Interpolation performance of the midmost frames on ACDC cardiac. The choice of midmost frames: if the frame number  $N$  is odd, three intermediate frames are selected, otherwise only two frames are chosen."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>26.01±0.467</td><td>2.673±0.361</td><td>38.9</td><td>142.8</td></tr><tr><td>DDM [29]</td><td>24.37±0.511</td><td>2.756±0.330</td><td>41.5</td><td>145.1</td></tr><tr><td>UVI-Net [30]</td><td>26.25±0.410</td><td>2.542±0.374</td><td>37.0</td><td>137.1</td></tr><tr><td>FB-Diff</td><td>26.18±0.413</td><td>2.287±0.305</td><td>32.7</td><td>128.9</td></tr><tr><td>Δ value</td><td>0.07 ↓</td><td>0.255 ↓</td><td>4.3 ↓</td><td>8.2 ↓</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "tive PSNR value, which demonstrates the effectiveness of respiration-related modeling via Fourier bases.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Qualitative Comparison. Qualitative results on the interpolated midmost frame are depicted in Fig.5. SVIN [13], Voxelmorph [2], and DDM [29] leverage the single-direction flow estimation to interpolate intermediate frames with linear motions. Compared with that, UVI-Net [30] constructs the interpolation model with time-domain cycle-consistency, and achieves better reconstruction performance as expected. However, these methods essentially overlook the nonlinear and quasi-periodic motion discipline between temporal sequences, resulting in unsatisfactory interpolated results. Instead, FB-Diff exhibits advantageous predictions for midmost frames under the guidance of various motion patterns, indicating locally anisotropic motions with different intensities. Besides, other diffusion models do not work well due to the lack of fine-grained conditional guidance.",
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+    {
+        "type": "text",
+        "text": "4.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Key Components. An ablation study is conducted to investigate the significance of various components in FB-Diff as shown in Tab.3. (a) Physiology Motion Priors  $\\theta$ . By",
+        "bbox": [
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+        "type": "table",
+        "img_path": "images/f006ddcb334f88c13fa38ae31482e173fdb0836eb48bf0dd0ce0e5815b0219d4.jpg",
+        "table_caption": [
+            "Table 3. Ablation study on key components.  $\\theta$ : physiology motion priors,  $\\hat{B}$ : Fourier motion bases,  $\\hat{V}$ : coarsely inpainted videos."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Settings</td><td colspan=\"2\">ACDC Cardiac</td><td colspan=\"2\">4D Lung</td></tr><tr><td>θ</td><td>ˆB</td><td>ˆV</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>29.76</td><td>1.710</td><td>29.53</td><td>2.413</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>28.17</td><td>2.105</td><td>28.40</td><td>2.971</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>30.29</td><td>1.655</td><td>29.71</td><td>2.246</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "removing  $\\theta$  from the Fourier motion operator, interpolation performance decreases significantly due to the loss of general spectral characteristics from respiratory data. Therefore, Fourier bases lack the precise phase information. (b) Fourier bases  $\\hat{\\mathcal{B}}$ . Without  $\\hat{\\mathcal{B}}$  as conditional guidance, the conditional diffusion model fails to perceive explicit motion patterns with different frequencies, which provide the intensity of anisotropic motions. As a result, the generative model cannot well learn the regular temporal variations, with 2.78 dB  $\\downarrow$  and 1.78 dB  $\\downarrow$  PSNR values on ACDC and 4D Lung. (c) Inpainted Videos  $\\hat{V}$ . Here the coarsely reconstructed sequences serve as the output by the finedtuned VAE as revealed in Fig.2. And the joint optimization process boosts the spatial and temporal representations of  $\\hat{V}$ . Consequently, discarding this component will reduce fine-grained details of the diffusion model's output.",
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+    },
+    {
+        "type": "text",
+        "text": "Hyper-settings of Fourier Bases. (a) The number of Fourier Bases  $N_{Fb}$ . We first analyze the quantitative effects of the frequency number on the interpolation performance. As revealed in Tab.4, reducing the frequency number will cause degraded performance of the temporal simulation. Specifically, 1.30 dB lower PSNR and 0.535 higher LPIPS values are induced by decreasing  $N_{Fb}$  from 16 to 8. That phenomenon indicates that some elements in the group of",
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "28016",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c70cbbc9d0193a624785ed0adda338f619441ab48549cd94deb117f6ac5a06fa.jpg",
+        "image_caption": [
+            "Figure 6. Visualizations on the frequency spectral of Fourier bases.  $V_{0}$ ,  $V_{N - 1}$ : starting and ending frames.  $f_{1} - f_{8}$  refer to different motion patterns, which highlight different regions under different frequency. There also appear locally anisotropic motion intensities inside a specific motion pattern."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e1109913f67f4e7e5b943dde274bf8c0476fa60b1a7c67b26c2d1d3363d2b6ea.jpg",
+        "table_caption": [
+            "Table 4. Ablation study on the hyper-settings of Fourier bases.  $N_{Fb}$ : the frequency number of Fourier bases."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Settings</td><td colspan=\"2\">ACDC Cardiac</td><td colspan=\"2\">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>\\(N_{Fb}\\)=16 (Ours)</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr><tr><td>\\(N_{Fb}\\)=12</td><td>30.76</td><td>1.640</td><td>29.97</td><td>2.570</td></tr><tr><td>\\(N_{Fb}\\)=8</td><td>29.65</td><td>1.987</td><td>29.50</td><td>2.745</td></tr><tr><td>w/o Real part</td><td>29.18</td><td>1.872</td><td>29.56</td><td>2.453</td></tr><tr><td>w/o Imaginary part</td><td>29.88</td><td>1.681</td><td>29.67</td><td>2.401</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "bases with the frequency ranging from  $f_{8}$  to  $f_{15}$  are consistent with specific frequencies of the respiratory process. (b) Real & Imaginary Parts.  $\\hat{\\mathcal{B}}$  bears real and imaginary parts after combining generic priors and case-specific spectral representations, which perform as the phase and magnitude information. Eliminating either the real or imaginary part will convert the complex data type into the real one, resulting in the loss of phase information and influencing the temporal interpolation.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.4. Visualization Analysis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Visualization of Fourier bases. To further validate the effectiveness and interpretability of our proposed Fourier bases, we visualize extracted motion bases from the most shadow layer. As revealed in Fig.6,  $f_{0} - f_{7}$  refers to the magnitude of the first eight motion bases in ascending order of frequency. Specifically,  $f_{0}$  shows a low-frequency motion pattern highlighting no region, which is strongly related to static backgrounds.  $f_{1} - f_{3}$  exhibit a large motion intensity in the highlighted right and left ventricle regions. Those regions are indeed dynamic foregrounds requiring special attention.  $f_{4}$  depicts an activation in the myocardial region, which contracts inward along the circumferential direction.  $f_{5} - f_{7}$  highlight regions with vast deformations in the temporal domain. Particularly,  $f_{6}$  illustrates a large motion on boundaries of anatomical structures. In summary, these motion patterns reveal locally anisotropic motion intensities, and are harmonized with specific frequencies of the respiratory process, thus promoting the temporal interpolation.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Visualization of temporal anatomical variations. To demonstrate the effectiveness of FB-Diff on temporal simulation, we visualize temporal variation maps for a perceptual comparison. Fig.7 provides interpolated intermediate",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/bfd652572d8a4fb20e6f20ddca808de4f098967ae86b12ade2703c4b76e21236.jpg",
+        "image_caption": [
+            "Figure 7. Temporal variation comparison between FB-Diff and existing methods with the linear motion hypothesis."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            531,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "frames at different timepoints. According to the referenced video, the anatomical motion in the temporal domain is nonlinear, which cannot be precisely simulated by existing methods with the linear motion hypothesis. In contrast, our predictions show better temporal consistency and continuity, particularly for frames at  $t = 0.6$  and 0.8.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our proposed FB-Diff resolves the temporal interpolation of 4D medical imaging from a frequency perspective, and can model the respiration-related process with nonlinear and quasi-periodic motions. A Fourier motion operator is devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space. And the diffusion model further leverages Fourier bases and two prompting frames to achieve the precise interpolation. Extensive results show that FB-Diff achieves SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Ultimately, it requires more conditional guidance such as electrocardiogram signals to simulate the highly unstable breathing, which is promising in future work.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "28017",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. We thank the anonymous reviewers for their thorough and constructive feedbacks. This research was supported in part by the project of the National Natural Science Foundation of China (No. 62376153), in part by the institute of Munich Center of Machine Learning.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "page_idx": 8
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+            "[49] Lu Wang, Shelly Hayes, Kamen Paskalev, Lihui Jin, Mark K Buyyounouski, Charlie C-M Ma, and Steve Feigenberg. Dosimetric comparison of stereotactic body radiotherapy using 4d ct and multiphase ct images for treatment planning of lung cancer: evaluation of the impact on daily dose coverage. *Radiotherapy and Oncology*, 91(3):314–324, 2009. 1",
+            "[50] Yihan Wang, Lahav Lipson, and Jia Deng. Sea-raft: Simple, efficient, accurate raft for optical flow. In ECCV, pages 36-54. Springer, 2024. 3",
+            "[51] Tzu-Ti Wei, Chin Kuo, Yu-Chee Tseng, and Jen-Jee Chen. Mpvf: 4d medical image inpainting by multi-pyramid voxel flows. IEEE Journal of Biomedical and Health Informatics, 2023. 1, 2, 3, 6",
+            "[52] Xin You, Ming Ding, Minghui Zhang, Yangqian Wu, Yi Yu, Yun Gu, and Jie Yang. Semantic difference guidance for the uncertain boundary segmentation of ct left atrial appendage. In MICCAI, pages 121-131. Springer, 2023. 1",
+            "[53] Xin You, Junjun He, Jie Yang, and Yun Gu. Learning with explicit shape priors for medical image segmentation. IEEE Transactions on Medical Imaging, 2024. 6"
+        ],
+        "bbox": [
+            516,
+            92,
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+        ],
+        "page_idx": 9
+    },
+    {
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+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[54] Xin You, Yixin Lou, Minghui Zhang, Jie Yang, and Yun Gu. Slord: Structural low-rank descriptors for shape consistency in vertebrae segmentation. IEEE Journal of Biomedical and Health Informatics, 2025. 4",
+            "[55] Xin You, Minghui Zhang, Hanxiao Zhang, Jie Yang, and Nassir Navab. Temporal differential fields for 4d motion modeling via image-to-video synthesis. arXiv preprint arXiv:2505.17333, 2025. 6",
+            "[56] Weihao Yu, Yuanhao Cai, Ruyi Zha, Zhiwen Fan, Chenxin Li, and Yixuan Yuan. X $^2$ -gaussian: 4d radiative gaussian splatting for continuous-time tomographic reconstruction. arXiv preprint arXiv:2503.21779, 2025. 1",
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+        ],
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+]

2025/FB-Diff_ Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging/c8ad7765-483e-400a-90bd-72090b0597d0_model.json

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+[
+    [
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "CVF"
+        },
+        {
+            "type": "header",
+            "bbox": [
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+            "angle": 0,
+            "content": "This ICCV 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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+            "angle": 0,
+            "content": "FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Xin You\\(^{1,2,3}\\) Runze Yang\\(^{1}\\) Chuyan Zhang\\(^{1}\\) Zhongliang Jiang\\(^{2}\\) Jie Yang\\(^{1,*}\\) Nassir Navab\\(^{2,*}\\)"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{1}\\) Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\) Computer Aided Medical Procedures, Technical University of Munich, Munich, Germany"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.272,
+                0.276,
+                0.732,
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+            ],
+            "angle": 0,
+            "content": "3 Munich Center for Machine Learning, Munich, Germany"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.362,
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+                0.637,
+                0.31
+            ],
+            "angle": 0,
+            "content": "xin.you@tum.de, nassir.navab@tum.de"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.249,
+                0.347,
+                0.327,
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+            ],
+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.092,
+                0.379,
+                0.485,
+                0.771
+            ],
+            "angle": 0,
+            "content": "The temporal interpolation task for 4D medical imaging, plays a crucial role in clinical practice of respiratory motion modeling. Following the simplified linear-motion hypothesis, existing approaches adopt optical flow-based models to interpolate intermediate frames. However, realistic respiratory motions should be nonlinear and quasi-periodic with specific frequencies. Intuited by this property, we resolve the temporal interpolation task from the frequency perspective, and propose a Fourier Basis-guided Diffusion model, termed FB-Diff. Specifically, due to the regular motion discipline of respiration, physiological motion priors are introduced to describe general characteristics of temporal data distributions. Then a Fourier motion operator is elaborately devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space of Variational Autoencoder. Well-learned Fourier bases can better simulate respiratory motions with motion patterns of specific frequencies. Conditioned on starting and ending frames, the diffusion model further leverages well-learned Fourier bases via the basis interaction operator, which promotes the temporal interpolation task in a generative manner. Extensive results demonstrate that FB-Diff achieves state-of-the-art (SOTA) perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Codes are available here."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.092,
+                0.8,
+                0.222,
+                0.815
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.825,
+                0.484,
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+            ],
+            "angle": 0,
+            "content": "4D medical images, which depict 3D volumes with temporal variations, are essential in clinical practice for capturing dynamic changes and monitoring the progression of diseases over time [12, 25, 49, 52]. A significant application is the temporal modeling for breathing-induced motions of"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.348,
+                0.907,
+                0.424
+            ],
+            "angle": 0,
+            "content": "cardiac or pulmonary anatomical structures. That task aims to enrich motion visualizations by generating intermediate frames under the condition of starting and ending frames, which is consistent with the concept of Video Frame Interpolation (VFI) in natural scenarios."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.427,
+                0.909,
+                0.639
+            ],
+            "angle": 0,
+            "content": "VFI has been thoroughly investigated through systematic studies in recent years [10, 24, 31, 37, 39, 41, 58, 61, 62]. However, due to unique properties and constraints of medical imaging, it remains a challenge to directly implement these frameworks into 4D medical video interpolation with maintaining equally promising performance. Specifically, the quality of ground truth intermediate frames in medical imaging is often compromised due to factors such as imaging noise, unstable breathing, causing unexpected artifacts [17, 25, 43, 49]. Thus, the lower image quality compared to videos in the natural domain, will degrade the interpolation performance of VFI models. Besides, potential patients' movement might induce an additional disturbance to the temporal modeling [5, 38]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.642,
+                0.909,
+                0.778
+            ],
+            "angle": 0,
+            "content": "Furthermore, there exists a discrepancy on the type of motions between natural and medical scenes. The former focuses on the object movement and illumination intensity change. While in the medical domain, motions can be depicted as subtle anatomical variance with quasi-periodic motion discipline [51, 56]. Thus, a specific motion prior of anatomies is effective to boost the temporal interpolation, especially for the medical data with limited resources from a small pool of individuals."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.78,
+                0.909,
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+            ],
+            "angle": 0,
+            "content": "On account of these challenges, we present the following question: \"How can we devise a specialist VFI model tailored for 4D temporal medical volumes?\" Existing methods [2, 13, 29, 30, 51] on medical VFI face a major shortcoming: the linear motion hypothesis in a breathing period is required for the regression of intermediate frames as revealed in Fig.1(a). However, respiratory motions should be a nonlinear oscillatory process that cannot be simply mod-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
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+            ],
+            "angle": 0,
+            "content": "28010"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.141,
+                0.089,
+                0.862,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.334,
+                0.363,
+                0.684,
+                0.379
+            ],
+            "angle": 0,
+            "content": "(b) Nonlinear & quasi-periodic motion \\(\\Longrightarrow\\) Our model"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.39,
+                0.908,
+                0.434
+            ],
+            "angle": 0,
+            "content": "Figure 1. Temporal Interpolation for respiratory motions. (a) Simplified linear-motion hypothesis: interpolating intermediate frames by regressing optical flows with linear variations. (b) Nonlinear & quasi-periodic motions: leveraging diffusion models conditioned on Fourier motion bases, which represent various motion patterns indicating nonlinear and locally inconsistent anatomical variations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.459,
+                0.483,
+                0.7
+            ],
+            "angle": 0,
+            "content": "eled with a linear equation [32, 51]. Also, these methods fail to recognize that respiratory motions in heart or lung, are indeed a quasi-periodic motion process with specific frequencies by extending the timeline. Intuited by this, we resolve the respiratory motion simulation from a frequency perspective. In Fig.1(b), each medical volume in the temporal domain can be viewed as a specific value in the periodic curve. That periodic curve can be decomposed as a group of sine and cosine bases with multiple frequencies [46]. Comparatively, there exists a group of Fourier bases, which are capable of reconstructing original temporal sequences. Here Fourier bases with different frequencies refer to various motion patterns, which indicate nonlinear and locally anisotropic variations of anatomical structures. In our work, Fourier bases are acquired by the Fast Fourier Transform (FFT) on the temporal domain."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.705,
+                0.484,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this work, 4D data distributions of the respiratory process depict a regular motion discipline, with temporal variations from inhaling to exhaling, or from diastole to systole. Motivated by that observation, physiology motion priors are introduced to encode generic characteristics of the respiratory process. Then a Fourier Motion Operator \\(O_{FM}\\) is elaborately devised to yield enhanced motion bases by incorporating physiology motion priors and case-specific spectral information in the feature space. Specifically, A Variational Autoencoder (VAE) is introduced to map the video space into the feature space. Physiology motion priors are defined as learnable frequency embeddings, which can be updated by pretraining a Variational Autoen"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.459,
+                0.907,
+                0.732
+            ],
+            "angle": 0,
+            "content": "coder (VAE) on given temporal data. And case-specific frequency information can be extracted by FFT in the temporal domain. Well-learned physiology motion priors can enrich Fourier bases with generic properties of respiratory motions. Then enhanced Fourier motion bases can better simulate the quasi-periodic respiratory process with motion patterns of specific frequencies. On the grounds that diffusion models show promising performance in generating realistic videos [15, 16, 35, 48], a Markov chain process is learned to transform Gaussian noise into target videos by the proposed Fourier Bases-guided Diffusion, termed FB-Diff. Since only starting and ending frames are available during inference, they serve as conditional prompts for intermediate frame interpolation. Meanwhile, we devise the basis interaction operator to inject enhanced Fourier bases into the conditional diffusion model. Then, FB-Diff can well address the temporal interpolation task in a generative manner."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.735,
+                0.909,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Our proposed method has achieved state-of-the-art (SOTA) interpolation performance compared with other methods for 4D medical imaging, particularly on the mid-most frames. For quantitative results, more comprehensive evaluation metrics are adopted in this work, including traditional reconstruction metrics and feature-level perceptual metrics. FB-Diff not only presents promising reconstruction metrics but also superior perceptual results. Qualitative visualizations reveal better temporal consistency by FB-Diff compared with other linear-motion-based methods. Our main contributions are summarized as follows:"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28011"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.129,
+                0.089,
+                0.87,
+                0.497
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.507,
+                0.907,
+                0.568
+            ],
+            "angle": 0,
+            "content": "Figure 2. The pipeline of FB-Diff. (a) The Fourier motion operator is proposed to extract Fourier bases in a feature space of VAE. Bases consist of learnable generic motion priors and case-specific frequency information. (b) Fourier bases are first adapted to the masked video domain under the guidance of well-learned motion priors and pretrained VAE weights. Domain-adapted bases serve as the conditional input to boost the video synthesis by diffusion models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.59,
+                0.483,
+                0.666
+            ],
+            "angle": 0,
+            "content": "- We propose a diffusion model termed FB-Diff for the temporal interpolation of 4D medical imaging. FB-Diff leverages Fourier motion bases, which indicate motion patterns with specific frequencies to resolve the respiratory modeling with nonlinear and quasi-periodic motions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.666,
+                0.483,
+                0.711
+            ],
+            "angle": 0,
+            "content": "- We introduce the Fourier motion operator \\( O_{FM} \\) to extract Fourier bases, containing physiology motion priors and case-specific frequency representations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.711,
+                0.483,
+                0.756
+            ],
+            "angle": 0,
+            "content": "- We devise the basis interaction operator to inject Fourier bases into the diffusion model. Fourier bases can boost the video synthesis for temporal interpolation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.756,
+                0.483,
+                0.801
+            ],
+            "angle": 0,
+            "content": "- Extensive results demonstrate that FB-Diff reveals SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.091,
+                0.59,
+                0.483,
+                0.801
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.815,
+                0.233,
+                0.831
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.84,
+                0.483,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Video Frame Interpolation. Popular VFI techniques are mainly classified into motion-free and motion-based approaches, depending on whether optical flows are incorporated or not. Motion-based: These approaches warp"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.59,
+                0.907,
+                0.788
+            ],
+            "angle": 0,
+            "content": "input frames forward or backward based on optical flows acquired by either off-the-shelf networks [11, 23, 44, 45, 50] or custom-designed flow estimators [20, 21, 27, 31, 33, 58]. Warped intermediate frames are then refined by delicately designed networks [3, 26] to enhance visual quality. Recently, Transformer-based motion estimators are proposed to raise the upper limit of VFI performance [36, 41, 58] Motion-Free: Motion-free methods rely on implicit spatiotemporal modeling [8, 9, 19, 28] to generate the intermediate frame. However, due to a limited quality of 4D medical videos and quasi-periodic motion priors, existing VFI frameworks are not feasible. That is why we aim to propose a specialist VFI model for 4D medical sequences."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.795,
+                0.909,
+                0.903
+            ],
+            "angle": 0,
+            "content": "4D Medical VFI. Existing methods on this topic mainly leverage volumetric motions for 4D temporal interpolation. Specifically, SVIN [13] estimates forward and backward deformation fields, which will yield precise intermediate frames by linearly combining bidirectional information. MPVF [51] resolves various magnitudes of motions by proposing a multi-pyramid voxel flows model that takes"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "28012"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.485,
+                0.227
+            ],
+            "angle": 0,
+            "content": "multi-scale voxel flows into account. DDM [29] can learn spatial deformation information between the source and target volumes and provide a latent code for generating intermediate frames along a geodesic path. UVI-Net [30] utilizes the flow calculation model with the time-domain cycle-consistency constraint and linear motion hypothesis, to realize motion modeling in an unsupervised style. However, the linear hypothesis for motions will induce temporal inconsistency and spatial distortion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.231,
+                0.485,
+                0.429
+            ],
+            "angle": 0,
+            "content": "Diffusion-based Video Interpolation. Denoising diffusion probabilistic models [15, 16, 35] reveal promising performance in generating realistic images or videos. Some methods maximize the potential of diffusion models to resolve video interpolation tasks. Essentially, these approaches implicitly learn the temporal motions from the starting frame to the ending frame [1, 7, 24]. LDMVFI [10] proposes a latent diffusion model, which approaches the VFI problem from a generative perspective by formulating it as a conditional synthesis issue. However, these diffusion models do not leverage effective conditional guidance, which is crucial for medical VFI with intrinsic motion priors. Thus, we introduce Fourier bases to enhance the conditional synthesis."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.44,
+                0.226,
+                0.458
+            ],
+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.465,
+                0.295,
+                0.48
+            ],
+            "angle": 0,
+            "content": "3.1. Fourier Motion Bases"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.487,
+                0.484,
+                0.653
+            ],
+            "angle": 0,
+            "content": "Since respiratory motions for heart or lung exhibit a quasi-periodic characteristic, we intend to resolve this task from a frequency perspective. Specifically, the respiration can be viewed as an oscillatory process with certain frequencies. Thus, we draw an analogy between 2D time-varying curves and 4D temporal medical volumes. Curves can be decomposed into a group of harmonic oscillators with various frequencies [46]. Similarly, temporal volumes can be restored via a stack of extracted Fourier bases, which are embodied with various motion patterns of anatomical deformation. The whole process can be formulated as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.131,
+                0.654,
+                0.483,
+                0.694
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {B} _ {k} = \\sum_ {n = 0} ^ {N - 1} V _ {n} e ^ {- i 2 \\pi k \\frac {n}{N}}, k = 0, 1, \\dots , N - 1, \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.126,
+                0.697,
+                0.483,
+                0.737
+            ],
+            "angle": 0,
+            "content": "\\[\nV _ {n} = \\frac {1}{T} \\sum_ {k = 0} ^ {N - 1} \\mathcal {B} _ {k} e ^ {i 2 \\pi n \\frac {k}{N}}, n = 0, 1, \\dots , N - 1, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.747,
+                0.484,
+                0.868
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{B}_k\\) means the \\(k_{th}\\) Fourier basis in the frequency domain, \\(V_{n}\\) refers to the \\(n_{th}\\) medical volume, and \\(N\\) is the frame number. These Fourier bases describe locally anisotropic anatomical variations with different motion intensities, promoting the performance of the temporal interpolation model \\(\\mathcal{I}\\). Thus, the goal of our work is to deduce 4D medical videos \\(V\\) conditioned on two prompting frames \\(V_{0}, V_{N-1}\\) and Fourier motion bases \\(\\mathcal{B}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.15,
+                0.879,
+                0.483,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {I} ^ {*} = \\underset {\\mathcal {I}} {\\arg \\min } \\| \\boldsymbol {V} - \\mathcal {I} \\left(V _ {0}, V _ {N - 1}; \\mathcal {B}\\right) \\| _ {\\mathcal {D}}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.529,
+                0.089,
+                0.895,
+                0.264
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.276,
+                0.907,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Figure 3. The details of Fourier motion operator. Fourier bases are decomposed as physiology motion priors and case-specific Fourier features, corresponding to phase and magnitude components."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.326,
+                0.907,
+                0.476
+            ],
+            "angle": 0,
+            "content": "\\(\\mathcal{I}^*\\) refers to the optimal solution in the interpolation model set, and \\(\\mathcal{D}\\) represents the distance-based normed space. We systematically organize the following sections along Fourier bases. Section 3.2 introduces the design of the Fourier Motion Operator, which constructs Fourier bases with physiology motion priors and case-specific frequency information. Section 3.3 adapts Fourier bases to the to-be-interpolated video domain with well-learned physiology motion priors. Section 3.4 provides details of the diffusion model conditioned on Fourier bases."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.487,
+                0.747,
+                0.503
+            ],
+            "angle": 0,
+            "content": "3.2. Fourier Motion Operator"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.509,
+                0.907,
+                0.735
+            ],
+            "angle": 0,
+            "content": "To explicitly extract the Fourier bases with various motion patterns for the respiration process, we introduce the Fourier Operator \\(O_{\\mathcal{F}}\\) as a neural operator. As stated in Eq.(2), \\(O_{\\mathcal{F}}\\) will operate in the temporal domain, not the spatial domain. Since the common Fourier operator \\(O_{\\mathcal{F}}\\) only mines case-specific frequency representations, general physiology characteristics inside respiratory data are ignored. Inspired by that notion, we devise the Fourier motion operator \\(O_{FM}\\) as a neural operator in the feature space. To map the image space into feature space, we introduce a Variational Autoencoder (VAE) as revealed in Fig.2(a). Due to no built-in 4D convolutional operator, we replace it with 3D spatial convolution and 1D temporal convolution as [34, 59] did. The spatial layer in Fig.2(a) consists of spatial convolution, GELU, and group normalization operations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.736,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The Fourier motion operator \\(O_{FM}\\) is devised to acquire spectral characteristics with both physiology motion priors and case-specific representations in the feature space. Firstly, physiology motion priors are introduced as learnable frequency embeddings, which are updated by backward gradients of restoring given temporal data via VAE. Well-trained frequency embeddings \\(\\theta\\) can represent the generic discipline of the regular respiration process [54], with \\(\\theta_{k}\\) referring to the \\(k_{th}\\) element \\((k = 0,1,\\dots,N - 1)\\). Then Fourier bases \\(\\mathcal{B}\\) are made up of physiology motion priors \\(\\theta\\) and case-specific features \\(F\\), which arise from the output of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28013"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.486,
+                0.123
+            ],
+            "angle": 0,
+            "content": "spatial and temporal layers. As depicted by Fig.3, \\(\\mathcal{B}\\) with a complex type is yielded in the following style:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.174,
+                0.131,
+                0.483,
+                0.173
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {B} = \\underbrace {\\mathcal {M} (\\left\\| O _ {\\mathcal {F}} (F) \\right\\| _ {2})} _ {\\text {C a s e - S p e c i f i c}} \\cdot \\underbrace {e ^ {i U (\\tau (\\theta))}} _ {\\text {G e n e r a l}}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.183,
+                0.485,
+                0.318
+            ],
+            "angle": 0,
+            "content": "\\(\\tau\\) means the channel transform, \\(U\\) refers to the upsampling which unifies the resolution of \\(\\theta\\) and \\(\\pmb{F}\\). These operations transform general motion priors into the phase part of Fourier bases, which determines the motion variation standing for the whole dataset distribution. Then \\(\\| \\cdot \\| _2\\) means the \\(L_{2}\\) norm, \\(\\mathcal{M}\\) is the convolutional mapping operation. They will output motion bases' magnitude information, which selectively highlights regions in spectral maps relevant to case-specific information."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.319,
+                0.485,
+                0.365
+            ],
+            "angle": 0,
+            "content": "Meanwhile, feature maps \\(F\\) are further enriched with more fine-grained frequency details. The specific mechanism can be described with Eq.(5):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.218,
+                0.374,
+                0.483,
+                0.395
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {\\boldsymbol {F}} = \\boldsymbol {F} + \\sigma \\mathcal {O} _ {\\mathcal {F}} ^ {- 1} (\\mathcal {B}), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.404,
+                0.484,
+                0.453
+            ],
+            "angle": 0,
+            "content": "here \\(O_{\\mathcal{F}}^{-1}\\) and \\(\\sigma\\) refer to the inverse Fourier transform and Sigmoid operators, which will boost deep features \\(\\hat{F}\\) with enriched details, including shape and texture information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.463,
+                0.435,
+                0.479
+            ],
+            "angle": 0,
+            "content": "3.3. Frame Inpainting-based Basis Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.485,
+                0.485,
+                0.68
+            ],
+            "angle": 0,
+            "content": "Due to the fact that only starting and ending frames can be acquired during inference, a significant step is to adapt Fourier bases to the masked video domain. Motivated by the fact that strong correlations exist between Fourier motion bases and inpainted temporal sequences, we plan to jointly optimize these two variables. To accomplish that goal, we repurpose well-calibrated physiology motion priors from VAE, which prove to be effective in providing the motion guidance for intermediate frame inpainting. Also, pretrained weights of VAE encode implicit temporal dependencies between frames, enhancing the reconstruction of masked video sequences via the finetuned VAE noted as \\(\\mathcal{G}\\). A mathematical formulation is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.69,
+                0.483,
+                0.711
+            ],
+            "angle": 0,
+            "content": "\\[\n\\hat {V}, \\hat {\\mathcal {B}} = \\mathcal {G} (\\hat {\\boldsymbol {\\theta}}, V _ {\\boldsymbol {M}}) = \\mathcal {G} (\\hat {\\boldsymbol {\\theta}}, V _ {0},.., \\mathbf {0},.., V _ {N - 1}), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.719,
+                0.483,
+                0.764
+            ],
+            "angle": 0,
+            "content": "\\(\\hat{\\theta}\\) and \\(V_{M}\\) correspond to well-trained general motions and zero-masked videos, \\(\\hat{V}\\) and \\(\\hat{B}\\) refer to inpainted videos and domain-adapted Fourier bases."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.765,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The interaction between temporal video representations and \\(\\hat{\\mathcal{B}}\\) is implemented via the Fourier motion operator as shown in Fig.2(b). For the joint optimization process, video sequences will contribute temporal variations, enhancing the synthesis of adapted Fourier bases. Conversely, Fourier bases for zero-masked inputs inherently generate a spectral map that emphasizes regions with motion in the temporal axis. This activated map aids in temporal frame inpainting by exerting attention on regions with different magnitudes."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.536,
+                0.091,
+                0.887,
+                0.232
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.244,
+                0.906,
+                0.313
+            ],
+            "angle": 0,
+            "content": "Figure 4. The architecture of basis interaction operator. Fourier motion bases selectively enhance video representations by measuring the motion intensity of different regions. Then those enhanced temporal representations can enrich denoised embeddings from the diffusion model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.321,
+                0.845,
+                0.337
+            ],
+            "angle": 0,
+            "content": "3.4. Basis-guided 4D Conditional Diffusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.342,
+                0.906,
+                0.448
+            ],
+            "angle": 0,
+            "content": "VAE in Fig.2(a) is not only devised for universal motion priors, but also for the latent diffusion model (LDM), which shows better compatibility for extra conditional inputs. Besides, LDM synthesizes latent embeddings occupying less GPU memory compared to 4D temporal volumes. And the VAE decoder is leveraged to reconstruct interpolated video sequences with synthesized latent embeddings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.449,
+                0.906,
+                0.495
+            ],
+            "angle": 0,
+            "content": "For the specific diffusion process, the whole video sequence \\( V \\) is first encoded as a latent embedding \\( z_0 = \\mathcal{G}_e(V) \\). Then the latent code \\( z_0 \\) is perturbed as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.579,
+                0.499,
+                0.905,
+                0.518
+            ],
+            "angle": 0,
+            "content": "\\[\nz _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\epsilon \\sim \\mathcal {N} (0, 1), \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.523,
+                0.906,
+                0.63
+            ],
+            "angle": 0,
+            "content": "where \\(\\overline{\\alpha}_t = \\prod_{i=1}^t (1 - \\beta_t)\\) with \\(\\beta_t\\) is the noise coefficient at time step \\(t\\), and \\(t\\) is uniformly sampled from the timestep index set \\([1,2,\\dots,T]\\). This process can be regarded as a Markov chain, which incrementally adds Gaussian noise to the latent code \\(z_0\\). The denoising model \\(d\\) receives \\(z_t\\) as input and is optimized under conditional guidance to learn the latent space distribution with the objective function:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.539,
+                0.634,
+                0.905,
+                0.654
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\epsilon} = E _ {z _ {t}, \\epsilon \\sim \\mathcal {N} (0, 1)} \\| \\epsilon - \\epsilon_ {d} \\left(z _ {t}, t; \\hat {\\mathcal {B}}, \\mathcal {G} _ {e} \\left(\\boldsymbol {V} _ {\\boldsymbol {M}}\\right), \\hat {\\boldsymbol {V}}\\right) \\| ^ {2}. \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.658,
+                0.906,
+                0.765
+            ],
+            "angle": 0,
+            "content": "here \\(\\epsilon_d\\) is the regressed noise, adapted Fourier bases \\(\\hat{\\mathcal{B}}\\) and inpainted coarse videos \\(\\hat{V}\\) are incorporated as the conditional guidance. Moreover, feature maps of starting and ending frames by the VAE encoder \\(\\mathcal{G}_e\\) serve as a strong prompt for the 4D video synthesis. Then during the training process of FB-Diff, the total loss \\(\\mathcal{L}\\) consists of the denoising loss \\(\\mathcal{L}_{\\epsilon}\\) and the \\(L_{2}\\)-norm reconstruction loss \\(\\mathcal{L}_r(\\hat{V},V)\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.766,
+                0.907,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To inject Fourier motion bases into LDM and harness coarsely inpainted results, we design the Basis Interaction Operator (BIO) as shown in Fig.4. Specifically, inpainted videos are mapped into video feature representations via spatial & temporal layers and the downsampling operation. Fourier motion bases with various motion patterns, selectively enhance video representations by measuring the motion intensity of different regions. Those enhanced temporal representations can enrich denoised embeddings from"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28014"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.089,
+                0.908,
+                0.119
+            ],
+            "angle": 0,
+            "content": "Table 1. Baseline comparison with flow-based and diffusion-based models. (Bold: the best, Underlined: the second best. Δ values represent the relative difference between our model and UVI-Net, and red and blue numbers stand for better and worse results)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.137,
+                0.128,
+                0.868,
+                0.334
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"4\">ACDC Cardiac</td><td colspan=\"4\">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>31.43±0.421</td><td>1.563±0.206</td><td>26.3</td><td>93.6</td><td>30.49±0.304</td><td>2.650±0.245</td><td>38.5</td><td>125.6</td></tr><tr><td>Voxelmorph [2]</td><td>30.77±0.502</td><td>1.969±0.197</td><td>29.4</td><td>102.1</td><td>29.90±0.373</td><td>2.815±0.260</td><td>43.2</td><td>149.0</td></tr><tr><td>Transmorph [6]</td><td>29.81±0.532</td><td>2.136±0.255</td><td>31.5</td><td>109.5</td><td>29.04±0.403</td><td>2.946±0.291</td><td>40.5</td><td>143.5</td></tr><tr><td>MPVF [51]</td><td>31.53±0.410</td><td>1.594±0.201</td><td>24.8</td><td>91.3</td><td>30.76±0.265</td><td>2.418±0.246</td><td>39.4</td><td>120.3</td></tr><tr><td>UVI-Net [30]</td><td>32.16±0.402</td><td>1.662±0.245</td><td>23.0</td><td>94.2</td><td>31.57±0.311</td><td>2.211±0.216</td><td>37.8</td><td>121.7</td></tr><tr><td>IFRNet [31]</td><td>30.58±0.408</td><td>1.752±0.249</td><td>27.8</td><td>97.5</td><td>30.05±0.280</td><td>2.316±0.273</td><td>39.7</td><td>124.0</td></tr><tr><td>LDMVFI [10]</td><td>27.11±0.460</td><td>2.943±0.410</td><td>28.8</td><td>99.2</td><td>26.31±0.453</td><td>3.659±0.341</td><td>42.1</td><td>142.7</td></tr><tr><td>LDDM [7]</td><td>24.53±0.481</td><td>2.634±0.308</td><td>33.4</td><td>105.7</td><td>25.19±0.273</td><td>2.914±0.287</td><td>48.7</td><td>146.3</td></tr><tr><td>Conditional Diff [16]</td><td>26.59±0.545</td><td>2.460±0.357</td><td>30.1</td><td>95.7</td><td>25.95±0.391</td><td>3.294±0.375</td><td>45.0</td><td>133.0</td></tr><tr><td>DDM [29]</td><td>29.79±0.504</td><td>2.089±0.352</td><td>27.4</td><td>110.3</td><td>29.67±0.420</td><td>2.705±0.330</td><td>40.8</td><td>165.5</td></tr><tr><td>FB-Diff</td><td>30.95±0.386</td><td>1.452±0.205</td><td>21.5</td><td>88.9</td><td>30.18±0.287</td><td>2.066±0.215</td><td>37.7</td><td>113.6</td></tr><tr><td>Δ value</td><td>1.21 ↓</td><td>0.210 ↓</td><td>1.5 ↓</td><td>5.3 ↓</td><td>1.39 ↓</td><td>0.145 ↓</td><td>0.1 ↓</td><td>8.1 ↓</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.37,
+                0.486,
+                0.418
+            ],
+            "angle": 0,
+            "content": "the diffusion model, promoting a promising synthesis of highlighted regions. Thus, BIO can boost well-interpolated videos with spatial and temporal consistency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.43,
+                0.226,
+                0.447
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.455,
+                0.3,
+                0.472
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.478,
+                0.483,
+                0.705
+            ],
+            "angle": 0,
+            "content": "Dataset. To evaluate the interpolation performance of our framework, we conduct experiments on public ACDC cardiac [4] and 4D-Lung datasets [22]. For ACDC with the MRI modality, volume sequences between the end-diastolic and end-systolic phases are extracted as valid 4D data. Of all the 150 4D sequences, cases with identity 1-100, 101-120, and 121-150 serve as the training, validation, and testing sets. Besides, all MRI volumes are cropped to \\(128 \\times 128 \\times 32\\), and the frame number ranges from 6 to 16 [53, 57]. For 4D-Lung CT images, the end-inspiratory and end-expiratory scans are set as the initial and final images. We collect 125 4D videos from [22], with the resolution equal to \\(6 \\times 128 \\times 128 \\times 128\\). They are split as \\(80 / 15 / 30\\) cases for training, validation, and inference. We uniform the frame number as 16 with zero paddings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.705,
+                0.483,
+                0.886
+            ],
+            "angle": 0,
+            "content": "**Evaluations.** We select quantitative evaluation metrics including Peak Signal-to-Noise Ratio (PSNR) [18], Learned Perceptual Image Patch Similarity (LPIPS) [55, 60], Fréchet Inception Distance (FID) [14], and Fréchet Video Distance (FVD) [47]. Compared to PSNR, which is the traditional pixel-wise reconstruction metric, LPIPS and FVD evaluate perceptual quality from the perspective of human vision [10, 24, 61], which is more feasible and favored in clinical practice. Specifically, LPIPS reveals important perceptual similarity like human vision. FID and FVD evaluate the dataset distribution bias between realistic and synthesized data, including spatial and temporal consistency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.886,
+                0.484,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Training Details. The VAE maps the image space into"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.37,
+                0.907,
+                0.492
+            ],
+            "angle": 0,
+            "content": "the downsampled latent space with a ratio of \\(1/8\\). And the proposed conditional diffusion model is implemented with a lightweight UNet. All models are trained using the AdamW optimizer with the linear warm-up strategy. The batch size, diffusion step \\(T\\), and training epoch are equal to 2, 1000, and 500. Experiments are implemented based on Pytorch and 2 NVIDIA RTX 4090 GPUs. More details about the network and training settings are described in the Appendix."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.501,
+                0.816,
+                0.517
+            ],
+            "angle": 0,
+            "content": "4.2. Comparisons with SOTA baselines"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.523,
+                0.907,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Quantitative Comparison. We comprehensively conduct experiments on ACDC cardiac and 4D Lung datasets. Quantitative results are illustrated in Tab.1. Our model achieves the best performance across the benchmark on perceptual evaluation metrics from the perspective of human vision [10, 61], which are clinically favored compared with the pixel-centric reconstruction metric [7]. Specifically, FB-Diff outperforms UVI-Net [30] with \\(0.210 \\downarrow\\) LPIPS and \\(5.3 \\downarrow\\) FVD values on ACDC. Also, our model maintains quite satisfactory PSNR values of \\(30.95\\mathrm{dB}\\) and \\(30.18\\mathrm{dB}\\) on ACDC and 4D Lung. Although diffusion models are not sensitive to pixel-wise intensities [15], the conditional guidance of Fourier bases and coarsely inpainted videos is effective to boost the interpolation performance of diffusion models. Tab.1 reveals that FB-Diff significantly surpasses existing diffusion models on all metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.766,
+                0.909,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Furthermore, the interpolation process becomes most challenging for the midmost frames since they are positioned farthest from the two reference frames [24]. And our model can better resolve this issue due to stronger temporal representations based on quasi-periodic motion modeling. Thus, a quantitative evaluation of central frames is necessary. As shown in Tab.2, FB-Diff demonstrates greater performance advantages, with \\(4.3\\downarrow\\) FID and \\(8.2\\downarrow\\) FVD values compared with UVI-Net. Additionally, FB-Diff acquires a competi"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "28015"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.138,
+                0.09,
+                0.868,
+                0.35
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.159,
+                0.358,
+                0.837,
+                0.373
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative comparison of the midmost frame interpolation between different models. VM: Voxelmorph."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.397,
+                0.484,
+                0.455
+            ],
+            "angle": 0,
+            "content": "Table 2. Interpolation performance of the midmost frames on ACDC cardiac. The choice of midmost frames: if the frame number \\( N \\) is odd, three intermediate frames are selected, otherwise only two frames are chosen."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.106,
+                0.463,
+                0.475,
+                0.548
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>26.01±0.467</td><td>2.673±0.361</td><td>38.9</td><td>142.8</td></tr><tr><td>DDM [29]</td><td>24.37±0.511</td><td>2.756±0.330</td><td>41.5</td><td>145.1</td></tr><tr><td>UVI-Net [30]</td><td>26.25±0.410</td><td>2.542±0.374</td><td>37.0</td><td>137.1</td></tr><tr><td>FB-Diff</td><td>26.18±0.413</td><td>2.287±0.305</td><td>32.7</td><td>128.9</td></tr><tr><td>Δ value</td><td>0.07 ↓</td><td>0.255 ↓</td><td>4.3 ↓</td><td>8.2 ↓</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.565,
+                0.484,
+                0.595
+            ],
+            "angle": 0,
+            "content": "tive PSNR value, which demonstrates the effectiveness of respiration-related modeling via Fourier bases."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.596,
+                0.484,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Qualitative Comparison. Qualitative results on the interpolated midmost frame are depicted in Fig.5. SVIN [13], Voxelmorph [2], and DDM [29] leverage the single-direction flow estimation to interpolate intermediate frames with linear motions. Compared with that, UVI-Net [30] constructs the interpolation model with time-domain cycle-consistency, and achieves better reconstruction performance as expected. However, these methods essentially overlook the nonlinear and quasi-periodic motion discipline between temporal sequences, resulting in unsatisfactory interpolated results. Instead, FB-Diff exhibits advantageous predictions for midmost frames under the guidance of various motion patterns, indicating locally anisotropic motions with different intensities. Besides, other diffusion models do not work well due to the lack of fine-grained conditional guidance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.833,
+                0.245,
+                0.849
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.484,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Key Components. An ablation study is conducted to investigate the significance of various components in FB-Diff as shown in Tab.3. (a) Physiology Motion Priors \\(\\theta\\). By"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.397,
+                0.907,
+                0.426
+            ],
+            "angle": 0,
+            "content": "Table 3. Ablation study on key components. \\(\\theta\\): physiology motion priors, \\(\\hat{B}\\): Fourier motion bases, \\(\\hat{V}\\): coarsely inpainted videos."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.528,
+                0.435,
+                0.897,
+                0.519
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"3\">Settings</td><td colspan=\"2\">ACDC Cardiac</td><td colspan=\"2\">4D Lung</td></tr><tr><td>θ</td><td>ˆB</td><td>ˆV</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>29.76</td><td>1.710</td><td>29.53</td><td>2.413</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>28.17</td><td>2.105</td><td>28.40</td><td>2.971</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>30.29</td><td>1.655</td><td>29.71</td><td>2.246</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.537,
+                0.907,
+                0.779
+            ],
+            "angle": 0,
+            "content": "removing \\(\\theta\\) from the Fourier motion operator, interpolation performance decreases significantly due to the loss of general spectral characteristics from respiratory data. Therefore, Fourier bases lack the precise phase information. (b) Fourier bases \\(\\hat{\\mathcal{B}}\\). Without \\(\\hat{\\mathcal{B}}\\) as conditional guidance, the conditional diffusion model fails to perceive explicit motion patterns with different frequencies, which provide the intensity of anisotropic motions. As a result, the generative model cannot well learn the regular temporal variations, with 2.78 dB \\(\\downarrow\\) and 1.78 dB \\(\\downarrow\\) PSNR values on ACDC and 4D Lung. (c) Inpainted Videos \\(\\hat{V}\\). Here the coarsely reconstructed sequences serve as the output by the finedtuned VAE as revealed in Fig.2. And the joint optimization process boosts the spatial and temporal representations of \\(\\hat{V}\\). Consequently, discarding this component will reduce fine-grained details of the diffusion model's output."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.78,
+                0.909,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Hyper-settings of Fourier Bases. (a) The number of Fourier Bases \\( N_{Fb} \\). We first analyze the quantitative effects of the frequency number on the interpolation performance. As revealed in Tab.4, reducing the frequency number will cause degraded performance of the temporal simulation. Specifically, 1.30 dB lower PSNR and 0.535 higher LPIPS values are induced by decreasing \\( N_{Fb} \\) from 16 to 8. That phenomenon indicates that some elements in the group of"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28016"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.113,
+                0.089,
+                0.887,
+                0.179
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.188,
+                0.908,
+                0.232
+            ],
+            "angle": 0,
+            "content": "Figure 6. Visualizations on the frequency spectral of Fourier bases. \\( V_{0} \\), \\( V_{N - 1} \\): starting and ending frames. \\( f_{1} - f_{8} \\) refer to different motion patterns, which highlight different regions under different frequency. There also appear locally anisotropic motion intensities inside a specific motion pattern."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.255,
+                0.483,
+                0.283
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study on the hyper-settings of Fourier bases. \\(N_{Fb}\\): the frequency number of Fourier bases."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.094,
+                0.294,
+                0.485,
+                0.387
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Settings</td><td colspan=\"2\">ACDC Cardiac</td><td colspan=\"2\">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>\\(N_{Fb}\\)=16 (Ours)</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr><tr><td>\\(N_{Fb}\\)=12</td><td>30.76</td><td>1.640</td><td>29.97</td><td>2.570</td></tr><tr><td>\\(N_{Fb}\\)=8</td><td>29.65</td><td>1.987</td><td>29.50</td><td>2.745</td></tr><tr><td>w/o Real part</td><td>29.18</td><td>1.872</td><td>29.56</td><td>2.453</td></tr><tr><td>w/o Imaginary part</td><td>29.88</td><td>1.681</td><td>29.67</td><td>2.401</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.404,
+                0.484,
+                0.541
+            ],
+            "angle": 0,
+            "content": "bases with the frequency ranging from \\( f_{8} \\) to \\( f_{15} \\) are consistent with specific frequencies of the respiratory process. (b) Real & Imaginary Parts. \\( \\hat{\\mathcal{B}} \\) bears real and imaginary parts after combining generic priors and case-specific spectral representations, which perform as the phase and magnitude information. Eliminating either the real or imaginary part will convert the complex data type into the real one, resulting in the loss of phase information and influencing the temporal interpolation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.547,
+                0.3,
+                0.563
+            ],
+            "angle": 0,
+            "content": "4.4. Visualization Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.569,
+                0.483,
+                0.841
+            ],
+            "angle": 0,
+            "content": "Visualization of Fourier bases. To further validate the effectiveness and interpretability of our proposed Fourier bases, we visualize extracted motion bases from the most shadow layer. As revealed in Fig.6, \\( f_{0} - f_{7} \\) refers to the magnitude of the first eight motion bases in ascending order of frequency. Specifically, \\( f_{0} \\) shows a low-frequency motion pattern highlighting no region, which is strongly related to static backgrounds. \\( f_{1} - f_{3} \\) exhibit a large motion intensity in the highlighted right and left ventricle regions. Those regions are indeed dynamic foregrounds requiring special attention. \\( f_{4} \\) depicts an activation in the myocardial region, which contracts inward along the circumferential direction. \\( f_{5} - f_{7} \\) highlight regions with vast deformations in the temporal domain. Particularly, \\( f_{6} \\) illustrates a large motion on boundaries of anatomical structures. In summary, these motion patterns reveal locally anisotropic motion intensities, and are harmonized with specific frequencies of the respiratory process, thus promoting the temporal interpolation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.841,
+                0.484,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Visualization of temporal anatomical variations. To demonstrate the effectiveness of FB-Diff on temporal simulation, we visualize temporal variation maps for a perceptual comparison. Fig.7 provides interpolated intermediate"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.532,
+                0.254,
+                0.891,
+                0.502
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.513,
+                0.907,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Figure 7. Temporal variation comparison between FB-Diff and existing methods with the linear motion hypothesis."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.549,
+                0.907,
+                0.641
+            ],
+            "angle": 0,
+            "content": "frames at different timepoints. According to the referenced video, the anatomical motion in the temporal domain is nonlinear, which cannot be precisely simulated by existing methods with the linear motion hypothesis. In contrast, our predictions show better temporal consistency and continuity, particularly for frames at \\( t = 0.6 \\) and 0.8."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.661,
+                0.634,
+                0.679
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.689,
+                0.907,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Our proposed FB-Diff resolves the temporal interpolation of 4D medical imaging from a frequency perspective, and can model the respiration-related process with nonlinear and quasi-periodic motions. A Fourier motion operator is devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space. And the diffusion model further leverages Fourier bases and two prompting frames to achieve the precise interpolation. Extensive results show that FB-Diff achieves SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Ultimately, it requires more conditional guidance such as electrocardiogram signals to simulate the highly unstable breathing, which is promising in future work."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "28017"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.092,
+                0.486,
+                0.168
+            ],
+            "angle": 0,
+            "content": "Acknowledgement. We thank the anonymous reviewers for their thorough and constructive feedbacks. This research was supported in part by the project of the National Natural Science Foundation of China (No. 62376153), in part by the institute of Munich Center of Machine Learning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.093,
+                0.182,
+                0.188,
+                0.198
+            ],
+            "angle": 0,
+            "content": "References"
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2025/FB-Diff_ Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging/c8ad7765-483e-400a-90bd-72090b0597d0_origin.pdf

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2025/FB-Diff_ Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging/full.md

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+# FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging
+
+Xin You $^{1,2,3}$  Runze Yang $^{1}$  Chuyan Zhang $^{1}$  Zhongliang Jiang $^{2}$  Jie Yang $^{1,*}$  Nassir Navab $^{2,*}$
+
+$^{1}$  Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China
+
+$^{2}$  Computer Aided Medical Procedures, Technical University of Munich, Munich, Germany
+
+3 Munich Center for Machine Learning, Munich, Germany
+
+xin.you@tum.de, nassir.navab@tum.de
+
+# Abstract
+
+The temporal interpolation task for 4D medical imaging, plays a crucial role in clinical practice of respiratory motion modeling. Following the simplified linear-motion hypothesis, existing approaches adopt optical flow-based models to interpolate intermediate frames. However, realistic respiratory motions should be nonlinear and quasi-periodic with specific frequencies. Intuited by this property, we resolve the temporal interpolation task from the frequency perspective, and propose a Fourier Basis-guided Diffusion model, termed FB-Diff. Specifically, due to the regular motion discipline of respiration, physiological motion priors are introduced to describe general characteristics of temporal data distributions. Then a Fourier motion operator is elaborately devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space of Variational Autoencoder. Well-learned Fourier bases can better simulate respiratory motions with motion patterns of specific frequencies. Conditioned on starting and ending frames, the diffusion model further leverages well-learned Fourier bases via the basis interaction operator, which promotes the temporal interpolation task in a generative manner. Extensive results demonstrate that FB-Diff achieves state-of-the-art (SOTA) perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Codes are available here.
+
+# 1. Introduction
+
+4D medical images, which depict 3D volumes with temporal variations, are essential in clinical practice for capturing dynamic changes and monitoring the progression of diseases over time [12, 25, 49, 52]. A significant application is the temporal modeling for breathing-induced motions of
+
+cardiac or pulmonary anatomical structures. That task aims to enrich motion visualizations by generating intermediate frames under the condition of starting and ending frames, which is consistent with the concept of Video Frame Interpolation (VFI) in natural scenarios.
+
+VFI has been thoroughly investigated through systematic studies in recent years [10, 24, 31, 37, 39, 41, 58, 61, 62]. However, due to unique properties and constraints of medical imaging, it remains a challenge to directly implement these frameworks into 4D medical video interpolation with maintaining equally promising performance. Specifically, the quality of ground truth intermediate frames in medical imaging is often compromised due to factors such as imaging noise, unstable breathing, causing unexpected artifacts [17, 25, 43, 49]. Thus, the lower image quality compared to videos in the natural domain, will degrade the interpolation performance of VFI models. Besides, potential patients' movement might induce an additional disturbance to the temporal modeling [5, 38].
+
+Furthermore, there exists a discrepancy on the type of motions between natural and medical scenes. The former focuses on the object movement and illumination intensity change. While in the medical domain, motions can be depicted as subtle anatomical variance with quasi-periodic motion discipline [51, 56]. Thus, a specific motion prior of anatomies is effective to boost the temporal interpolation, especially for the medical data with limited resources from a small pool of individuals.
+
+On account of these challenges, we present the following question: "How can we devise a specialist VFI model tailored for 4D temporal medical volumes?" Existing methods [2, 13, 29, 30, 51] on medical VFI face a major shortcoming: the linear motion hypothesis in a breathing period is required for the regression of intermediate frames as revealed in Fig.1(a). However, respiratory motions should be a nonlinear oscillatory process that cannot be simply mod-
+
+![](images/49b55a0a073f7468310942ce3ca259cec8925fa39bd51feff78d4aec58660ba8.jpg)  
+(b) Nonlinear & quasi-periodic motion  $\Longrightarrow$  Our model  
+Figure 1. Temporal Interpolation for respiratory motions. (a) Simplified linear-motion hypothesis: interpolating intermediate frames by regressing optical flows with linear variations. (b) Nonlinear & quasi-periodic motions: leveraging diffusion models conditioned on Fourier motion bases, which represent various motion patterns indicating nonlinear and locally inconsistent anatomical variations.
+
+eled with a linear equation [32, 51]. Also, these methods fail to recognize that respiratory motions in heart or lung, are indeed a quasi-periodic motion process with specific frequencies by extending the timeline. Intuited by this, we resolve the respiratory motion simulation from a frequency perspective. In Fig.1(b), each medical volume in the temporal domain can be viewed as a specific value in the periodic curve. That periodic curve can be decomposed as a group of sine and cosine bases with multiple frequencies [46]. Comparatively, there exists a group of Fourier bases, which are capable of reconstructing original temporal sequences. Here Fourier bases with different frequencies refer to various motion patterns, which indicate nonlinear and locally anisotropic variations of anatomical structures. In our work, Fourier bases are acquired by the Fast Fourier Transform (FFT) on the temporal domain.
+
+In this work, 4D data distributions of the respiratory process depict a regular motion discipline, with temporal variations from inhaling to exhaling, or from diastole to systole. Motivated by that observation, physiology motion priors are introduced to encode generic characteristics of the respiratory process. Then a Fourier Motion Operator  $O_{FM}$  is elaborately devised to yield enhanced motion bases by incorporating physiology motion priors and case-specific spectral information in the feature space. Specifically, A Variational Autoencoder (VAE) is introduced to map the video space into the feature space. Physiology motion priors are defined as learnable frequency embeddings, which can be updated by pretraining a Variational Autoen
+
+coder (VAE) on given temporal data. And case-specific frequency information can be extracted by FFT in the temporal domain. Well-learned physiology motion priors can enrich Fourier bases with generic properties of respiratory motions. Then enhanced Fourier motion bases can better simulate the quasi-periodic respiratory process with motion patterns of specific frequencies. On the grounds that diffusion models show promising performance in generating realistic videos [15, 16, 35, 48], a Markov chain process is learned to transform Gaussian noise into target videos by the proposed Fourier Bases-guided Diffusion, termed FB-Diff. Since only starting and ending frames are available during inference, they serve as conditional prompts for intermediate frame interpolation. Meanwhile, we devise the basis interaction operator to inject enhanced Fourier bases into the conditional diffusion model. Then, FB-Diff can well address the temporal interpolation task in a generative manner.
+
+Our proposed method has achieved state-of-the-art (SOTA) interpolation performance compared with other methods for 4D medical imaging, particularly on the mid-most frames. For quantitative results, more comprehensive evaluation metrics are adopted in this work, including traditional reconstruction metrics and feature-level perceptual metrics. FB-Diff not only presents promising reconstruction metrics but also superior perceptual results. Qualitative visualizations reveal better temporal consistency by FB-Diff compared with other linear-motion-based methods. Our main contributions are summarized as follows:
+
+![](images/ea0242ad2ded6b4b4995d4b5240260ecbefd64127560851e8856bf2d9f92bc00.jpg)  
+Figure 2. The pipeline of FB-Diff. (a) The Fourier motion operator is proposed to extract Fourier bases in a feature space of VAE. Bases consist of learnable generic motion priors and case-specific frequency information. (b) Fourier bases are first adapted to the masked video domain under the guidance of well-learned motion priors and pretrained VAE weights. Domain-adapted bases serve as the conditional input to boost the video synthesis by diffusion models.
+
+- We propose a diffusion model termed FB-Diff for the temporal interpolation of 4D medical imaging. FB-Diff leverages Fourier motion bases, which indicate motion patterns with specific frequencies to resolve the respiratory modeling with nonlinear and quasi-periodic motions.  
+- We introduce the Fourier motion operator  $O_{FM}$  to extract Fourier bases, containing physiology motion priors and case-specific frequency representations.  
+- We devise the basis interaction operator to inject Fourier bases into the diffusion model. Fourier bases can boost the video synthesis for temporal interpolation.  
+- Extensive results demonstrate that FB-Diff reveals SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics.
+
+# 2. Related Work
+
+Video Frame Interpolation. Popular VFI techniques are mainly classified into motion-free and motion-based approaches, depending on whether optical flows are incorporated or not. Motion-based: These approaches warp
+
+input frames forward or backward based on optical flows acquired by either off-the-shelf networks [11, 23, 44, 45, 50] or custom-designed flow estimators [20, 21, 27, 31, 33, 58]. Warped intermediate frames are then refined by delicately designed networks [3, 26] to enhance visual quality. Recently, Transformer-based motion estimators are proposed to raise the upper limit of VFI performance [36, 41, 58] Motion-Free: Motion-free methods rely on implicit spatiotemporal modeling [8, 9, 19, 28] to generate the intermediate frame. However, due to a limited quality of 4D medical videos and quasi-periodic motion priors, existing VFI frameworks are not feasible. That is why we aim to propose a specialist VFI model for 4D medical sequences.
+
+4D Medical VFI. Existing methods on this topic mainly leverage volumetric motions for 4D temporal interpolation. Specifically, SVIN [13] estimates forward and backward deformation fields, which will yield precise intermediate frames by linearly combining bidirectional information. MPVF [51] resolves various magnitudes of motions by proposing a multi-pyramid voxel flows model that takes
+
+multi-scale voxel flows into account. DDM [29] can learn spatial deformation information between the source and target volumes and provide a latent code for generating intermediate frames along a geodesic path. UVI-Net [30] utilizes the flow calculation model with the time-domain cycle-consistency constraint and linear motion hypothesis, to realize motion modeling in an unsupervised style. However, the linear hypothesis for motions will induce temporal inconsistency and spatial distortion.
+
+Diffusion-based Video Interpolation. Denoising diffusion probabilistic models [15, 16, 35] reveal promising performance in generating realistic images or videos. Some methods maximize the potential of diffusion models to resolve video interpolation tasks. Essentially, these approaches implicitly learn the temporal motions from the starting frame to the ending frame [1, 7, 24]. LDMVFI [10] proposes a latent diffusion model, which approaches the VFI problem from a generative perspective by formulating it as a conditional synthesis issue. However, these diffusion models do not leverage effective conditional guidance, which is crucial for medical VFI with intrinsic motion priors. Thus, we introduce Fourier bases to enhance the conditional synthesis.
+
+# 3. Methodology
+
+# 3.1. Fourier Motion Bases
+
+Since respiratory motions for heart or lung exhibit a quasi-periodic characteristic, we intend to resolve this task from a frequency perspective. Specifically, the respiration can be viewed as an oscillatory process with certain frequencies. Thus, we draw an analogy between 2D time-varying curves and 4D temporal medical volumes. Curves can be decomposed into a group of harmonic oscillators with various frequencies [46]. Similarly, temporal volumes can be restored via a stack of extracted Fourier bases, which are embodied with various motion patterns of anatomical deformation. The whole process can be formulated as:
+
+$$
+\mathcal {B} _ {k} = \sum_ {n = 0} ^ {N - 1} V _ {n} e ^ {- i 2 \pi k \frac {n}{N}}, k = 0, 1, \dots , N - 1, \tag {1}
+$$
+
+$$
+V _ {n} = \frac {1}{T} \sum_ {k = 0} ^ {N - 1} \mathcal {B} _ {k} e ^ {i 2 \pi n \frac {k}{N}}, n = 0, 1, \dots , N - 1, \tag {2}
+$$
+
+where  $\mathcal{B}_k$  means the  $k_{th}$  Fourier basis in the frequency domain,  $V_{n}$  refers to the  $n_{th}$  medical volume, and  $N$  is the frame number. These Fourier bases describe locally anisotropic anatomical variations with different motion intensities, promoting the performance of the temporal interpolation model  $\mathcal{I}$ . Thus, the goal of our work is to deduce 4D medical videos  $V$  conditioned on two prompting frames  $V_{0}, V_{N-1}$  and Fourier motion bases  $\mathcal{B}$ :
+
+$$
+\mathcal {I} ^ {*} = \underset {\mathcal {I}} {\arg \min } \| \boldsymbol {V} - \mathcal {I} \left(V _ {0}, V _ {N - 1}; \mathcal {B}\right) \| _ {\mathcal {D}}, \tag {3}
+$$
+
+![](images/3a5fb39ec16e2282dd96e4173cb949fd02dec76d57657897bdfbad4585e8955a.jpg)  
+Figure 3. The details of Fourier motion operator. Fourier bases are decomposed as physiology motion priors and case-specific Fourier features, corresponding to phase and magnitude components.
+
+$\mathcal{I}^*$  refers to the optimal solution in the interpolation model set, and  $\mathcal{D}$  represents the distance-based normed space. We systematically organize the following sections along Fourier bases. Section 3.2 introduces the design of the Fourier Motion Operator, which constructs Fourier bases with physiology motion priors and case-specific frequency information. Section 3.3 adapts Fourier bases to the to-be-interpolated video domain with well-learned physiology motion priors. Section 3.4 provides details of the diffusion model conditioned on Fourier bases.
+
+# 3.2. Fourier Motion Operator
+
+To explicitly extract the Fourier bases with various motion patterns for the respiration process, we introduce the Fourier Operator  $O_{\mathcal{F}}$  as a neural operator. As stated in Eq.(2),  $O_{\mathcal{F}}$  will operate in the temporal domain, not the spatial domain. Since the common Fourier operator  $O_{\mathcal{F}}$  only mines case-specific frequency representations, general physiology characteristics inside respiratory data are ignored. Inspired by that notion, we devise the Fourier motion operator  $O_{FM}$  as a neural operator in the feature space. To map the image space into feature space, we introduce a Variational Autoencoder (VAE) as revealed in Fig.2(a). Due to no built-in 4D convolutional operator, we replace it with 3D spatial convolution and 1D temporal convolution as [34, 59] did. The spatial layer in Fig.2(a) consists of spatial convolution, GELU, and group normalization operations.
+
+The Fourier motion operator  $O_{FM}$  is devised to acquire spectral characteristics with both physiology motion priors and case-specific representations in the feature space. Firstly, physiology motion priors are introduced as learnable frequency embeddings, which are updated by backward gradients of restoring given temporal data via VAE. Well-trained frequency embeddings  $\theta$  can represent the generic discipline of the regular respiration process [54], with  $\theta_{k}$  referring to the  $k_{th}$  element  $(k = 0,1,\dots,N - 1)$ . Then Fourier bases  $\mathcal{B}$  are made up of physiology motion priors  $\theta$  and case-specific features  $F$ , which arise from the output of
+
+spatial and temporal layers. As depicted by Fig.3,  $\mathcal{B}$  with a complex type is yielded in the following style:
+
+$$
+\mathcal {B} = \underbrace {\mathcal {M} (\left\| O _ {\mathcal {F}} (F) \right\| _ {2})} _ {\text {C a s e - S p e c i f i c}} \cdot \underbrace {e ^ {i U (\tau (\theta))}} _ {\text {G e n e r a l}}, \tag {4}
+$$
+
+$\tau$  means the channel transform,  $U$  refers to the upsampling which unifies the resolution of  $\theta$  and  $\pmb{F}$ . These operations transform general motion priors into the phase part of Fourier bases, which determines the motion variation standing for the whole dataset distribution. Then  $\| \cdot \| _2$  means the  $L_{2}$  norm,  $\mathcal{M}$  is the convolutional mapping operation. They will output motion bases' magnitude information, which selectively highlights regions in spectral maps relevant to case-specific information.
+
+Meanwhile, feature maps  $F$  are further enriched with more fine-grained frequency details. The specific mechanism can be described with Eq.(5):
+
+$$
+\hat {\boldsymbol {F}} = \boldsymbol {F} + \sigma \mathcal {O} _ {\mathcal {F}} ^ {- 1} (\mathcal {B}), \tag {5}
+$$
+
+here  $O_{\mathcal{F}}^{-1}$  and  $\sigma$  refer to the inverse Fourier transform and Sigmoid operators, which will boost deep features  $\hat{F}$  with enriched details, including shape and texture information.
+
+# 3.3. Frame Inpainting-based Basis Synthesis
+
+Due to the fact that only starting and ending frames can be acquired during inference, a significant step is to adapt Fourier bases to the masked video domain. Motivated by the fact that strong correlations exist between Fourier motion bases and inpainted temporal sequences, we plan to jointly optimize these two variables. To accomplish that goal, we repurpose well-calibrated physiology motion priors from VAE, which prove to be effective in providing the motion guidance for intermediate frame inpainting. Also, pretrained weights of VAE encode implicit temporal dependencies between frames, enhancing the reconstruction of masked video sequences via the finetuned VAE noted as  $\mathcal{G}$ . A mathematical formulation is defined as:
+
+$$
+\hat {V}, \hat {\mathcal {B}} = \mathcal {G} (\hat {\boldsymbol {\theta}}, V _ {\boldsymbol {M}}) = \mathcal {G} (\hat {\boldsymbol {\theta}}, V _ {0},.., \mathbf {0},.., V _ {N - 1}), \tag {6}
+$$
+
+$\hat{\theta}$  and  $V_{M}$  correspond to well-trained general motions and zero-masked videos,  $\hat{V}$  and  $\hat{B}$  refer to inpainted videos and domain-adapted Fourier bases.
+
+The interaction between temporal video representations and  $\hat{\mathcal{B}}$  is implemented via the Fourier motion operator as shown in Fig.2(b). For the joint optimization process, video sequences will contribute temporal variations, enhancing the synthesis of adapted Fourier bases. Conversely, Fourier bases for zero-masked inputs inherently generate a spectral map that emphasizes regions with motion in the temporal axis. This activated map aids in temporal frame inpainting by exerting attention on regions with different magnitudes.
+
+![](images/e46e1aa2636d3a69e2489f0e0819f6dad5bd9bb3792fe805fd5471e932837caa.jpg)  
+Figure 4. The architecture of basis interaction operator. Fourier motion bases selectively enhance video representations by measuring the motion intensity of different regions. Then those enhanced temporal representations can enrich denoised embeddings from the diffusion model.
+
+# 3.4. Basis-guided 4D Conditional Diffusion
+
+VAE in Fig.2(a) is not only devised for universal motion priors, but also for the latent diffusion model (LDM), which shows better compatibility for extra conditional inputs. Besides, LDM synthesizes latent embeddings occupying less GPU memory compared to 4D temporal volumes. And the VAE decoder is leveraged to reconstruct interpolated video sequences with synthesized latent embeddings.
+
+For the specific diffusion process, the whole video sequence  $V$  is first encoded as a latent embedding  $z_0 = \mathcal{G}_e(V)$ . Then the latent code  $z_0$  is perturbed as:
+
+$$
+z _ {t} = \sqrt {\bar {\alpha} _ {t}} z _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \epsilon \sim \mathcal {N} (0, 1), \tag {7}
+$$
+
+where  $\overline{\alpha}_t = \prod_{i=1}^t (1 - \beta_t)$  with  $\beta_t$  is the noise coefficient at time step  $t$ , and  $t$  is uniformly sampled from the timestep index set  $[1,2,\dots,T]$ . This process can be regarded as a Markov chain, which incrementally adds Gaussian noise to the latent code  $z_0$ . The denoising model  $d$  receives  $z_t$  as input and is optimized under conditional guidance to learn the latent space distribution with the objective function:
+
+$$
+\mathcal {L} _ {\epsilon} = E _ {z _ {t}, \epsilon \sim \mathcal {N} (0, 1)} \| \epsilon - \epsilon_ {d} \left(z _ {t}, t; \hat {\mathcal {B}}, \mathcal {G} _ {e} \left(\boldsymbol {V} _ {\boldsymbol {M}}\right), \hat {\boldsymbol {V}}\right) \| ^ {2}. \tag {8}
+$$
+
+here  $\epsilon_d$  is the regressed noise, adapted Fourier bases  $\hat{\mathcal{B}}$  and inpainted coarse videos  $\hat{V}$  are incorporated as the conditional guidance. Moreover, feature maps of starting and ending frames by the VAE encoder  $\mathcal{G}_e$  serve as a strong prompt for the 4D video synthesis. Then during the training process of FB-Diff, the total loss  $\mathcal{L}$  consists of the denoising loss  $\mathcal{L}_{\epsilon}$  and the  $L_{2}$ -norm reconstruction loss  $\mathcal{L}_r(\hat{V},V)$ .
+
+To inject Fourier motion bases into LDM and harness coarsely inpainted results, we design the Basis Interaction Operator (BIO) as shown in Fig.4. Specifically, inpainted videos are mapped into video feature representations via spatial & temporal layers and the downsampling operation. Fourier motion bases with various motion patterns, selectively enhance video representations by measuring the motion intensity of different regions. Those enhanced temporal representations can enrich denoised embeddings from
+
+Table 1. Baseline comparison with flow-based and diffusion-based models. (Bold: the best, Underlined: the second best. Δ values represent the relative difference between our model and UVI-Net, and red and blue numbers stand for better and worse results).  
+
+<table><tr><td rowspan="2">Model</td><td colspan="4">ACDC Cardiac</td><td colspan="4">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>31.43±0.421</td><td>1.563±0.206</td><td>26.3</td><td>93.6</td><td>30.49±0.304</td><td>2.650±0.245</td><td>38.5</td><td>125.6</td></tr><tr><td>Voxelmorph [2]</td><td>30.77±0.502</td><td>1.969±0.197</td><td>29.4</td><td>102.1</td><td>29.90±0.373</td><td>2.815±0.260</td><td>43.2</td><td>149.0</td></tr><tr><td>Transmorph [6]</td><td>29.81±0.532</td><td>2.136±0.255</td><td>31.5</td><td>109.5</td><td>29.04±0.403</td><td>2.946±0.291</td><td>40.5</td><td>143.5</td></tr><tr><td>MPVF [51]</td><td>31.53±0.410</td><td>1.594±0.201</td><td>24.8</td><td>91.3</td><td>30.76±0.265</td><td>2.418±0.246</td><td>39.4</td><td>120.3</td></tr><tr><td>UVI-Net [30]</td><td>32.16±0.402</td><td>1.662±0.245</td><td>23.0</td><td>94.2</td><td>31.57±0.311</td><td>2.211±0.216</td><td>37.8</td><td>121.7</td></tr><tr><td>IFRNet [31]</td><td>30.58±0.408</td><td>1.752±0.249</td><td>27.8</td><td>97.5</td><td>30.05±0.280</td><td>2.316±0.273</td><td>39.7</td><td>124.0</td></tr><tr><td>LDMVFI [10]</td><td>27.11±0.460</td><td>2.943±0.410</td><td>28.8</td><td>99.2</td><td>26.31±0.453</td><td>3.659±0.341</td><td>42.1</td><td>142.7</td></tr><tr><td>LDDM [7]</td><td>24.53±0.481</td><td>2.634±0.308</td><td>33.4</td><td>105.7</td><td>25.19±0.273</td><td>2.914±0.287</td><td>48.7</td><td>146.3</td></tr><tr><td>Conditional Diff [16]</td><td>26.59±0.545</td><td>2.460±0.357</td><td>30.1</td><td>95.7</td><td>25.95±0.391</td><td>3.294±0.375</td><td>45.0</td><td>133.0</td></tr><tr><td>DDM [29]</td><td>29.79±0.504</td><td>2.089±0.352</td><td>27.4</td><td>110.3</td><td>29.67±0.420</td><td>2.705±0.330</td><td>40.8</td><td>165.5</td></tr><tr><td>FB-Diff</td><td>30.95±0.386</td><td>1.452±0.205</td><td>21.5</td><td>88.9</td><td>30.18±0.287</td><td>2.066±0.215</td><td>37.7</td><td>113.6</td></tr><tr><td>Δ value</td><td>1.21 ↓</td><td>0.210 ↓</td><td>1.5 ↓</td><td>5.3 ↓</td><td>1.39 ↓</td><td>0.145 ↓</td><td>0.1 ↓</td><td>8.1 ↓</td></tr></table>
+
+the diffusion model, promoting a promising synthesis of highlighted regions. Thus, BIO can boost well-interpolated videos with spatial and temporal consistency.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Dataset. To evaluate the interpolation performance of our framework, we conduct experiments on public ACDC cardiac [4] and 4D-Lung datasets [22]. For ACDC with the MRI modality, volume sequences between the end-diastolic and end-systolic phases are extracted as valid 4D data. Of all the 150 4D sequences, cases with identity 1-100, 101-120, and 121-150 serve as the training, validation, and testing sets. Besides, all MRI volumes are cropped to  $128 \times 128 \times 32$ , and the frame number ranges from 6 to 16 [53, 57]. For 4D-Lung CT images, the end-inspiratory and end-expiratory scans are set as the initial and final images. We collect 125 4D videos from [22], with the resolution equal to  $6 \times 128 \times 128 \times 128$ . They are split as  $80 / 15 / 30$  cases for training, validation, and inference. We uniform the frame number as 16 with zero paddings.
+
+**Evaluations.** We select quantitative evaluation metrics including Peak Signal-to-Noise Ratio (PSNR) [18], Learned Perceptual Image Patch Similarity (LPIPS) [55, 60], Fréchet Inception Distance (FID) [14], and Fréchet Video Distance (FVD) [47]. Compared to PSNR, which is the traditional pixel-wise reconstruction metric, LPIPS and FVD evaluate perceptual quality from the perspective of human vision [10, 24, 61], which is more feasible and favored in clinical practice. Specifically, LPIPS reveals important perceptual similarity like human vision. FID and FVD evaluate the dataset distribution bias between realistic and synthesized data, including spatial and temporal consistency.
+
+Training Details. The VAE maps the image space into
+
+the downsampled latent space with a ratio of  $1/8$ . And the proposed conditional diffusion model is implemented with a lightweight UNet. All models are trained using the AdamW optimizer with the linear warm-up strategy. The batch size, diffusion step  $T$ , and training epoch are equal to 2, 1000, and 500. Experiments are implemented based on Pytorch and 2 NVIDIA RTX 4090 GPUs. More details about the network and training settings are described in the Appendix.
+
+# 4.2. Comparisons with SOTA baselines
+
+Quantitative Comparison. We comprehensively conduct experiments on ACDC cardiac and 4D Lung datasets. Quantitative results are illustrated in Tab.1. Our model achieves the best performance across the benchmark on perceptual evaluation metrics from the perspective of human vision [10, 61], which are clinically favored compared with the pixel-centric reconstruction metric [7]. Specifically, FB-Diff outperforms UVI-Net [30] with  $0.210 \downarrow$  LPIPS and  $5.3 \downarrow$  FVD values on ACDC. Also, our model maintains quite satisfactory PSNR values of  $30.95\mathrm{dB}$  and  $30.18\mathrm{dB}$  on ACDC and 4D Lung. Although diffusion models are not sensitive to pixel-wise intensities [15], the conditional guidance of Fourier bases and coarsely inpainted videos is effective to boost the interpolation performance of diffusion models. Tab.1 reveals that FB-Diff significantly surpasses existing diffusion models on all metrics.
+
+Furthermore, the interpolation process becomes most challenging for the midmost frames since they are positioned farthest from the two reference frames [24]. And our model can better resolve this issue due to stronger temporal representations based on quasi-periodic motion modeling. Thus, a quantitative evaluation of central frames is necessary. As shown in Tab.2, FB-Diff demonstrates greater performance advantages, with  $4.3\downarrow$  FID and  $8.2\downarrow$  FVD values compared with UVI-Net. Additionally, FB-Diff acquires a competi
+
+![](images/8da4c198ac582ec7f985250dd8520efe4944f7261aca5a0b3ecc632bc930d0c8.jpg)  
+Figure 5. Qualitative comparison of the midmost frame interpolation between different models. VM: Voxelmorph.
+
+Table 2. Interpolation performance of the midmost frames on ACDC cardiac. The choice of midmost frames: if the frame number  $N$  is odd, three intermediate frames are selected, otherwise only two frames are chosen.  
+
+<table><tr><td>Model</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>FID ↓</td><td>FVD ↓</td></tr><tr><td>SVIN [13]</td><td>26.01±0.467</td><td>2.673±0.361</td><td>38.9</td><td>142.8</td></tr><tr><td>DDM [29]</td><td>24.37±0.511</td><td>2.756±0.330</td><td>41.5</td><td>145.1</td></tr><tr><td>UVI-Net [30]</td><td>26.25±0.410</td><td>2.542±0.374</td><td>37.0</td><td>137.1</td></tr><tr><td>FB-Diff</td><td>26.18±0.413</td><td>2.287±0.305</td><td>32.7</td><td>128.9</td></tr><tr><td>Δ value</td><td>0.07 ↓</td><td>0.255 ↓</td><td>4.3 ↓</td><td>8.2 ↓</td></tr></table>
+
+tive PSNR value, which demonstrates the effectiveness of respiration-related modeling via Fourier bases.
+
+Qualitative Comparison. Qualitative results on the interpolated midmost frame are depicted in Fig.5. SVIN [13], Voxelmorph [2], and DDM [29] leverage the single-direction flow estimation to interpolate intermediate frames with linear motions. Compared with that, UVI-Net [30] constructs the interpolation model with time-domain cycle-consistency, and achieves better reconstruction performance as expected. However, these methods essentially overlook the nonlinear and quasi-periodic motion discipline between temporal sequences, resulting in unsatisfactory interpolated results. Instead, FB-Diff exhibits advantageous predictions for midmost frames under the guidance of various motion patterns, indicating locally anisotropic motions with different intensities. Besides, other diffusion models do not work well due to the lack of fine-grained conditional guidance.
+
+# 4.3. Ablation Study
+
+Key Components. An ablation study is conducted to investigate the significance of various components in FB-Diff as shown in Tab.3. (a) Physiology Motion Priors  $\theta$ . By
+
+Table 3. Ablation study on key components.  $\theta$ : physiology motion priors,  $\hat{B}$ : Fourier motion bases,  $\hat{V}$ : coarsely inpainted videos.  
+
+<table><tr><td colspan="3">Settings</td><td colspan="2">ACDC Cardiac</td><td colspan="2">4D Lung</td></tr><tr><td>θ</td><td>ˆB</td><td>ˆV</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>X</td><td>✓</td><td>✓</td><td>29.76</td><td>1.710</td><td>29.53</td><td>2.413</td></tr><tr><td>X</td><td>X</td><td>✓</td><td>28.17</td><td>2.105</td><td>28.40</td><td>2.971</td></tr><tr><td>✓</td><td>✓</td><td>X</td><td>30.29</td><td>1.655</td><td>29.71</td><td>2.246</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr></table>
+
+removing  $\theta$  from the Fourier motion operator, interpolation performance decreases significantly due to the loss of general spectral characteristics from respiratory data. Therefore, Fourier bases lack the precise phase information. (b) Fourier bases  $\hat{\mathcal{B}}$ . Without  $\hat{\mathcal{B}}$  as conditional guidance, the conditional diffusion model fails to perceive explicit motion patterns with different frequencies, which provide the intensity of anisotropic motions. As a result, the generative model cannot well learn the regular temporal variations, with 2.78 dB  $\downarrow$  and 1.78 dB  $\downarrow$  PSNR values on ACDC and 4D Lung. (c) Inpainted Videos  $\hat{V}$ . Here the coarsely reconstructed sequences serve as the output by the finedtuned VAE as revealed in Fig.2. And the joint optimization process boosts the spatial and temporal representations of  $\hat{V}$ . Consequently, discarding this component will reduce fine-grained details of the diffusion model's output.
+
+Hyper-settings of Fourier Bases. (a) The number of Fourier Bases  $N_{Fb}$ . We first analyze the quantitative effects of the frequency number on the interpolation performance. As revealed in Tab.4, reducing the frequency number will cause degraded performance of the temporal simulation. Specifically, 1.30 dB lower PSNR and 0.535 higher LPIPS values are induced by decreasing  $N_{Fb}$  from 16 to 8. That phenomenon indicates that some elements in the group of
+
+![](images/c70cbbc9d0193a624785ed0adda338f619441ab48549cd94deb117f6ac5a06fa.jpg)  
+Figure 6. Visualizations on the frequency spectral of Fourier bases.  $V_{0}$ ,  $V_{N - 1}$ : starting and ending frames.  $f_{1} - f_{8}$  refer to different motion patterns, which highlight different regions under different frequency. There also appear locally anisotropic motion intensities inside a specific motion pattern.
+
+Table 4. Ablation study on the hyper-settings of Fourier bases.  $N_{Fb}$ : the frequency number of Fourier bases.  
+
+<table><tr><td rowspan="2">Settings</td><td colspan="2">ACDC Cardiac</td><td colspan="2">4D Lung</td></tr><tr><td>PSNR (dB) ↑</td><td>LPIPS ↓</td><td>PSNR (dB) ↑</td><td>LPIPS ↓</td></tr><tr><td>\(N_{Fb}\)=16 (Ours)</td><td>30.95</td><td>1.452</td><td>30.18</td><td>2.066</td></tr><tr><td>\(N_{Fb}\)=12</td><td>30.76</td><td>1.640</td><td>29.97</td><td>2.570</td></tr><tr><td>\(N_{Fb}\)=8</td><td>29.65</td><td>1.987</td><td>29.50</td><td>2.745</td></tr><tr><td>w/o Real part</td><td>29.18</td><td>1.872</td><td>29.56</td><td>2.453</td></tr><tr><td>w/o Imaginary part</td><td>29.88</td><td>1.681</td><td>29.67</td><td>2.401</td></tr></table>
+
+bases with the frequency ranging from  $f_{8}$  to  $f_{15}$  are consistent with specific frequencies of the respiratory process. (b) Real & Imaginary Parts.  $\hat{\mathcal{B}}$  bears real and imaginary parts after combining generic priors and case-specific spectral representations, which perform as the phase and magnitude information. Eliminating either the real or imaginary part will convert the complex data type into the real one, resulting in the loss of phase information and influencing the temporal interpolation.
+
+# 4.4. Visualization Analysis
+
+Visualization of Fourier bases. To further validate the effectiveness and interpretability of our proposed Fourier bases, we visualize extracted motion bases from the most shadow layer. As revealed in Fig.6,  $f_{0} - f_{7}$  refers to the magnitude of the first eight motion bases in ascending order of frequency. Specifically,  $f_{0}$  shows a low-frequency motion pattern highlighting no region, which is strongly related to static backgrounds.  $f_{1} - f_{3}$  exhibit a large motion intensity in the highlighted right and left ventricle regions. Those regions are indeed dynamic foregrounds requiring special attention.  $f_{4}$  depicts an activation in the myocardial region, which contracts inward along the circumferential direction.  $f_{5} - f_{7}$  highlight regions with vast deformations in the temporal domain. Particularly,  $f_{6}$  illustrates a large motion on boundaries of anatomical structures. In summary, these motion patterns reveal locally anisotropic motion intensities, and are harmonized with specific frequencies of the respiratory process, thus promoting the temporal interpolation.
+
+Visualization of temporal anatomical variations. To demonstrate the effectiveness of FB-Diff on temporal simulation, we visualize temporal variation maps for a perceptual comparison. Fig.7 provides interpolated intermediate
+
+![](images/bfd652572d8a4fb20e6f20ddca808de4f098967ae86b12ade2703c4b76e21236.jpg)  
+Figure 7. Temporal variation comparison between FB-Diff and existing methods with the linear motion hypothesis.
+
+frames at different timepoints. According to the referenced video, the anatomical motion in the temporal domain is nonlinear, which cannot be precisely simulated by existing methods with the linear motion hypothesis. In contrast, our predictions show better temporal consistency and continuity, particularly for frames at  $t = 0.6$  and 0.8.
+
+# 5. Conclusion
+
+Our proposed FB-Diff resolves the temporal interpolation of 4D medical imaging from a frequency perspective, and can model the respiration-related process with nonlinear and quasi-periodic motions. A Fourier motion operator is devised to extract Fourier bases by incorporating physiological motion priors and case-specific spectral information in the feature space. And the diffusion model further leverages Fourier bases and two prompting frames to achieve the precise interpolation. Extensive results show that FB-Diff achieves SOTA perceptual performance with better temporal consistency while maintaining promising reconstruction metrics. Ultimately, it requires more conditional guidance such as electrocardiogram signals to simulate the highly unstable breathing, which is promising in future work.
+
+Acknowledgement. We thank the anonymous reviewers for their thorough and constructive feedbacks. This research was supported in part by the project of the National Natural Science Foundation of China (No. 62376153), in part by the institute of Munich Center of Machine Learning.
+
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+        "text": "FDPT: Federated Discrete Prompt Tuning for Black-Box Visual-Language Models",
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+        "text": "Jiaqi Wu $^{1,8,10\\dagger}$ , Simin Chen $^{2\\dagger}$ , Jing Tang $^{3}$ , Yuzhe YANG $^{4}$ , Yiming Chen $^{5}$ , Lixu Wang $^{6}$ , Song Lin $^{7}$ , Zehua Wang $^{8,9}$ , Wei Chen $^{9*}$ , and Zijian Tian $^{10}$",
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+        "text": "$^{1}$ Tsinghua University,  $^{2}$ University of Texas at Dallas,  $^{3}$ Huazhong University of Science and Technology,",
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+    {
+        "type": "text",
+        "text": "<sup>4</sup>The Chinese University of Hong Kong, <sup>5</sup>National University of Singapore, <sup>6</sup>Nanyang Technological University,",
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+        "text": "$^{9}$ China University of Mining and Technology,  $^{10}$ China University of Mining and Technology (Beijing)",
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+        "text": "wjq11346@student.ubc.ca, sxc180080@utdallas.edu, focusers@163.com, yuzheyang@link.cuhk.edu.cn,",
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+        "text": "yiming.chen@u.nus.edu, wanglixu4334@gmail.com, linsong04@baidu.com, zwang@ece.ubc.ca,",
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+        "type": "text",
+        "text": "chenwdavior@163.com，Tianzj0726@126.com",
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+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Vision-Language Models (VLMs) have driven significant advancements in multimodal AI. Fine-tuning these models with user data enhances adaptability but poses privacy risks. While federated learning (FL) mitigates user data privacy concerns, it fails to protect model properties. Existing methods relying on black-box VLM APIs often require access to prediction logits, making them vulnerable to inversion attacks. Additionally, optimizing tuning complexity and data transmission efficiency in federated VLM scenarios remains a challenge. To address these challenges, we propose FDPT—the first federated discrete prompt tuning method utilizing black-box VLMs. During client optimization stage, FDPT employs an agent-driven framework leveraging large language models (LLMs) with enhanced reasoning capacities to systematically optimize discrete prompt representations, and also utilizes feedback mechanisms and chain of thought to enhance prediction accuracy. Importantly, it performs optimization by relying not on the predicted logic vectors output by LLMs but on textual results, avoiding reverse attack risks. During global aggregation stage, We mimic human electoral activities by employing evolutionary computation methods underpinned by semantic similarity computation to implement enhanced zero-order optimization for acquiring representative global tokens, thereby achieving knowledge aggregation. FDPT significantly outperforms nine state-of-the-art methods in image classification and visual question-answering, reducing communication overhead while generating highly transferable optimized prompts. Additionally, it exhibits im",
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+        "text": "proved robustness to data heterogeneity.",
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+        "text": "1. Introduction",
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+        "text": "General-purpose Vision-Language Models (VLMs) [45] integrate vast visual and linguistic information, advancing various vision tasks [36]. To better adapt to user needs, these models can undergo fine-tuning or prompt-tuning [27], but such modifications introduce privacy risks [13, 18, 34, 38]. Federated Learning (FL) [22] addresses these concerns by decentralizing data storage, reducing single-point breaches, and exchanging model weights or embeddings instead of raw data. Various FL-based approaches [19, 29, 39] have been explored for tuning large models, effectively preserving user data privacy.",
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+        "text": "Despite the success of FL, protecting the privacy of VLMs themselves remains a critical yet largely unexplored challenge. Existing FL approaches use zero-order optimization to estimate gradients for prompt tuning on black-box VLMs [31, 41]. For example, FedBPT [31] employs prompt exchange and gradient-free optimization, reducing communication and memory costs by avoiding direct parameter access and backpropagation on client devices. However, several limitations remain. First, these methods remain vulnerable to security risks as they rely on prediction logits, exposing them to inversion attacks that can infer model parameters [7, 47]. Second, zero-order optimization techniques [31, 41] often suffer from limited accuracy and adaptability in prompt fine-tuning. Finally, soft prompt methods [15, 46] lack interpretability and incur high communication costs in federated settings.",
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+        "text": "This ICCV 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": "federated discrete prompt optimization method comprising two stages: client-side optimization and global aggregation. In the client-side optimization phase, we introduce AI Agent-based Client Prompt Optimization, which refines token-level prompts using large language models (LLMs). We design a feedback mechanism and Chain-of-Thought measures to guide the agent in selecting optimal discrete tokens, overcoming the limitations of existing zero-order optimization methods in prompt tuning. Unlike traditional approaches that rely on prediction logits, our method uses only black-box VLM text outputs, reducing the risk of inversion attacks and enhancing model privacy protection. Afterwards, in the global aggregation phase, to reduce communication overhead in federated settings, we use discrete tokens for knowledge exchange instead of soft prompts. Inspired by human voting mechanisms, we propose a Self-Attention-Guided Evolutionary Computation method to identify representative tokens for constructing global prompts. Unlike the coarse sampling in traditional zero-order optimization, our approach clusters tokens in semantic space and then applies similarity calculations to refine the most accurate results, enhancing tuning efficiency.",
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+        "text": "Detailed experimental results demonstrate the advantages of our method. In Visual Question Answering (VQA) tasks, under the GPT-4 black-box setting, our method outperforms the classic black-box prompt optimization method FedBPT [31], achieving  $11.1\\%$  and  $7.4\\%$  improvements on the Art and Chemistry categories of the MMMU dataset [43], respectively. In traditional computer vision (CV) classification tasks, using the Qwen2-VL-72B model [3], our approach achieves  $71.8\\%$  accuracy on CIFAR-100, surpassing FedBPT by  $5.3\\%$ , demonstrating its superior performance. Additionally, FDPT significantly reduces communication costs without compromising optimization performance and enhances interpretability through discrete prompts. The contributions of this paper are as follows:",
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+        "list_items": [
+            "- We propose FDPT, a first federated black-box discrete prompt optimization framework that aggregates knowledge from multiple parties to optimize prompts while ensuring the privacy of both users and easily overlooked VLMs.",
+            "- We introduce an AI Agent-based Client Prompt Optimization for token-level prompts and a Self-attention-guided Evolutionary Computation method for selecting global tokens, offering better predictive performance than traditional zero-order optimization.",
+            "- Extensive experiments demonstrate that our method achieves superior performance across various text-vision tasks, exhibits low communication overhead, and is resilient to data heterogeneity."
+        ],
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+    {
+        "type": "text",
+        "text": "2. Background & Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Visual Language Models. Visual-Language Models (VLMs) [5, 45] are AI systems designed to process and understand both visual and textual information, enabling them to perform tasks such as Visual Question Answering (VQA) [43] and traditional visual classification tasks [20]. Traditional VLMs, like Qwen-VL [3], effectively integrate visual features with textual data, excelling in both VQA and image classification tasks. Flamingo [1] leverages few-shot learning capabilities, allowing it to quickly adapt to new tasks and perform well across both VQA and classification. Gemini [32] focuses on reasoning and multimodal understanding, achieving strong results in complex VQA tasks while also performing well in image and text classification. LLaVA [25] benefits from large-scale pretraining, efficiently handling intricate visuals and long-form text, with exceptional performance in both VQA and classification tasks. Newer models like InternVL2 [8], Qwen2-VL [35], and GPT-4o [16] build on these foundations, enhancing multimodal reasoning, improving the fusion of visual and textual data, and offering broader adaptability across both VQA and classification tasks.",
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+        "text": "Federated Learning. Federated Learning (FL) [22] is a decentralized approach allowing multiple clients to collaboratively train a shared model without sharing raw data, thus preserving privacy and defending against attacks [6, 24]. Recent works have further improved FL's robustness in handling data heterogeneity [26, 33], label noise [17], and personalization needs [11]. With the rise of large language models (LLMs), Federated Learning (FL) has gained new applications, effectively addressing the challenges of knowledge exchange and privacy protection between independent LLMs. FedPrompt [46] combines FL with prompt tuning, utilizing split aggregation to significantly reduce communication costs. FedBPT [31] presents a federated black-box prompt tuning framework that avoids direct access to model parameters, instead optimizing prompts using gradient-free methods. FedDTPT [40] realizes discrete prompt tuning for Large Language Models (LLMs). However, these methods still face issues such as security risks in large models and high communication overhead. We propose a Federated Discrete Prompt Tuning method, which, compared to existing approaches, performs zero-order optimization at the token level, mitigating the risk of adversarial users leveraging logits generated by the large model for backdoor attacks. Additionally, by utilizing discrete tokens for knowledge exchange, it significantly reduces communication overhead.",
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+        "type": "text",
+        "text": "Prompt Tuning. Prompt tuning [49] is an emerging technique for adapting large pre-trained models to specific tasks",
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+        "type": "page_number",
+        "text": "2462",
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+        "img_path": "images/750758aadf814a2906dd59c770d1ad113ac648049b233a009a000c5306cbf8d5.jpg",
+        "image_caption": [
+            "Figure 1. Overview of FDPT. The proposed framework consists of the client-side local Agent-based Client Prompt Optimization and the server-side Semantic-Similarity-Guided Evolutionary Computation for global selection. The detailed process is described in Sec. 3.2."
+        ],
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+        "type": "text",
+        "text": "with minimal additional training. In VLMs, prompt tuning [14] bridges visual and textual modalities, enabling tasks like image captioning [42, 44]. The Prompt tuning can be represented as finding an optimal prompt  $\\mathbf{p}^*$  to maximize the model's performance on the dataset  $\\mathcal{D} = \\{(\\mathbf{x},\\mathbf{y})\\}$ :",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {p} ^ {*} = \\arg \\max  f _ {\\mathrm {V L M}} (\\mathbf {p}; \\mathcal {D}) \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $f_{\\mathrm{VLM}}(\\mathbf{p};\\mathcal{D})$  denotes the performance of the VLM using prompt  $\\mathbf{p}$  over the dataset  $\\mathcal{D}$ . Continual Prompt Tuning (soft prompt tuning) involves fine-tuning a small set of trainable parameters (soft prompts) while keeping the core model fixed. However, it suffers from poor interpretability, and in Federated Learning (FL), it incurs high communication overhead between clients. Discrete Prompt Tuning (DPT), in contrast, optimizes specific discrete tokens from a fixed vocabulary. A notable approach, RLPrompt, uses reinforcement learning (RL) to select the best tokens based on rewards. However, it has limited optimization efficiency due to the computationally intensive nature of RL. Regarding above limitations, the proposed Federated Discrete Prompt Tuning method aims to combine the strengths of discrete prompt tuning with the constraints and needs of Federated Learning. By leveraging an AI agent (based on large language models) with robust reasoning capabilities, the method can generate more accurate and efficient local discrete tokens. Furthermore, by incorporating semantic similarity calculations into an evolutionary computing framework, the method can generate more precise global tokens that are shared across clients. Additionally, this reduces communication costs between clients, as discrete tokens are much smaller in parameters compared to soft prompts.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
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+        "text": "In this work, we consider a distributed scenario [22], where  $N$  clients each possess a private dataset  $\\mathcal{D}_k = \\{(\\mathcal{X}_k,\\mathcal{Y}_k)\\}$  consisting of  $n_k$  samples  $\\{(x_i^k,y_i^k)\\}_{i\\in [n_k]}$ . Each client can only access its own private data and does not wish to share it with others. This scenario is realistic, as hospitals and other organizations prioritize protecting sensitive data. Moreover, such distributed settings have been widely studied in existing research.",
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+        "type": "text",
+        "text": "Then, our federated discrete prompt optimization can be formulated as an optimization problem that aims to find the optimal prompt instruction  $p^*$  that satisfies the following equation:",
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+        "type": "equation",
+        "text": "\n$$\np ^ {*} = \\arg \\min  _ {p} \\sum_ {k \\in [ K ]} \\frac {n ^ {k}}{\\sum_ {k \\in [ K ]} n ^ {k}} \\sum_ {i \\in [ n ^ {k} ]} \\mathcal {L} \\left(\\mathrm {V L M} \\left(p; x _ {i} ^ {k}\\right), y _ {i} ^ {k}\\right) \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}(\\cdot)$  is the objective function, which could be the error rate, and  $\\mathrm{VLM}(\\cdot)$  represents the Vision-Language Model (VLM). The above equation can be interpreted as learning a globally optimal natural language prompt by minimizing the weighted average loss across all clients, where each client's contribution is proportional to its dataset size.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Notice that if clients were permitted to share their private data and had white-box access to the VLM, the equation above could be easily solved by approximating the objective function with a differentiable function, such as cross-entropy loss. In this case, standard backpropagation could be applied to the global dataset to search for the optimal prompt instruction. However, due to commercial concerns, modern VLMs are typically deployed as API ser",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "2463",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "vices, which are black-boxes to the clients. Additionally, each client is unwilling to share their data with others due to privacy concerns. Consequently, we must impose the following constraints:",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Blackbox:  $\\frac{\\partial\\mathcal{L}(\\mathrm{VLM}(p;x),y)}{\\partial p} = \\emptyset$",
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+    {
+        "type": "text",
+        "text": "Privacy:  $\\forall k,j\\in [K],k\\neq j,$ $\\mathrm{Client}_k$  cannot access  $\\mathcal{D}_j$  (3)",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The first constraint indicates that the gradient is not feasible, while the second constraint specifies that each client can only access its own data.",
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+    {
+        "type": "text",
+        "text": "3.2. Design Overview",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The algorithm overview is illustrated in Figure 1. Consistent with the traditional federated learning paradigm [22], each client communicates solely with the server using the prompt information, while keeping their data local. This ensures compliance with the data privacy constraints outlined in Eq.(3). Specifically, at the beginning, the server distributes the Global Prompt to each client. Then our approach follows these steps during each global communication round to search an optimal prompt: (1) Client Optimization: Each client utilizes an Agent-based Client Prompt Optimization method for personalized token-level prompt optimization. This method is preferred over backpropagation and ensures adherence to the black-box constraints in Eq.(3), which is more realistic in the context of VLM as a service; (2) Server Aggregation: Each client uploads its locally optimized prompt to the server, where knowledge aggregation is performed using the Semantic-similarity-guided Evolutionary Computation method. The subsequent sections provide a detailed explanation of each step in our approach.",
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+    {
+        "type": "text",
+        "text": "3.3. Client Optimization",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Upon receiving the global discrete prompt  $p_0$  from the server in the current round, each client iteratively updates it using an agent-based approach, as shown in Alg. 1. Initially, the agent queries the LLM to randomly replace some tokens in  $p_0$ , generating a set of prompt mutants  $p_1, p_2, \\ldots, p_M$  (Line 1). Each prompt is then combined with the client's local dataset and fed into the VLM to measure the accuracy, which serves as the prompt mutant's score. FDPT maintains a priority queue to manage these mutants, prioritizing those with higher accuracy (Lines 2-6). FDPT iteratively selects the highest-priority prompt from the queue as the seed, asks the LLM to mutate the important tokens of the seed, and updates the priority queue with the newly generated prompt mutants (Lines 7-13). Specifically, token importance is computed as follows: (1), FDPT compares each prompt mutant  $p_i$  with the seed prompt  $p_0$  token by token, constructing a difference matrix  $M$ , where  $M_i^j = 0$  if the",
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+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Agent-Based Prompt Optimization"
+        ],
+        "code_body": "Input: Initial discrete prompt  $p_0$ , Large Language Model (LLM), Vision-Language Model (VLM), client local dataset  $\\mathcal{D}$ , number of mutants  $M$   \nOutput: Optimized prompt  $\\hat{p}$   \n1: Initialization:  $\\{p_1, p_2, \\ldots, p_M\\} =$  Mutator(  $LLM, p_0$  )  $\\triangleright$  Mutate  $p_0$  by randomly replacing tokens  \n2:  $\\mathcal{Q} =$  Priority Queue  $\\triangleright$  Initialize an empty queue  \n3: for each prompt  $p_i$  in  $\\{p_0, p_1, \\ldots, p_M\\}$  do  \n4:  $Acc_i =$  Evaluate(VLM,  $p_i$ ,  $\\mathcal{D}$ )  $\\triangleright$  Evaluation  \n5: Push  $(\\mathcal{Q}, p_i, Acc_i)$ $\\triangleright$  Update the priority queue  \n6: end for  \n7: while stopping criterion not met do  \n8:  $p_{seed} =$  Pop  $(\\mathcal{Q}) \\triangleright$  Get the highest-priority prompt  \n9: Position = Importance Estimator  $\\triangleright$  Select important tokens  \n10:  $p_{new} =$  Mutator(  $LLM, p_{seed}$ , Position)  \n11:  $Acc_{new} =$  Evaluate(VLM,  $p_{new}$ ,  $\\mathcal{D}$ )  $\\triangleright$  Evaluation  \n12: Push  $(\\mathcal{Q}, p_{new}, Acc_{new})$ $\\triangleright$  Update the queue  \n13: end while  \n14: Return highest-scoring prompt from  $\\mathcal{Q}$",
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+    {
+        "type": "text",
+        "text": "$j$ -th token of  $p_i$  and  $p_0$  are different, and  $M_i^j = 1$  otherwise. (2), FDPT computes the accuracy gains  $V$ , where  $V_i = \\mathrm{Acc}_i - \\mathrm{Acc}_0$ . (3) The importance score of each token position is then given by  $S = M^{-1}V$ . This score estimation equation reflects the degree to which a token's presence or absence affects accuracy, weighted by its position in the prompt. Finally, the top  $K$  token positions are selected based on the importance score  $S$ .",
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+    {
+        "type": "text",
+        "text": "3.4. Server Aggregation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "After local client optimization, each client uploads its optimized discrete prompt to the server for knowledge exchange. The server then aggregates these local optimal prompts for the next round of optimization. Specifically, the server aggregation includes the following steps (as shown in Algorithm 2):",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Token-level Semantic Representation. In total client uploaded prompts, e.g. the initial population  $\\mathcal{P}_{\\mathrm{init}}$ , for each token in a prompt, we use a pre-trained text encoder of the Roberta to get its token-level semantic representation, denoted as",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} _ {i} = [ e _ {i} ^ {1}, e _ {i} ^ {2}, \\dots , e _ {i} ^ {K} ] e _ {i} ^ {j} = f _ {e m b e d} (t k _ {i} ^ {j}) \\qquad (4)\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where  $f_{embed}(\\cdot)$  is the pre-trained encoder, and  $tk_i^j$  is the  $j^{th}$  token of the  $i^{th}$  prompt.",
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+    {
+        "type": "text",
+        "text": "Reputation Test. We first evaluate the reputation of each token, defined as the semantic-similarity weight (denoted",
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+    {
+        "type": "page_number",
+        "text": "2464",
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+    {
+        "type": "text",
+        "text": "$\\alpha_{g,h})$  that each token assigns to all other tokens. This is computed using a cosine-similarity mechanism [12] based on embeddings:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {g} = \\sum_ {h} \\alpha_ {g, h} = \\sum_ {h} \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {e} _ {g} \\cdot \\mathbf {e} _ {h}}{\\sqrt {d}}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{e}_g$  and  $\\mathbf{e}_h$  represent the embedding of a token  $g$  and  $h$ , respectively, and  $d$  is the dimensionality of the embeddings. A higher semantic-similarity weight  $\\alpha_{g,h}$  signifies a stronger influence over other tokens. We define the total semantic-similarity weight of token  $g$  as  $\\alpha_{g}$ , which represents the token's semantic importance among all other tokens, referred to as its Reputation.",
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+    {
+        "type": "text",
+        "text": "Aggregation. Next, tokens are clustered based on their semantic similarity by grouping embeddings that are close to each other in the high-dimensional semantic space:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} = \\left\\{\\mathcal {C} _ {1}, \\mathcal {C} _ {2}, \\dots , \\mathcal {C} _ {Z} \\right\\}, \\mathcal {C} _ {z} = \\left\\{\\mathbf {e} _ {h} \\mid \\| \\mathbf {e} _ {h} - \\mathbf {e} _ {g} \\| <   \\epsilon , \\forall h \\in \\mathcal {P} _ {\\text {i n i t}} \\right\\}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "where  $\\epsilon$  is a pre-defined distance threshold.  $C_z$  denotes a cluster, or Community. Embeddings with equivalent syntactic meanings are grouped into a cluster, from which a single representative is subsequently selected.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Election. Finally, within each cluster (Community), the representative token is determined by semantic-similarity weights (reputation). Tokens with higher weights have stronger semantic dependencies on other tokens and are more likely to be selected:",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {r} _ {z} = \\underset {\\mathbf {e} _ {n} \\in \\mathcal {C} _ {z}} {\\arg \\max } \\alpha_ {n}, \\tag {7}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathbf{r}_z$  denotes the representative token in Community  $\\mathcal{C}_z$ . Importantly, communities containing only a single token are discarded, as these tokens contain only client-specific information, following the principle of \"majority rule\" [30] in Voting. The selected tokens are then arranged in their original order (using, for example, a bubble sort [2]) to form a representative prompt, or the \"Representatives\", denoted as  $\\mathcal{P}_{\\mathrm{new}} = \\{\\mathbf{r}_1,\\mathbf{r}_2,\\dots ,\\mathbf{r}_Z\\}$ .",
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+    {
+        "type": "text",
+        "text": "4. Evaluation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1. Evaluation Setup",
+        "text_level": 1,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Backbone API. In our experiments, we selected four backbone models: Qwen2-VL-72B [35], InternVL2-Llama3-76B, TeleMM [23], and GPT4o.",
+        "bbox": [
+            89,
+            790,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Dataset and Evaluation. We conduct experiments on two tasks: traditional image classification and Visual Question Answer (VQA). For image classification, we use the",
+        "bbox": [
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+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 2 Semantic-similarity-Guided Evolutionary Computation for Discrete Prompt Optimization"
+        ],
+        "code_body": "Input: I clients with discrete prompt tokens  $\\{\\mathcal{P}_{\\mathrm{client}_i}\\}_{i = 1}^I$    \nOutput: Global prompt tokens  $\\mathcal{P}_{\\mathrm{new}}$    \n1: Initialization Initial population  $\\mathcal{P}_{\\mathrm{init}}$    \n2: for each token  $tk$  in a prompt  $\\in \\mathcal{P}_{\\mathrm{init}}$  do   \n3: Achieve mapping according to Eq.4   \n4: end for   \n5: for each token  $\\mathbf{t}_g$  do  $\\triangleright$  Reputation Test   \n6: for each token  $\\mathbf{t}_h$  do   \n7: Semantic-similarity weight according to Eq.5   \n8: end for   \n9: Get total semantic-similarity weight  $\\alpha_{g} = \\sum_{h}\\alpha_{g,h}$    \n10: end for   \n11: Cluster tokens according to Eq.6 Aggregation   \n12: for each Community  $C_z\\in \\mathcal{C}$  do Election   \n13: Select representative token according to Eq.7   \n14: if  $C_z$  contains only one token then   \n15: Discard Community  $C_z$    \n16: end if   \n17: end for   \n18: Form Representatives  $\\mathcal{P}_{\\mathrm{new}} = \\{\\mathbf{r}_1,\\mathbf{r}_2,\\dots ,\\mathbf{r}_Z\\}$  from selected representative tokens",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "MNIST [9], CIFAR-10, CIFAR-100, and TinyImageNet (TinyImg) [20] datasets. For VQA, we utilize the Art, Chemistry, and Finance sections of the MMMU dataset [43], along with the RealWorldQA (RWQA) dataset. The task objective is to leverage optimized prompts for accurate image classification on the image datasets, and for VQA, to assist in parsing textual content within the datasets to enable accurate classification or decision-making.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use Accuracy as the evaluation metric for the image classification task. To maintain consistency across tasks, we also constrain predictions in the VQA task to the range of available labels and evaluate performance using Accuracy.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison Baselines. We compare our method against eight state-of-the-art (SOTA) approaches: FedPrompt [46], FedPepTAO [4], FedTPG [29], HPT [37], CoOp [48], BBT [10], FedBPT [31], BPTVLM [41], and a manual prompting method (Manual Prompt). Notably, HPT [37], CoOp [48], BBT[10], and BPTVLM [41] are not originally designed for federated learning. To adapt these methods to a federated setting, we apply a weighted averaging aggregation approach, following the implementations of FedPrompt [46]and FedBPT [31]. The results are reported using federated versions of these models: FedAvg-HPT, FedAvg-CoOp, FedAvg-BBT, and Fed-BPTVLM. Additionally, we categorize these methods into White-box and Black-box approaches based on whether they require access to model parameters. The White-box methods include FedPrompt [46],",
+        "bbox": [
+            511,
+            674,
+            908,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "2465",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9aaa57d4b4beb88de6977a74ffcc74e8af97332a32ca82a86645ed5c709770d7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">Method</td><td colspan=\"4\">CV Classification</td><td colspan=\"4\">VQA</td><td rowspan=\"2\">Average</td></tr><tr><td>MNIST</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td><td>Art</td><td>Chemistry</td><td>Finance</td><td>RWQA</td></tr><tr><td rowspan=\"10\">Qwen2-VL-72B</td><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>90.4</td><td>79.5</td><td>73.5</td><td>60.9</td><td>74.6</td><td>63.3</td><td>70.5</td><td>80.4</td></tr><tr><td>FedPepTAO</td><td>86.7</td><td>78.3</td><td>72.9</td><td>59.5</td><td>69.1</td><td>58.8</td><td>68.5</td><td>77.9</td></tr><tr><td>FedTPG</td><td>84.2</td><td>76.8</td><td>71.3</td><td>59.2</td><td>72.4</td><td>57.5</td><td>62.6</td><td>75.4</td></tr><tr><td>FedAvg-HPT</td><td>86.9</td><td>78.4</td><td>70.2</td><td>58.7</td><td>75.7</td><td>53.5</td><td>65.9</td><td>78.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>78.1</td><td>71.4</td><td>59.2</td><td>70.2</td><td>61.8</td><td>63.3</td><td>76.5</td></tr><tr><td rowspan=\"5\">Black Box</td><td>Manual</td><td>70.7</td><td>62.2</td><td>53.5</td><td>47.3</td><td>54.7</td><td>45.8</td><td>51.8</td><td>58.3</td></tr><tr><td>FedAvg-BBT</td><td>78.9</td><td>72.3</td><td>62.7</td><td>51.7</td><td>63.5</td><td>53.9</td><td>60.3</td><td>69.7</td></tr><tr><td>FedBPT</td><td>80.0</td><td>72.0</td><td>64.2</td><td>53.1</td><td>68.0</td><td>50.6</td><td>59.0</td><td>67.8</td></tr><tr><td>Fed-BPTVLM</td><td>80.7</td><td>73.1</td><td>62.3</td><td>50.9</td><td>65.2</td><td>53.3</td><td>63.3</td><td>70.8</td></tr><tr><td>Our method</td><td>90.5</td><td>78.5</td><td>71.8</td><td>57.8</td><td>74.0</td><td>60.8</td><td>67.2</td><td>78.5</td></tr><tr><td rowspan=\"10\">InternVL2-Llama3-76B</td><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>88.1</td><td>81.3</td><td>74.4</td><td>60.2</td><td>70.2</td><td>58.8</td><td>62.9</td><td>76.1</td></tr><tr><td>FedPepTAO</td><td>87.3</td><td>77.8</td><td>71.2</td><td>58.5</td><td>65.2</td><td>55.3</td><td>63.0</td><td>75.4</td></tr><tr><td>FedTPG</td><td>86.2</td><td>79.3</td><td>71.7</td><td>57.4</td><td>68.0</td><td>54.2</td><td>60.7</td><td>73.8</td></tr><tr><td>FedAvg-HPT</td><td>85.1</td><td>78.7</td><td>72.3</td><td>58.4</td><td>69.1</td><td>53.0</td><td>62.0</td><td>74.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>79.1</td><td>71.6</td><td>58.1</td><td>71.8</td><td>56.2</td><td>63.9</td><td>71.7</td></tr><tr><td rowspan=\"5\">Black Box</td><td>Manual</td><td>71.8</td><td>63.7</td><td>51.8</td><td>45.4</td><td>52.5</td><td>46.3</td><td>53.8</td><td>61.3</td></tr><tr><td>FedAvg-BBT</td><td>80.0</td><td>71.1</td><td>65.2</td><td>52.7</td><td>60.2</td><td>51.9</td><td>53.8</td><td>70.5</td></tr><tr><td>FedBPT</td><td>80.7</td><td>72.7</td><td>66.6</td><td>52.3</td><td>61.3</td><td>50.6</td><td>58.4</td><td>67.1</td></tr><tr><td>Fed-BPTVLM</td><td>79.5</td><td>71.4</td><td>67.2</td><td>53.0</td><td>64.1</td><td>53.0</td><td>56.7</td><td>69.8</td></tr><tr><td>Our method</td><td>89.6</td><td>79.0</td><td>71.5</td><td>57.3</td><td>70.7</td><td>55.9</td><td>63.6</td><td>75.5</td></tr><tr><td rowspan=\"5\">TeleMM</td><td rowspan=\"5\">Black Box</td><td>Manual</td><td>69.4</td><td>65.5</td><td>53.3</td><td>45.8</td><td>53.0</td><td>45.0</td><td>52.5</td><td>57.9</td></tr><tr><td>FedAvg-BBT</td><td>80.9</td><td>70.6</td><td>63.1</td><td>49.1</td><td>56.9</td><td>48.8</td><td>56.4</td><td>64.1</td></tr><tr><td>FedBPT</td><td>80.0</td><td>71.3</td><td>61.9</td><td>50.9</td><td>60.8</td><td>51.5</td><td>57.4</td><td>66.3</td></tr><tr><td>Fed-BPTVLM</td><td>79.1</td><td>71.0</td><td>62.7</td><td>49.7</td><td>59.1</td><td>52.3</td><td>57.7</td><td>68.5</td></tr><tr><td>Our method</td><td>88.4</td><td>78.9</td><td>69.3</td><td>57.4</td><td>64.6</td><td>55.7</td><td>61.6</td><td>75.0</td></tr><tr><td rowspan=\"5\">GPT4o</td><td rowspan=\"5\">Black Box</td><td>Manual</td><td>74.4</td><td>68.2</td><td>59.1</td><td>52.8</td><td>61.9</td><td>58.6</td><td>61.6</td><td>71.9</td></tr><tr><td>FedAvg-BBT</td><td>81.0</td><td>76.7</td><td>67.6</td><td>56.1</td><td>64.6</td><td>57.5</td><td>63.6</td><td>69.2</td></tr><tr><td>FedBPT</td><td>83.2</td><td>78.3</td><td>68.4</td><td>56.6</td><td>69.1</td><td>59.3</td><td>68.5</td><td>69.9</td></tr><tr><td>Fed-BPTVLM</td><td>81.7</td><td>79.0</td><td>67.9</td><td>57.3</td><td>67.4</td><td>57.9</td><td>65.2</td><td>71.6</td></tr><tr><td>Our method</td><td>92.5</td><td>85.3</td><td>73.9</td><td>62.7</td><td>76.8</td><td>66.7</td><td>72.8</td><td>78.5</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Performance Comparison on CV Classification and VQA Tasks. The accuracy results are measured in percentages (\\%). Bold values indicate the overall best results, and underlined values indicate the best results among Black Box methods.",
+        "bbox": [
+            89,
+            595,
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+            625
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "FedPepTAO [4], FedTPG [29], FedAvg-HPT, and FedAvg-CoOp, while the Black-box methods consist of Manual, FedAvg-BBT, FedBPT [31], and Fed-BPTVLM. Detailed descriptions of all baselines are provided in Appendix A.",
+        "bbox": [
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+            651,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation. The federated learning setup for our experiments is as follows: we use a default of 10 clients, with a client participation rate of  $100\\%$  in each training round. Additionally, we adopt a  $k$ -shot mechanism for prompt tuning, following the approach in work [31], with the default value of  $k$  set to 50. For image classification datasets, we use the original training and test sets. For each Visual QA dataset, we randomly select 50 samples as the training set (from the validation set for MMMU and the test set for RealWorldQA), with the remaining samples used for testing. In terms of baseline implementations, we adapt traditional",
+        "bbox": [
+            89,
+            734,
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+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "prompt optimization methods (HPT, CoOp, BBT, BBT-VLM) to the federated learning framework by employing the classical Federated Averaging (FedAvg) approach. For black-box backbone model configurations, we extend soft prompt tuning methodologies, such as FedBPT, by mapping the soft tokens to discrete tokens, through the RoBERTa encoder's tokenization mechanism, before feeding them into API-based models. In addition, all experiments are conducted on two NVIDIA GeForce RTX A800 GPUs. Detailed hyperparameter settings are provided in Appendix B.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Effectiveness Results",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We first evaluate the effectiveness of our method on traditional CV classification tasks and VQA tasks. Experimental results show that, compared to other methods, our method demonstrates significant performance improvements in both",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "2466",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tasks, particularly excelling in black-box environments, with only a small gap from white-box algorithms.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Traditional CV Classification Tasks. In traditional CV classification tasks, our method achieves outstanding performance across all model configurations. For example, in the GPT4o black-box setting, our method achieves improvements of  $11.2\\%$ ,  $7.0\\%$ ,  $5.5\\%$ , and  $6.1\\%$  over the closest-performing FedBPT [31] method on the MNIST, Cifar-10, Cifar-100, and TinyImg datasets, respectively. In the TeleMM black-box setting, our method also performs exceptionally well, achieving  $88.4\\%$  and  $78.9\\%$  accuracy on MNIST and Cifar-10, respectively, which is an improvement of  $9.3\\%$  and  $8.3\\%$  over FedAvg-BBT. Additionally, for the Qwen2-VL-72B model, our method achieves accuracies of  $78.5\\%$  and  $71.8\\%$  on the Cifar-10 and Cifar-100 datasets, respectively, representing improvements of  $7.1\\%$  and  $5.3\\%$  over FedBPT [31], further demonstrating its advantage in traditional CV tasks.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "VQA Tasks. Our method also shows strong performance in VQA tasks. In the GPT4o black-box setting, our method achieves improvements of  $11.1\\%$ ,  $7.4\\%$ ,  $4.3\\%$ , and  $8.6\\%$  over the FedBPT [31] method on the Art, Chemistry, Finance, and RWQA datasets, respectively. In TeleMM setting, our method's performance remains very stable, achieving improvements of  $7.7\\%$  and  $10.9\\%$  over FedAvg-BBT on the Art and RWQA datasets, respectively.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Prompt Transferability Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In the prompt transferability experiment, we evaluate the performance of prompts optimized on one backbone model when applied to another, as shown in Table 2. The results indicate that prompts exhibit a degree of transferability, maintaining high robustness across models with minimal accuracy loss, as referenced in Table 1. Additionally, compared to the Qwen2-VL transfer results, the InternVL2 transfer showed better accuracy, further validating the high applicability and robustness of prompts between certain models.",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/329c6aa54a41fb62a1627c40a1023d44ac408383efbb017c4bba9319fb55c93f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td>Qwen2-VL→TeleMM</td><td>80</td><td>70.5</td><td>58.1</td></tr><tr><td>InternVL2→GPT4o</td><td>87.8</td><td>72.3</td><td>63.5</td></tr></table>",
+        "bbox": [
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+            717,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Communication Overhead Experiment",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In the communication overhead experiment, our method shows a significant advantage in parameter efficiency, as illustrated in Table 3. Specifically, white-box methods like",
+        "bbox": [
+            89,
+            854,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "FedPrompt [46] and FedTPG [29] and most black-box methods such as FedAvg-BBT and Fed-BPTVLM require hundreds of thousands of parameters, whereas our method requires only 150. This substantial reduction effectively minimizes latency and resource consumption associated with communication. This advantage primarily arises from a key difference in algorithm design: while other methods use soft prompts for knowledge exchange between clients, our method employs discrete prompt tokens. Soft prompts typically require a large number of continuous parameters, whereas discrete prompt tokens enable knowledge transfer with only a small set of parameters, significantly reducing communication overhead.",
+        "bbox": [
+            511,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/aa4c6eea7331c9d07ab9724ccd8d4dca825b99624935b534b17ae42878f44315.jpg",
+        "table_caption": [
+            "Table 2. Transferability Experiment Results. The accuracy results are measured in percentages  $(\\%)$ ."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Type</td><td>Method</td><td>Parameters</td></tr><tr><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>614k</td></tr><tr><td>FedPepTAO</td><td>1796k</td></tr><tr><td>FedTPG</td><td>614k</td></tr><tr><td>FedAvg-HPT</td><td>614k</td></tr><tr><td>FedAvg-CoOp</td><td>614k</td></tr><tr><td rowspan=\"3\">Black Box</td><td>FedAvg-BBT</td><td>614k</td></tr><tr><td>FedBPT</td><td>40.8k</td></tr><tr><td>Fed-BPTVLM</td><td>614k</td></tr><tr><td colspan=\"2\">Our method</td><td>150</td></tr></table>",
+        "bbox": [
+            517,
+            297,
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+            448
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Communication Overhead Experiment results. The measurements are in Tensors within the PyTorch Framework. Bold values indicate the best results, and underlined values indicate the second-best results.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "In the improvements ablation study based on Qwen2-VL72B API, our method consistently achieves the best performance across all metrics, further validating the effectiveness of its key components, as shown in Table 4. Compared to cases where specific modules are removed or replaced, our method demonstrates significant improvements on the Cifar-10, Cifar-100, and TinyImg datasets. Server-side experiments. Our method improves accuracy on the Cifar-10 and Cifar-100 datasets by  $2.0\\%$  and  $1.2\\%$ , respectively, compared to the setting without the clustering strategy. Furthermore, compared to the fixed clustering approach, our method achieves accuracy gains of  $0.7\\%$  on Cifar-10 and  $2.5\\%$  on Cifar-100, underscoring the importance of a dynamic clustering strategy. Client-side experiments. Removing the G-F mechanism results in a significant accuracy drop across all datasets. Furthermore, our method achieves a  $1.0\\%$  accuracy improvement on Cifar-100 and  $1.6\\%$  on TinyImg compared to the configuration without the E-EB strategy. Compared to the configuration without the PPR-CoT strategy, our method improves accuracy by  $3.2\\%$  on Cifar-10 and  $2.5\\%$  on Cifar-100, underscoring the pivotal role of the PPR-CoT strategy in enhancing model perfor",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "2467",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/014723ac8c30ea6bf4eb63108b72b1e7123449f98af58dfb737d99169f31fe74.jpg",
+        "table_caption": [
+            "mance."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Site</td><td>Method</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td rowspan=\"4\">Server</td><td>w Embedding-fedavg</td><td>71.9</td><td>62.5</td><td>54.2</td></tr><tr><td>w Random search</td><td>65.3</td><td>57.3</td><td>53.9</td></tr><tr><td>w/o Clustering Strategy</td><td>76.5</td><td>70.6</td><td>55.9</td></tr><tr><td>w Fixed Clusters</td><td>77.8</td><td>69.3</td><td>56.3</td></tr><tr><td rowspan=\"3\">Client</td><td>w/o G-F Mechanism</td><td>71.8</td><td>65.5</td><td>53.5</td></tr><tr><td>w/o E-EB Strategy</td><td>76.9</td><td>70.8</td><td>56.2</td></tr><tr><td>w/o PPR-CoT</td><td>75.3</td><td>69.3</td><td>56.7</td></tr><tr><td colspan=\"2\">Our method</td><td>78.5</td><td>71.8</td><td>57.8</td></tr></table>",
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+        "text": "Table 4. The Improvements Ablation Studies Results. The accuracy is measured in percentages (\\%). Performance decreases with the removal or modification of any key component, underscoring the effectiveness of the improvements. \"w Embedding-fedavg\" denotes the use of a weighted averaging aggregation method, as in FedBPT [31] and FedAvg-BBT. \"w Random search\" refers to the removal of weight comparison, using random search instead to select representative tokens. \"w/o Clustering Strategy\" indicates the removal of the clustering step. \"w Fixed Clusters\" implies a fixed number of clusters, which affects the count of representative tokens.",
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+        "text": "Initial Prompt Impact. We evaluate the impact of the Initial Prompt on performance using GPT-4o as the backbone black-box VLM for classification tasks across datasets, comparing it with three typical black-box algorithms. Figure 2 shows that different prompt configurations significantly affect model performance, with our algorithm consistently achieving the best outcomes. Specifically, detailed prompts enhance model accuracy by providing richer information, which supports more effective learning and adaptation. In contrast, shorter prompts reduce accuracy, indicating that limited information constrains performance. Thus, prompt design is critical in classification tasks, and our algorithm exhibits strong robustness and performance across various prompt configurations. We present all Initial Prompts in Appendix C.",
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+        "image_caption": [
+            "Figure 2. Initial Prompt Impact. Prompt-1 represents a \"shorter initial prompt,\" Prompt-2 a \"standard initial prompt,\" and Prompt-3 a \"detailed initial prompt.\""
+        ],
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+        "text": "4.6. Heterogeneous Data Robustness Experiment",
+        "text_level": 1,
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+        "text": "In the heterogeneous data robustness experiment, we use the Qwen2-VL-72B API as the backbone VLM model to evaluate the performance of different algorithms on heterogeneous data in the TinyImagenet dataset, as shown in Figure 3. Data is distributed across 10 clients using a Dirichlet Distribution [21] with varying hyperparameters dir, where a smaller Dirichlet parameter (e.g., dir=0.05) indicates greater data heterogeneity. Details of these heterogeneous data distributions are provided in Appendix D. The results demonstrate that all methods show some robustness to data heterogeneity, aligning with expectations [28, 31] for model stability on heterogeneous data. Additionally, as heterogeneity increases, our method exhibits superior performance, with minimal accuracy reduction, outperforming other methods under all heterogeneity conditions.",
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+        "img_path": "images/da5f1c208403cb7a251f64a0194070670d99b45fd8172029e77c6a9e485be995.jpg",
+        "image_caption": [
+            "Figure 3. Heterogeneous Data Robustness Experiment results on the TinyImageNet dataset. The parameter \"dir\" is the Dirichlet Distribution hyperparameter; smaller values of dir indicate higher data heterogeneity across the 10 clients."
+        ],
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+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose FDPT, the first federated black-box discrete prompt tuning framework based on visual language models. FDPT uses an Agent-based Client Prompt Optimization strategy to achieve token-level prompt optimization on the client side without traditional prediction logits, thereby preventing inversion attacks. On the server side, a Semantic-Similarity-Guided Evolutionary Computation framework is implemented to execute more precise zeroth-order optimization, which enables the obtention of representative global tokens. Moreover, discrete token exchange between clients offers high security and low communication overhead. Moreover, discrete tokens exhibit enhanced interpretability compared to soft prompts, which facilitates human experts in designing corresponding instructions. Our framework exhibits: (1) statistically significant accuracy enhancements in conventional visual recognition and cross-modal reasoning tasks; (2) optimized communication efficiency through adaptive token selection mechanisms; (3) cross-domain transferability of learned prompt representations; and (4) strengthened resilience to data distribution shifts, particularly in heterogeneous learning environments.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. This research was supported by the National Natural Science Foundation of China under Grant 52074305, 52274160, 51874300 and the National Natural Science Foundation of China-Shanxi Provincial People's Government Coal-based Low Carbon Joint Fund U1510115, the Academic Research Projects of Beijing Union University (No.ZK90202106) and R&D Program of Beijing Municipal Education Commission (KM202211417005).",
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+    {
+        "type": "text",
+        "text": "References",
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+            "content": "Vision-Language Models (VLMs) have driven significant advancements in multimodal AI. Fine-tuning these models with user data enhances adaptability but poses privacy risks. While federated learning (FL) mitigates user data privacy concerns, it fails to protect model properties. Existing methods relying on black-box VLM APIs often require access to prediction logits, making them vulnerable to inversion attacks. Additionally, optimizing tuning complexity and data transmission efficiency in federated VLM scenarios remains a challenge. To address these challenges, we propose FDPT—the first federated discrete prompt tuning method utilizing black-box VLMs. During client optimization stage, FDPT employs an agent-driven framework leveraging large language models (LLMs) with enhanced reasoning capacities to systematically optimize discrete prompt representations, and also utilizes feedback mechanisms and chain of thought to enhance prediction accuracy. Importantly, it performs optimization by relying not on the predicted logic vectors output by LLMs but on textual results, avoiding reverse attack risks. During global aggregation stage, We mimic human electoral activities by employing evolutionary computation methods underpinned by semantic similarity computation to implement enhanced zero-order optimization for acquiring representative global tokens, thereby achieving knowledge aggregation. FDPT significantly outperforms nine state-of-the-art methods in image classification and visual question-answering, reducing communication overhead while generating highly transferable optimized prompts. Additionally, it exhibits im"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.4,
+                0.78,
+                0.415
+            ],
+            "angle": 0,
+            "content": "proved robustness to data heterogeneity."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.448,
+                0.646,
+                0.464
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.475,
+                0.907,
+                0.642
+            ],
+            "angle": 0,
+            "content": "General-purpose Vision-Language Models (VLMs) [45] integrate vast visual and linguistic information, advancing various vision tasks [36]. To better adapt to user needs, these models can undergo fine-tuning or prompt-tuning [27], but such modifications introduce privacy risks [13, 18, 34, 38]. Federated Learning (FL) [22] addresses these concerns by decentralizing data storage, reducing single-point breaches, and exchanging model weights or embeddings instead of raw data. Various FL-based approaches [19, 29, 39] have been explored for tuning large models, effectively preserving user data privacy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.643,
+                0.909,
+                0.884
+            ],
+            "angle": 0,
+            "content": "Despite the success of FL, protecting the privacy of VLMs themselves remains a critical yet largely unexplored challenge. Existing FL approaches use zero-order optimization to estimate gradients for prompt tuning on black-box VLMs [31, 41]. For example, FedBPT [31] employs prompt exchange and gradient-free optimization, reducing communication and memory costs by avoiding direct parameter access and backpropagation on client devices. However, several limitations remain. First, these methods remain vulnerable to security risks as they rely on prediction logits, exposing them to inversion attacks that can infer model parameters [7, 47]. Second, zero-order optimization techniques [31, 41] often suffer from limited accuracy and adaptability in prompt fine-tuning. Finally, soft prompt methods [15, 46] lack interpretability and incur high communication costs in federated settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.534,
+                0.886,
+                0.907,
+                0.902
+            ],
+            "angle": 0,
+            "content": "To address these challenges, we propose FDPT, the first"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.109,
+                0.875,
+                0.218,
+                0.888
+            ],
+            "angle": 0,
+            "content": "\\(\\dagger\\) Equal contribution"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.112,
+                0.888,
+                0.235,
+                0.9
+            ],
+            "angle": 0,
+            "content": "* Corresponding author"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2461"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.424
+            ],
+            "angle": 0,
+            "content": "federated discrete prompt optimization method comprising two stages: client-side optimization and global aggregation. In the client-side optimization phase, we introduce AI Agent-based Client Prompt Optimization, which refines token-level prompts using large language models (LLMs). We design a feedback mechanism and Chain-of-Thought measures to guide the agent in selecting optimal discrete tokens, overcoming the limitations of existing zero-order optimization methods in prompt tuning. Unlike traditional approaches that rely on prediction logits, our method uses only black-box VLM text outputs, reducing the risk of inversion attacks and enhancing model privacy protection. Afterwards, in the global aggregation phase, to reduce communication overhead in federated settings, we use discrete tokens for knowledge exchange instead of soft prompts. Inspired by human voting mechanisms, we propose a Self-Attention-Guided Evolutionary Computation method to identify representative tokens for constructing global prompts. Unlike the coarse sampling in traditional zero-order optimization, our approach clusters tokens in semantic space and then applies similarity calculations to refine the most accurate results, enhancing tuning efficiency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.45,
+                0.483,
+                0.661
+            ],
+            "angle": 0,
+            "content": "Detailed experimental results demonstrate the advantages of our method. In Visual Question Answering (VQA) tasks, under the GPT-4 black-box setting, our method outperforms the classic black-box prompt optimization method FedBPT [31], achieving \\(11.1\\%\\) and \\(7.4\\%\\) improvements on the Art and Chemistry categories of the MMMU dataset [43], respectively. In traditional computer vision (CV) classification tasks, using the Qwen2-VL-72B model [3], our approach achieves \\(71.8\\%\\) accuracy on CIFAR-100, surpassing FedBPT by \\(5.3\\%\\), demonstrating its superior performance. Additionally, FDPT significantly reduces communication costs without compromising optimization performance and enhances interpretability through discrete prompts. The contributions of this paper are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.687,
+                0.48,
+                0.759
+            ],
+            "angle": 0,
+            "content": "- We propose FDPT, a first federated black-box discrete prompt optimization framework that aggregates knowledge from multiple parties to optimize prompts while ensuring the privacy of both users and easily overlooked VLMs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.763,
+                0.48,
+                0.834
+            ],
+            "angle": 0,
+            "content": "- We introduce an AI Agent-based Client Prompt Optimization for token-level prompts and a Self-attention-guided Evolutionary Computation method for selecting global tokens, offering better predictive performance than traditional zero-order optimization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.838,
+                0.48,
+                0.895
+            ],
+            "angle": 0,
+            "content": "- Extensive experiments demonstrate that our method achieves superior performance across various text-vision tasks, exhibits low communication overhead, and is resilient to data heterogeneity."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.091,
+                0.687,
+                0.48,
+                0.895
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.09,
+                0.783,
+                0.107
+            ],
+            "angle": 0,
+            "content": "2. Background & Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.115,
+                0.905,
+                0.433
+            ],
+            "angle": 0,
+            "content": "Visual Language Models. Visual-Language Models (VLMs) [5, 45] are AI systems designed to process and understand both visual and textual information, enabling them to perform tasks such as Visual Question Answering (VQA) [43] and traditional visual classification tasks [20]. Traditional VLMs, like Qwen-VL [3], effectively integrate visual features with textual data, excelling in both VQA and image classification tasks. Flamingo [1] leverages few-shot learning capabilities, allowing it to quickly adapt to new tasks and perform well across both VQA and classification. Gemini [32] focuses on reasoning and multimodal understanding, achieving strong results in complex VQA tasks while also performing well in image and text classification. LLaVA [25] benefits from large-scale pretraining, efficiently handling intricate visuals and long-form text, with exceptional performance in both VQA and classification tasks. Newer models like InternVL2 [8], Qwen2-VL [35], and GPT-4o [16] build on these foundations, enhancing multimodal reasoning, improving the fusion of visual and textual data, and offering broader adaptability across both VQA and classification tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.453,
+                0.905,
+                0.845
+            ],
+            "angle": 0,
+            "content": "Federated Learning. Federated Learning (FL) [22] is a decentralized approach allowing multiple clients to collaboratively train a shared model without sharing raw data, thus preserving privacy and defending against attacks [6, 24]. Recent works have further improved FL's robustness in handling data heterogeneity [26, 33], label noise [17], and personalization needs [11]. With the rise of large language models (LLMs), Federated Learning (FL) has gained new applications, effectively addressing the challenges of knowledge exchange and privacy protection between independent LLMs. FedPrompt [46] combines FL with prompt tuning, utilizing split aggregation to significantly reduce communication costs. FedBPT [31] presents a federated black-box prompt tuning framework that avoids direct access to model parameters, instead optimizing prompts using gradient-free methods. FedDTPT [40] realizes discrete prompt tuning for Large Language Models (LLMs). However, these methods still face issues such as security risks in large models and high communication overhead. We propose a Federated Discrete Prompt Tuning method, which, compared to existing approaches, performs zero-order optimization at the token level, mitigating the risk of adversarial users leveraging logits generated by the large model for backdoor attacks. Additionally, by utilizing discrete tokens for knowledge exchange, it significantly reduces communication overhead."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.871,
+                0.905,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Prompt Tuning. Prompt tuning [49] is an emerging technique for adapting large pre-trained models to specific tasks"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "2462"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.172,
+                0.089,
+                0.825,
+                0.322
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.332,
+                0.908,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of FDPT. The proposed framework consists of the client-side local Agent-based Client Prompt Optimization and the server-side Semantic-Similarity-Guided Evolutionary Computation for global selection. The detailed process is described in Sec. 3.2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.387,
+                0.483,
+                0.464
+            ],
+            "angle": 0,
+            "content": "with minimal additional training. In VLMs, prompt tuning [14] bridges visual and textual modalities, enabling tasks like image captioning [42, 44]. The Prompt tuning can be represented as finding an optimal prompt \\(\\mathbf{p}^*\\) to maximize the model's performance on the dataset \\(\\mathcal{D} = \\{(\\mathbf{x},\\mathbf{y})\\}\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.196,
+                0.485,
+                0.483,
+                0.502
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {p} ^ {*} = \\arg \\max  f _ {\\mathrm {V L M}} (\\mathbf {p}; \\mathcal {D}) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.093,
+                0.524,
+                0.485,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\( f_{\\mathrm{VLM}}(\\mathbf{p};\\mathcal{D}) \\) denotes the performance of the VLM using prompt \\( \\mathbf{p} \\) over the dataset \\( \\mathcal{D} \\). Continual Prompt Tuning (soft prompt tuning) involves fine-tuning a small set of trainable parameters (soft prompts) while keeping the core model fixed. However, it suffers from poor interpretability, and in Federated Learning (FL), it incurs high communication overhead between clients. Discrete Prompt Tuning (DPT), in contrast, optimizes specific discrete tokens from a fixed vocabulary. A notable approach, RLPrompt, uses reinforcement learning (RL) to select the best tokens based on rewards. However, it has limited optimization efficiency due to the computationally intensive nature of RL. Regarding above limitations, the proposed Federated Discrete Prompt Tuning method aims to combine the strengths of discrete prompt tuning with the constraints and needs of Federated Learning. By leveraging an AI agent (based on large language models) with robust reasoning capabilities, the method can generate more accurate and efficient local discrete tokens. Furthermore, by incorporating semantic similarity calculations into an evolutionary computing framework, the method can generate more precise global tokens that are shared across clients. Additionally, this reduces communication costs between clients, as discrete tokens are much smaller in parameters compared to soft prompts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.385,
+                0.605,
+                0.401
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.41,
+                0.718,
+                0.424
+            ],
+            "angle": 0,
+            "content": "3.1. Problem Formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.432,
+                0.907,
+                0.552
+            ],
+            "angle": 0,
+            "content": "In this work, we consider a distributed scenario [22], where \\(N\\) clients each possess a private dataset \\(\\mathcal{D}_k = \\{(\\mathcal{X}_k,\\mathcal{Y}_k)\\}\\) consisting of \\(n_k\\) samples \\(\\{(x_i^k,y_i^k)\\}_{i\\in [n_k]}\\). Each client can only access its own private data and does not wish to share it with others. This scenario is realistic, as hospitals and other organizations prioritize protecting sensitive data. Moreover, such distributed settings have been widely studied in existing research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.553,
+                0.907,
+                0.613
+            ],
+            "angle": 0,
+            "content": "Then, our federated discrete prompt optimization can be formulated as an optimization problem that aims to find the optimal prompt instruction \\( p^* \\) that satisfies the following equation:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.512,
+                0.621,
+                0.905,
+                0.674
+            ],
+            "angle": 0,
+            "content": "\\[\np ^ {*} = \\arg \\min  _ {p} \\sum_ {k \\in [ K ]} \\frac {n ^ {k}}{\\sum_ {k \\in [ K ]} n ^ {k}} \\sum_ {i \\in [ n ^ {k} ]} \\mathcal {L} \\left(\\mathrm {V L M} \\left(p; x _ {i} ^ {k}\\right), y _ {i} ^ {k}\\right) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.675,
+                0.907,
+                0.779
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}(\\cdot)\\) is the objective function, which could be the error rate, and \\(\\mathrm{VLM}(\\cdot)\\) represents the Vision-Language Model (VLM). The above equation can be interpreted as learning a globally optimal natural language prompt by minimizing the weighted average loss across all clients, where each client's contribution is proportional to its dataset size."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.78,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Notice that if clients were permitted to share their private data and had white-box access to the VLM, the equation above could be easily solved by approximating the objective function with a differentiable function, such as cross-entropy loss. In this case, standard backpropagation could be applied to the global dataset to search for the optimal prompt instruction. However, due to commercial concerns, modern VLMs are typically deployed as API ser"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2463"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.485,
+                0.152
+            ],
+            "angle": 0,
+            "content": "vices, which are black-boxes to the clients. Additionally, each client is unwilling to share their data with others due to privacy concerns. Consequently, we must impose the following constraints:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.093,
+                0.16,
+                0.358,
+                0.193
+            ],
+            "angle": 0,
+            "content": "Blackbox: \\(\\frac{\\partial\\mathcal{L}(\\mathrm{VLM}(p;x),y)}{\\partial p} = \\emptyset\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.092,
+                0.195,
+                0.483,
+                0.227
+            ],
+            "angle": 0,
+            "content": "Privacy: \\(\\forall k,j\\in [K],k\\neq j,\\) \\(\\mathrm{Client}_k\\) cannot access \\(\\mathcal{D}_j\\) (3)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.236,
+                0.484,
+                0.282
+            ],
+            "angle": 0,
+            "content": "The first constraint indicates that the gradient is not feasible, while the second constraint specifies that each client can only access its own data."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.29,
+                0.258,
+                0.306
+            ],
+            "angle": 0,
+            "content": "3.2. Design Overview"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.312,
+                0.485,
+                0.614
+            ],
+            "angle": 0,
+            "content": "The algorithm overview is illustrated in Figure 1. Consistent with the traditional federated learning paradigm [22], each client communicates solely with the server using the prompt information, while keeping their data local. This ensures compliance with the data privacy constraints outlined in Eq.(3). Specifically, at the beginning, the server distributes the Global Prompt to each client. Then our approach follows these steps during each global communication round to search an optimal prompt: (1) Client Optimization: Each client utilizes an Agent-based Client Prompt Optimization method for personalized token-level prompt optimization. This method is preferred over backpropagation and ensures adherence to the black-box constraints in Eq.(3), which is more realistic in the context of VLM as a service; (2) Server Aggregation: Each client uploads its locally optimized prompt to the server, where knowledge aggregation is performed using the Semantic-similarity-guided Evolutionary Computation method. The subsequent sections provide a detailed explanation of each step in our approach."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.623,
+                0.282,
+                0.639
+            ],
+            "angle": 0,
+            "content": "3.3. Client Optimization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.645,
+                0.484,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Upon receiving the global discrete prompt \\( p_0 \\) from the server in the current round, each client iteratively updates it using an agent-based approach, as shown in Alg. 1. Initially, the agent queries the LLM to randomly replace some tokens in \\( p_0 \\), generating a set of prompt mutants \\( p_1, p_2, \\ldots, p_M \\) (Line 1). Each prompt is then combined with the client's local dataset and fed into the VLM to measure the accuracy, which serves as the prompt mutant's score. FDPT maintains a priority queue to manage these mutants, prioritizing those with higher accuracy (Lines 2-6). FDPT iteratively selects the highest-priority prompt from the queue as the seed, asks the LLM to mutate the important tokens of the seed, and updates the priority queue with the newly generated prompt mutants (Lines 7-13). Specifically, token importance is computed as follows: (1), FDPT compares each prompt mutant \\( p_i \\) with the seed prompt \\( p_0 \\) token by token, constructing a difference matrix \\( M \\), where \\( M_i^j = 0 \\) if the"
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.515,
+                0.091,
+                0.836,
+                0.107
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Agent-Based Prompt Optimization"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.514,
+                0.11,
+                0.907,
+                0.433
+            ],
+            "angle": 0,
+            "content": "Input: Initial discrete prompt \\(p_0\\), Large Language Model (LLM), Vision-Language Model (VLM), client local dataset \\(\\mathcal{D}\\), number of mutants \\(M\\)  \nOutput: Optimized prompt \\(\\hat{p}\\)  \n1: Initialization: \\(\\{p_1, p_2, \\ldots, p_M\\} =\\) Mutator( \\(LLM, p_0\\) ) \\(\\triangleright\\) Mutate \\(p_0\\) by randomly replacing tokens  \n2: \\(\\mathcal{Q} =\\) Priority Queue \\(\\triangleright\\) Initialize an empty queue  \n3: for each prompt \\(p_i\\) in \\(\\{p_0, p_1, \\ldots, p_M\\}\\) do  \n4: \\(Acc_i =\\) Evaluate(VLM, \\(p_i\\), \\(\\mathcal{D}\\)) \\(\\triangleright\\) Evaluation  \n5: Push \\((\\mathcal{Q}, p_i, Acc_i)\\) \\(\\triangleright\\) Update the priority queue  \n6: end for  \n7: while stopping criterion not met do  \n8: \\(p_{seed} =\\) Pop \\((\\mathcal{Q}) \\triangleright\\) Get the highest-priority prompt  \n9: Position = Importance Estimator \\(\\triangleright\\) Select important tokens  \n10: \\(p_{new} =\\) Mutator( \\(LLM, p_{seed}\\), Position)  \n11: \\(Acc_{new} =\\) Evaluate(VLM, \\(p_{new}\\), \\(\\mathcal{D}\\)) \\(\\triangleright\\) Evaluation  \n12: Push \\((\\mathcal{Q}, p_{new}, Acc_{new})\\) \\(\\triangleright\\) Update the queue  \n13: end while  \n14: Return highest-scoring prompt from \\(\\mathcal{Q}\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.459,
+                0.907,
+                0.581
+            ],
+            "angle": 0,
+            "content": "\\(j\\)-th token of \\(p_i\\) and \\(p_0\\) are different, and \\(M_i^j = 1\\) otherwise. (2), FDPT computes the accuracy gains \\(V\\), where \\(V_i = \\mathrm{Acc}_i - \\mathrm{Acc}_0\\). (3) The importance score of each token position is then given by \\(S = M^{-1}V\\). This score estimation equation reflects the degree to which a token's presence or absence affects accuracy, weighted by its position in the prompt. Finally, the top \\(K\\) token positions are selected based on the importance score \\(S\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.59,
+                0.7,
+                0.606
+            ],
+            "angle": 0,
+            "content": "3.4. Server Aggregation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.612,
+                0.906,
+                0.702
+            ],
+            "angle": 0,
+            "content": "After local client optimization, each client uploads its optimized discrete prompt to the server for knowledge exchange. The server then aggregates these local optimal prompts for the next round of optimization. Specifically, the server aggregation includes the following steps (as shown in Algorithm 2):"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.703,
+                0.906,
+                0.778
+            ],
+            "angle": 0,
+            "content": "Token-level Semantic Representation. In total client uploaded prompts, e.g. the initial population \\(\\mathcal{P}_{\\mathrm{init}}\\), for each token in a prompt, we use a pre-trained text encoder of the Roberta to get its token-level semantic representation, denoted as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.57,
+                0.789,
+                0.907,
+                0.809
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {E} _ {i} = [ e _ {i} ^ {1}, e _ {i} ^ {2}, \\dots , e _ {i} ^ {K} ] e _ {i} ^ {j} = f _ {e m b e d} (t k _ {i} ^ {j}) \\qquad (4)\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.82,
+                0.906,
+                0.852
+            ],
+            "angle": 0,
+            "content": "where \\( f_{embed}(\\cdot) \\) is the pre-trained encoder, and \\( tk_i^j \\) is the \\( j^{th} \\) token of the \\( i^{th} \\) prompt."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.871,
+                0.907,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Reputation Test. We first evaluate the reputation of each token, defined as the semantic-similarity weight (denoted"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2464"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.486,
+                0.138
+            ],
+            "angle": 0,
+            "content": "\\(\\alpha_{g,h})\\) that each token assigns to all other tokens. This is computed using a cosine-similarity mechanism [12] based on embeddings:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.145,
+                0.148,
+                0.483,
+                0.185
+            ],
+            "angle": 0,
+            "content": "\\[\n\\alpha_ {g} = \\sum_ {h} \\alpha_ {g, h} = \\sum_ {h} \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {e} _ {g} \\cdot \\mathbf {e} _ {h}}{\\sqrt {d}}\\right), \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.196,
+                0.485,
+                0.304
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{e}_g\\) and \\(\\mathbf{e}_h\\) represent the embedding of a token \\(g\\) and \\(h\\), respectively, and \\(d\\) is the dimensionality of the embeddings. A higher semantic-similarity weight \\(\\alpha_{g,h}\\) signifies a stronger influence over other tokens. We define the total semantic-similarity weight of token \\(g\\) as \\(\\alpha_{g}\\), which represents the token's semantic importance among all other tokens, referred to as its Reputation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.321,
+                0.485,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Aggregation. Next, tokens are clustered based on their semantic similarity by grouping embeddings that are close to each other in the high-dimensional semantic space:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.378,
+                0.484,
+                0.408
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {C} = \\left\\{\\mathcal {C} _ {1}, \\mathcal {C} _ {2}, \\dots , \\mathcal {C} _ {Z} \\right\\}, \\mathcal {C} _ {z} = \\left\\{\\mathbf {e} _ {h} \\mid \\| \\mathbf {e} _ {h} - \\mathbf {e} _ {g} \\| <   \\epsilon , \\forall h \\in \\mathcal {P} _ {\\text {i n i t}} \\right\\}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.409,
+                0.485,
+                0.47
+            ],
+            "angle": 0,
+            "content": "where \\(\\epsilon\\) is a pre-defined distance threshold. \\(C_z\\) denotes a cluster, or Community. Embeddings with equivalent syntactic meanings are grouped into a cluster, from which a single representative is subsequently selected."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.488,
+                0.484,
+                0.564
+            ],
+            "angle": 0,
+            "content": "Election. Finally, within each cluster (Community), the representative token is determined by semantic-similarity weights (reputation). Tokens with higher weights have stronger semantic dependencies on other tokens and are more likely to be selected:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.22,
+                0.578,
+                0.483,
+                0.6
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathbf {r} _ {z} = \\underset {\\mathbf {e} _ {n} \\in \\mathcal {C} _ {z}} {\\arg \\max } \\alpha_ {n}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.61,
+                0.484,
+                0.732
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbf{r}_z\\) denotes the representative token in Community \\(\\mathcal{C}_z\\). Importantly, communities containing only a single token are discarded, as these tokens contain only client-specific information, following the principle of \"majority rule\" [30] in Voting. The selected tokens are then arranged in their original order (using, for example, a bubble sort [2]) to form a representative prompt, or the \"Representatives\", denoted as \\(\\mathcal{P}_{\\mathrm{new}} = \\{\\mathbf{r}_1,\\mathbf{r}_2,\\dots ,\\mathbf{r}_Z\\}\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.745,
+                0.208,
+                0.76
+            ],
+            "angle": 0,
+            "content": "4. Evaluation"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.769,
+                0.26,
+                0.787
+            ],
+            "angle": 0,
+            "content": "4.1. Evaluation Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.791,
+                0.484,
+                0.838
+            ],
+            "angle": 0,
+            "content": "Backbone API. In our experiments, we selected four backbone models: Qwen2-VL-72B [35], InternVL2-Llama3-76B, TeleMM [23], and GPT4o."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Dataset and Evaluation. We conduct experiments on two tasks: traditional image classification and Visual Question Answer (VQA). For image classification, we use the"
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.515,
+                0.091,
+                0.907,
+                0.122
+            ],
+            "angle": 0,
+            "content": "Algorithm 2 Semantic-similarity-Guided Evolutionary Computation for Discrete Prompt Optimization"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.513,
+                0.125,
+                0.907,
+                0.451
+            ],
+            "angle": 0,
+            "content": "Input: I clients with discrete prompt tokens \\(\\{\\mathcal{P}_{\\mathrm{client}_i}\\}_{i = 1}^I\\)   \nOutput: Global prompt tokens \\(\\mathcal{P}_{\\mathrm{new}}\\)   \n1: Initialization Initial population \\(\\mathcal{P}_{\\mathrm{init}}\\)   \n2: for each token \\(tk\\) in a prompt \\(\\in \\mathcal{P}_{\\mathrm{init}}\\) do   \n3: Achieve mapping according to Eq.4   \n4: end for   \n5: for each token \\(\\mathbf{t}_g\\) do \\(\\triangleright\\) Reputation Test   \n6: for each token \\(\\mathbf{t}_h\\) do   \n7: Semantic-similarity weight according to Eq.5   \n8: end for   \n9: Get total semantic-similarity weight \\(\\alpha_{g} = \\sum_{h}\\alpha_{g,h}\\)   \n10: end for   \n11: Cluster tokens according to Eq.6 Aggregation   \n12: for each Community \\(C_z\\in \\mathcal{C}\\) do Election   \n13: Select representative token according to Eq.7   \n14: if \\(C_z\\) contains only one token then   \n15: Discard Community \\(C_z\\)   \n16: end if   \n17: end for   \n18: Form Representatives \\(\\mathcal{P}_{\\mathrm{new}} = \\{\\mathbf{r}_1,\\mathbf{r}_2,\\dots ,\\mathbf{r}_Z\\}\\) from selected representative tokens"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.474,
+                0.907,
+                0.596
+            ],
+            "angle": 0,
+            "content": "MNIST [9], CIFAR-10, CIFAR-100, and TinyImageNet (TinyImg) [20] datasets. For VQA, we utilize the Art, Chemistry, and Finance sections of the MMMU dataset [43], along with the RealWorldQA (RWQA) dataset. The task objective is to leverage optimized prompts for accurate image classification on the image datasets, and for VQA, to assist in parsing textual content within the datasets to enable accurate classification or decision-making."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.597,
+                0.907,
+                0.658
+            ],
+            "angle": 0,
+            "content": "We use Accuracy as the evaluation metric for the image classification task. To maintain consistency across tasks, we also constrain predictions in the VQA task to the range of available labels and evaluate performance using Accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.675,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Comparison Baselines. We compare our method against eight state-of-the-art (SOTA) approaches: FedPrompt [46], FedPepTAO [4], FedTPG [29], HPT [37], CoOp [48], BBT [10], FedBPT [31], BPTVLM [41], and a manual prompting method (Manual Prompt). Notably, HPT [37], CoOp [48], BBT[10], and BPTVLM [41] are not originally designed for federated learning. To adapt these methods to a federated setting, we apply a weighted averaging aggregation approach, following the implementations of FedPrompt [46]and FedBPT [31]. The results are reported using federated versions of these models: FedAvg-HPT, FedAvg-CoOp, FedAvg-BBT, and Fed-BPTVLM. Additionally, we categorize these methods into White-box and Black-box approaches based on whether they require access to model parameters. The White-box methods include FedPrompt [46],"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2465"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.107,
+                0.088,
+                0.892,
+                0.588
+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\">Backbone</td><td rowspan=\"2\">Method</td><td colspan=\"4\">CV Classification</td><td colspan=\"4\">VQA</td><td rowspan=\"2\">Average</td></tr><tr><td>MNIST</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td><td>Art</td><td>Chemistry</td><td>Finance</td><td>RWQA</td></tr><tr><td rowspan=\"10\">Qwen2-VL-72B</td><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>90.4</td><td>79.5</td><td>73.5</td><td>60.9</td><td>74.6</td><td>63.3</td><td>70.5</td><td>80.4</td></tr><tr><td>FedPepTAO</td><td>86.7</td><td>78.3</td><td>72.9</td><td>59.5</td><td>69.1</td><td>58.8</td><td>68.5</td><td>77.9</td></tr><tr><td>FedTPG</td><td>84.2</td><td>76.8</td><td>71.3</td><td>59.2</td><td>72.4</td><td>57.5</td><td>62.6</td><td>75.4</td></tr><tr><td>FedAvg-HPT</td><td>86.9</td><td>78.4</td><td>70.2</td><td>58.7</td><td>75.7</td><td>53.5</td><td>65.9</td><td>78.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>78.1</td><td>71.4</td><td>59.2</td><td>70.2</td><td>61.8</td><td>63.3</td><td>76.5</td></tr><tr><td rowspan=\"5\">Black Box</td><td>Manual</td><td>70.7</td><td>62.2</td><td>53.5</td><td>47.3</td><td>54.7</td><td>45.8</td><td>51.8</td><td>58.3</td></tr><tr><td>FedAvg-BBT</td><td>78.9</td><td>72.3</td><td>62.7</td><td>51.7</td><td>63.5</td><td>53.9</td><td>60.3</td><td>69.7</td></tr><tr><td>FedBPT</td><td>80.0</td><td>72.0</td><td>64.2</td><td>53.1</td><td>68.0</td><td>50.6</td><td>59.0</td><td>67.8</td></tr><tr><td>Fed-BPTVLM</td><td>80.7</td><td>73.1</td><td>62.3</td><td>50.9</td><td>65.2</td><td>53.3</td><td>63.3</td><td>70.8</td></tr><tr><td>Our method</td><td>90.5</td><td>78.5</td><td>71.8</td><td>57.8</td><td>74.0</td><td>60.8</td><td>67.2</td><td>78.5</td></tr><tr><td rowspan=\"10\">InternVL2-Llama3-76B</td><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>88.1</td><td>81.3</td><td>74.4</td><td>60.2</td><td>70.2</td><td>58.8</td><td>62.9</td><td>76.1</td></tr><tr><td>FedPepTAO</td><td>87.3</td><td>77.8</td><td>71.2</td><td>58.5</td><td>65.2</td><td>55.3</td><td>63.0</td><td>75.4</td></tr><tr><td>FedTPG</td><td>86.2</td><td>79.3</td><td>71.7</td><td>57.4</td><td>68.0</td><td>54.2</td><td>60.7</td><td>73.8</td></tr><tr><td>FedAvg-HPT</td><td>85.1</td><td>78.7</td><td>72.3</td><td>58.4</td><td>69.1</td><td>53.0</td><td>62.0</td><td>74.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>79.1</td><td>71.6</td><td>58.1</td><td>71.8</td><td>56.2</td><td>63.9</td><td>71.7</td></tr><tr><td rowspan=\"5\">Black Box</td><td>Manual</td><td>71.8</td><td>63.7</td><td>51.8</td><td>45.4</td><td>52.5</td><td>46.3</td><td>53.8</td><td>61.3</td></tr><tr><td>FedAvg-BBT</td><td>80.0</td><td>71.1</td><td>65.2</td><td>52.7</td><td>60.2</td><td>51.9</td><td>53.8</td><td>70.5</td></tr><tr><td>FedBPT</td><td>80.7</td><td>72.7</td><td>66.6</td><td>52.3</td><td>61.3</td><td>50.6</td><td>58.4</td><td>67.1</td></tr><tr><td>Fed-BPTVLM</td><td>79.5</td><td>71.4</td><td>67.2</td><td>53.0</td><td>64.1</td><td>53.0</td><td>56.7</td><td>69.8</td></tr><tr><td>Our method</td><td>89.6</td><td>79.0</td><td>71.5</td><td>57.3</td><td>70.7</td><td>55.9</td><td>63.6</td><td>75.5</td></tr><tr><td rowspan=\"5\">TeleMM</td><td rowspan=\"5\">Black Box</td><td>Manual</td><td>69.4</td><td>65.5</td><td>53.3</td><td>45.8</td><td>53.0</td><td>45.0</td><td>52.5</td><td>57.9</td></tr><tr><td>FedAvg-BBT</td><td>80.9</td><td>70.6</td><td>63.1</td><td>49.1</td><td>56.9</td><td>48.8</td><td>56.4</td><td>64.1</td></tr><tr><td>FedBPT</td><td>80.0</td><td>71.3</td><td>61.9</td><td>50.9</td><td>60.8</td><td>51.5</td><td>57.4</td><td>66.3</td></tr><tr><td>Fed-BPTVLM</td><td>79.1</td><td>71.0</td><td>62.7</td><td>49.7</td><td>59.1</td><td>52.3</td><td>57.7</td><td>68.5</td></tr><tr><td>Our method</td><td>88.4</td><td>78.9</td><td>69.3</td><td>57.4</td><td>64.6</td><td>55.7</td><td>61.6</td><td>75.0</td></tr><tr><td rowspan=\"5\">GPT4o</td><td rowspan=\"5\">Black Box</td><td>Manual</td><td>74.4</td><td>68.2</td><td>59.1</td><td>52.8</td><td>61.9</td><td>58.6</td><td>61.6</td><td>71.9</td></tr><tr><td>FedAvg-BBT</td><td>81.0</td><td>76.7</td><td>67.6</td><td>56.1</td><td>64.6</td><td>57.5</td><td>63.6</td><td>69.2</td></tr><tr><td>FedBPT</td><td>83.2</td><td>78.3</td><td>68.4</td><td>56.6</td><td>69.1</td><td>59.3</td><td>68.5</td><td>69.9</td></tr><tr><td>Fed-BPTVLM</td><td>81.7</td><td>79.0</td><td>67.9</td><td>57.3</td><td>67.4</td><td>57.9</td><td>65.2</td><td>71.6</td></tr><tr><td>Our method</td><td>92.5</td><td>85.3</td><td>73.9</td><td>62.7</td><td>76.8</td><td>66.7</td><td>72.8</td><td>78.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.597,
+                0.908,
+                0.626
+            ],
+            "angle": 0,
+            "content": "Table 1. Performance Comparison on CV Classification and VQA Tasks. The accuracy results are measured in percentages (\\%). Bold values indicate the overall best results, and underlined values indicate the best results among Black Box methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.652,
+                0.483,
+                0.713
+            ],
+            "angle": 0,
+            "content": "FedPepTAO [4], FedTPG [29], FedAvg-HPT, and FedAvg-CoOp, while the Black-box methods consist of Manual, FedAvg-BBT, FedBPT [31], and Fed-BPTVLM. Detailed descriptions of all baselines are provided in Appendix A."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.735,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Implementation. The federated learning setup for our experiments is as follows: we use a default of 10 clients, with a client participation rate of \\(100\\%\\) in each training round. Additionally, we adopt a \\(k\\)-shot mechanism for prompt tuning, following the approach in work [31], with the default value of \\(k\\) set to 50. For image classification datasets, we use the original training and test sets. For each Visual QA dataset, we randomly select 50 samples as the training set (from the validation set for MMMU and the test set for RealWorldQA), with the remaining samples used for testing. In terms of baseline implementations, we adapt traditional"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.652,
+                0.907,
+                0.804
+            ],
+            "angle": 0,
+            "content": "prompt optimization methods (HPT, CoOp, BBT, BBT-VLM) to the federated learning framework by employing the classical Federated Averaging (FedAvg) approach. For black-box backbone model configurations, we extend soft prompt tuning methodologies, such as FedBPT, by mapping the soft tokens to discrete tokens, through the RoBERTa encoder's tokenization mechanism, before feeding them into API-based models. In addition, all experiments are conducted on two NVIDIA GeForce RTX A800 GPUs. Detailed hyperparameter settings are provided in Appendix B."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.817,
+                0.71,
+                0.832
+            ],
+            "angle": 0,
+            "content": "4.2. Effectiveness Results"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.84,
+                0.907,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We first evaluate the effectiveness of our method on traditional CV classification tasks and VQA tasks. Experimental results show that, compared to other methods, our method demonstrates significant performance improvements in both"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "2466"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.092,
+                0.482,
+                0.123
+            ],
+            "angle": 0,
+            "content": "tasks, particularly excelling in black-box environments, with only a small gap from white-box algorithms."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.142,
+                0.483,
+                0.385
+            ],
+            "angle": 0,
+            "content": "Traditional CV Classification Tasks. In traditional CV classification tasks, our method achieves outstanding performance across all model configurations. For example, in the GPT4o black-box setting, our method achieves improvements of \\(11.2\\%\\), \\(7.0\\%\\), \\(5.5\\%\\), and \\(6.1\\%\\) over the closest-performing FedBPT [31] method on the MNIST, Cifar-10, Cifar-100, and TinyImg datasets, respectively. In the TeleMM black-box setting, our method also performs exceptionally well, achieving \\(88.4\\%\\) and \\(78.9\\%\\) accuracy on MNIST and Cifar-10, respectively, which is an improvement of \\(9.3\\%\\) and \\(8.3\\%\\) over FedAvg-BBT. Additionally, for the Qwen2-VL-72B model, our method achieves accuracies of \\(78.5\\%\\) and \\(71.8\\%\\) on the Cifar-10 and Cifar-100 datasets, respectively, representing improvements of \\(7.1\\%\\) and \\(5.3\\%\\) over FedBPT [31], further demonstrating its advantage in traditional CV tasks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.404,
+                0.483,
+                0.526
+            ],
+            "angle": 0,
+            "content": "VQA Tasks. Our method also shows strong performance in VQA tasks. In the GPT4o black-box setting, our method achieves improvements of \\(11.1\\%\\), \\(7.4\\%\\), \\(4.3\\%\\), and \\(8.6\\%\\) over the FedBPT [31] method on the Art, Chemistry, Finance, and RWQA datasets, respectively. In TeleMM setting, our method's performance remains very stable, achieving improvements of \\(7.7\\%\\) and \\(10.9\\%\\) over FedAvg-BBT on the Art and RWQA datasets, respectively."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.535,
+                0.395,
+                0.551
+            ],
+            "angle": 0,
+            "content": "4.3. Prompt Transferability Evaluation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.558,
+                0.483,
+                0.709
+            ],
+            "angle": 0,
+            "content": "In the prompt transferability experiment, we evaluate the performance of prompts optimized on one backbone model when applied to another, as shown in Table 2. The results indicate that prompts exhibit a degree of transferability, maintaining high robustness across models with minimal accuracy loss, as referenced in Table 1. Additionally, compared to the Qwen2-VL transfer results, the InternVL2 transfer showed better accuracy, further validating the high applicability and robustness of prompts between certain models."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.095,
+                0.718,
+                0.48,
+                0.766
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Model</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td>Qwen2-VL→TeleMM</td><td>80</td><td>70.5</td><td>58.1</td></tr><tr><td>InternVL2→GPT4o</td><td>87.8</td><td>72.3</td><td>63.5</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.091,
+                0.775,
+                0.483,
+                0.804
+            ],
+            "angle": 0,
+            "content": "Table 2. Transferability Experiment Results. The accuracy results are measured in percentages \\((\\%)\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.833,
+                0.427,
+                0.851
+            ],
+            "angle": 0,
+            "content": "4.4. Communication Overhead Experiment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In the communication overhead experiment, our method shows a significant advantage in parameter efficiency, as illustrated in Table 3. Specifically, white-box methods like"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.092,
+                0.905,
+                0.288
+            ],
+            "angle": 0,
+            "content": "FedPrompt [46] and FedTPG [29] and most black-box methods such as FedAvg-BBT and Fed-BPTVLM require hundreds of thousands of parameters, whereas our method requires only 150. This substantial reduction effectively minimizes latency and resource consumption associated with communication. This advantage primarily arises from a key difference in algorithm design: while other methods use soft prompts for knowledge exchange between clients, our method employs discrete prompt tokens. Soft prompts typically require a large number of continuous parameters, whereas discrete prompt tokens enable knowledge transfer with only a small set of parameters, significantly reducing communication overhead."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.299,
+                0.903,
+                0.449
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Type</td><td>Method</td><td>Parameters</td></tr><tr><td rowspan=\"5\">White Box</td><td>FedPrompt</td><td>614k</td></tr><tr><td>FedPepTAO</td><td>1796k</td></tr><tr><td>FedTPG</td><td>614k</td></tr><tr><td>FedAvg-HPT</td><td>614k</td></tr><tr><td>FedAvg-CoOp</td><td>614k</td></tr><tr><td rowspan=\"3\">Black Box</td><td>FedAvg-BBT</td><td>614k</td></tr><tr><td>FedBPT</td><td>40.8k</td></tr><tr><td>Fed-BPTVLM</td><td>614k</td></tr><tr><td colspan=\"2\">Our method</td><td>150</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.458,
+                0.907,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Table 3. Communication Overhead Experiment results. The measurements are in Tensors within the PyTorch Framework. Bold values indicate the best results, and underlined values indicate the second-best results."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.546,
+                0.679,
+                0.561
+            ],
+            "angle": 0,
+            "content": "4.5. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.569,
+                0.907,
+                0.903
+            ],
+            "angle": 0,
+            "content": "In the improvements ablation study based on Qwen2-VL72B API, our method consistently achieves the best performance across all metrics, further validating the effectiveness of its key components, as shown in Table 4. Compared to cases where specific modules are removed or replaced, our method demonstrates significant improvements on the Cifar-10, Cifar-100, and TinyImg datasets. Server-side experiments. Our method improves accuracy on the Cifar-10 and Cifar-100 datasets by \\(2.0\\%\\) and \\(1.2\\%\\), respectively, compared to the setting without the clustering strategy. Furthermore, compared to the fixed clustering approach, our method achieves accuracy gains of \\(0.7\\%\\) on Cifar-10 and \\(2.5\\%\\) on Cifar-100, underscoring the importance of a dynamic clustering strategy. Client-side experiments. Removing the G-F mechanism results in a significant accuracy drop across all datasets. Furthermore, our method achieves a \\(1.0\\%\\) accuracy improvement on Cifar-100 and \\(1.6\\%\\) on TinyImg compared to the configuration without the E-EB strategy. Compared to the configuration without the PPR-CoT strategy, our method improves accuracy by \\(3.2\\%\\) on Cifar-10 and \\(2.5\\%\\) on Cifar-100, underscoring the pivotal role of the PPR-CoT strategy in enhancing model perfor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "2467"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.092,
+                0.093,
+                0.143,
+                0.105
+            ],
+            "angle": 0,
+            "content": "mance."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.096,
+                0.119,
+                0.481,
+                0.263
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Site</td><td>Method</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td rowspan=\"4\">Server</td><td>w Embedding-fedavg</td><td>71.9</td><td>62.5</td><td>54.2</td></tr><tr><td>w Random search</td><td>65.3</td><td>57.3</td><td>53.9</td></tr><tr><td>w/o Clustering Strategy</td><td>76.5</td><td>70.6</td><td>55.9</td></tr><tr><td>w Fixed Clusters</td><td>77.8</td><td>69.3</td><td>56.3</td></tr><tr><td rowspan=\"3\">Client</td><td>w/o G-F Mechanism</td><td>71.8</td><td>65.5</td><td>53.5</td></tr><tr><td>w/o E-EB Strategy</td><td>76.9</td><td>70.8</td><td>56.2</td></tr><tr><td>w/o PPR-CoT</td><td>75.3</td><td>69.3</td><td>56.7</td></tr><tr><td colspan=\"2\">Our method</td><td>78.5</td><td>71.8</td><td>57.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.272,
+                0.484,
+                0.425
+            ],
+            "angle": 0,
+            "content": "Table 4. The Improvements Ablation Studies Results. The accuracy is measured in percentages (\\%). Performance decreases with the removal or modification of any key component, underscoring the effectiveness of the improvements. \"w Embedding-fedavg\" denotes the use of a weighted averaging aggregation method, as in FedBPT [31] and FedAvg-BBT. \"w Random search\" refers to the removal of weight comparison, using random search instead to select representative tokens. \"w/o Clustering Strategy\" indicates the removal of the clustering step. \"w Fixed Clusters\" implies a fixed number of clusters, which affects the count of representative tokens."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.474,
+                0.487,
+                0.702
+            ],
+            "angle": 0,
+            "content": "Initial Prompt Impact. We evaluate the impact of the Initial Prompt on performance using GPT-4o as the backbone black-box VLM for classification tasks across datasets, comparing it with three typical black-box algorithms. Figure 2 shows that different prompt configurations significantly affect model performance, with our algorithm consistently achieving the best outcomes. Specifically, detailed prompts enhance model accuracy by providing richer information, which supports more effective learning and adaptation. In contrast, shorter prompts reduce accuracy, indicating that limited information constrains performance. Thus, prompt design is critical in classification tasks, and our algorithm exhibits strong robustness and performance across various prompt configurations. We present all Initial Prompts in Appendix C."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.123,
+                0.73,
+                0.446,
+                0.842
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.855,
+                0.483,
+                0.898
+            ],
+            "angle": 0,
+            "content": "Figure 2. Initial Prompt Impact. Prompt-1 represents a \"shorter initial prompt,\" Prompt-2 a \"standard initial prompt,\" and Prompt-3 a \"detailed initial prompt.\""
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.091,
+                0.892,
+                0.108
+            ],
+            "angle": 0,
+            "content": "4.6. Heterogeneous Data Robustness Experiment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.115,
+                0.908,
+                0.342
+            ],
+            "angle": 0,
+            "content": "In the heterogeneous data robustness experiment, we use the Qwen2-VL-72B API as the backbone VLM model to evaluate the performance of different algorithms on heterogeneous data in the TinyImagenet dataset, as shown in Figure 3. Data is distributed across 10 clients using a Dirichlet Distribution [21] with varying hyperparameters dir, where a smaller Dirichlet parameter (e.g., dir=0.05) indicates greater data heterogeneity. Details of these heterogeneous data distributions are provided in Appendix D. The results demonstrate that all methods show some robustness to data heterogeneity, aligning with expectations [28, 31] for model stability on heterogeneous data. Additionally, as heterogeneity increases, our method exhibits superior performance, with minimal accuracy reduction, outperforming other methods under all heterogeneity conditions."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.553,
+                0.355,
+                0.866,
+                0.457
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.466,
+                0.909,
+                0.522
+            ],
+            "angle": 0,
+            "content": "Figure 3. Heterogeneous Data Robustness Experiment results on the TinyImageNet dataset. The parameter \"dir\" is the Dirichlet Distribution hyperparameter; smaller values of dir indicate higher data heterogeneity across the 10 clients."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.557,
+                0.634,
+                0.573
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.584,
+                0.909,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We propose FDPT, the first federated black-box discrete prompt tuning framework based on visual language models. FDPT uses an Agent-based Client Prompt Optimization strategy to achieve token-level prompt optimization on the client side without traditional prediction logits, thereby preventing inversion attacks. On the server side, a Semantic-Similarity-Guided Evolutionary Computation framework is implemented to execute more precise zeroth-order optimization, which enables the obtention of representative global tokens. Moreover, discrete token exchange between clients offers high security and low communication overhead. Moreover, discrete tokens exhibit enhanced interpretability compared to soft prompts, which facilitates human experts in designing corresponding instructions. Our framework exhibits: (1) statistically significant accuracy enhancements in conventional visual recognition and cross-modal reasoning tasks; (2) optimized communication efficiency through adaptive token selection mechanisms; (3) cross-domain transferability of learned prompt representations; and (4) strengthened resilience to data distribution shifts, particularly in heterogeneous learning environments."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.956
+            ],
+            "angle": 0,
+            "content": "2468"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.486,
+                0.228
+            ],
+            "angle": 0,
+            "content": "Acknowledgements. This research was supported by the National Natural Science Foundation of China under Grant 52074305, 52274160, 51874300 and the National Natural Science Foundation of China-Shanxi Provincial People's Government Coal-based Low Carbon Joint Fund U1510115, the Academic Research Projects of Beijing Union University (No.ZK90202106) and R&D Program of Beijing Municipal Education Commission (KM202211417005)."
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+        {
+            "type": "title",
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+            "angle": 0,
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2025/FDPT_ Federated Discrete Prompt Tuning for Black-Box Visual-Language Models/5d5a1b2f-9957-4fb4-b461-7bf3e1ebccfb_origin.pdf

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2025/FDPT_ Federated Discrete Prompt Tuning for Black-Box Visual-Language Models/full.md

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+# FDPT: Federated Discrete Prompt Tuning for Black-Box Visual-Language Models
+
+Jiaqi Wu $^{1,8,10\dagger}$ , Simin Chen $^{2\dagger}$ , Jing Tang $^{3}$ , Yuzhe YANG $^{4}$ , Yiming Chen $^{5}$ , Lixu Wang $^{6}$ , Song Lin $^{7}$ , Zehua Wang $^{8,9}$ , Wei Chen $^{9*}$ , and Zijian Tian $^{10}$
+
+$^{1}$ Tsinghua University,  $^{2}$ University of Texas at Dallas,  $^{3}$ Huazhong University of Science and Technology,
+
+<sup>4</sup>The Chinese University of Hong Kong, <sup>5</sup>National University of Singapore, <sup>6</sup>Nanyang Technological University,
+
+<sup>7</sup>Beijing Baidu Netcom Science Technology Co., Ltd., <sup>8</sup>University of British Columbia,
+
+$^{9}$ China University of Mining and Technology,  $^{10}$ China University of Mining and Technology (Beijing)
+
+wjq11346@student.ubc.ca, sxc180080@utdallas.edu, focusers@163.com, yuzheyang@link.cuhk.edu.cn,
+
+yiming.chen@u.nus.edu, wanglixu4334@gmail.com, linsong04@baidu.com, zwang@ece.ubc.ca,
+
+chenwdavior@163.com，Tianzj0726@126.com
+
+# Abstract
+
+Vision-Language Models (VLMs) have driven significant advancements in multimodal AI. Fine-tuning these models with user data enhances adaptability but poses privacy risks. While federated learning (FL) mitigates user data privacy concerns, it fails to protect model properties. Existing methods relying on black-box VLM APIs often require access to prediction logits, making them vulnerable to inversion attacks. Additionally, optimizing tuning complexity and data transmission efficiency in federated VLM scenarios remains a challenge. To address these challenges, we propose FDPT—the first federated discrete prompt tuning method utilizing black-box VLMs. During client optimization stage, FDPT employs an agent-driven framework leveraging large language models (LLMs) with enhanced reasoning capacities to systematically optimize discrete prompt representations, and also utilizes feedback mechanisms and chain of thought to enhance prediction accuracy. Importantly, it performs optimization by relying not on the predicted logic vectors output by LLMs but on textual results, avoiding reverse attack risks. During global aggregation stage, We mimic human electoral activities by employing evolutionary computation methods underpinned by semantic similarity computation to implement enhanced zero-order optimization for acquiring representative global tokens, thereby achieving knowledge aggregation. FDPT significantly outperforms nine state-of-the-art methods in image classification and visual question-answering, reducing communication overhead while generating highly transferable optimized prompts. Additionally, it exhibits im
+
+proved robustness to data heterogeneity.
+
+# 1. Introduction
+
+General-purpose Vision-Language Models (VLMs) [45] integrate vast visual and linguistic information, advancing various vision tasks [36]. To better adapt to user needs, these models can undergo fine-tuning or prompt-tuning [27], but such modifications introduce privacy risks [13, 18, 34, 38]. Federated Learning (FL) [22] addresses these concerns by decentralizing data storage, reducing single-point breaches, and exchanging model weights or embeddings instead of raw data. Various FL-based approaches [19, 29, 39] have been explored for tuning large models, effectively preserving user data privacy.
+
+Despite the success of FL, protecting the privacy of VLMs themselves remains a critical yet largely unexplored challenge. Existing FL approaches use zero-order optimization to estimate gradients for prompt tuning on black-box VLMs [31, 41]. For example, FedBPT [31] employs prompt exchange and gradient-free optimization, reducing communication and memory costs by avoiding direct parameter access and backpropagation on client devices. However, several limitations remain. First, these methods remain vulnerable to security risks as they rely on prediction logits, exposing them to inversion attacks that can infer model parameters [7, 47]. Second, zero-order optimization techniques [31, 41] often suffer from limited accuracy and adaptability in prompt fine-tuning. Finally, soft prompt methods [15, 46] lack interpretability and incur high communication costs in federated settings.
+
+To address these challenges, we propose FDPT, the first
+
+federated discrete prompt optimization method comprising two stages: client-side optimization and global aggregation. In the client-side optimization phase, we introduce AI Agent-based Client Prompt Optimization, which refines token-level prompts using large language models (LLMs). We design a feedback mechanism and Chain-of-Thought measures to guide the agent in selecting optimal discrete tokens, overcoming the limitations of existing zero-order optimization methods in prompt tuning. Unlike traditional approaches that rely on prediction logits, our method uses only black-box VLM text outputs, reducing the risk of inversion attacks and enhancing model privacy protection. Afterwards, in the global aggregation phase, to reduce communication overhead in federated settings, we use discrete tokens for knowledge exchange instead of soft prompts. Inspired by human voting mechanisms, we propose a Self-Attention-Guided Evolutionary Computation method to identify representative tokens for constructing global prompts. Unlike the coarse sampling in traditional zero-order optimization, our approach clusters tokens in semantic space and then applies similarity calculations to refine the most accurate results, enhancing tuning efficiency.
+
+Detailed experimental results demonstrate the advantages of our method. In Visual Question Answering (VQA) tasks, under the GPT-4 black-box setting, our method outperforms the classic black-box prompt optimization method FedBPT [31], achieving  $11.1\%$  and  $7.4\%$  improvements on the Art and Chemistry categories of the MMMU dataset [43], respectively. In traditional computer vision (CV) classification tasks, using the Qwen2-VL-72B model [3], our approach achieves  $71.8\%$  accuracy on CIFAR-100, surpassing FedBPT by  $5.3\%$ , demonstrating its superior performance. Additionally, FDPT significantly reduces communication costs without compromising optimization performance and enhances interpretability through discrete prompts. The contributions of this paper are as follows:
+
+- We propose FDPT, a first federated black-box discrete prompt optimization framework that aggregates knowledge from multiple parties to optimize prompts while ensuring the privacy of both users and easily overlooked VLMs.  
+- We introduce an AI Agent-based Client Prompt Optimization for token-level prompts and a Self-attention-guided Evolutionary Computation method for selecting global tokens, offering better predictive performance than traditional zero-order optimization.  
+- Extensive experiments demonstrate that our method achieves superior performance across various text-vision tasks, exhibits low communication overhead, and is resilient to data heterogeneity.
+
+# 2. Background & Related Work
+
+Visual Language Models. Visual-Language Models (VLMs) [5, 45] are AI systems designed to process and understand both visual and textual information, enabling them to perform tasks such as Visual Question Answering (VQA) [43] and traditional visual classification tasks [20]. Traditional VLMs, like Qwen-VL [3], effectively integrate visual features with textual data, excelling in both VQA and image classification tasks. Flamingo [1] leverages few-shot learning capabilities, allowing it to quickly adapt to new tasks and perform well across both VQA and classification. Gemini [32] focuses on reasoning and multimodal understanding, achieving strong results in complex VQA tasks while also performing well in image and text classification. LLaVA [25] benefits from large-scale pretraining, efficiently handling intricate visuals and long-form text, with exceptional performance in both VQA and classification tasks. Newer models like InternVL2 [8], Qwen2-VL [35], and GPT-4o [16] build on these foundations, enhancing multimodal reasoning, improving the fusion of visual and textual data, and offering broader adaptability across both VQA and classification tasks.
+
+Federated Learning. Federated Learning (FL) [22] is a decentralized approach allowing multiple clients to collaboratively train a shared model without sharing raw data, thus preserving privacy and defending against attacks [6, 24]. Recent works have further improved FL's robustness in handling data heterogeneity [26, 33], label noise [17], and personalization needs [11]. With the rise of large language models (LLMs), Federated Learning (FL) has gained new applications, effectively addressing the challenges of knowledge exchange and privacy protection between independent LLMs. FedPrompt [46] combines FL with prompt tuning, utilizing split aggregation to significantly reduce communication costs. FedBPT [31] presents a federated black-box prompt tuning framework that avoids direct access to model parameters, instead optimizing prompts using gradient-free methods. FedDTPT [40] realizes discrete prompt tuning for Large Language Models (LLMs). However, these methods still face issues such as security risks in large models and high communication overhead. We propose a Federated Discrete Prompt Tuning method, which, compared to existing approaches, performs zero-order optimization at the token level, mitigating the risk of adversarial users leveraging logits generated by the large model for backdoor attacks. Additionally, by utilizing discrete tokens for knowledge exchange, it significantly reduces communication overhead.
+
+Prompt Tuning. Prompt tuning [49] is an emerging technique for adapting large pre-trained models to specific tasks
+
+![](images/750758aadf814a2906dd59c770d1ad113ac648049b233a009a000c5306cbf8d5.jpg)  
+Figure 1. Overview of FDPT. The proposed framework consists of the client-side local Agent-based Client Prompt Optimization and the server-side Semantic-Similarity-Guided Evolutionary Computation for global selection. The detailed process is described in Sec. 3.2.
+
+with minimal additional training. In VLMs, prompt tuning [14] bridges visual and textual modalities, enabling tasks like image captioning [42, 44]. The Prompt tuning can be represented as finding an optimal prompt  $\mathbf{p}^*$  to maximize the model's performance on the dataset  $\mathcal{D} = \{(\mathbf{x},\mathbf{y})\}$ :
+
+$$
+\mathbf {p} ^ {*} = \arg \max  f _ {\mathrm {V L M}} (\mathbf {p}; \mathcal {D}) \tag {1}
+$$
+
+where  $f_{\mathrm{VLM}}(\mathbf{p};\mathcal{D})$  denotes the performance of the VLM using prompt  $\mathbf{p}$  over the dataset  $\mathcal{D}$ . Continual Prompt Tuning (soft prompt tuning) involves fine-tuning a small set of trainable parameters (soft prompts) while keeping the core model fixed. However, it suffers from poor interpretability, and in Federated Learning (FL), it incurs high communication overhead between clients. Discrete Prompt Tuning (DPT), in contrast, optimizes specific discrete tokens from a fixed vocabulary. A notable approach, RLPrompt, uses reinforcement learning (RL) to select the best tokens based on rewards. However, it has limited optimization efficiency due to the computationally intensive nature of RL. Regarding above limitations, the proposed Federated Discrete Prompt Tuning method aims to combine the strengths of discrete prompt tuning with the constraints and needs of Federated Learning. By leveraging an AI agent (based on large language models) with robust reasoning capabilities, the method can generate more accurate and efficient local discrete tokens. Furthermore, by incorporating semantic similarity calculations into an evolutionary computing framework, the method can generate more precise global tokens that are shared across clients. Additionally, this reduces communication costs between clients, as discrete tokens are much smaller in parameters compared to soft prompts.
+
+# 3. Method
+
+# 3.1. Problem Formulation
+
+In this work, we consider a distributed scenario [22], where  $N$  clients each possess a private dataset  $\mathcal{D}_k = \{(\mathcal{X}_k,\mathcal{Y}_k)\}$  consisting of  $n_k$  samples  $\{(x_i^k,y_i^k)\}_{i\in [n_k]}$ . Each client can only access its own private data and does not wish to share it with others. This scenario is realistic, as hospitals and other organizations prioritize protecting sensitive data. Moreover, such distributed settings have been widely studied in existing research.
+
+Then, our federated discrete prompt optimization can be formulated as an optimization problem that aims to find the optimal prompt instruction  $p^*$  that satisfies the following equation:
+
+$$
+p ^ {*} = \arg \min  _ {p} \sum_ {k \in [ K ]} \frac {n ^ {k}}{\sum_ {k \in [ K ]} n ^ {k}} \sum_ {i \in [ n ^ {k} ]} \mathcal {L} \left(\mathrm {V L M} \left(p; x _ {i} ^ {k}\right), y _ {i} ^ {k}\right) \tag {2}
+$$
+
+where  $\mathcal{L}(\cdot)$  is the objective function, which could be the error rate, and  $\mathrm{VLM}(\cdot)$  represents the Vision-Language Model (VLM). The above equation can be interpreted as learning a globally optimal natural language prompt by minimizing the weighted average loss across all clients, where each client's contribution is proportional to its dataset size.
+
+Notice that if clients were permitted to share their private data and had white-box access to the VLM, the equation above could be easily solved by approximating the objective function with a differentiable function, such as cross-entropy loss. In this case, standard backpropagation could be applied to the global dataset to search for the optimal prompt instruction. However, due to commercial concerns, modern VLMs are typically deployed as API ser
+
+vices, which are black-boxes to the clients. Additionally, each client is unwilling to share their data with others due to privacy concerns. Consequently, we must impose the following constraints:
+
+Blackbox:  $\frac{\partial\mathcal{L}(\mathrm{VLM}(p;x),y)}{\partial p} = \emptyset$
+
+Privacy:  $\forall k,j\in [K],k\neq j,$ $\mathrm{Client}_k$  cannot access  $\mathcal{D}_j$  (3)
+
+The first constraint indicates that the gradient is not feasible, while the second constraint specifies that each client can only access its own data.
+
+# 3.2. Design Overview
+
+The algorithm overview is illustrated in Figure 1. Consistent with the traditional federated learning paradigm [22], each client communicates solely with the server using the prompt information, while keeping their data local. This ensures compliance with the data privacy constraints outlined in Eq.(3). Specifically, at the beginning, the server distributes the Global Prompt to each client. Then our approach follows these steps during each global communication round to search an optimal prompt: (1) Client Optimization: Each client utilizes an Agent-based Client Prompt Optimization method for personalized token-level prompt optimization. This method is preferred over backpropagation and ensures adherence to the black-box constraints in Eq.(3), which is more realistic in the context of VLM as a service; (2) Server Aggregation: Each client uploads its locally optimized prompt to the server, where knowledge aggregation is performed using the Semantic-similarity-guided Evolutionary Computation method. The subsequent sections provide a detailed explanation of each step in our approach.
+
+# 3.3. Client Optimization
+
+Upon receiving the global discrete prompt  $p_0$  from the server in the current round, each client iteratively updates it using an agent-based approach, as shown in Alg. 1. Initially, the agent queries the LLM to randomly replace some tokens in  $p_0$ , generating a set of prompt mutants  $p_1, p_2, \ldots, p_M$  (Line 1). Each prompt is then combined with the client's local dataset and fed into the VLM to measure the accuracy, which serves as the prompt mutant's score. FDPT maintains a priority queue to manage these mutants, prioritizing those with higher accuracy (Lines 2-6). FDPT iteratively selects the highest-priority prompt from the queue as the seed, asks the LLM to mutate the important tokens of the seed, and updates the priority queue with the newly generated prompt mutants (Lines 7-13). Specifically, token importance is computed as follows: (1), FDPT compares each prompt mutant  $p_i$  with the seed prompt  $p_0$  token by token, constructing a difference matrix  $M$ , where  $M_i^j = 0$  if the
+
+Algorithm 1 Agent-Based Prompt Optimization  
+Input: Initial discrete prompt  $p_0$ , Large Language Model (LLM), Vision-Language Model (VLM), client local dataset  $\mathcal{D}$ , number of mutants  $M$   
+Output: Optimized prompt  $\hat{p}$   
+1: Initialization:  $\{p_1, p_2, \ldots, p_M\} =$  Mutator(  $LLM, p_0$  )  $\triangleright$  Mutate  $p_0$  by randomly replacing tokens  
+2:  $\mathcal{Q} =$  Priority Queue  $\triangleright$  Initialize an empty queue  
+3: for each prompt  $p_i$  in  $\{p_0, p_1, \ldots, p_M\}$  do  
+4:  $Acc_i =$  Evaluate(VLM,  $p_i$ ,  $\mathcal{D}$ )  $\triangleright$  Evaluation  
+5: Push  $(\mathcal{Q}, p_i, Acc_i)$ $\triangleright$  Update the priority queue  
+6: end for  
+7: while stopping criterion not met do  
+8:  $p_{seed} =$  Pop  $(\mathcal{Q}) \triangleright$  Get the highest-priority prompt  
+9: Position = Importance Estimator  $\triangleright$  Select important tokens  
+10:  $p_{new} =$  Mutator(  $LLM, p_{seed}$ , Position)  
+11:  $Acc_{new} =$  Evaluate(VLM,  $p_{new}$ ,  $\mathcal{D}$ )  $\triangleright$  Evaluation  
+12: Push  $(\mathcal{Q}, p_{new}, Acc_{new})$ $\triangleright$  Update the queue  
+13: end while  
+14: Return highest-scoring prompt from  $\mathcal{Q}$
+
+$j$ -th token of  $p_i$  and  $p_0$  are different, and  $M_i^j = 1$  otherwise. (2), FDPT computes the accuracy gains  $V$ , where  $V_i = \mathrm{Acc}_i - \mathrm{Acc}_0$ . (3) The importance score of each token position is then given by  $S = M^{-1}V$ . This score estimation equation reflects the degree to which a token's presence or absence affects accuracy, weighted by its position in the prompt. Finally, the top  $K$  token positions are selected based on the importance score  $S$ .
+
+# 3.4. Server Aggregation
+
+After local client optimization, each client uploads its optimized discrete prompt to the server for knowledge exchange. The server then aggregates these local optimal prompts for the next round of optimization. Specifically, the server aggregation includes the following steps (as shown in Algorithm 2):
+
+Token-level Semantic Representation. In total client uploaded prompts, e.g. the initial population  $\mathcal{P}_{\mathrm{init}}$ , for each token in a prompt, we use a pre-trained text encoder of the Roberta to get its token-level semantic representation, denoted as
+
+$$
+\mathcal {E} _ {i} = [ e _ {i} ^ {1}, e _ {i} ^ {2}, \dots , e _ {i} ^ {K} ] e _ {i} ^ {j} = f _ {e m b e d} (t k _ {i} ^ {j}) \qquad (4)
+$$
+
+where  $f_{embed}(\cdot)$  is the pre-trained encoder, and  $tk_i^j$  is the  $j^{th}$  token of the  $i^{th}$  prompt.
+
+Reputation Test. We first evaluate the reputation of each token, defined as the semantic-similarity weight (denoted
+
+$\alpha_{g,h})$  that each token assigns to all other tokens. This is computed using a cosine-similarity mechanism [12] based on embeddings:
+
+$$
+\alpha_ {g} = \sum_ {h} \alpha_ {g, h} = \sum_ {h} \operatorname {s o f t m a x} \left(\frac {\mathbf {e} _ {g} \cdot \mathbf {e} _ {h}}{\sqrt {d}}\right), \tag {5}
+$$
+
+where  $\mathbf{e}_g$  and  $\mathbf{e}_h$  represent the embedding of a token  $g$  and  $h$ , respectively, and  $d$  is the dimensionality of the embeddings. A higher semantic-similarity weight  $\alpha_{g,h}$  signifies a stronger influence over other tokens. We define the total semantic-similarity weight of token  $g$  as  $\alpha_{g}$ , which represents the token's semantic importance among all other tokens, referred to as its Reputation.
+
+Aggregation. Next, tokens are clustered based on their semantic similarity by grouping embeddings that are close to each other in the high-dimensional semantic space:
+
+$$
+\mathcal {C} = \left\{\mathcal {C} _ {1}, \mathcal {C} _ {2}, \dots , \mathcal {C} _ {Z} \right\}, \mathcal {C} _ {z} = \left\{\mathbf {e} _ {h} \mid \| \mathbf {e} _ {h} - \mathbf {e} _ {g} \| <   \epsilon , \forall h \in \mathcal {P} _ {\text {i n i t}} \right\}, \tag {6}
+$$
+
+where  $\epsilon$  is a pre-defined distance threshold.  $C_z$  denotes a cluster, or Community. Embeddings with equivalent syntactic meanings are grouped into a cluster, from which a single representative is subsequently selected.
+
+Election. Finally, within each cluster (Community), the representative token is determined by semantic-similarity weights (reputation). Tokens with higher weights have stronger semantic dependencies on other tokens and are more likely to be selected:
+
+$$
+\mathbf {r} _ {z} = \underset {\mathbf {e} _ {n} \in \mathcal {C} _ {z}} {\arg \max } \alpha_ {n}, \tag {7}
+$$
+
+where  $\mathbf{r}_z$  denotes the representative token in Community  $\mathcal{C}_z$ . Importantly, communities containing only a single token are discarded, as these tokens contain only client-specific information, following the principle of "majority rule" [30] in Voting. The selected tokens are then arranged in their original order (using, for example, a bubble sort [2]) to form a representative prompt, or the "Representatives", denoted as  $\mathcal{P}_{\mathrm{new}} = \{\mathbf{r}_1,\mathbf{r}_2,\dots ,\mathbf{r}_Z\}$ .
+
+# 4. Evaluation
+
+# 4.1. Evaluation Setup
+
+Backbone API. In our experiments, we selected four backbone models: Qwen2-VL-72B [35], InternVL2-Llama3-76B, TeleMM [23], and GPT4o.
+
+Dataset and Evaluation. We conduct experiments on two tasks: traditional image classification and Visual Question Answer (VQA). For image classification, we use the
+
+Algorithm 2 Semantic-similarity-Guided Evolutionary Computation for Discrete Prompt Optimization  
+Input: I clients with discrete prompt tokens  $\{\mathcal{P}_{\mathrm{client}_i}\}_{i = 1}^I$    
+Output: Global prompt tokens  $\mathcal{P}_{\mathrm{new}}$    
+1: Initialization Initial population  $\mathcal{P}_{\mathrm{init}}$    
+2: for each token  $tk$  in a prompt  $\in \mathcal{P}_{\mathrm{init}}$  do   
+3: Achieve mapping according to Eq.4   
+4: end for   
+5: for each token  $\mathbf{t}_g$  do  $\triangleright$  Reputation Test   
+6: for each token  $\mathbf{t}_h$  do   
+7: Semantic-similarity weight according to Eq.5   
+8: end for   
+9: Get total semantic-similarity weight  $\alpha_{g} = \sum_{h}\alpha_{g,h}$    
+10: end for   
+11: Cluster tokens according to Eq.6 Aggregation   
+12: for each Community  $C_z\in \mathcal{C}$  do Election   
+13: Select representative token according to Eq.7   
+14: if  $C_z$  contains only one token then   
+15: Discard Community  $C_z$    
+16: end if   
+17: end for   
+18: Form Representatives  $\mathcal{P}_{\mathrm{new}} = \{\mathbf{r}_1,\mathbf{r}_2,\dots ,\mathbf{r}_Z\}$  from selected representative tokens
+
+MNIST [9], CIFAR-10, CIFAR-100, and TinyImageNet (TinyImg) [20] datasets. For VQA, we utilize the Art, Chemistry, and Finance sections of the MMMU dataset [43], along with the RealWorldQA (RWQA) dataset. The task objective is to leverage optimized prompts for accurate image classification on the image datasets, and for VQA, to assist in parsing textual content within the datasets to enable accurate classification or decision-making.
+
+We use Accuracy as the evaluation metric for the image classification task. To maintain consistency across tasks, we also constrain predictions in the VQA task to the range of available labels and evaluate performance using Accuracy.
+
+Comparison Baselines. We compare our method against eight state-of-the-art (SOTA) approaches: FedPrompt [46], FedPepTAO [4], FedTPG [29], HPT [37], CoOp [48], BBT [10], FedBPT [31], BPTVLM [41], and a manual prompting method (Manual Prompt). Notably, HPT [37], CoOp [48], BBT[10], and BPTVLM [41] are not originally designed for federated learning. To adapt these methods to a federated setting, we apply a weighted averaging aggregation approach, following the implementations of FedPrompt [46]and FedBPT [31]. The results are reported using federated versions of these models: FedAvg-HPT, FedAvg-CoOp, FedAvg-BBT, and Fed-BPTVLM. Additionally, we categorize these methods into White-box and Black-box approaches based on whether they require access to model parameters. The White-box methods include FedPrompt [46],
+
+<table><tr><td rowspan="2">Backbone</td><td rowspan="2">Method</td><td colspan="4">CV Classification</td><td colspan="4">VQA</td><td rowspan="2">Average</td></tr><tr><td>MNIST</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td><td>Art</td><td>Chemistry</td><td>Finance</td><td>RWQA</td></tr><tr><td rowspan="10">Qwen2-VL-72B</td><td rowspan="5">White Box</td><td>FedPrompt</td><td>90.4</td><td>79.5</td><td>73.5</td><td>60.9</td><td>74.6</td><td>63.3</td><td>70.5</td><td>80.4</td></tr><tr><td>FedPepTAO</td><td>86.7</td><td>78.3</td><td>72.9</td><td>59.5</td><td>69.1</td><td>58.8</td><td>68.5</td><td>77.9</td></tr><tr><td>FedTPG</td><td>84.2</td><td>76.8</td><td>71.3</td><td>59.2</td><td>72.4</td><td>57.5</td><td>62.6</td><td>75.4</td></tr><tr><td>FedAvg-HPT</td><td>86.9</td><td>78.4</td><td>70.2</td><td>58.7</td><td>75.7</td><td>53.5</td><td>65.9</td><td>78.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>78.1</td><td>71.4</td><td>59.2</td><td>70.2</td><td>61.8</td><td>63.3</td><td>76.5</td></tr><tr><td rowspan="5">Black Box</td><td>Manual</td><td>70.7</td><td>62.2</td><td>53.5</td><td>47.3</td><td>54.7</td><td>45.8</td><td>51.8</td><td>58.3</td></tr><tr><td>FedAvg-BBT</td><td>78.9</td><td>72.3</td><td>62.7</td><td>51.7</td><td>63.5</td><td>53.9</td><td>60.3</td><td>69.7</td></tr><tr><td>FedBPT</td><td>80.0</td><td>72.0</td><td>64.2</td><td>53.1</td><td>68.0</td><td>50.6</td><td>59.0</td><td>67.8</td></tr><tr><td>Fed-BPTVLM</td><td>80.7</td><td>73.1</td><td>62.3</td><td>50.9</td><td>65.2</td><td>53.3</td><td>63.3</td><td>70.8</td></tr><tr><td>Our method</td><td>90.5</td><td>78.5</td><td>71.8</td><td>57.8</td><td>74.0</td><td>60.8</td><td>67.2</td><td>78.5</td></tr><tr><td rowspan="10">InternVL2-Llama3-76B</td><td rowspan="5">White Box</td><td>FedPrompt</td><td>88.1</td><td>81.3</td><td>74.4</td><td>60.2</td><td>70.2</td><td>58.8</td><td>62.9</td><td>76.1</td></tr><tr><td>FedPepTAO</td><td>87.3</td><td>77.8</td><td>71.2</td><td>58.5</td><td>65.2</td><td>55.3</td><td>63.0</td><td>75.4</td></tr><tr><td>FedTPG</td><td>86.2</td><td>79.3</td><td>71.7</td><td>57.4</td><td>68.0</td><td>54.2</td><td>60.7</td><td>73.8</td></tr><tr><td>FedAvg-HPT</td><td>85.1</td><td>78.7</td><td>72.3</td><td>58.4</td><td>69.1</td><td>53.0</td><td>62.0</td><td>74.3</td></tr><tr><td>FedAvg-CoOp</td><td>85.7</td><td>79.1</td><td>71.6</td><td>58.1</td><td>71.8</td><td>56.2</td><td>63.9</td><td>71.7</td></tr><tr><td rowspan="5">Black Box</td><td>Manual</td><td>71.8</td><td>63.7</td><td>51.8</td><td>45.4</td><td>52.5</td><td>46.3</td><td>53.8</td><td>61.3</td></tr><tr><td>FedAvg-BBT</td><td>80.0</td><td>71.1</td><td>65.2</td><td>52.7</td><td>60.2</td><td>51.9</td><td>53.8</td><td>70.5</td></tr><tr><td>FedBPT</td><td>80.7</td><td>72.7</td><td>66.6</td><td>52.3</td><td>61.3</td><td>50.6</td><td>58.4</td><td>67.1</td></tr><tr><td>Fed-BPTVLM</td><td>79.5</td><td>71.4</td><td>67.2</td><td>53.0</td><td>64.1</td><td>53.0</td><td>56.7</td><td>69.8</td></tr><tr><td>Our method</td><td>89.6</td><td>79.0</td><td>71.5</td><td>57.3</td><td>70.7</td><td>55.9</td><td>63.6</td><td>75.5</td></tr><tr><td rowspan="5">TeleMM</td><td rowspan="5">Black Box</td><td>Manual</td><td>69.4</td><td>65.5</td><td>53.3</td><td>45.8</td><td>53.0</td><td>45.0</td><td>52.5</td><td>57.9</td></tr><tr><td>FedAvg-BBT</td><td>80.9</td><td>70.6</td><td>63.1</td><td>49.1</td><td>56.9</td><td>48.8</td><td>56.4</td><td>64.1</td></tr><tr><td>FedBPT</td><td>80.0</td><td>71.3</td><td>61.9</td><td>50.9</td><td>60.8</td><td>51.5</td><td>57.4</td><td>66.3</td></tr><tr><td>Fed-BPTVLM</td><td>79.1</td><td>71.0</td><td>62.7</td><td>49.7</td><td>59.1</td><td>52.3</td><td>57.7</td><td>68.5</td></tr><tr><td>Our method</td><td>88.4</td><td>78.9</td><td>69.3</td><td>57.4</td><td>64.6</td><td>55.7</td><td>61.6</td><td>75.0</td></tr><tr><td rowspan="5">GPT4o</td><td rowspan="5">Black Box</td><td>Manual</td><td>74.4</td><td>68.2</td><td>59.1</td><td>52.8</td><td>61.9</td><td>58.6</td><td>61.6</td><td>71.9</td></tr><tr><td>FedAvg-BBT</td><td>81.0</td><td>76.7</td><td>67.6</td><td>56.1</td><td>64.6</td><td>57.5</td><td>63.6</td><td>69.2</td></tr><tr><td>FedBPT</td><td>83.2</td><td>78.3</td><td>68.4</td><td>56.6</td><td>69.1</td><td>59.3</td><td>68.5</td><td>69.9</td></tr><tr><td>Fed-BPTVLM</td><td>81.7</td><td>79.0</td><td>67.9</td><td>57.3</td><td>67.4</td><td>57.9</td><td>65.2</td><td>71.6</td></tr><tr><td>Our method</td><td>92.5</td><td>85.3</td><td>73.9</td><td>62.7</td><td>76.8</td><td>66.7</td><td>72.8</td><td>78.5</td></tr></table>
+
+Table 1. Performance Comparison on CV Classification and VQA Tasks. The accuracy results are measured in percentages (\%). Bold values indicate the overall best results, and underlined values indicate the best results among Black Box methods.
+
+FedPepTAO [4], FedTPG [29], FedAvg-HPT, and FedAvg-CoOp, while the Black-box methods consist of Manual, FedAvg-BBT, FedBPT [31], and Fed-BPTVLM. Detailed descriptions of all baselines are provided in Appendix A.
+
+Implementation. The federated learning setup for our experiments is as follows: we use a default of 10 clients, with a client participation rate of  $100\%$  in each training round. Additionally, we adopt a  $k$ -shot mechanism for prompt tuning, following the approach in work [31], with the default value of  $k$  set to 50. For image classification datasets, we use the original training and test sets. For each Visual QA dataset, we randomly select 50 samples as the training set (from the validation set for MMMU and the test set for RealWorldQA), with the remaining samples used for testing. In terms of baseline implementations, we adapt traditional
+
+prompt optimization methods (HPT, CoOp, BBT, BBT-VLM) to the federated learning framework by employing the classical Federated Averaging (FedAvg) approach. For black-box backbone model configurations, we extend soft prompt tuning methodologies, such as FedBPT, by mapping the soft tokens to discrete tokens, through the RoBERTa encoder's tokenization mechanism, before feeding them into API-based models. In addition, all experiments are conducted on two NVIDIA GeForce RTX A800 GPUs. Detailed hyperparameter settings are provided in Appendix B.
+
+# 4.2. Effectiveness Results
+
+We first evaluate the effectiveness of our method on traditional CV classification tasks and VQA tasks. Experimental results show that, compared to other methods, our method demonstrates significant performance improvements in both
+
+tasks, particularly excelling in black-box environments, with only a small gap from white-box algorithms.
+
+Traditional CV Classification Tasks. In traditional CV classification tasks, our method achieves outstanding performance across all model configurations. For example, in the GPT4o black-box setting, our method achieves improvements of  $11.2\%$ ,  $7.0\%$ ,  $5.5\%$ , and  $6.1\%$  over the closest-performing FedBPT [31] method on the MNIST, Cifar-10, Cifar-100, and TinyImg datasets, respectively. In the TeleMM black-box setting, our method also performs exceptionally well, achieving  $88.4\%$  and  $78.9\%$  accuracy on MNIST and Cifar-10, respectively, which is an improvement of  $9.3\%$  and  $8.3\%$  over FedAvg-BBT. Additionally, for the Qwen2-VL-72B model, our method achieves accuracies of  $78.5\%$  and  $71.8\%$  on the Cifar-10 and Cifar-100 datasets, respectively, representing improvements of  $7.1\%$  and  $5.3\%$  over FedBPT [31], further demonstrating its advantage in traditional CV tasks.
+
+VQA Tasks. Our method also shows strong performance in VQA tasks. In the GPT4o black-box setting, our method achieves improvements of  $11.1\%$ ,  $7.4\%$ ,  $4.3\%$ , and  $8.6\%$  over the FedBPT [31] method on the Art, Chemistry, Finance, and RWQA datasets, respectively. In TeleMM setting, our method's performance remains very stable, achieving improvements of  $7.7\%$  and  $10.9\%$  over FedAvg-BBT on the Art and RWQA datasets, respectively.
+
+# 4.3. Prompt Transferability Evaluation
+
+In the prompt transferability experiment, we evaluate the performance of prompts optimized on one backbone model when applied to another, as shown in Table 2. The results indicate that prompts exhibit a degree of transferability, maintaining high robustness across models with minimal accuracy loss, as referenced in Table 1. Additionally, compared to the Qwen2-VL transfer results, the InternVL2 transfer showed better accuracy, further validating the high applicability and robustness of prompts between certain models.
+
+<table><tr><td>Model</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td>Qwen2-VL→TeleMM</td><td>80</td><td>70.5</td><td>58.1</td></tr><tr><td>InternVL2→GPT4o</td><td>87.8</td><td>72.3</td><td>63.5</td></tr></table>
+
+# 4.4. Communication Overhead Experiment
+
+In the communication overhead experiment, our method shows a significant advantage in parameter efficiency, as illustrated in Table 3. Specifically, white-box methods like
+
+FedPrompt [46] and FedTPG [29] and most black-box methods such as FedAvg-BBT and Fed-BPTVLM require hundreds of thousands of parameters, whereas our method requires only 150. This substantial reduction effectively minimizes latency and resource consumption associated with communication. This advantage primarily arises from a key difference in algorithm design: while other methods use soft prompts for knowledge exchange between clients, our method employs discrete prompt tokens. Soft prompts typically require a large number of continuous parameters, whereas discrete prompt tokens enable knowledge transfer with only a small set of parameters, significantly reducing communication overhead.
+
+Table 2. Transferability Experiment Results. The accuracy results are measured in percentages  $(\%)$ .  
+
+<table><tr><td>Type</td><td>Method</td><td>Parameters</td></tr><tr><td rowspan="5">White Box</td><td>FedPrompt</td><td>614k</td></tr><tr><td>FedPepTAO</td><td>1796k</td></tr><tr><td>FedTPG</td><td>614k</td></tr><tr><td>FedAvg-HPT</td><td>614k</td></tr><tr><td>FedAvg-CoOp</td><td>614k</td></tr><tr><td rowspan="3">Black Box</td><td>FedAvg-BBT</td><td>614k</td></tr><tr><td>FedBPT</td><td>40.8k</td></tr><tr><td>Fed-BPTVLM</td><td>614k</td></tr><tr><td colspan="2">Our method</td><td>150</td></tr></table>
+
+Table 3. Communication Overhead Experiment results. The measurements are in Tensors within the PyTorch Framework. Bold values indicate the best results, and underlined values indicate the second-best results.
+
+# 4.5. Ablation Studies
+
+In the improvements ablation study based on Qwen2-VL72B API, our method consistently achieves the best performance across all metrics, further validating the effectiveness of its key components, as shown in Table 4. Compared to cases where specific modules are removed or replaced, our method demonstrates significant improvements on the Cifar-10, Cifar-100, and TinyImg datasets. Server-side experiments. Our method improves accuracy on the Cifar-10 and Cifar-100 datasets by  $2.0\%$  and  $1.2\%$ , respectively, compared to the setting without the clustering strategy. Furthermore, compared to the fixed clustering approach, our method achieves accuracy gains of  $0.7\%$  on Cifar-10 and  $2.5\%$  on Cifar-100, underscoring the importance of a dynamic clustering strategy. Client-side experiments. Removing the G-F mechanism results in a significant accuracy drop across all datasets. Furthermore, our method achieves a  $1.0\%$  accuracy improvement on Cifar-100 and  $1.6\%$  on TinyImg compared to the configuration without the E-EB strategy. Compared to the configuration without the PPR-CoT strategy, our method improves accuracy by  $3.2\%$  on Cifar-10 and  $2.5\%$  on Cifar-100, underscoring the pivotal role of the PPR-CoT strategy in enhancing model perfor
+
+mance.  
+
+<table><tr><td>Site</td><td>Method</td><td>Cifar-10</td><td>Cifar-100</td><td>TinyImg</td></tr><tr><td rowspan="4">Server</td><td>w Embedding-fedavg</td><td>71.9</td><td>62.5</td><td>54.2</td></tr><tr><td>w Random search</td><td>65.3</td><td>57.3</td><td>53.9</td></tr><tr><td>w/o Clustering Strategy</td><td>76.5</td><td>70.6</td><td>55.9</td></tr><tr><td>w Fixed Clusters</td><td>77.8</td><td>69.3</td><td>56.3</td></tr><tr><td rowspan="3">Client</td><td>w/o G-F Mechanism</td><td>71.8</td><td>65.5</td><td>53.5</td></tr><tr><td>w/o E-EB Strategy</td><td>76.9</td><td>70.8</td><td>56.2</td></tr><tr><td>w/o PPR-CoT</td><td>75.3</td><td>69.3</td><td>56.7</td></tr><tr><td colspan="2">Our method</td><td>78.5</td><td>71.8</td><td>57.8</td></tr></table>
+
+Table 4. The Improvements Ablation Studies Results. The accuracy is measured in percentages (\%). Performance decreases with the removal or modification of any key component, underscoring the effectiveness of the improvements. "w Embedding-fedavg" denotes the use of a weighted averaging aggregation method, as in FedBPT [31] and FedAvg-BBT. "w Random search" refers to the removal of weight comparison, using random search instead to select representative tokens. "w/o Clustering Strategy" indicates the removal of the clustering step. "w Fixed Clusters" implies a fixed number of clusters, which affects the count of representative tokens.
+
+Initial Prompt Impact. We evaluate the impact of the Initial Prompt on performance using GPT-4o as the backbone black-box VLM for classification tasks across datasets, comparing it with three typical black-box algorithms. Figure 2 shows that different prompt configurations significantly affect model performance, with our algorithm consistently achieving the best outcomes. Specifically, detailed prompts enhance model accuracy by providing richer information, which supports more effective learning and adaptation. In contrast, shorter prompts reduce accuracy, indicating that limited information constrains performance. Thus, prompt design is critical in classification tasks, and our algorithm exhibits strong robustness and performance across various prompt configurations. We present all Initial Prompts in Appendix C.
+
+![](images/bdf692c71c5accc0fa2d0073f9c851bbd72af7066710b1a942b3d1ad6d0a7bcb.jpg)  
+Figure 2. Initial Prompt Impact. Prompt-1 represents a "shorter initial prompt," Prompt-2 a "standard initial prompt," and Prompt-3 a "detailed initial prompt."
+
+# 4.6. Heterogeneous Data Robustness Experiment
+
+In the heterogeneous data robustness experiment, we use the Qwen2-VL-72B API as the backbone VLM model to evaluate the performance of different algorithms on heterogeneous data in the TinyImagenet dataset, as shown in Figure 3. Data is distributed across 10 clients using a Dirichlet Distribution [21] with varying hyperparameters dir, where a smaller Dirichlet parameter (e.g., dir=0.05) indicates greater data heterogeneity. Details of these heterogeneous data distributions are provided in Appendix D. The results demonstrate that all methods show some robustness to data heterogeneity, aligning with expectations [28, 31] for model stability on heterogeneous data. Additionally, as heterogeneity increases, our method exhibits superior performance, with minimal accuracy reduction, outperforming other methods under all heterogeneity conditions.
+
+![](images/da5f1c208403cb7a251f64a0194070670d99b45fd8172029e77c6a9e485be995.jpg)  
+Figure 3. Heterogeneous Data Robustness Experiment results on the TinyImageNet dataset. The parameter "dir" is the Dirichlet Distribution hyperparameter; smaller values of dir indicate higher data heterogeneity across the 10 clients.
+
+# 5. Conclusion
+
+We propose FDPT, the first federated black-box discrete prompt tuning framework based on visual language models. FDPT uses an Agent-based Client Prompt Optimization strategy to achieve token-level prompt optimization on the client side without traditional prediction logits, thereby preventing inversion attacks. On the server side, a Semantic-Similarity-Guided Evolutionary Computation framework is implemented to execute more precise zeroth-order optimization, which enables the obtention of representative global tokens. Moreover, discrete token exchange between clients offers high security and low communication overhead. Moreover, discrete tokens exhibit enhanced interpretability compared to soft prompts, which facilitates human experts in designing corresponding instructions. Our framework exhibits: (1) statistically significant accuracy enhancements in conventional visual recognition and cross-modal reasoning tasks; (2) optimized communication efficiency through adaptive token selection mechanisms; (3) cross-domain transferability of learned prompt representations; and (4) strengthened resilience to data distribution shifts, particularly in heterogeneous learning environments.
+
+Acknowledgements. This research was supported by the National Natural Science Foundation of China under Grant 52074305, 52274160, 51874300 and the National Natural Science Foundation of China-Shanxi Provincial People's Government Coal-based Low Carbon Joint Fund U1510115, the Academic Research Projects of Beijing Union University (No.ZK90202106) and R&D Program of Beijing Municipal Education Commission (KM202211417005).
+
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2025/FE-CLIP_ Frequency Enhanced CLIP Model for Zero-Shot Anomaly Detection and Segmentation/e20fdad0-0c02-434f-a4f5-0e729b38aab0_content_list.json

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+        "type": "text",
+        "text": "FE-CLIP: Frequency Enhanced CLIP Model for Zero-Shot Anomaly Detection and Segmentation",
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+        "text": "Tao Gong  $^{1,2,3}$ , Qi Chu  $^{1,2,3*}$ , Bin Liu  $^{1,2,3}$ , Wei Zhou  $^{4}$ , Nenghai Yu  $^{1,2,3}$",
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+        "text": "$^{4}$ Ling Yang Industrial Internet Co., Ltd.",
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+        "type": "text",
+        "text": "{tgong, qchu, flowice, ynh} @ustc.edu.cn, weizhou8@iflytek.com",
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+        "text": "Abstract",
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+        "text": "Zero-shot anomaly detection (ZSAD) requires detection models trained using auxiliary data to detect anomalies without any training sample in a target dataset. It is challenging since the models need to generalize to anomalies across different domains. Recently, CLIP-based anomaly detection methods, such as WinCLIP and AnomalyCLIP, have demonstrated superior performance in the ZSAD task, due to the strong zero-shot recognition of the CLIP model. However, they overlook the utilization of frequency information of images. In this paper, we find that frequency information could benefit the ZSAD task, since some properties of the anomaly area, such as appearance defects, can also be reflected based on its frequency information. To this end, We propose Frequency Enhanced CLIP (FE-CLIP), taking advantage of two different but complementary frequency-aware clues, (1) Frequency-aware Feature Extraction adapter, and (2) Local Frequency Statistics adapter, in the visual encoder of CLIP, to deeply mine frequency information for the ZSAD task. We apply DCT as the frequency-domain transformation. Through comprehensive experiments, we show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Besides, FE-CLIP also achieves superior performance under the few-normal-shot anomaly detection settings.",
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+        "text": "1. Introduction",
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+        "text": "Anomaly Detection aims to predict an image or a pixel as normal or anomalous, and has been widely applied in",
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+        "text": "various applications, such as industrial defect inspection [4, 5, 7, 16, 28, 35, 37, 47, 51] and medical image analysis [11, 27, 31, 42, 43]. Existing AD approaches typically assume that training examples in a target application domain are available for learning the detection models. However, this assumption may not hold in various scenarios, such as i) when accessing training data violates data privacy policies, or ii) when the target domain does not have relevant training data. Therefore, Zero-shot anomaly detection (ZSAD) is an emerging task for AD in such scenarios, to which the AD methods mentioned above are not viable, as it requires detection models to detect anomalies without any training sample in a target dataset. ZSAD is challenging since the models need to generalize to anomalies across different domains where the appearance of foreground objects, abnormal regions, and background features can vary significantly.",
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+        "text": "Recently, large pre-trained vision-language models (VLMs) have demonstrated strong zero-shot recognition ability in various vision tasks. Particularly, being pretrained using millions/billions of image-text pairs, CLIP [33] has been applied to empower various downstream tasks with its strong generalization capability. WinCLIP [17] is the first work to apply the CLIP model in the ZSAD line. It uses a large number of hand-crafted text prompts and extraction of window/patch/image-level features aligned with text to finish the ZSAD task. However, WinCLIP involves multiple forward passes of image patches for anomaly segmentation, which leads to inefficiency. Besides, WinCLIP only performs the testing of the CLIP model in the ZSAD without any fine-tuning using the anomaly detection task data, which also limits its performance in the ZSAD task. Subsequently, several works [8, 22, 32, 52] attempt to adapt the CLIP into the ZSAD task by fintuning. Specifically, AnomalyCLIP [52] learns object-agnostic text prompts that capture generic normality and abnormality in an image regardless of its foreground objects. ClipSAM [22] introduces",
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+        "image_caption": [
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+        "image_caption": [
+            "(c) crack",
+            "Figure 1. The local frequency statistics of images. The second row represents the local frequency statistics of non-overlapped image regions. There are four columns, standing for the normal object, object with a hole, object with a crack, and object with print, respectively. Please zoom in and pay attention to the red region (i.e. the anomaly region of the input image) for a better view."
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+    {
+        "type": "text",
+        "text": "a unified multiscale cross-modal interaction module for interacting language with visual features at multiple stages of the CLIP visual encoder to reason anomaly positions. VCP-CLIP [32] propose the Pre-VCP module and PostVCP module to perform visual context prompting to activate CLIP's anomalous semantic perception ability. AdaCLIP [8] incorporates static and dynamic learnable prompts to adapt CLIP for ZSAD. However, all of the methods mentioned above overlook the utilization of frequency information of images.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In this paper, we find that frequency information could benefit the ZSAD task. Some properties of the anomaly area, such as appearance defects, can also be reflected based on its frequency information, since high-frequency components represent fine details (e.g. soft borders) that often exist in the anomaly area. For example, as shown in Figure 1, the frequency statistics in the red region are different from the frequency statistics in the surrounding regions of the input abnormal image and the corresponding region of the normal image. These specific frequency patterns could be helpful for anomaly detection.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To this end, we introduce a novel approach, namely the Frequency Enhanced CLIP (FE-CLIP), to inject frequency information into CLIP for accurate ZSAD across different domains. FE-CLIP takes advantage of two different but complementary frequency-aware clues, (1) Frequency-aware Feature Extraction (FFE) adapter, and (2) Local Frequency Statistics (LFS) adapter, in the visual encoder of CLIP, to deeply mine frequency information. Specifically, the FFE adapter uses DCT [1] to transform the image features into the frequency domain in order to mine the frequency information, then uses inverse DCT to transform back to the spatial domain. The FFE adapter describes the frequency-aware patterns in the spatial domain, but does not explicitly render the frequency information directly in",
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "the neural networks. Therefore, we use LFS to render the frequency information directly in the frequency domain. In each densely but regularly sampled local spatial patch, the statistics are gathered by counting the mean frequency responses. The averaged frequency statistics are a multichannel spatial map, where the number of channels is identical to the number of channels in the spatial domain. The local frequency statistics also follow the spatial layouts as the features of the CLIP visual encoder, thus also enjoying effective representation learning powered by the CLIP visual encoder. Meanwhile, since the frequency-aware feature extraction and local frequency statistics are complementary to each other but both of them share inherently similar frequency-aware semantics, thus they can be progressively fused during the feature learning process.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Through comprehensive experiments, we show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Our contributions in this paper are summarized as follows:",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. We find that frequency information could benefit the ZSAD task, and propose a novel Frequency Enhanced CLIP (FE-CLIP) method to inject frequency information into CLIP for accurate ZSAD across different domains.",
+            "2. We propose two different but complementary frequency-aware adapters, Frequency-aware Feature Extraction (FFE) adapter, and Local Frequency Statistics (LFS) adapter, in the visual encoder of CLIP, to deeply mine the frequency patterns of anomaly region.",
+            "3. Extensive experiments show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Besides, the proposed FE-CLIP also achieves superior performance under the few-normal-shot anomaly detection settings."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            513,
+            700,
+            653,
+            715
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Vision-language modeling",
+        "text_level": 1,
+        "bbox": [
+            511,
+            726,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Among recent successes of large pre-trained vision-language models (VLM) [2, 20, 33], CLIP [33] is the first to perform pre-training on web-scale image-text data, showing unprecedented generality: e.g., its language-driven zero-shot inference, improved both effective robustness [40] and perceptual alignment [12]. Many following VLM works explored large-scale pre-training in different aspects, e.g., scaling up data [20], efficient designs [21], multi-tasks [29], etc. To democratize large-scale VLM for the usages in different domains, a billion-scale data LAION5B [39], a",
+        "bbox": [
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+            750,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "21221",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa8fb52490b307caa182158c166aa25e1db21b01264cdc8cc19722b5bec154fb.jpg",
+        "image_caption": [
+            "Figure 2. The framework of the proposed FE-CLIP. The text encoder and visual encoder are from the CLIP model, and the FFE and LFS are the proposed adapters. We only show the class token embedding after the last block of the CLIP visual encoder for convenience. Actually, the CLIP visual encoder can output the class token after every block."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            158,
+            98,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "code base of OpenCLIP with pre-trained models are open-sourced. Other works presented CLIP's promise in zero/few-shot transfer to downstream tasks beyond classification [13, 36, 41, 46]. Good prompt engineering and tuning [33, 50] can non-trivially benefit generalization performances. Moreover, some other works [34, 48, 49] leverage the pre-trained CLIP for language-guided detection and segmentation with promising performances. In this paper, we mainly focus on adapting CLIP into the ZSAD task with superior performance by injecting the frequency information into the visual encoder of CLIP.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Zero-shot Anomaly detection",
+        "text_level": 1,
+        "bbox": [
+            89,
+            621,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ZSAD relies on the model's strong transferability to handle unseen anomalies [3]. A very recent approach WinCLIP [17] presents a seminal work that leverages CLIP [33] for zero-shot anomaly classification and segmentation. WinCLIP proposes a compositional ensemble on state words and prompt templates and efficient extraction and aggregation of window/patch/image-level features aligned with text to finish the ZSAD task. To tackle this inefficiency, APRILGAN [9] introduces a fine-tuning strategy by adding extra learnable linear projection layers in multiple stages of the CLIP visual encoder to enhance the modeling of local visual semantics. AnomalyCLIP [52] learns object-agnostic text prompts that capture generic normality and abnormality in an image regardless of its foreground objects. ClipSAM [22] introduces a unified multiscale cross-modal interaction module for interacting language with visual features at multiple stages of the CLIP visual encoder to reason anomaly",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "positions. Myriad [25] and AnomalyGPT [14] utilize large language models for zero-shot/few-shot anomaly detection. They employ an image decoder to provide fine-grained semantics and design a prompt learner to fine-tune the large language models using prompt embeddings. However, all of the methods mentioned above overlook the utilization of frequency information of images. In this paper, we find that frequency information could benefit the ZSAD task, and propose the FE-CLIP method which utilizes two different but complementary adapters, the FFE adapter and the LFS adapter, into the visual encoder of CLIP, to deeply mine the frequency information for ZSAD task.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Preliminary",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "CLIP [33] is a large-scale pretraining method offering a joint vision-language representation. It consists of a text encoder  $T(\\cdot)$  and a visual encoder  $F(\\cdot)$ . Both encoders are mainstream multi-block networks such as ViT [10]. Using text prompts is a typical way to acquire the embeddings of different classes for zero-shot classification. The text prompts usually combine a text prompt template  $\\Omega$  with the category name  $c$ , where the text prompt template  $\\Omega$  usually is defined as A photo of a [cls] and [cls] represents the target category name. The text prompts are passed through  $T(\\cdot)$  to obtain its corresponding textual embedding  $g_{c} \\in \\mathbb{R}^{D}$  where  $D$  denotes the channel dimension. Then, an input image is passed through  $F(\\cdot)$  to get the visual representations, where the class token  $f \\in \\mathbb{R}^{D}$  is the",
+        "bbox": [
+            511,
+            688,
+            908,
+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "21222",
+        "bbox": [
+            478,
+            944,
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+            957
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "global visual embedding of the input image, and patch tokens  $f^{m} \\in \\mathbb{R}^{H \\times W \\times D}$  are treated as local visual embeddings of the input image.  $H$  and  $W$  denote the height and width of the patch tokens, respectively. CLIP can perform zero-shot recognition by measuring the similarity between textual and visual embeddings. Specifically, given a target class set  $\\mathcal{C}$  and an image, CLIP predicts the probability of the image belonging to the  $c$  category as follows:",
+        "bbox": [
+            89,
+            90,
+            483,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np (y = c) = P \\left(g _ {c}, f\\right) = \\frac {\\exp \\left(<   g _ {c} , f > / \\tau\\right)}{\\sum_ {c \\in \\mathcal {C}} \\exp \\left(<   g _ {c} , f >\\right) / \\tau} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            222,
+            482,
+            258
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\tau$  denotes the temperature and the operator  $<  ,\\cdot ,>$  represents the computation of cosine similarity. The computation can be extended from global visual embeddings to local visual embeddings to derive the corresponding segmentation maps  $M_{c}\\in \\mathbb{R}^{H\\times W}$  , if each entry  $(i,j)$  is computed as  $P\\left(g_c,f^{m(i,j)}\\right)$",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Frequency Enhanced CLIP",
+        "text_level": 1,
+        "bbox": [
+            89,
+            366,
+            338,
+            382
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we find that frequency information could benefit the ZSAD task, and propose a novel Frequency Enhanced CLIP (FE-CLIP) method to inject frequency information into CLIP [33] for accurate ZSAD across different domains. We inject the frequency information by the features of the CLIP visual encoder rather than the frequency of the input image, since the CLIP visual encoder is trained to take RGB image as input. Typically, the CLIP visual encoder comprises a series of block layers. From the bottom to the top of the layers, the visual encoder gradually learns the visual patterns at different levels of abstraction. As shown in Figure 2, we add Frequency-aware Feature Extraction (FFE) adapter and Local Frequency Statistics (LFS) adapter across multiple blocks levels in the visual encoder  $F(\\cdot)$  of CLIP, while keeping its original backbone unchanged, thus enabling frequency information injection at multiple feature levels. To be specific, assuming the visual encoder consists of  $N$  blocks ( $N = 4$ ), the features (i.e. the patch tokens) after the  $n$ -th block are denoted as  $f_{n}^{m} \\in \\mathbb{R}^{H \\times W \\times D}$ , and the class token after the  $n$ -th block is denoted as  $f_{n} \\in \\mathbb{R}^{D}$ , where  $n = 1, 2,.., N$ . Firstly, the features  $f_{n}^{m}$  are passed through an FFE adapter and an LFS adapter to get the features  $f_{n,ffe}^{m}$  and  $f_{n,lfs}^{m}$ , respectively, which contain the frequency information. We can get the frequency-aware feature  $\\hat{f}_{n}^{m}$  as follows:",
+        "bbox": [
+            89,
+            388,
+            483,
+            767
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {f} _ {n} ^ {m} = \\lambda (f _ {n, f f e} ^ {m} + f _ {n, l f s} ^ {m}) + (1 - \\lambda) f _ {n} ^ {m} \\qquad (2)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            153,
+            777,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with  $\\hat{f}_n^m$  serving as the input for the next block. The class token  $f_n$  will also be injected with frequency information after the next block due to the self-attention mechanism [44] in the blocks. We set  $\\lambda = 0.1$  to preserve the original knowledge of the CLIP visual encoder. Then, the normal text prompt and abnormal text prompt are passed through",
+        "bbox": [
+            89,
+            809,
+            483,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ada198cb4923503e658aeebf6adf459bb11b39ce42a82b39c983defa58a9c7c5.jpg",
+        "image_caption": [
+            "Figure 3. The proposed Frequency-aware Feature Extraction (FFE) adapter."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            524,
+            88,
+            897,
+            157
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "text encoder  $T(\\cdot)$  to get corresponding textual embedding  $g_{r}$  and  $g_{a}$ , respectively.  $g_{r}$  and  $g_{a}$  constitute the target class set  $\\mathcal{C}$ . We simply use A photo of a normal object and A photo of a damaged object for the normal text prompt and abnormal text prompt, respectively, rather than the complex compositional ensemble on state words and prompt templates used in WinCLIP [17], since we find that the simple text prompt also works well. Finally, we compute the abnormal segmentation map  $M_{a,n} \\in \\mathbb{R}^{H \\times W}$  based on the equation 1, where each entry  $(i,j)$  is computed as  $P\\left(g_{a}, fc(\\hat{f}_{n}^{m(i,j)})\\right)$ . The  $fc$  means that we use a single learnable fc to align the dimension of visual features  $\\hat{f}_{n}^{m}$  to the dimension of text features. The abnormal score  $S_{a,n}$  is also computed based on the equation 1 as  $P\\left(g_{a}, fc_{clip}(f_{n})\\right)$ . The  $fc_{clip}$  denotes the frozen project layer of the visual encoder in CLIP to align the dimension of class token  $f_{n}$  and the dimension of text features. The final prediction of the abnormal score  $S_{a}$  and abnormal segmentation map  $M_{a}$  are computed by averaging  $S_{a,n}$  and  $M_{a,n}$  across  $N$  blocks, respectively, as follows:",
+        "bbox": [
+            511,
+            220,
+            906,
+            531
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {a} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} S _ {a, n}, \\quad M _ {a} = \\frac {1}{N} \\sum_ {n = 1} ^ {N} M _ {a, n} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Frequency-aware Feature Extraction Adapter",
+        "text_level": 1,
+        "bbox": [
+            511,
+            590,
+            901,
+            607
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The specific frequency patterns could be beneficial for anomaly detection. To mine the frequency information, we propose the Frequency-aware Feature Extraction (FFE) adapter in the visual encoder of CLIP. Specifically, given the patch tokens of the  $n$ -th block  $f_{n}^{m}\\in \\mathbb{R}^{H\\times W\\times D}$ , we first split the  $f_{n}^{m}$  into non-overlapped windows with total  $(H / P)\\times (W / P)$  windows and each window containing  $P\\times P$  patch tokens ( $P$  is set to 3 by default). As shown in Figure 3, we apply DCT [1] transformation to each window to extract the DCT features  $f_{n,ffe,1}^{m}$  which represents the frequency information. Then, we pass  $f_{n,ffe,1}^{m}$  through one linear layer followed by one GELU( $\\cdot$ ) activation layer to further extract the frequency features  $f_{n,ffe,2}^{m}$ . Finally, we apply the inverse DCT transformation to  $f_{n,ffe,2}^{m}$  to get the frequency-aware features  $f_{n,ffe}^{m}$  in the spatial domain. The FFE adapter describes the frequency-aware patterns in the spatial domain, but does not explicitly render the frequency information directly in the neural networks. In the next sub-section, we propose an adapter that renders the fre",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "21223",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/5e04a0e617d3013bf98a724038f9b30a721e7183e7309f2327e0716c29a434c0.jpg",
+        "image_caption": [
+            "Figure 4. The proposed Local Frequency Statistics (LFS) adapter."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            101,
+            89,
+            473,
+            165
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "quency information directly in the neural networks.",
+        "bbox": [
+            89,
+            231,
+            429,
+            247
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Local Frequency Statistics Adapter",
+        "text_level": 1,
+        "bbox": [
+            89,
+            253,
+            397,
+            272
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The aforementioned FFE adapter has provided frequency-aware representation, but it has to represent the frequency-aware patterns back into the spatial domain, thus failing to directly utilize the frequency patterns in the frequency domain. Therefore, we propose the Local Frequency Statistics (LFS) adapter in the visual encoder of CLIP to render the frequency patterns directly in the frequency domain. As shown in Figure 4, given the patch tokens of the  $n$ -th block  $f_{n}^{m}\\in \\mathbb{R}^{H\\times W\\times D}$ , we first apply a Sliding Window DCT (SW DCT) on  $f_{n}^{m}$  (i.e., taking DCT [1] densely on sliding windows of the features) to extract the localized frequency responses  $f_{n,lfs,1}^{m}$ . The size of sliding windows is  $Q\\times Q$  ( $Q$  is set to 3 by default). Therefore, there are  $Q\\times Q$  group frequency responses in  $f_{n,lfs,1}^{m}$ , where the first one represents the low-frequency responses and the last one represents the high-frequency responses. Then we count the mean of  $f_{n,lfs,1}^{m}$  across  $Q\\times Q$  groups to get the mean frequency responses  $f_{n,lfs,2}^{m}$ . The  $f_{n,lfs,2}^{m}$  is a multi-channel spatial map that shares the same layout as  $f_{n}^{m}$ . The LFS adapter outputs  $f_{n,lfs}^{m}$  after  $f_{n,lfs,2}^{m}$  being passed through a convolutional layer followed by one  $GELU(\\cdot)$  activation layer. The LFS adapter provides a localized aperture to detect detailed abnormal frequency distributions.",
+        "bbox": [
+            91,
+            277,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Loss Functions",
+        "text_level": 1,
+        "bbox": [
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+            632,
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+            647
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $S_{gt}$  denote the ground-truth image label where 1 represents the abnormal image and 0 represents the normal image. The loss for the anomaly classification is defined as follows:",
+        "bbox": [
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+            654,
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {c l s} = - \\frac {1}{N} \\sum_ {N} ^ {n = 1} \\left[ S _ {g t} \\log \\left(S _ {a, n}\\right) + \\left(1 - S _ {g t}\\right) \\log \\left(1 - S _ {a, n}\\right) \\right] \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            94,
+            723,
+            480,
+            775
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\log$  denotes the log operation. Similarly, let  $M_{gt}$  denote the ground-truth pixel label of the input image, where 1 means abnormal pixel region and 0 means normal pixel region. The loss for the anomaly segmentation is defined as follows:",
+        "bbox": [
+            89,
+            776,
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {m a s k}} = \\frac {1}{N} \\sum_ {N} ^ {n = 1} [ \\operatorname {F o c a l} (U p (M _ {a, n}), M _ {g t}) + D i c e (U p (M _ {a, n}), M _ {g t}) ] \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            89,
+            851,
+            506,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $Focal(\\cdot, \\cdot)$  and  $Dice(\\cdot, \\cdot)$  denote the focal loss [26] and dice loss [23], respectively. The operator  $Up(\\cdot)$  represents the unsampling operation. During training, both the visual encoder and the text encoder of CLIP [33] are Frozen. Only the FFE adapters and LFS adapters are optimized by the loss function  $L_{total} = L_{cls} + L_{mask}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            511,
+            196,
+            645,
+            213
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets and Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            511,
+            222,
+            799,
+            237
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To verify the effectiveness of the proposed method FE-CLIP, we conduct comprehensive experiments across 10 real-world anomaly detection datasets, covering various industrial inspection scenarios and medical imaging domains. In industrial inspection, we use MVtec AD [4], VisA [54], MPDD [18], BTAD [30], DAGM [45], and DTD-Synthetic [3]. In medical imaging, we use colon polyp detection datasets CVC-ClinicDB [6] and Kvasir [19], brain tumor detection datasets BrainMRI [38] and Br35H [15].",
+        "bbox": [
+            511,
+            244,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As for the evaluation metrics, following previous works [17, 52], we use Area Under the Receiver Operating Characteristic curve (AUROC). Additionally, Average Precision (AP) for Zero-Shot Anomaly Detection (ZSAD) and PRO [5] for Zeor-Shot Anomaly Segmentation (ZSAS) are also used to provide a more in-depth analysis of the results.",
+        "bbox": [
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+            381,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            511,
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use the publicly available CLIP model (VITL/14@336px) as our backbone. Model parameters of CLIP are all frozen, and only the parameters of FFE adapters and LFS adapters are learnable. Following AnomalyCLIP [52], we fine-tune FE-CLIP using the test data of MVtec AD and evaluate the ZSAD performance on other datasets. As for MVtec AD, we fine-tune FE-CLIP on the test data of VisA. The proposed FE-CLIP is trained by 9 epochs with Adam optimizer. The learning rate is set to 5e-4 and the total batch size is 16. All experiments are conducted in PyTorch-1.13.0 with four NVIDIA RTX 3090 24GB GPUs. All experiment results are averaged under five runs. We report dataset-level results, which are averaged across their respective sub-datasets.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Main Results",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ZSAD performance on diverse anomaly scenarios. Table 1 shows the ZSAD results of FE-CLIP with other competing methods over six industrial defect datasets and two medical domain datasets. As shown in Table 1, FE-CLIP can achieve higher AUROC and AP for the ZSAD task on most industrial inspection datasets and medical datasets, such as MVTec AD, DTD-Synthetic, and BrainMRI, when compared with other competing methods, such as WinCLIP [17], AnomalyCLIP [52] and AdaCLIP [8]. This shows that (1) the frequency information can benefit the ZSAD task",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "21224",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/88e54f6673c8da6d807a01d5faebda72997adb2739eb01cc3f9d34d01e05d850.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">Industrial Defects</td><td colspan=\"2\">Medical Anomalies</td></tr><tr><td>MVTec AD</td><td>VisA</td><td>MPDD</td><td>BTAD</td><td>DAGM</td><td>DTD-Synthetic</td><td>BrainMRI</td><td>Br35H</td></tr><tr><td>CLIP [33]</td><td>74.1 / 87.6</td><td>66.4 / 71.5</td><td>54.3 / 65.4</td><td>34.5 / 52.5</td><td>79.6 / 59.0</td><td>71.6 / 85.7</td><td>73.9 / 81.7</td><td>78.4 / 78.8</td></tr><tr><td>CoOp [50]</td><td>88.8 / 94.8</td><td>62.8 / 68.1</td><td>55.1 / 64.2</td><td>66.8 / 77.4</td><td>87.5 / 74.6</td><td>- / -</td><td>61.3 / 44.9</td><td>86.0 / 87.5</td></tr><tr><td>WinCLIP [17]</td><td>91.8 / 96.5</td><td>78.1 / 81.2</td><td>63.6 / 69.9</td><td>68.2 / 70.9</td><td>91.8 / 79.5</td><td>93.2 / 92.6</td><td>86.6 / 91.5</td><td>80.5 / 82.2</td></tr><tr><td>APRIL-GAN [9]</td><td>86.1 / 93.5</td><td>78.0 / 81.4</td><td>78.0 / 81.4</td><td>73.6 / 68.6</td><td>94.4 / 83.8</td><td>86.4 / 95.0</td><td>89.3 / 90.9</td><td>93.1 / 92.9</td></tr><tr><td>AnomalyCLIP [52]</td><td>91.5 / 96.2</td><td>82.1 / 85.4</td><td>77.0 / 82.0</td><td>88.3 / 87.3</td><td>97.5 / 92.3</td><td>93.5 / 97.0</td><td>90.3 / 92.2</td><td>94.6 / 94.7</td></tr><tr><td>AdaCLIP [8]</td><td>89.2 / -</td><td>85.8 / -</td><td>76.0 / -</td><td>88.6 / -</td><td>99.1 / -</td><td>95.5 / -</td><td>94.8 / -</td><td>97.7 / -</td></tr><tr><td>FE-CLIP</td><td>91.9 / 96.5</td><td>84.6 / 86.6</td><td>78.0 / 82.6</td><td>90.3 / 90.0</td><td>97.5 / 92.3</td><td>98.3 / 99.4</td><td>94.8 / 93.8</td><td>96.8 / 93.8</td></tr></table>",
+        "bbox": [
+            99,
+            88,
+            903,
+            224
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/c57f4830242ac8bbbdc5be1a89ca7c3e40937918fd9fef0a46665eef220eb416.jpg",
+        "table_caption": [
+            "Table 1. AUROC / AP results for Zero-Shot Anomaly Detection (ZSAD) task on eight real-world anomaly detection datasets. Best results are highlighted in red."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"6\">Industrial Defects</td><td colspan=\"2\">Medical Anomalies</td></tr><tr><td>MVTec AD</td><td>VisA</td><td>MPDD</td><td>BTAD</td><td>DAGM</td><td>DTD-Synthetic</td><td>CVC-ClinicDB</td><td>Kvasir</td></tr><tr><td>CLIP [33]</td><td>38.4 / 11.3</td><td>46.6 / 14.8</td><td>62.1, 33.0</td><td>30.6 / 4.4</td><td>30.6 / 4.4</td><td>33.9 / 12.5</td><td>47.5 / 18.9</td><td>44.6 / 17.7</td></tr><tr><td>CoOp [50]</td><td>33.3 / 6.7</td><td>24.2 / 3.8</td><td>15.4 / 2.3</td><td>15.4 / 2.3</td><td>17.5 / 2.1</td><td>- / -</td><td>17.5 / 2.1</td><td>44.1 / 3.5</td></tr><tr><td>WinCLIP [17]</td><td>85.1 / 64.6</td><td>79.6 / 56.8</td><td>79.6 / 56.8</td><td>72.7 / 27.3</td><td>87.6 / 65.7</td><td>83.9 / 57.8</td><td>51.2 / 13.8</td><td>69.7 / 24.5</td></tr><tr><td>APRIL-GAN [9]</td><td>87.6 / 84.0</td><td>94.2 / 86.8</td><td>94.1 / 83.2</td><td>60.8 / 25.0</td><td>82.4 / 66.2</td><td>95.3 / 86.9</td><td>80.5 / 60.7</td><td>75.0 / 36.2</td></tr><tr><td>AnomalyCLIP [52]</td><td>91.1 / 81.4</td><td>95.5 / 87.0</td><td>96.5 / 88.7</td><td>94.2 / 74.8</td><td>95.6 / 91.0</td><td>97.9 / 92.3</td><td>82.9 / 67.8</td><td>78.9 / 45.6</td></tr><tr><td>AdaCLIP [8]</td><td>88.7 / -</td><td>95.5 / -</td><td>96.1 / -</td><td>92.1 / -</td><td>91.5 / -</td><td>97.9 / -</td><td>84.4 / -</td><td>- / -</td></tr><tr><td>VCP-CLIP [32]</td><td>92.0 / 87.3</td><td>95.7 / 90.7</td><td>- / -</td><td>94.1 / 74.6</td><td>99.4 / 98.3</td><td>- / -</td><td>- / -</td><td>- / -</td></tr><tr><td>FE-CLIP</td><td>92.6 / 88.3</td><td>95.9 / 92.8</td><td>97.0 / 90.5</td><td>95.6 / 80.4</td><td>98.5 / 96.6</td><td>99.0 / 97.4</td><td>84.5 / 69.2</td><td>79.8 / 60.6</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. AUROC / PRO results for Zero-Shot Anomaly Segmentation (ZSAS) task on eight real-world anomaly detection datasets. Best results are highlighted in red. Note that the image-level medical AD datasets do not contain segmentation ground truth, so the pixel-level medical AD datasets are different from the image-level datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "due to the superior performance of FE-CLIP, and (2) the frequency information helps FE-CLIP achieve good generalization across datasets from different domains.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ZSAS performance on diverse anomaly scenarios. We show the ZSAS results of FE-CLIP with other competing methods over six industrial defect datasets and two medical domain datasets in Table 2. Table 2 shows that FE-CLIP achieves higher AUROC and PRO for the ZSAS task on almost all of the industrial inspection datasets and medical datasets, except for the DAGM dataset, when compared with other competing methods, such as WinCLIP [17], AnomalyCLIP [52], AdaCLIP [8] and VCP-CLIP [32]. This further demonstrates that (1) the frequency information can benefit the ZSAS task and (2) the frequency information helps FE-CLIP achieve good generalization across datasets from different domains.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Discussion. We also note that the FE-CLIP can defeat almost all of the competing methods on the ZSAS task, while FE-CLIP only performs better than other methods over most of the datasets on ZSAD task. The reason may be that the frequency information can be directly injected into the patch tokens (i.e. the feature map used for the ZSAS task) through the FFE adapter and LFS adapter, while the frequency information can only be implicitly involved in the global class token (i.e. the feature vector used for the ZSAD task) from the patch tokens based on the self",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "attention mechanism.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Overall, the proposed FE-CLIP achieves superior zero-shot performance of detecting and segmenting anomalies in datasets of highly diverse class semantics from various defect inspection and medical imaging domains.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The effectiveness of FFE and LFS We conduct ablation experiments on MVTec AD dataset and VisA dataset to validate the effectiveness of the proposed FFE adapter and LFS adapter. The results are shown in Table 3. The \"CLIP  $[33] + \\text{Conv Adapter}\"$  means we add  $N$  conv adapters, where each of them consists of one convolutional layer followed by one  $GELU(\\cdot)$  activation layer to keep the same learnable parameters with the LFS adapter into the visual encoder of CLIP. It can be concluded that both the FFE adapter and LFS adapter can achieve better performance than the conv adapter in MVTec AD dataset and VisA dataset across the ZSAD task and ZSAS task. This also shows that the frequency information can benefit the ZSAD task and ZSAS task. When combined the FFE adapter with the LFS adapter, the FE-CLIP achieves higher performance than the FFE adapter and LFS adapter. This demonstrates that the FFE adapter and LFS adapter can mine different but complementary frequency information to further boost the performance of model on the ZSAD and ZSAS tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "21225",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/e3bab8a5ceac6a321f616e8e408d0e1a32fed1ffdfa9a58e13fc88d7235db46a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td>CLIP[33] + Conv Adapter</td><td>89.0 / 85.1</td><td>87.8 / 94.5</td><td>94.8 / 89.8</td><td>82.3 / 83.5</td></tr><tr><td>CLIP[33] + FFE Adapter</td><td>90.6 / 86.2</td><td>90.0 / 95.4</td><td>95.1 / 91.3</td><td>83.3 / 85.0</td></tr><tr><td>CLIP[33] + LFS Adapter</td><td>91.5 / 87.1</td><td>90.6 / 95.7</td><td>95.5 / 91.8</td><td>83.9 / 85.7</td></tr><tr><td>FE-CLIP</td><td>92.6 / 88.3</td><td>91.9 / 96.5</td><td>95.9 / 92.8</td><td>84.6 / 86.6</td></tr></table>",
+        "bbox": [
+            215,
+            88,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/9555c9f026c27fb73638766794429890f5e41a7a55540e2c1819321e780ef512.jpg",
+        "table_caption": [
+            "Table 3. Module ablation on the MVTec AD and the VisA datasets. The metric of Pixel-level is AUROC / PRO for ZSAS task, and the metric of Image-level is AUROC / AP for ZSAD task. Best results are highlighted in red."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td>FFT</td><td>92.8 / 88.3</td><td>92.0 / 96.2</td><td>95.5 / 93.0</td><td>84.1 / 86.8</td></tr><tr><td>DCT</td><td>92.6 / 88.3</td><td>91.9 / 96.5</td><td>95.9 / 92.8</td><td>84.6 / 86.6</td></tr></table>",
+        "bbox": [
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+            258,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Compared with using FFT to extract the frequency information in the FFE and LFS modules. The metric of Pixel-level is AUROC / PRO for ZSAS task, and the metric of Image-level is AUROC / AP for ZSAD task. Best results are highlighted in red.",
+        "bbox": [
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+            401
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d6f13747d83cf192722772b460591f1b66576a4774d0cb3f468528e3c50c073d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/19181edfeb38d426337f67abc575606f9e563ded07ed5ace7016579f93df73eb.jpg",
+        "image_caption": [
+            "(a) Input Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/919a719e30bba0e8afc8a81c79f7db0966c64af1ac9771609e1bf42911a92bc0.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/5131f2a5216916bc8b7df84d3705250873a75f7cc4c87f10966a1a98a7f44d48.jpg",
+        "image_caption": [
+            "(b)  $f_{fe}^{m}$  from FFE Adapter"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            488,
+            248,
+            545
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2d4704cb6283321213688f49e1fcf5b6c8a811acb9be816fdb5fea86e934c725.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/61cd967df442bba1adb5db52b48daa51e95ab22d3049bf2ad4684b7194503f66.jpg",
+        "image_caption": [
+            "(c)  $f_{N,lf_s}^m$  from LFS Adapter"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            251,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/1aa7f5f88c38dc5ab12d1f85613f49cf78fae46ee08df725bb534ffe4d2c00ce.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e7f85ba6cab1ad3ddce06249e23fbd3b3b9a739c90497e16a7968c548736d774.jpg",
+        "image_caption": [
+            "(d)  $\\hat{f}_N^m$  from equation (2)",
+            "Figure 5. The visualization of the learned frequency features. Please zoom in for a better view."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            326,
+            488,
+            401,
+            545
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8dacbcc1c5ca34bb5c9e58ea87bc5dfde841ac5e0ddc160659a58225a04e3901.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            401,
+            426,
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+            487
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/d9d43740d3f9c1df4bb794417b67fcfcae4ceb31aa44f2b19cc30e03997fc358.jpg",
+        "image_caption": [
+            "(e) Final prediction"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            401,
+            488,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Would FFT work instead of DCT We attempt to use FFT to replace the DCT in the FFE and LFS modules to extract the frequency information. However, there are real values and imaginary values after FFT. To deal with this, the real values and imaginary values are separately processed and then combined to transform back to the spatial domain in the FFE module. As for the LFS module, the averaged local frequency statistics are computed from the real values and imaginary values, respectively, to get the averaged real local frequency statistics and the averaged imaginary local frequency statistics, and then they are summed to get the final averaged local frequency statistics. The results are shown in Table 4. This shows that using FFT achieves similar results with DCT, which means that the key is to inject the frequency information rather than the way of frequency transformation. We choose DCT since DCT is more convenient to extract frequency.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.5. Analysis",
+        "text_level": 1,
+        "bbox": [
+            511,
+            261,
+            614,
+            277
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Time cost. We report the inference time of APRIL-GAN, AnomalyCLIP, VCP-CLIP, AdaCLIP, and FE-CLIP with PyTorch-1.13.0 on one NVIDIA RTX 3090 24GB GPU. The inference time is 105, 120, 128, 160, and  $125\\mathrm{ms}$ , respectively. FE-CLIP achieves a better trade-off between performance and speed.",
+        "bbox": [
+            511,
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+            376
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visualization of learned frequency features. To show why frequency information is effective for the ZSAD task, we visualize the frequency-aware features from the last block of the visual encoder of CLIP as example, where the FFE and LFS adapters are added. As shown in Figure 5, both the features  $f_{N,ffe}^{m}$  from FFE adapter and the features  $f_{N,lfs}^{m}$  from LFS adapter highlight the abnormal region of images. By injecting the features  $f_{N,ffe}^{m}$  and  $f_{N,lfs}^{m}$  into the visual encoder of CLIP, the obtained features  $\\hat{f}_N^m$  can successfully localize the main abnormal region, in favor of the final prediction of the model.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "When frequency information can be beneficial. Some properties of anomaly area, such as appearance defects, can be reflected based on its frequency information, since high-frequency components represent fine details (e.g. soft borders) that often exist in anomaly area. In these cases, These specific frequency patterns could be beneficial for anomaly detection. For example, as shown in Figure 1, the frequency statistics in the red region are different from the frequency statistics in the surrounding regions of the input abnormal image and the corresponding region of the normal image.",
+        "bbox": [
+            511,
+            549,
+            905,
+            700
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Let's consider images of normal dumplings and images of squashed dumplings, where squashed dumplings are anomalies. In this case, if the squashed dumplings reveal the meat filling, the frequency of squashed dumplings could still stand out and frequency information could be helpful to detect anomalies. However, if the dumplings are squashed to be more like a meat pie without revealing the meat filling, the frequency of this squashed dumpling might not stand out and frequency information might not work well.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We validate the FE-CLIP across different domains with 10 datasets of highly diverse class semantics from various industrial inspections and medical domains, and the results of FE-CLIP on the datasets of medical domains are trained",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "21226",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f2dc48cc22edaa802f805f5bb14bad245619d22856f888d906f56cd06a4950e7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Setup</td><td rowspan=\"2\">Methods</td><td colspan=\"2\">MVTec AD</td><td colspan=\"2\">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td rowspan=\"5\">1-shot</td><td>PatchCore [37]</td><td>92.0 / 79.7</td><td>83.4 / 92.2</td><td>95.4 / 80.5</td><td>79.9 / 82.8</td></tr><tr><td>WinCLIP [17]</td><td>95.2 / 87.1</td><td>93.1 / 96.5</td><td>96.4 / 85.1</td><td>83.8 / 85.1</td></tr><tr><td>AnomalyGPT [14]</td><td>95.3 / -</td><td>94.1 / -</td><td>96.2 / -</td><td>87.4 / -</td></tr><tr><td>PromptAD [24]</td><td>95.9 / -</td><td>94.6 / -</td><td>96.7 / -</td><td>86.9 / -</td></tr><tr><td>FE-CLIP</td><td>96.1 / 90.9</td><td>95.6 / 98.1</td><td>97.9 / 93.9</td><td>88.7 / 90.5</td></tr><tr><td rowspan=\"6\">2-shot</td><td>PatchCore [37]</td><td>93.3 / 82.3</td><td>86.3 / 93.8</td><td>96.1 / 82.6</td><td>81.6 / 84.8</td></tr><tr><td>WinCLIP [17]</td><td>96.0 / 88.4</td><td>94.4 / 97.0</td><td>96.8 / 86.2</td><td>84.6 / 85.8</td></tr><tr><td>AnomalyGPT [14]</td><td>95.6 / -</td><td>95.5 / -</td><td>96.4 / -</td><td>88.6 / -</td></tr><tr><td>PromptAD [24]</td><td>96.2 / -</td><td>95.7 / -</td><td>97.1 / -</td><td>88.3 / -</td></tr><tr><td>InCTRL [53]</td><td>- / -</td><td>94.0 / 96.9</td><td>- / -</td><td>85.8 / 87.7</td></tr><tr><td>FE-CLIP</td><td>96.5 / 91.5</td><td>96.2 / 98.3</td><td>98.2 / 94.3</td><td>90.3 / 91.6</td></tr><tr><td rowspan=\"6\">4-shot</td><td>PatchCore [37]</td><td>94.3 / 84.3</td><td>88.8 / 94.5</td><td>96.8 / 84.9</td><td>85.3 / 87.5</td></tr><tr><td>WinCLIP [17]</td><td>96.2 / 89.0</td><td>95.2 / 97.3</td><td>97.2 / 87.6</td><td>87.3 / 88.8</td></tr><tr><td>AnomalyGPT [14]</td><td>96.2 / -</td><td>96.3 / -</td><td>96.7 / -</td><td>90.6 / -</td></tr><tr><td>PromptAD [24]</td><td>96.5 / -</td><td>96.6 / -</td><td>97.4 / -</td><td>89.1 / -</td></tr><tr><td>InCTRL [53]</td><td>- / -</td><td>94.5 / 97.2</td><td>- / -</td><td>87.7 / 90.2</td></tr><tr><td>FE-CLIP</td><td>96.7 / 91.7</td><td>96.6 / 98.4</td><td>98.4 / 95.0</td><td>90.7 / 91.9</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 5. Compared with other competing methods under few-normal-shot anomaly detection setting. The metric of Pixel-level is AUROC / PRO for the few-normal-shot anomaly segmentation task, and the metric of Image-level is AUROC / AP for the few-normal-shot anomaly detection task. Best results are highlighted in red.",
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+        "type": "text",
+        "text": "by the industrial inspection MVTec AD dataset, as shown in Table 1 and Table 2. The superior performance of FE-CLIP demonstrates that frequency information could be beneficial for many cases of anomaly detection, and the proposed FE-CLIP has good generalization across different domains.",
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+        "type": "text",
+        "text": "4.6. FE-CLIP with Few Normal Shots",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The performance of FE-CLIP can also be further boosted when equipped with few-shot normal images, just like WinCLIP [17] and AnomalyGPT [14]. We adopt the same way as AnomalyGPT to compute the anomaly segmentation map with few-shot normal images. In short words, we use the same visual encoder of FE-CLIP to extract intermediate patch-level features from normal images and store them in memory banks, then calculate the cosine similarity distance between each patch token of input image and its most similar counterpart in the memory banks to obtain the anomaly segmentation map  $S_{a,few\\_shot}$ . Finally, we add the anomaly segmentation map  $S_{a}$  from the FE-CLIP model with  $S_{a,few\\_shot}$  to get the final anomaly segmentation map, and add the anomaly score  $M_{a}$  from the FE-CLIP model with the max value of  $S_{a,few\\_shot}$  to get the final anomaly score. Please refer to [14] for more technical details.",
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+        "type": "text",
+        "text": "We compare the FE-CLIP with other competing methods, such as AnomalyGPT [14], PromptAD [24], and InCTRL [53], under the few-shot anomaly detection setting. As shown in Table 5, the FE-CLIP outperforms all other com",
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+        "type": "text",
+        "text": "peting methods across different metrics, including AUROC and PRO metrics for the anomaly detection task, and AUROC and AP metrics for the anomaly segmentation task, on both datasets. The experiments under few-normal-shot setting further demonstrate the superiority of the FE-CLIP.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we find that frequency information can benefit the ZSAD task. To this end, we propose FE-CLIP, which adds the proposed FFE and LFS adapters into the visual encoder of CLIP, to deeply mine the frequency patterns for the visual features. Extensive experiments on 10 datasets of highly diverse class semantics from various defect inspections and medical domains demonstrate that (1) the frequency information can benefit the ZSAD task, and (2) the frequency information can help the model have good generalization across datasets from different domains. We also conduct experiments under the few-normal-shot anomaly detection setting to further validate the superiority of the proposed FE-CLIP. We hope the community of anomaly detection will be aware of the effectiveness of frequency information from our work and explore more ways to utilize the frequency information for anomaly detection in the future.",
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+        "text": "Acknowledgements",
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+        "type": "text",
+        "text": "This work was supported by the Anhui Provincial Science and Technology Major Project (No. 2023z020006).",
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+        "text": "21227",
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2025/FE-CLIP_ Frequency Enhanced CLIP Model for Zero-Shot Anomaly Detection and Segmentation/full.md

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+# FE-CLIP: Frequency Enhanced CLIP Model for Zero-Shot Anomaly Detection and Segmentation
+
+Tao Gong  $^{1,2,3}$ , Qi Chu  $^{1,2,3*}$ , Bin Liu  $^{1,2,3}$ , Wei Zhou  $^{4}$ , Nenghai Yu  $^{1,2,3}$
+
+<sup>1</sup>School of Cyber Science and Technology, University of Science and Technology of China
+
+<sup>2</sup>Anhui Province Key Laboratory of Digital Security
+
+3the CCCD Key Lab of Ministry of Culture and Tourism
+
+$^{4}$ Ling Yang Industrial Internet Co., Ltd.
+
+{tgong, qchu, flowice, ynh} @ustc.edu.cn, weizhou8@iflytek.com
+
+# Abstract
+
+Zero-shot anomaly detection (ZSAD) requires detection models trained using auxiliary data to detect anomalies without any training sample in a target dataset. It is challenging since the models need to generalize to anomalies across different domains. Recently, CLIP-based anomaly detection methods, such as WinCLIP and AnomalyCLIP, have demonstrated superior performance in the ZSAD task, due to the strong zero-shot recognition of the CLIP model. However, they overlook the utilization of frequency information of images. In this paper, we find that frequency information could benefit the ZSAD task, since some properties of the anomaly area, such as appearance defects, can also be reflected based on its frequency information. To this end, We propose Frequency Enhanced CLIP (FE-CLIP), taking advantage of two different but complementary frequency-aware clues, (1) Frequency-aware Feature Extraction adapter, and (2) Local Frequency Statistics adapter, in the visual encoder of CLIP, to deeply mine frequency information for the ZSAD task. We apply DCT as the frequency-domain transformation. Through comprehensive experiments, we show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Besides, FE-CLIP also achieves superior performance under the few-normal-shot anomaly detection settings.
+
+# 1. Introduction
+
+Anomaly Detection aims to predict an image or a pixel as normal or anomalous, and has been widely applied in
+
+various applications, such as industrial defect inspection [4, 5, 7, 16, 28, 35, 37, 47, 51] and medical image analysis [11, 27, 31, 42, 43]. Existing AD approaches typically assume that training examples in a target application domain are available for learning the detection models. However, this assumption may not hold in various scenarios, such as i) when accessing training data violates data privacy policies, or ii) when the target domain does not have relevant training data. Therefore, Zero-shot anomaly detection (ZSAD) is an emerging task for AD in such scenarios, to which the AD methods mentioned above are not viable, as it requires detection models to detect anomalies without any training sample in a target dataset. ZSAD is challenging since the models need to generalize to anomalies across different domains where the appearance of foreground objects, abnormal regions, and background features can vary significantly.
+
+Recently, large pre-trained vision-language models (VLMs) have demonstrated strong zero-shot recognition ability in various vision tasks. Particularly, being pretrained using millions/billions of image-text pairs, CLIP [33] has been applied to empower various downstream tasks with its strong generalization capability. WinCLIP [17] is the first work to apply the CLIP model in the ZSAD line. It uses a large number of hand-crafted text prompts and extraction of window/patch/image-level features aligned with text to finish the ZSAD task. However, WinCLIP involves multiple forward passes of image patches for anomaly segmentation, which leads to inefficiency. Besides, WinCLIP only performs the testing of the CLIP model in the ZSAD without any fine-tuning using the anomaly detection task data, which also limits its performance in the ZSAD task. Subsequently, several works [8, 22, 32, 52] attempt to adapt the CLIP into the ZSAD task by fintuning. Specifically, AnomalyCLIP [52] learns object-agnostic text prompts that capture generic normality and abnormality in an image regardless of its foreground objects. ClipSAM [22] introduces
+
+![](images/1c26cd97864a68e083005162dfc3547c7765e45f23d3c57b6e61b7a48aa42a10.jpg)
+
+![](images/9d558e64152f6531e8db98707af6e0a4f628d3d575aee100ae81214939f2f93e.jpg)
+
+![](images/481e6f3295a2142aeb98cd2466fb958c8eb1f96e00ab27f6e11da1e0a5400fcb.jpg)
+
+![](images/e0912137d64943e50914be6d383485a7da6123f6874c46937667ee4e5b732b41.jpg)
+
+![](images/624acac42e6ce9861fb5a31243faba7f9dca38d1893b808927d4a803f61fb3d6.jpg)  
+(a) normal
+
+![](images/1d0eda1e2bd73fd2b08f254c32a05142fe642f32d8b33e44f39c0fe41c77365b.jpg)  
+(b) hole
+
+![](images/43a1f479838ef21d8c8f7fbcfdcdee60401235314c45aa66c30cbcd9d46cca12.jpg)  
+(c) crack  
+Figure 1. The local frequency statistics of images. The second row represents the local frequency statistics of non-overlapped image regions. There are four columns, standing for the normal object, object with a hole, object with a crack, and object with print, respectively. Please zoom in and pay attention to the red region (i.e. the anomaly region of the input image) for a better view.
+
+![](images/c6e47206040e53189505e927df62368744ab12c30d1fdec37db0117a4990442e.jpg)  
+(d) print
+
+a unified multiscale cross-modal interaction module for interacting language with visual features at multiple stages of the CLIP visual encoder to reason anomaly positions. VCP-CLIP [32] propose the Pre-VCP module and PostVCP module to perform visual context prompting to activate CLIP's anomalous semantic perception ability. AdaCLIP [8] incorporates static and dynamic learnable prompts to adapt CLIP for ZSAD. However, all of the methods mentioned above overlook the utilization of frequency information of images.
+
+In this paper, we find that frequency information could benefit the ZSAD task. Some properties of the anomaly area, such as appearance defects, can also be reflected based on its frequency information, since high-frequency components represent fine details (e.g. soft borders) that often exist in the anomaly area. For example, as shown in Figure 1, the frequency statistics in the red region are different from the frequency statistics in the surrounding regions of the input abnormal image and the corresponding region of the normal image. These specific frequency patterns could be helpful for anomaly detection.
+
+To this end, we introduce a novel approach, namely the Frequency Enhanced CLIP (FE-CLIP), to inject frequency information into CLIP for accurate ZSAD across different domains. FE-CLIP takes advantage of two different but complementary frequency-aware clues, (1) Frequency-aware Feature Extraction (FFE) adapter, and (2) Local Frequency Statistics (LFS) adapter, in the visual encoder of CLIP, to deeply mine frequency information. Specifically, the FFE adapter uses DCT [1] to transform the image features into the frequency domain in order to mine the frequency information, then uses inverse DCT to transform back to the spatial domain. The FFE adapter describes the frequency-aware patterns in the spatial domain, but does not explicitly render the frequency information directly in
+
+the neural networks. Therefore, we use LFS to render the frequency information directly in the frequency domain. In each densely but regularly sampled local spatial patch, the statistics are gathered by counting the mean frequency responses. The averaged frequency statistics are a multichannel spatial map, where the number of channels is identical to the number of channels in the spatial domain. The local frequency statistics also follow the spatial layouts as the features of the CLIP visual encoder, thus also enjoying effective representation learning powered by the CLIP visual encoder. Meanwhile, since the frequency-aware feature extraction and local frequency statistics are complementary to each other but both of them share inherently similar frequency-aware semantics, thus they can be progressively fused during the feature learning process.
+
+Through comprehensive experiments, we show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Our contributions in this paper are summarized as follows:
+
+1. We find that frequency information could benefit the ZSAD task, and propose a novel Frequency Enhanced CLIP (FE-CLIP) method to inject frequency information into CLIP for accurate ZSAD across different domains.  
+2. We propose two different but complementary frequency-aware adapters, Frequency-aware Feature Extraction (FFE) adapter, and Local Frequency Statistics (LFS) adapter, in the visual encoder of CLIP, to deeply mine the frequency patterns of anomaly region.  
+3. Extensive experiments show that the proposed FE-CLIP has good generalization across different domains and achieves superior zero-shot performance of detecting and segmenting anomalies in 10 datasets of highly diverse class semantics from various defect inspections and medical domains. Besides, the proposed FE-CLIP also achieves superior performance under the few-normal-shot anomaly detection settings.
+
+# 2. Related Work
+
+# 2.1. Vision-language modeling
+
+Among recent successes of large pre-trained vision-language models (VLM) [2, 20, 33], CLIP [33] is the first to perform pre-training on web-scale image-text data, showing unprecedented generality: e.g., its language-driven zero-shot inference, improved both effective robustness [40] and perceptual alignment [12]. Many following VLM works explored large-scale pre-training in different aspects, e.g., scaling up data [20], efficient designs [21], multi-tasks [29], etc. To democratize large-scale VLM for the usages in different domains, a billion-scale data LAION5B [39], a
+
+![](images/aa8fb52490b307caa182158c166aa25e1db21b01264cdc8cc19722b5bec154fb.jpg)  
+Figure 2. The framework of the proposed FE-CLIP. The text encoder and visual encoder are from the CLIP model, and the FFE and LFS are the proposed adapters. We only show the class token embedding after the last block of the CLIP visual encoder for convenience. Actually, the CLIP visual encoder can output the class token after every block.
+
+code base of OpenCLIP with pre-trained models are open-sourced. Other works presented CLIP's promise in zero/few-shot transfer to downstream tasks beyond classification [13, 36, 41, 46]. Good prompt engineering and tuning [33, 50] can non-trivially benefit generalization performances. Moreover, some other works [34, 48, 49] leverage the pre-trained CLIP for language-guided detection and segmentation with promising performances. In this paper, we mainly focus on adapting CLIP into the ZSAD task with superior performance by injecting the frequency information into the visual encoder of CLIP.
+
+# 2.2. Zero-shot Anomaly detection
+
+ZSAD relies on the model's strong transferability to handle unseen anomalies [3]. A very recent approach WinCLIP [17] presents a seminal work that leverages CLIP [33] for zero-shot anomaly classification and segmentation. WinCLIP proposes a compositional ensemble on state words and prompt templates and efficient extraction and aggregation of window/patch/image-level features aligned with text to finish the ZSAD task. To tackle this inefficiency, APRILGAN [9] introduces a fine-tuning strategy by adding extra learnable linear projection layers in multiple stages of the CLIP visual encoder to enhance the modeling of local visual semantics. AnomalyCLIP [52] learns object-agnostic text prompts that capture generic normality and abnormality in an image regardless of its foreground objects. ClipSAM [22] introduces a unified multiscale cross-modal interaction module for interacting language with visual features at multiple stages of the CLIP visual encoder to reason anomaly
+
+positions. Myriad [25] and AnomalyGPT [14] utilize large language models for zero-shot/few-shot anomaly detection. They employ an image decoder to provide fine-grained semantics and design a prompt learner to fine-tune the large language models using prompt embeddings. However, all of the methods mentioned above overlook the utilization of frequency information of images. In this paper, we find that frequency information could benefit the ZSAD task, and propose the FE-CLIP method which utilizes two different but complementary adapters, the FFE adapter and the LFS adapter, into the visual encoder of CLIP, to deeply mine the frequency information for ZSAD task.
+
+# 3. Method
+
+# 3.1. Preliminary
+
+CLIP [33] is a large-scale pretraining method offering a joint vision-language representation. It consists of a text encoder  $T(\cdot)$  and a visual encoder  $F(\cdot)$ . Both encoders are mainstream multi-block networks such as ViT [10]. Using text prompts is a typical way to acquire the embeddings of different classes for zero-shot classification. The text prompts usually combine a text prompt template  $\Omega$  with the category name  $c$ , where the text prompt template  $\Omega$  usually is defined as A photo of a [cls] and [cls] represents the target category name. The text prompts are passed through  $T(\cdot)$  to obtain its corresponding textual embedding  $g_{c} \in \mathbb{R}^{D}$  where  $D$  denotes the channel dimension. Then, an input image is passed through  $F(\cdot)$  to get the visual representations, where the class token  $f \in \mathbb{R}^{D}$  is the
+
+global visual embedding of the input image, and patch tokens  $f^{m} \in \mathbb{R}^{H \times W \times D}$  are treated as local visual embeddings of the input image.  $H$  and  $W$  denote the height and width of the patch tokens, respectively. CLIP can perform zero-shot recognition by measuring the similarity between textual and visual embeddings. Specifically, given a target class set  $\mathcal{C}$  and an image, CLIP predicts the probability of the image belonging to the  $c$  category as follows:
+
+$$
+p (y = c) = P \left(g _ {c}, f\right) = \frac {\exp \left(<   g _ {c} , f > / \tau\right)}{\sum_ {c \in \mathcal {C}} \exp \left(<   g _ {c} , f >\right) / \tau} \tag {1}
+$$
+
+where  $\tau$  denotes the temperature and the operator  $<  ,\cdot ,>$  represents the computation of cosine similarity. The computation can be extended from global visual embeddings to local visual embeddings to derive the corresponding segmentation maps  $M_{c}\in \mathbb{R}^{H\times W}$  , if each entry  $(i,j)$  is computed as  $P\left(g_c,f^{m(i,j)}\right)$
+
+# 3.2. Frequency Enhanced CLIP
+
+In this paper, we find that frequency information could benefit the ZSAD task, and propose a novel Frequency Enhanced CLIP (FE-CLIP) method to inject frequency information into CLIP [33] for accurate ZSAD across different domains. We inject the frequency information by the features of the CLIP visual encoder rather than the frequency of the input image, since the CLIP visual encoder is trained to take RGB image as input. Typically, the CLIP visual encoder comprises a series of block layers. From the bottom to the top of the layers, the visual encoder gradually learns the visual patterns at different levels of abstraction. As shown in Figure 2, we add Frequency-aware Feature Extraction (FFE) adapter and Local Frequency Statistics (LFS) adapter across multiple blocks levels in the visual encoder  $F(\cdot)$  of CLIP, while keeping its original backbone unchanged, thus enabling frequency information injection at multiple feature levels. To be specific, assuming the visual encoder consists of  $N$  blocks ( $N = 4$ ), the features (i.e. the patch tokens) after the  $n$ -th block are denoted as  $f_{n}^{m} \in \mathbb{R}^{H \times W \times D}$ , and the class token after the  $n$ -th block is denoted as  $f_{n} \in \mathbb{R}^{D}$ , where  $n = 1, 2,.., N$ . Firstly, the features  $f_{n}^{m}$  are passed through an FFE adapter and an LFS adapter to get the features  $f_{n,ffe}^{m}$  and  $f_{n,lfs}^{m}$ , respectively, which contain the frequency information. We can get the frequency-aware feature  $\hat{f}_{n}^{m}$  as follows:
+
+$$
+\hat {f} _ {n} ^ {m} = \lambda (f _ {n, f f e} ^ {m} + f _ {n, l f s} ^ {m}) + (1 - \lambda) f _ {n} ^ {m} \qquad (2)
+$$
+
+with  $\hat{f}_n^m$  serving as the input for the next block. The class token  $f_n$  will also be injected with frequency information after the next block due to the self-attention mechanism [44] in the blocks. We set  $\lambda = 0.1$  to preserve the original knowledge of the CLIP visual encoder. Then, the normal text prompt and abnormal text prompt are passed through
+
+![](images/ada198cb4923503e658aeebf6adf459bb11b39ce42a82b39c983defa58a9c7c5.jpg)  
+Figure 3. The proposed Frequency-aware Feature Extraction (FFE) adapter.
+
+text encoder  $T(\cdot)$  to get corresponding textual embedding  $g_{r}$  and  $g_{a}$ , respectively.  $g_{r}$  and  $g_{a}$  constitute the target class set  $\mathcal{C}$ . We simply use A photo of a normal object and A photo of a damaged object for the normal text prompt and abnormal text prompt, respectively, rather than the complex compositional ensemble on state words and prompt templates used in WinCLIP [17], since we find that the simple text prompt also works well. Finally, we compute the abnormal segmentation map  $M_{a,n} \in \mathbb{R}^{H \times W}$  based on the equation 1, where each entry  $(i,j)$  is computed as  $P\left(g_{a}, fc(\hat{f}_{n}^{m(i,j)})\right)$ . The  $fc$  means that we use a single learnable fc to align the dimension of visual features  $\hat{f}_{n}^{m}$  to the dimension of text features. The abnormal score  $S_{a,n}$  is also computed based on the equation 1 as  $P\left(g_{a}, fc_{clip}(f_{n})\right)$ . The  $fc_{clip}$  denotes the frozen project layer of the visual encoder in CLIP to align the dimension of class token  $f_{n}$  and the dimension of text features. The final prediction of the abnormal score  $S_{a}$  and abnormal segmentation map  $M_{a}$  are computed by averaging  $S_{a,n}$  and  $M_{a,n}$  across  $N$  blocks, respectively, as follows:
+
+$$
+S _ {a} = \frac {1}{N} \sum_ {n = 1} ^ {N} S _ {a, n}, \quad M _ {a} = \frac {1}{N} \sum_ {n = 1} ^ {N} M _ {a, n} \tag {3}
+$$
+
+# 3.3. Frequency-aware Feature Extraction Adapter
+
+The specific frequency patterns could be beneficial for anomaly detection. To mine the frequency information, we propose the Frequency-aware Feature Extraction (FFE) adapter in the visual encoder of CLIP. Specifically, given the patch tokens of the  $n$ -th block  $f_{n}^{m}\in \mathbb{R}^{H\times W\times D}$ , we first split the  $f_{n}^{m}$  into non-overlapped windows with total  $(H / P)\times (W / P)$  windows and each window containing  $P\times P$  patch tokens ( $P$  is set to 3 by default). As shown in Figure 3, we apply DCT [1] transformation to each window to extract the DCT features  $f_{n,ffe,1}^{m}$  which represents the frequency information. Then, we pass  $f_{n,ffe,1}^{m}$  through one linear layer followed by one GELU( $\cdot$ ) activation layer to further extract the frequency features  $f_{n,ffe,2}^{m}$ . Finally, we apply the inverse DCT transformation to  $f_{n,ffe,2}^{m}$  to get the frequency-aware features  $f_{n,ffe}^{m}$  in the spatial domain. The FFE adapter describes the frequency-aware patterns in the spatial domain, but does not explicitly render the frequency information directly in the neural networks. In the next sub-section, we propose an adapter that renders the fre
+
+![](images/5e04a0e617d3013bf98a724038f9b30a721e7183e7309f2327e0716c29a434c0.jpg)  
+Figure 4. The proposed Local Frequency Statistics (LFS) adapter.
+
+quency information directly in the neural networks.
+
+# 3.4. Local Frequency Statistics Adapter
+
+The aforementioned FFE adapter has provided frequency-aware representation, but it has to represent the frequency-aware patterns back into the spatial domain, thus failing to directly utilize the frequency patterns in the frequency domain. Therefore, we propose the Local Frequency Statistics (LFS) adapter in the visual encoder of CLIP to render the frequency patterns directly in the frequency domain. As shown in Figure 4, given the patch tokens of the  $n$ -th block  $f_{n}^{m}\in \mathbb{R}^{H\times W\times D}$ , we first apply a Sliding Window DCT (SW DCT) on  $f_{n}^{m}$  (i.e., taking DCT [1] densely on sliding windows of the features) to extract the localized frequency responses  $f_{n,lfs,1}^{m}$ . The size of sliding windows is  $Q\times Q$  ( $Q$  is set to 3 by default). Therefore, there are  $Q\times Q$  group frequency responses in  $f_{n,lfs,1}^{m}$ , where the first one represents the low-frequency responses and the last one represents the high-frequency responses. Then we count the mean of  $f_{n,lfs,1}^{m}$  across  $Q\times Q$  groups to get the mean frequency responses  $f_{n,lfs,2}^{m}$ . The  $f_{n,lfs,2}^{m}$  is a multi-channel spatial map that shares the same layout as  $f_{n}^{m}$ . The LFS adapter outputs  $f_{n,lfs}^{m}$  after  $f_{n,lfs,2}^{m}$  being passed through a convolutional layer followed by one  $GELU(\cdot)$  activation layer. The LFS adapter provides a localized aperture to detect detailed abnormal frequency distributions.
+
+# 3.5. Loss Functions
+
+Let  $S_{gt}$  denote the ground-truth image label where 1 represents the abnormal image and 0 represents the normal image. The loss for the anomaly classification is defined as follows:
+
+$$
+L _ {c l s} = - \frac {1}{N} \sum_ {N} ^ {n = 1} \left[ S _ {g t} \log \left(S _ {a, n}\right) + \left(1 - S _ {g t}\right) \log \left(1 - S _ {a, n}\right) \right] \tag {4}
+$$
+
+where  $\log$  denotes the log operation. Similarly, let  $M_{gt}$  denote the ground-truth pixel label of the input image, where 1 means abnormal pixel region and 0 means normal pixel region. The loss for the anomaly segmentation is defined as follows:
+
+$$
+L _ {\text {m a s k}} = \frac {1}{N} \sum_ {N} ^ {n = 1} [ \operatorname {F o c a l} (U p (M _ {a, n}), M _ {g t}) + D i c e (U p (M _ {a, n}), M _ {g t}) ] \tag {5}
+$$
+
+where  $Focal(\cdot, \cdot)$  and  $Dice(\cdot, \cdot)$  denote the focal loss [26] and dice loss [23], respectively. The operator  $Up(\cdot)$  represents the unsampling operation. During training, both the visual encoder and the text encoder of CLIP [33] are Frozen. Only the FFE adapters and LFS adapters are optimized by the loss function  $L_{total} = L_{cls} + L_{mask}$ .
+
+# 4. Experiments
+
+# 4.1. Datasets and Evaluation Metrics
+
+To verify the effectiveness of the proposed method FE-CLIP, we conduct comprehensive experiments across 10 real-world anomaly detection datasets, covering various industrial inspection scenarios and medical imaging domains. In industrial inspection, we use MVtec AD [4], VisA [54], MPDD [18], BTAD [30], DAGM [45], and DTD-Synthetic [3]. In medical imaging, we use colon polyp detection datasets CVC-ClinicDB [6] and Kvasir [19], brain tumor detection datasets BrainMRI [38] and Br35H [15].
+
+As for the evaluation metrics, following previous works [17, 52], we use Area Under the Receiver Operating Characteristic curve (AUROC). Additionally, Average Precision (AP) for Zero-Shot Anomaly Detection (ZSAD) and PRO [5] for Zeor-Shot Anomaly Segmentation (ZSAS) are also used to provide a more in-depth analysis of the results.
+
+# 4.2. Implementation Details
+
+We use the publicly available CLIP model (VITL/14@336px) as our backbone. Model parameters of CLIP are all frozen, and only the parameters of FFE adapters and LFS adapters are learnable. Following AnomalyCLIP [52], we fine-tune FE-CLIP using the test data of MVtec AD and evaluate the ZSAD performance on other datasets. As for MVtec AD, we fine-tune FE-CLIP on the test data of VisA. The proposed FE-CLIP is trained by 9 epochs with Adam optimizer. The learning rate is set to 5e-4 and the total batch size is 16. All experiments are conducted in PyTorch-1.13.0 with four NVIDIA RTX 3090 24GB GPUs. All experiment results are averaged under five runs. We report dataset-level results, which are averaged across their respective sub-datasets.
+
+# 4.3. Main Results
+
+ZSAD performance on diverse anomaly scenarios. Table 1 shows the ZSAD results of FE-CLIP with other competing methods over six industrial defect datasets and two medical domain datasets. As shown in Table 1, FE-CLIP can achieve higher AUROC and AP for the ZSAD task on most industrial inspection datasets and medical datasets, such as MVTec AD, DTD-Synthetic, and BrainMRI, when compared with other competing methods, such as WinCLIP [17], AnomalyCLIP [52] and AdaCLIP [8]. This shows that (1) the frequency information can benefit the ZSAD task
+
+<table><tr><td rowspan="2">Methods</td><td colspan="6">Industrial Defects</td><td colspan="2">Medical Anomalies</td></tr><tr><td>MVTec AD</td><td>VisA</td><td>MPDD</td><td>BTAD</td><td>DAGM</td><td>DTD-Synthetic</td><td>BrainMRI</td><td>Br35H</td></tr><tr><td>CLIP [33]</td><td>74.1 / 87.6</td><td>66.4 / 71.5</td><td>54.3 / 65.4</td><td>34.5 / 52.5</td><td>79.6 / 59.0</td><td>71.6 / 85.7</td><td>73.9 / 81.7</td><td>78.4 / 78.8</td></tr><tr><td>CoOp [50]</td><td>88.8 / 94.8</td><td>62.8 / 68.1</td><td>55.1 / 64.2</td><td>66.8 / 77.4</td><td>87.5 / 74.6</td><td>- / -</td><td>61.3 / 44.9</td><td>86.0 / 87.5</td></tr><tr><td>WinCLIP [17]</td><td>91.8 / 96.5</td><td>78.1 / 81.2</td><td>63.6 / 69.9</td><td>68.2 / 70.9</td><td>91.8 / 79.5</td><td>93.2 / 92.6</td><td>86.6 / 91.5</td><td>80.5 / 82.2</td></tr><tr><td>APRIL-GAN [9]</td><td>86.1 / 93.5</td><td>78.0 / 81.4</td><td>78.0 / 81.4</td><td>73.6 / 68.6</td><td>94.4 / 83.8</td><td>86.4 / 95.0</td><td>89.3 / 90.9</td><td>93.1 / 92.9</td></tr><tr><td>AnomalyCLIP [52]</td><td>91.5 / 96.2</td><td>82.1 / 85.4</td><td>77.0 / 82.0</td><td>88.3 / 87.3</td><td>97.5 / 92.3</td><td>93.5 / 97.0</td><td>90.3 / 92.2</td><td>94.6 / 94.7</td></tr><tr><td>AdaCLIP [8]</td><td>89.2 / -</td><td>85.8 / -</td><td>76.0 / -</td><td>88.6 / -</td><td>99.1 / -</td><td>95.5 / -</td><td>94.8 / -</td><td>97.7 / -</td></tr><tr><td>FE-CLIP</td><td>91.9 / 96.5</td><td>84.6 / 86.6</td><td>78.0 / 82.6</td><td>90.3 / 90.0</td><td>97.5 / 92.3</td><td>98.3 / 99.4</td><td>94.8 / 93.8</td><td>96.8 / 93.8</td></tr></table>
+
+Table 1. AUROC / AP results for Zero-Shot Anomaly Detection (ZSAD) task on eight real-world anomaly detection datasets. Best results are highlighted in red.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="6">Industrial Defects</td><td colspan="2">Medical Anomalies</td></tr><tr><td>MVTec AD</td><td>VisA</td><td>MPDD</td><td>BTAD</td><td>DAGM</td><td>DTD-Synthetic</td><td>CVC-ClinicDB</td><td>Kvasir</td></tr><tr><td>CLIP [33]</td><td>38.4 / 11.3</td><td>46.6 / 14.8</td><td>62.1, 33.0</td><td>30.6 / 4.4</td><td>30.6 / 4.4</td><td>33.9 / 12.5</td><td>47.5 / 18.9</td><td>44.6 / 17.7</td></tr><tr><td>CoOp [50]</td><td>33.3 / 6.7</td><td>24.2 / 3.8</td><td>15.4 / 2.3</td><td>15.4 / 2.3</td><td>17.5 / 2.1</td><td>- / -</td><td>17.5 / 2.1</td><td>44.1 / 3.5</td></tr><tr><td>WinCLIP [17]</td><td>85.1 / 64.6</td><td>79.6 / 56.8</td><td>79.6 / 56.8</td><td>72.7 / 27.3</td><td>87.6 / 65.7</td><td>83.9 / 57.8</td><td>51.2 / 13.8</td><td>69.7 / 24.5</td></tr><tr><td>APRIL-GAN [9]</td><td>87.6 / 84.0</td><td>94.2 / 86.8</td><td>94.1 / 83.2</td><td>60.8 / 25.0</td><td>82.4 / 66.2</td><td>95.3 / 86.9</td><td>80.5 / 60.7</td><td>75.0 / 36.2</td></tr><tr><td>AnomalyCLIP [52]</td><td>91.1 / 81.4</td><td>95.5 / 87.0</td><td>96.5 / 88.7</td><td>94.2 / 74.8</td><td>95.6 / 91.0</td><td>97.9 / 92.3</td><td>82.9 / 67.8</td><td>78.9 / 45.6</td></tr><tr><td>AdaCLIP [8]</td><td>88.7 / -</td><td>95.5 / -</td><td>96.1 / -</td><td>92.1 / -</td><td>91.5 / -</td><td>97.9 / -</td><td>84.4 / -</td><td>- / -</td></tr><tr><td>VCP-CLIP [32]</td><td>92.0 / 87.3</td><td>95.7 / 90.7</td><td>- / -</td><td>94.1 / 74.6</td><td>99.4 / 98.3</td><td>- / -</td><td>- / -</td><td>- / -</td></tr><tr><td>FE-CLIP</td><td>92.6 / 88.3</td><td>95.9 / 92.8</td><td>97.0 / 90.5</td><td>95.6 / 80.4</td><td>98.5 / 96.6</td><td>99.0 / 97.4</td><td>84.5 / 69.2</td><td>79.8 / 60.6</td></tr></table>
+
+Table 2. AUROC / PRO results for Zero-Shot Anomaly Segmentation (ZSAS) task on eight real-world anomaly detection datasets. Best results are highlighted in red. Note that the image-level medical AD datasets do not contain segmentation ground truth, so the pixel-level medical AD datasets are different from the image-level datasets.
+
+due to the superior performance of FE-CLIP, and (2) the frequency information helps FE-CLIP achieve good generalization across datasets from different domains.
+
+ZSAS performance on diverse anomaly scenarios. We show the ZSAS results of FE-CLIP with other competing methods over six industrial defect datasets and two medical domain datasets in Table 2. Table 2 shows that FE-CLIP achieves higher AUROC and PRO for the ZSAS task on almost all of the industrial inspection datasets and medical datasets, except for the DAGM dataset, when compared with other competing methods, such as WinCLIP [17], AnomalyCLIP [52], AdaCLIP [8] and VCP-CLIP [32]. This further demonstrates that (1) the frequency information can benefit the ZSAS task and (2) the frequency information helps FE-CLIP achieve good generalization across datasets from different domains.
+
+Discussion. We also note that the FE-CLIP can defeat almost all of the competing methods on the ZSAS task, while FE-CLIP only performs better than other methods over most of the datasets on ZSAD task. The reason may be that the frequency information can be directly injected into the patch tokens (i.e. the feature map used for the ZSAS task) through the FFE adapter and LFS adapter, while the frequency information can only be implicitly involved in the global class token (i.e. the feature vector used for the ZSAD task) from the patch tokens based on the self
+
+attention mechanism.
+
+Overall, the proposed FE-CLIP achieves superior zero-shot performance of detecting and segmenting anomalies in datasets of highly diverse class semantics from various defect inspection and medical imaging domains.
+
+# 4.4. Ablation Study
+
+The effectiveness of FFE and LFS We conduct ablation experiments on MVTec AD dataset and VisA dataset to validate the effectiveness of the proposed FFE adapter and LFS adapter. The results are shown in Table 3. The "CLIP  $[33] + \text{Conv Adapter}"$  means we add  $N$  conv adapters, where each of them consists of one convolutional layer followed by one  $GELU(\cdot)$  activation layer to keep the same learnable parameters with the LFS adapter into the visual encoder of CLIP. It can be concluded that both the FFE adapter and LFS adapter can achieve better performance than the conv adapter in MVTec AD dataset and VisA dataset across the ZSAD task and ZSAS task. This also shows that the frequency information can benefit the ZSAD task and ZSAS task. When combined the FFE adapter with the LFS adapter, the FE-CLIP achieves higher performance than the FFE adapter and LFS adapter. This demonstrates that the FFE adapter and LFS adapter can mine different but complementary frequency information to further boost the performance of model on the ZSAD and ZSAS tasks.
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">MVTec AD</td><td colspan="2">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td>CLIP[33] + Conv Adapter</td><td>89.0 / 85.1</td><td>87.8 / 94.5</td><td>94.8 / 89.8</td><td>82.3 / 83.5</td></tr><tr><td>CLIP[33] + FFE Adapter</td><td>90.6 / 86.2</td><td>90.0 / 95.4</td><td>95.1 / 91.3</td><td>83.3 / 85.0</td></tr><tr><td>CLIP[33] + LFS Adapter</td><td>91.5 / 87.1</td><td>90.6 / 95.7</td><td>95.5 / 91.8</td><td>83.9 / 85.7</td></tr><tr><td>FE-CLIP</td><td>92.6 / 88.3</td><td>91.9 / 96.5</td><td>95.9 / 92.8</td><td>84.6 / 86.6</td></tr></table>
+
+Table 3. Module ablation on the MVTec AD and the VisA datasets. The metric of Pixel-level is AUROC / PRO for ZSAS task, and the metric of Image-level is AUROC / AP for ZSAD task. Best results are highlighted in red.  
+
+<table><tr><td rowspan="2">Methods</td><td colspan="2">MVTec AD</td><td colspan="2">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td>FFT</td><td>92.8 / 88.3</td><td>92.0 / 96.2</td><td>95.5 / 93.0</td><td>84.1 / 86.8</td></tr><tr><td>DCT</td><td>92.6 / 88.3</td><td>91.9 / 96.5</td><td>95.9 / 92.8</td><td>84.6 / 86.6</td></tr></table>
+
+Table 4. Compared with using FFT to extract the frequency information in the FFE and LFS modules. The metric of Pixel-level is AUROC / PRO for ZSAS task, and the metric of Image-level is AUROC / AP for ZSAD task. Best results are highlighted in red.
+
+![](images/d6f13747d83cf192722772b460591f1b66576a4774d0cb3f468528e3c50c073d.jpg)
+
+![](images/19181edfeb38d426337f67abc575606f9e563ded07ed5ace7016579f93df73eb.jpg)  
+(a) Input Image
+
+![](images/919a719e30bba0e8afc8a81c79f7db0966c64af1ac9771609e1bf42911a92bc0.jpg)
+
+![](images/5131f2a5216916bc8b7df84d3705250873a75f7cc4c87f10966a1a98a7f44d48.jpg)  
+(b)  $f_{fe}^{m}$  from FFE Adapter
+
+![](images/2d4704cb6283321213688f49e1fcf5b6c8a811acb9be816fdb5fea86e934c725.jpg)
+
+![](images/61cd967df442bba1adb5db52b48daa51e95ab22d3049bf2ad4684b7194503f66.jpg)  
+(c)  $f_{N,lf_s}^m$  from LFS Adapter
+
+![](images/1aa7f5f88c38dc5ab12d1f85613f49cf78fae46ee08df725bb534ffe4d2c00ce.jpg)
+
+![](images/e7f85ba6cab1ad3ddce06249e23fbd3b3b9a739c90497e16a7968c548736d774.jpg)  
+(d)  $\hat{f}_N^m$  from equation (2)  
+Figure 5. The visualization of the learned frequency features. Please zoom in for a better view.
+
+![](images/8dacbcc1c5ca34bb5c9e58ea87bc5dfde841ac5e0ddc160659a58225a04e3901.jpg)
+
+![](images/d9d43740d3f9c1df4bb794417b67fcfcae4ceb31aa44f2b19cc30e03997fc358.jpg)  
+(e) Final prediction
+
+Would FFT work instead of DCT We attempt to use FFT to replace the DCT in the FFE and LFS modules to extract the frequency information. However, there are real values and imaginary values after FFT. To deal with this, the real values and imaginary values are separately processed and then combined to transform back to the spatial domain in the FFE module. As for the LFS module, the averaged local frequency statistics are computed from the real values and imaginary values, respectively, to get the averaged real local frequency statistics and the averaged imaginary local frequency statistics, and then they are summed to get the final averaged local frequency statistics. The results are shown in Table 4. This shows that using FFT achieves similar results with DCT, which means that the key is to inject the frequency information rather than the way of frequency transformation. We choose DCT since DCT is more convenient to extract frequency.
+
+# 4.5. Analysis
+
+Time cost. We report the inference time of APRIL-GAN, AnomalyCLIP, VCP-CLIP, AdaCLIP, and FE-CLIP with PyTorch-1.13.0 on one NVIDIA RTX 3090 24GB GPU. The inference time is 105, 120, 128, 160, and  $125\mathrm{ms}$ , respectively. FE-CLIP achieves a better trade-off between performance and speed.
+
+Visualization of learned frequency features. To show why frequency information is effective for the ZSAD task, we visualize the frequency-aware features from the last block of the visual encoder of CLIP as example, where the FFE and LFS adapters are added. As shown in Figure 5, both the features  $f_{N,ffe}^{m}$  from FFE adapter and the features  $f_{N,lfs}^{m}$  from LFS adapter highlight the abnormal region of images. By injecting the features  $f_{N,ffe}^{m}$  and  $f_{N,lfs}^{m}$  into the visual encoder of CLIP, the obtained features  $\hat{f}_N^m$  can successfully localize the main abnormal region, in favor of the final prediction of the model.
+
+When frequency information can be beneficial. Some properties of anomaly area, such as appearance defects, can be reflected based on its frequency information, since high-frequency components represent fine details (e.g. soft borders) that often exist in anomaly area. In these cases, These specific frequency patterns could be beneficial for anomaly detection. For example, as shown in Figure 1, the frequency statistics in the red region are different from the frequency statistics in the surrounding regions of the input abnormal image and the corresponding region of the normal image.
+
+Let's consider images of normal dumplings and images of squashed dumplings, where squashed dumplings are anomalies. In this case, if the squashed dumplings reveal the meat filling, the frequency of squashed dumplings could still stand out and frequency information could be helpful to detect anomalies. However, if the dumplings are squashed to be more like a meat pie without revealing the meat filling, the frequency of this squashed dumpling might not stand out and frequency information might not work well.
+
+We validate the FE-CLIP across different domains with 10 datasets of highly diverse class semantics from various industrial inspections and medical domains, and the results of FE-CLIP on the datasets of medical domains are trained
+
+<table><tr><td rowspan="2">Setup</td><td rowspan="2">Methods</td><td colspan="2">MVTec AD</td><td colspan="2">VisA</td></tr><tr><td>Pixel-level</td><td>Image-level</td><td>Pixel-level</td><td>Image-level</td></tr><tr><td rowspan="5">1-shot</td><td>PatchCore [37]</td><td>92.0 / 79.7</td><td>83.4 / 92.2</td><td>95.4 / 80.5</td><td>79.9 / 82.8</td></tr><tr><td>WinCLIP [17]</td><td>95.2 / 87.1</td><td>93.1 / 96.5</td><td>96.4 / 85.1</td><td>83.8 / 85.1</td></tr><tr><td>AnomalyGPT [14]</td><td>95.3 / -</td><td>94.1 / -</td><td>96.2 / -</td><td>87.4 / -</td></tr><tr><td>PromptAD [24]</td><td>95.9 / -</td><td>94.6 / -</td><td>96.7 / -</td><td>86.9 / -</td></tr><tr><td>FE-CLIP</td><td>96.1 / 90.9</td><td>95.6 / 98.1</td><td>97.9 / 93.9</td><td>88.7 / 90.5</td></tr><tr><td rowspan="6">2-shot</td><td>PatchCore [37]</td><td>93.3 / 82.3</td><td>86.3 / 93.8</td><td>96.1 / 82.6</td><td>81.6 / 84.8</td></tr><tr><td>WinCLIP [17]</td><td>96.0 / 88.4</td><td>94.4 / 97.0</td><td>96.8 / 86.2</td><td>84.6 / 85.8</td></tr><tr><td>AnomalyGPT [14]</td><td>95.6 / -</td><td>95.5 / -</td><td>96.4 / -</td><td>88.6 / -</td></tr><tr><td>PromptAD [24]</td><td>96.2 / -</td><td>95.7 / -</td><td>97.1 / -</td><td>88.3 / -</td></tr><tr><td>InCTRL [53]</td><td>- / -</td><td>94.0 / 96.9</td><td>- / -</td><td>85.8 / 87.7</td></tr><tr><td>FE-CLIP</td><td>96.5 / 91.5</td><td>96.2 / 98.3</td><td>98.2 / 94.3</td><td>90.3 / 91.6</td></tr><tr><td rowspan="6">4-shot</td><td>PatchCore [37]</td><td>94.3 / 84.3</td><td>88.8 / 94.5</td><td>96.8 / 84.9</td><td>85.3 / 87.5</td></tr><tr><td>WinCLIP [17]</td><td>96.2 / 89.0</td><td>95.2 / 97.3</td><td>97.2 / 87.6</td><td>87.3 / 88.8</td></tr><tr><td>AnomalyGPT [14]</td><td>96.2 / -</td><td>96.3 / -</td><td>96.7 / -</td><td>90.6 / -</td></tr><tr><td>PromptAD [24]</td><td>96.5 / -</td><td>96.6 / -</td><td>97.4 / -</td><td>89.1 / -</td></tr><tr><td>InCTRL [53]</td><td>- / -</td><td>94.5 / 97.2</td><td>- / -</td><td>87.7 / 90.2</td></tr><tr><td>FE-CLIP</td><td>96.7 / 91.7</td><td>96.6 / 98.4</td><td>98.4 / 95.0</td><td>90.7 / 91.9</td></tr></table>
+
+Table 5. Compared with other competing methods under few-normal-shot anomaly detection setting. The metric of Pixel-level is AUROC / PRO for the few-normal-shot anomaly segmentation task, and the metric of Image-level is AUROC / AP for the few-normal-shot anomaly detection task. Best results are highlighted in red.
+
+by the industrial inspection MVTec AD dataset, as shown in Table 1 and Table 2. The superior performance of FE-CLIP demonstrates that frequency information could be beneficial for many cases of anomaly detection, and the proposed FE-CLIP has good generalization across different domains.
+
+# 4.6. FE-CLIP with Few Normal Shots
+
+The performance of FE-CLIP can also be further boosted when equipped with few-shot normal images, just like WinCLIP [17] and AnomalyGPT [14]. We adopt the same way as AnomalyGPT to compute the anomaly segmentation map with few-shot normal images. In short words, we use the same visual encoder of FE-CLIP to extract intermediate patch-level features from normal images and store them in memory banks, then calculate the cosine similarity distance between each patch token of input image and its most similar counterpart in the memory banks to obtain the anomaly segmentation map  $S_{a,few\_shot}$ . Finally, we add the anomaly segmentation map  $S_{a}$  from the FE-CLIP model with  $S_{a,few\_shot}$  to get the final anomaly segmentation map, and add the anomaly score  $M_{a}$  from the FE-CLIP model with the max value of  $S_{a,few\_shot}$  to get the final anomaly score. Please refer to [14] for more technical details.
+
+We compare the FE-CLIP with other competing methods, such as AnomalyGPT [14], PromptAD [24], and InCTRL [53], under the few-shot anomaly detection setting. As shown in Table 5, the FE-CLIP outperforms all other com
+
+peting methods across different metrics, including AUROC and PRO metrics for the anomaly detection task, and AUROC and AP metrics for the anomaly segmentation task, on both datasets. The experiments under few-normal-shot setting further demonstrate the superiority of the FE-CLIP.
+
+# 5. Conclusion
+
+In this paper, we find that frequency information can benefit the ZSAD task. To this end, we propose FE-CLIP, which adds the proposed FFE and LFS adapters into the visual encoder of CLIP, to deeply mine the frequency patterns for the visual features. Extensive experiments on 10 datasets of highly diverse class semantics from various defect inspections and medical domains demonstrate that (1) the frequency information can benefit the ZSAD task, and (2) the frequency information can help the model have good generalization across datasets from different domains. We also conduct experiments under the few-normal-shot anomaly detection setting to further validate the superiority of the proposed FE-CLIP. We hope the community of anomaly detection will be aware of the effectiveness of frequency information from our work and explore more ways to utilize the frequency information for anomaly detection in the future.
+
+# Acknowledgements
+
+This work was supported by the Anhui Provincial Science and Technology Major Project (No. 2023z020006).
+
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2025/FED-PsyAU_ Privacy-Preserving Micro-Expression Recognition via Psychological AU Coordination and Dynamic Facial Motion Modeling/e27ad4a5-3106-4216-bcea-a95709cd5f65_content_list.json

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+        "type": "text",
+        "text": "FED-PsyAU: Privacy-Preserving Micro-Expression Recognition via Psychological AU Coordination and Dynamic Facial Motion Modeling",
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+        "text": "Jingting Li $^{1,2}$ , Yu Qian $^{1,3}$ , Lin Zhao $^{1,2}$ , Su-Jing Wang $^{*1,2}$",
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+        "text": "$^{1}$ State Key Laboratory of Cognitive Science and Mental Health, Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101, China",
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+        "type": "text",
+        "text": "$^{2}$ Department of Psychology, University of the Chinese Academy of Sciences, Beijing, 100049, China",
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+        "type": "text",
+        "text": "$^{3}$ School of Computer, Jiangsu University of Science and Technology, Zhenjiang, 212100, China",
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+        "text": "$^{\\dagger}$ Equal contribution, \\*Corresponding author (wangsujing@psych.ac.cn)",
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+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Micro-expressions (MEs) are brief, low-intensity, often localized facial expressions. They could reveal genuine emotions individuals may attempt to conceal, valuable in contexts like criminal interrogation and psychological counseling. However, ME recognition (MER) faces challenges, such as small sample sizes and subtle features, which hinder efficient modeling. Additionally, real-world applications encounter ME data privacy issues, leaving the task of enhancing recognition across settings under privacy constraints largely unexplored. To address these issues, we propose a FED-PsyAU research framework. We begin with a psychological study on the coordination of upper and lower facial action units (AUs) to provide structured prior knowledge of facial muscle dynamics. We then develop a DPK-GAT network that combines these psychological priors with statistical AU patterns, enabling hierarchical learning of facial motion features from regional to global levels, effectively enhancing MER performance. Additionally, our federated learning (FL) framework advances MER capabilities across multiple clients without data sharing, preserving privacy and alleviating the limited-sample issue for each client. Extensive experiments on commonly-used ME databases demonstrate the effectiveness of our approach. Our implementation is publicly available at https://github.com/MELABIPCAS/FED-PsyAU.git.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Micro-expressions (MEs) [9], resulting from conflicts between voluntary and involuntary expressions, reveal true emotions, making them valuable in non-contact emotion detection applications like criminal interrogation and psychological counseling. MEs are characterized by their brief duration, low intensity, localized occurrence, and occasional",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "asymmetry [10]. These traits not only restrict large-scale data collection and annotation but also make it challenging for deep learning networks to effectively model their motion characteristics. Some methods focus on regions of interest (ROIs) [4, 21, 31, 49], while others utilize attention mechanisms [3, 14, 33] and transformer-based architectures [24, 50, 57] to capture salient features. Meanwhile, MEs are often complex manifestations involving the combination of multiple AUs. In contrast, individual action units (AUs) correspond to specific, anatomically-based facial muscle movements. Focusing on AUs allows us to model more fundamental and consistent facial appearance changes. Certain approaches use AU labels to construct adjacency matrices for graph convolutional networks (GCNs) [24, 39]. Yet, to the best of our knowledge, these methods often apply AU annotations directly without fully exploiting the anatomical structure and coordinated AU dynamics, limiting the network's understanding on ME.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To address these challenges, we leverage the theory that distinct neural pathways control upper and lower facial movements, resulting in two different motion patterns. Based on this, we conduct a psychological study to investigate upper/lower facial AU coordination, providing crucial prior knowledge on structural motion relationships underpinning MEs. Using both psychological priors and data-driven AU patterns, we design a Graph Attention Network (GAT) [47] based on dynamic prior knowledge, applied separately to the upper and lower regions. A final global GAT captures the topological relationships of muscle movements across the face. The resulting feature, combined with full-face optical flow (OF), is input into a subsequent dual-stream network, effectively integrating structural and dynamic information to enhance ME recognition (MER).",
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+    {
+        "type": "text",
+        "text": "Besides, as mentioned earlier, although MEs have valuable applications in many privacy-sensitive contexts, the sensitivity of biometric data makes it impractical to aggre",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV 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_number",
+        "text": "14453",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "gate ME data across clients for training. Meanwhile, the sample size in a single client is often insufficient to train a robust model. Yet, the challenge of enhancing MER performance across diverse clients while preserving privacy remains largely unexplored. To address this, we adopt a federated learning (FL) framework, improving performance by merging and updating model parameters across clients without exchanging local data. This approach preserves data privacy and supports the MER practical deployment.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Overall, our work leverages psychological and data-driven priors to enhance the network's learning of structured ME motion patterns, particularly in limited-sample conditions. Additionally, we introduce FL to advance MER in real-world scenarios. The contributions of this paper are:",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- We conduct a psychological experiment to derive AU coordination between the upper and lower facial regions, providing structural priors for ME and facial expression analysis in computer vision.",
+            "- We design a local-to-global GAT network that integrates psychological priors and data-driven AU patterns in the upper and lower facial regions, improving the network's ability to learn both local and global structural facial dynamics. This feature, combined with global OF feature in a dual-stream network, enhances MER performance.",
+            "- We employ FL in MER to improve data privacy and overcome small sample size challenges by aggregating features from distributed data-protected sources."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Micro-expression Recognition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In recent years, MER has gained increasing attention from computer vision researchers. Traditional machine learning methods primarily rely on handcrafted feature extraction. For instance, Local Binary Pattern (LBP) [43], effectively utilizes local texture features, has inspired various improvements [18, 49]. Furthermore, OF [26] has been explored for capturing object motion. Liu et al. [38] developed the Main Directional Mean OF (MDMO) method by aligning faces in the OF domain, while Liong et al. [34] added optical strain features for MER. However, traditional approaches depend heavily on manually crafted features, limiting both accuracy and generalizability. Meanwhile, deep learning methods, with robust feature extraction capabilities, can automatically learn multi-level representations to capture subtle ME changes. The availability of several spontaneous ME databases, such as CASME II [51], SAMM [6], CAS(ME) $^{3}$  [27], DFME [59] and others [1, 30, 32, 44, 54], has accelerated deep learning advancements in MER. Inspired by Liong et al.'s work [35] on sequence redundancy, many studies [4, 13, 50] now use keyframes (onset and apex) as input, reducing model parameters while achieving excellent results.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite advancements in preprocessing and feature extraction, deep learning alone has yet to achieve high MER accuracy. As MEs stem from physiological muscle activity, incorporating prior knowledge offers meaningful context. FACS [10], which defines expressions through AUs, provides a basic theoretical framework for MER. Recent studies explore AU-ME relationships to enhance MER performance. Lei et al. [24] applied GCN [21] to model AU co-occurrences, especially around the eyebrow and mouth regions. Xie et al. [53] introduced an AU-assisted GCN, with modules for AU feature extraction and ME image generation. Wang et al. [48] used transformers to learn dynamic AU adjacency, boosting model generalization. These networks typically rely on AU labels from databases, without fully integrating structured facial muscle movements, AU interrelations, or their links to expressions. In this work, we refine structured ME feature extraction using a local-to-global GAT network, which integrates priors on facial AU coordination from psychological experiments with data-driven movement patterns.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2. Federated Learning",
+        "text_level": 1,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To assess MER across databases, ME Grand Challenge (MEGC) 2018 [56] introduced the Holdout-database Evaluation and Composite Database Evaluation tasks, utilizing the CASME II and SAMM databases. MEGC 2019 [45] expanded the CDE task to include the SMIC databases. While research on MEs predominantly utilizes these public datasets, existing methodologies do not address the privacy concerns that arise in practical applications.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "FL [41] could addresses ME data scarcity and privacy concerns through collaborative training. It includes two main phases: local training and global aggregation. Many existing FL works for expressions, while insightful, are often not open-source or use highly customized frameworks (e.g., non-random client data allocation [12], specialized parameter aggregation [11]) making standard methods more suitable for implementation and comparisons in our study. For instance, McMahan et al. [41] proposed FedAvg, a basic aggregation method that uses weighted averaging based on each client's data volume. Li et al. [28] introduced FedProx by adding a regularization term to the client loss function, aligning updates more closely with the global model. However, the one-global model-fits-all approach ignores client data diversity. To solve this, our approach extends FedProx by distributing a personalized global model to each client.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Psychological Study on AU Incoordination",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "This study employed a behavioral experiment to investigate individuals' cognitive responses to AU incoordination in the upper and lower facial regions.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "14454",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/d0be976c39a1a2b1350002c8024a300f5603459bf08e9cad7c5424168a69b569.jpg",
+        "image_caption": [
+            "(a) AU  $4 + 9$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            96,
+            88,
+            161,
+            155
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6a6758a36e511f40688f624788965fb5f708c901579da499564d7275e17f1144.jpg",
+        "image_caption": [
+            "(b) AU 6+12"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            200,
+            88,
+            267,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/75bb2e5693552c09e2c1a618dc3ae130c5010e3798a28cb5539630fc5fb61851.jpg",
+        "image_caption": [
+            "(c) AU 4+12",
+            "Figure 1. Examples of AU composite images. (a) and (b) are coordinated composites. (c) and (d) are uncoordinated composites."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            305,
+            88,
+            372,
+            155
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/c488cf12372e861cf51dcda4ad2396759b6b73ada71b35e9bbaf1e1974f014a9.jpg",
+        "image_caption": [
+            "(d) AU 6+15"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            411,
+            88,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The study included 30 college participants (20 female, Mean= 22.22 years), a sample size considered adequate for statistical reliability under the Central Limit Theorem [23]. All procedures followed the Declaration of Helsinki and were approved by the institutional review board of the Institute of Psychology, Chinese Academy of Sciences.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This behavioral experiment employed a within-subjects design. The independent variable was the type of AU composite image (coordinated vs. uncoordinated AU composites), as shown in Fig. 1. The face images were segmented anatomically. The dividing line was consistently present in all stimuli, serving as a control variable and would not influence the experiment's outcomes. To control for individual facial differences in emotion recognition, the original images used for composites were sourced from the same person [10]. Seventy-two composite images were generated from upper and lower facial AUs across six basic emotions, with each emotion represented by six coordinated and six uncoordinated expressions.",
+        "bbox": [
+            89,
+            329,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The dependent variables are accuracy rates and scores. Specifically, participants made two judgments for each composite image: whether it was coordinated or uncoordinated, and the degree of coordination or incoordination.",
+        "bbox": [
+            89,
+            526,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Statistical analysis from this study showed that participants were significantly more accurate in recognizing coordinated AU composite images than uncoordinated ones (Please see Supplementary Materials (Suppl.) for more experimental details and statistical results). The study further highlighted specific AU combinations, such as AU4 and AU12, that participants quickly identified as uncoordinated, whereas combinations like AU6 and AU12 were rapidly recognized as coordinated. This suggests that these uncoordinated AU pairings may inherently convey emotional incoordination. Besides, the coordination patterns between specific AUs reveal systematic facial action structures. These patterns help the network distinguish both coordinated and uncoordinated facial movements, thus enhancing its ability to identify ME features more effectively.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. Our Proposed FED-PsyAU Framework",
+        "text_level": 1,
+        "bbox": [
+            89,
+            829,
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+            847
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We propose the FED-PsyAU framework (Fig. 2), which embeds a psychology-driven MER model within a federated aggregation module. The model features a hierarchi",
+        "bbox": [
+            89,
+            854,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "cal structure that learns from local ROIs to AU groups and finally to global facial regions, capturing dynamic topology while minimizing redundancy. It leverages a multiscale InceptionNet to extract and fuse global OF with structural facial features. The federated module enables privacy-preserving collaborative training to boost MER performance on each client.",
+        "bbox": [
+            511,
+            90,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Localized ROI Modeling",
+        "text_level": 1,
+        "bbox": [
+            511,
+            217,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Since MEs are manifested by muscle movements in key facial regions (e.g., eyes, mouth, nose) [10], we refine the standard 68 landmarks from Dlib [20] to precisely capture these changes. As shown in Fig. 3, we discard 10 less informative outer contour landmarks and add 7 new midpoints to better track movements in the cheek and eyebrow regions, resulting in a final set of 65 keypoints.",
+        "bbox": [
+            511,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Then, onset-apex OF inputs  $(128 \\times 128$  pixels) are cropped into 65 ROIs, each measuring  $5 \\times 5$  pixels, centered on selected facial landmarks  $\\mathbf{p}_k = (x_k, y_k)$ , where  $k \\in 1, 2, \\ldots, 65$ , denotes the landmark index. To enhance robustness to apex annotation, we also compute OF using a small window of frames around the apex. The ROI features input to the Local ROI Feature Extractor (LFE), denoted as  $\\Theta_k$ , contain the horizontal and vertical components of OF and optical strain. The LFE module consists of three convolutional layers, each followed by batch normalization and ReLU activation. All kernel sizes were  $3 \\times 3$ . The output channels in the first two layers increase from 32 to 64, while the final layer outputs 3 channels. This design helps the LFE capture complex local patterns, with the output features referred to as  $\\Phi_k = \\mathrm{LFE}(\\Theta_k)$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Inspired by Vision Transformer [8], we use a Spatial Structure Encoder (SSE), i.e., Transformer Encoder with three attention heads to capture diverse dependencies among ROIs, as MEs result from coordinated muscle movements across multiple areas. Precisely, we convert  $\\Phi_k$ , into a token. To retain the positional information of the facial landmarks, a positional embedding  $E_{k}$  is added based on the landmark index to each token, yielding  $X_{k} = \\Phi_{k} + E_{k}$ . We add the output of the three head attention module to the input feature  $X_{k}$ , and then normalize the result using LayerNorm. Finally, after passing through a feed-forward neural network and applying LayerNorm, the final output representation is obtained as  $Z_{k}\\in \\mathbb{R}^{3\\times 5\\times 5}$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.2. Relationship Modeling among AU Features",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our proposed Relationship Modeling among AU Features (AFR) module consists of two components: an AU Feature Extractor (AFE) to derive features from AU-specific facial regions, and a GAT-structure to model the topological relationships between these AUs.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "14455",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/32a7893b63bbeb533929b4b91016e08a888aebebc0656d7b79a2840f881c5d6b.jpg",
+        "image_caption": [
+            "Figure 2. The pipeline of our proposed FED-PsyAU framework, including MER network (black block) and the Federated Aggregation (FA) module (orange block). In MER network, the LRM module consists of the local ROI feature extractor (LFE) and the spatial structure encoder (SSE), which preserves spatial structure information while efficiently extracting ROI features; the AFR module includes the AU feature extractor (AFE) and the dynamic prior knowledge-based graph attention network (DPK-GAT) for effective AU feature extraction and capturing AU dynamic relationships, the DSI module use a dual-stream structure to capture multi-scale facial muscle topology and motion information for MER. Then, the FA module integrates the MER network into the FL framework."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/6fff2cada31386a5b011df13bd87f2c5f07231243518331d7ca049c484b4cd7c.jpg",
+        "image_caption": [
+            "Figure 3. ROI grouping strategy for AU. OF features from each ROI are processed through LFE and SSE to yield high-dimensional representations. ROIs are then grouped by AU movement patterns to create inputs for AFEs, ultimately producing AU node features for the GAT network."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2.1. AU Feature Extractor",
+        "text_level": 1,
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "MEs involve dynamic, coordinated interactions across multiple regions [10] and are characterized by subtle movements that differ from typical macro-expressions. Therefore, as shown in Fig. 3, when grouping ROIs for the AFE module, the AU selection and regionalization are based on: 1) AU frequency in MEs; 2) Grouping by primary/secondary muscle activation areas [7]. Notably, not all AUs employed in Section 3 are applied to MER. We specifically retain only the 12 AUs exhibiting the highest relevance to ME dynamics, as listed in Tab. 1. Detailed occurrences are provided in the Suppl.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The first step we construct in AFE is Group Squeeze and",
+        "bbox": [
+            109,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/4434210dc95c750de1434423c9b2d3c7ecffecf56f8da8459c219c8ad5f1d05b.jpg",
+        "table_caption": [
+            "Table 1. Selected AUs and Corresponding Regions (Primary and Secondary/ Coordinate).  $g$ ,  $N_g$  and  $N_{g\\_AU}$  represent ROI Group index, corresponding ROI number and AU amount."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>g</td><td>AU</td><td>Primary</td><td>Secondary/ Coordinate</td><td>Ng</td><td>Ng-AU</td></tr><tr><td>1</td><td>1,2,4</td><td>Eyebrows</td><td>Eyes</td><td>23</td><td>3</td></tr><tr><td>2</td><td>5,6,7</td><td>Eyes</td><td>Eyebrows, Cheeks, Mouth</td><td>48</td><td>3</td></tr><tr><td>3</td><td>9,10</td><td>Nose, Cheeks</td><td>Mouth, Chin</td><td>38</td><td>2</td></tr><tr><td>4</td><td>12,14,15,17</td><td>Mouth</td><td>Eyes, Eyebrows, Nose</td><td>52</td><td>4</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Excitation (GSE). It computes the attention for each group of AUs (ROI group), which makes the model pay more attention to the critical ROIs. Specifically, for each ROI group input  $R_{g} = \\{Z_{1}, Z_{2}, \\ldots, Z_{N_{g}}\\}$ ,  $g \\in \\{1, 2, 3, 4\\}$ , the GSE module performs global average pooling on each ROI and computes channel importance through a fully connected (FC) layer. The original features are then preserved through residual concatenation:",
+        "bbox": [
+            511,
+            537,
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+            657
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf _ {\\mathrm {G S E}} \\left(R _ {g}\\right) = \\left\\{W _ {k} ^ {\\text {a t t}} \\odot Z _ {k} + Z _ {k} \\mid Z _ {k} \\in R _ {g} \\right\\} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            562,
+            667,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{k}^{att}$  is the attention weight for each group of ROI,  $\\odot$  denotes element-wise multiplication along the channel dimension of  $Z_{k}$ . Next,  $f_{\\mathrm{GSE}}(R_g)$  undergoes further feature extraction, reducing from  $N_{g}$  composite features to  $N_{g\\_AU}$  representative AU features, yielding the output feature  $F_{g\\_AU}$ . Precisely, the process comprises two convolutional layers: a  $3 \\times 3$  layer that doubles the input dimensions and a  $1 \\times 1$  layer that restores them to the original size. Both layers are followed by Batch Normalization and ReLU activation for improved stability and representation.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2.2. AU Relationship Modeling",
+        "text_level": 1,
+        "bbox": [
+            511,
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+            867
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Prior Knowledge: To model AU dynamic relationships, we integrate two forms of prior knowledge: an \"intrinsic\" prior",
+        "bbox": [
+            511,
+            869,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "14456",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "from psychological principles and an \"extrinsic\" prior from data-driven patterns. The intrinsic prior, derived from our psychological findings on AU coordination (Sec. 3), provides structural guidance by defining the initial GAT adjacency matrix  $A$ . The extrinsic prior, based on statistical AU co-occurrence patterns in the data, offers data-driven refinement that theoretical models may overlook. This extrinsic prior forms a prior attention matrix  $D$  to guide weight allocation among AU nodes. By fusing this foundational psychological structure with real-world dynamics, our model achieves superior adaptability and generalization (see Suppl. for matrix details).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Facial Segmentation: As presented in Sec. 3, the upper and lower facial regions, controlled by different neural pathways, exhibit distinct muscle movement patterns. AUs and their associated primary muscles in the upper and lower face can exhibit coordination (potential co-occurrence) or lack of coordination (infrequent simultaneous appearance). Leveraging these intra- and inter-regional interactions, we model AU relationships for the upper face, lower face, and whole face. Consistent with the experimental setup in Sec. 3, we segment the face into upper and lower parts based on the orbicularis oculi muscle. Specifically, following the primary occurrence regions of 12 listed AUs, the AUs in the first two groups from Tab. 1 are classified as upper face AUs, while those in the last two groups are classified as lower face AUs.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {A U} ^ {U p p e r} = F _ {1 \\_ A U} \\cup F _ {2 \\_ A U}, F _ {A U} ^ {L o w e r} = F _ {3 \\_ A U} \\cup F _ {4 \\_ A U} (2)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We input the AU features from the upper and lower face:  $F_{AU}^{Upper}$ ,  $F_{AU}^{Lower}$  into our proposed Dynamic Prior Knowledge GATs (DPK-GATs) in parallel (Details are presented in the next part of this subsection). These networks use psychology prior knowledge to build AU adjacency relationships and data-driven priors to guide attention learning, producing outputs  $h^{Upper}$  and  $h^{Lower}$ , which are combined into  $h^{Local}$  for the next stage.",
+        "bbox": [
+            89,
+            530,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the whole-face DPK-GAT, we construct the network similarly but set adjacency values within the same region to zero, ignoring intra-regional AU relationships. By learning cross-regional topological structures and statistical patterns, we obtain global AU relationship features, denoted as  $h^{Global}$ , as illustrated in Fig. 4.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "DPK-GAT: We model dynamic AU node relationships combing GAT and the prior knowledge. In particular, for the input feature belonging to  $\\{F_{AU}^{Upper}, F_{AU}^{Lower}, h^{Local}\\}$ , a linear mapping projects it to a higher-dimensional space as  $f$ . The similarity score  $e_{ij}$  between AU nodes  $i$  and  $j$ , is calculated using the attention weight vector  $\\vec{a}$  and concatenated node features  $f_{i}$  and  $f_{j}$ :",
+        "bbox": [
+            89,
+            743,
+            482,
+            851
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ne _ {i j} = \\left\\{ \\begin{array}{l l} \\text {L e a k y R e L U} \\left(\\tilde {a} ^ {T} [ f _ {i} | | f _ {j} ]\\right), & \\text {i f} A _ {i j} > 0 \\\\ - \\infty , & \\text {i f} A _ {i j} = 0 \\end{array} \\right. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            863,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/3934cbe5af16a98d999e3491078e08adc38f6f6edc979040b58195a36422df20.jpg",
+        "image_caption": [
+            "Figure 4. DPK-GAT from facial segmentations to global face. First, intra-regional AU node relationships are learned within the upper and lower facial regions. Second, cross-regional relationships are modeled to integrate interactions between these regions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here, only neighboring nodes defined by the psychology-derived adjacency matrix  $A$  are considered.",
+        "bbox": [
+            511,
+            287,
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+            318
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The final attention  $\\alpha_{ij}$  is calculated by combining the data-driven prior attention  $D_{ij}$  and the self-attention, obtained by the softmax operation applied to  $e_{ij}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i j} = (1 - \\beta) \\cdot \\operatorname {s o f t m a x} \\left(e _ {i j}\\right) + \\beta \\cdot D _ {i j} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            576,
+            377,
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+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where,  $\\beta$  is the dynamic prior attention weight, updated based on the training rounds. Along with a residual concatenation, the final node representation  $h_i$  is aggregated as:",
+        "bbox": [
+            511,
+            404,
+            903,
+            463
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh _ {i} = \\operatorname {E L U} \\left(\\sum_ {j \\in \\mathcal {N} (i)} \\alpha_ {i j} \\cdot f _ {j}\\right) + f _ {i} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            593,
+            464,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{N}(i)$  denotes the neighboring nodes of  $i$ . In our implementation, we employ three attention heads and a two-layer structure, enabling the extraction of complex AU dependencies.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Dual-Stream-InceptionNet",
+        "text_level": 1,
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Muscle movements vary widely across facial regions, making multi-scale information essential for the MER task. InceptionNet's core concept is leveraging parallel convolutional kernels to extract multi-scale features, enhancing the network's ability to capture fine details and overall structure [46]. We build on this by using a dual-stream InceptionNet as the ME feature extractor. One stream processes the AU relationship features  $h^{Global}$ , while the other handles global OF features  $\\Theta$ . This dual-stream design allows the model to capture the topological relationships of facial muscles through AUs and holistic motion via OF. The output tensors from both streams are flattened, concatenated, and fed into a FC layer for ME prediction.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.4. Federated Aggregation",
+        "text_level": 1,
+        "bbox": [
+            511,
+            787,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Traditional centralized learning consolidates all data on a single server, enhancing model accuracy and generalization but neglecting privacy concerns in MER. FL could address this by training models locally and sharing only parameters, protecting data privacy and retaining each client's unique data characteristics.",
+        "bbox": [
+            511,
+            809,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "14457",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "FedProx [29] is a FL approach designed to address data heterogeneity among clients. It incorporates proximal terms during model aggregation to balance global and client-local learning, improving both performance and convergence speed. We extend FedProx by altering the server's processing and distribution strategy during aggregation, which we call Personalized FedProx (P-FedProx). Specifically, P-FedProx initializes each client's model  $W_{i}^{t}$  in round  $t$  by combining its previous model  $\\mathring{W}_{i}^{t-1}$  with models from other clients  $\\mathring{W}_{j}^{t-1}$ .",
+        "bbox": [
+            89,
+            90,
+            483,
+            238
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {i} ^ {t} = \\theta \\cdot \\mathring {W} _ {i} ^ {t - 1} + \\sum_ {\\substack {j = 1 \\\\ j \\neq i}} ^ {n} \\omega_ {j} \\cdot \\mathring {W} _ {j} ^ {t - 1}, \\text {where} \\sum_ {\\substack {j = 1 \\\\ j \\neq i}} ^ {n} \\omega_ {j} = 1 - \\theta \\tag{6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            246,
+            483,
+            272
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where weight  $\\omega_{j}$  is proportional to  $j$ th client's data size. For  $i$ th client,  $\\theta$  is set to 0.9 (optimal experimental result, see more detail in the Suppl.)",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.5. Loss Function",
+        "text_level": 1,
+        "bbox": [
+            89,
+            332,
+            235,
+            347
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "AU Prediction Loss: To enhance MER, our network models the topological relationships and statistical patterns of AUs, making AU prediction an auxiliary task. The prediction is utilized in two stages: one enhances the AU feature extraction performance of the AFE module, and the other improves the GAT network's ability to learn AU topological structures. AU recognition is formulated as a multi-label classification problem, with the Binary Cross-Entropy Loss for each AU label defined as:",
+        "bbox": [
+            89,
+            353,
+            483,
+            479
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\mathrm {A}} = \\frac {\\sum_ {j = 1} ^ {M} \\left[ y _ {j} \\cdot \\log \\left(\\sigma \\left(\\hat {y} _ {j}\\right)\\right) + \\left(1 - y _ {j}\\right) \\cdot \\log \\left(1 - \\sigma \\left(\\hat {y} _ {j}\\right)\\right) \\right]}{- M} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            484,
+            483,
+            516
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $M$  is the total number of AUs,  $y_{j}$ ,  $\\sigma (\\hat{y}_j)$  and  $\\hat{y}_j$  represent respectively the ground truth label (0 or 1), the logit output and prediction after applying the sigmoid function for the  $j$ -th AU. The loss function is consistent for both stages, i.e.,  $L_{\\mathrm{A}}^{\\mathrm{AFE}}$  and  $L_{\\mathrm{A}}^{\\mathrm{GAT}}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MER Loss: The Cross-Entropy Loss function is utilized for emotion classification. Thus, our overall MER loss is composed as follows:",
+        "bbox": [
+            89,
+            599,
+            483,
+            642
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {M E R}} = \\alpha_ {1} \\cdot \\left(- \\sum_ {i = 1} ^ {N} y _ {i} \\cdot \\log (\\hat {y} _ {i})\\right) + \\alpha_ {2} \\cdot L _ {\\mathrm {A}} ^ {\\mathrm {A F E}} + \\alpha_ {3} \\cdot L _ {\\mathrm {A}} ^ {\\mathrm {G A T}} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            99,
+            648,
+            482,
+            667
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where,  $N$  represents the number of classes,  $y_{i}$  and  $\\hat{y}_i$  are the one-hot encoded ground truth label and the predicted probability for class  $i$ ,  $\\alpha_{1}$ ,  $\\alpha_{2}$  and  $\\alpha_{3}$  are hyperparameters, set to 0.2, 0.8, and 0.8 to prioritize MER loss while balancing AU recognition (See parameter analysis in Suppl.).",
+        "bbox": [
+            89,
+            674,
+            482,
+            750
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Federated Loss: During federated training, the local client's loss function includes the MER loss  $L_{\\mathrm{MER}}$  and a proximal term:",
+        "bbox": [
+            89,
+            750,
+            483,
+            796
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\mathrm {F L}} = L _ {\\mathrm {M E R}} + \\frac {\\alpha_ {4}}{2} \\cdot \\left\\| W - W _ {t} \\right\\| ^ {2} \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            832
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{t}$  denotes the global model in the server's  $t$ -th round of distribution, and  $W$  represents the current model of the client.  $\\alpha_{4}$  is the hyperparameter for the weight of the proximal term.",
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+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1. Configuration",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Databases: We use two recently published large scale and challenging ME databases: CAS(ME) $^3$  and DFME. CAS(ME) $^3$ -Part A offers 860 samples from 100 participants. DFME includes three subsets with (participants, samples): A (72,1,118), B (92,969), C (492,5,439). For Apex-first-frame scenario, we compute the OF between the apex and mid-frame towards the offset.",
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+    {
+        "type": "text",
+        "text": "Pre-training: To enhance the model's ability to perceive facial motion patterns, we first pre-trained the AU module (LRM+AFR) on the DISFA [40] and CK [19] datasets. The effect of this pre-training is detailed in the Suppl.",
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+        "type": "text",
+        "text": "MER Experiment Settings: The evaluation follows standard protocols on two datasets. On  $\\mathrm{CAS(ME)^3}$ , we perform 3-class classification (positive, negative, surprised) [45] with Leave-One-Subject-Out (LOSO) validation. On DFME, we conduct 7-class classification (Happiness, Surprise, Disgust, Sadness, Anger, Fear, and Contempt) using scale-adapted 10-fold cross-validation [59]. To address class imbalance, performance is measured by the UF1 and UAR. Experiments were implemented in PyTorch 1.13.0 and run on five NVIDIA GeForce RTX 4090 GPUs.",
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+    {
+        "type": "text",
+        "text": "Federated Experiment Settings: The DFME and  $\\mathrm{CAS(ME)^3}$  datasets are randomly split into 5 and 2 local clients, respectively, with each client assigned an equal number of subjects. However, variations in microexpression (ME) counts per subject result in differing ME data distributions and quantities across clients, mirroring real-world data heterogeneity (See detailed data distributions in the Suppl.). Traditional LOSO and k-fold cross-validation can leak training samples in a federated setting, so we employ a random partition strategy with  $70\\%$  of samples for training and  $30\\%$  for testing, averaging results over 10 tests to minimize randomness. Furthermore, we assume an ideal FL scenario with no client dropouts and equal local updates per client. In FedAvg [41] and FedProx [28], the server assigns an identical global model to all clients each round; differently, FedProx adds a proximal term to reduce model bias in local training. Our P-FedProx enhances this by assigning tailored initial models, with  $90\\%$  ( $\\theta$ ) weight on each client's own model and  $10\\%$  on others'. Additionally, we compare against recent personalized FL methods: FedRep [5] uses shared representations with personalized heads, ELLP [61] employs parameter decoupling with Fisher Information weighting, and FedAS [55] applies parameter alignment and client synchronization. Unlike these approaches requiring architectural changes or complex procedures, P-FedProx achieves personalization through simple weighted initialization.",
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+    },
+    {
+        "type": "page_number",
+        "text": "14458",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/502801362957141a992ddc3c6071f9230c83567e960670e5400bcdd202050902.jpg",
+        "table_caption": [
+            "Table 2. SOTA methods comparison on DFME and CAS(ME)  ${}^{3}$"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Category</td><td rowspan=\"2\">Method</td><td rowspan=\"2\">Year</td><td colspan=\"2\">DFME</td><td colspan=\"2\">CAS(ME)3</td></tr><tr><td>UF1</td><td>UAR</td><td>UF1</td><td>UAR</td></tr><tr><td rowspan=\"2\">3D-CNN</td><td>I3D [2]</td><td>2017</td><td>0.2923</td><td>0.3058</td><td>-</td><td>-</td></tr><tr><td>R3D [17]</td><td>2018</td><td>0.2164</td><td>0.2313</td><td>-</td><td>-</td></tr><tr><td rowspan=\"2\">Hand-crafted</td><td>LBP-TOP [49]</td><td>2014</td><td>0.2336</td><td>0.2653</td><td>-</td><td>-</td></tr><tr><td>MDMO [37]</td><td>2015</td><td>0.2489</td><td>0.2939</td><td>-</td><td>-</td></tr><tr><td rowspan=\"13\">Deep Learning</td><td>OFF-ApexNet [15]</td><td>2019</td><td>0.2386</td><td>0.2806</td><td>-</td><td>-</td></tr><tr><td>AlexNet [22]</td><td>2012</td><td>-</td><td>-</td><td>0.2570</td><td>0.2634</td></tr><tr><td>STSTNet [36]</td><td>2019</td><td>0.2714</td><td>0.3108</td><td>0.3795</td><td>0.3792</td></tr><tr><td>RCN-A [52]</td><td>2020</td><td>0.2751</td><td>0.3123</td><td>0.3928</td><td>0.3893</td></tr><tr><td>MERSiam [58]</td><td>2021</td><td>0.3184</td><td>0.3532</td><td>0.3184</td><td>0.3532</td></tr><tr><td>FGRL [24]</td><td>2021</td><td>0.0736</td><td>0.1429</td><td>0.3333</td><td>0.2636</td></tr><tr><td>FR [24, 60]</td><td>2022</td><td>0.3559</td><td>0.3814</td><td>0.3493</td><td>0.3413</td></tr><tr><td>MMNet [25]</td><td>2022</td><td>0.2649</td><td>0.2776</td><td>0.3706</td><td>0.3646</td></tr><tr><td>BDCNN [4]</td><td>2022</td><td>0.2975</td><td>0.3314</td><td>0.5050</td><td>0.5164</td></tr><tr><td>Micro-BERT [42]</td><td>2023</td><td>-</td><td>-</td><td>0.5604</td><td>0.6125</td></tr><tr><td>HTNet [50]</td><td>2024</td><td>0.3243</td><td>0.3368</td><td>0.5767</td><td>0.5415</td></tr><tr><td>HSTA [16]</td><td>2024</td><td>-</td><td>-</td><td>0.593</td><td>0.618</td></tr><tr><td>Ours</td><td>-</td><td>0.3853</td><td>0.3978</td><td>0.6221</td><td>0.6226</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5.2. Comparison to State-of-the-art Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tab. 2 list the SOTA comparisons on DFME and CAS(ME) $^3$ . The confusion matrices are shown in the Suppl.",
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+    },
+    {
+        "type": "text",
+        "text": "Regarding DFME, classifying ME samples into seven categories poses significant challenges, resulting in relatively low UF1 and UAR scores across all methods. However, our proposed method outperforms all others in every metric. Specifically, Our method outperforms I3D by  $9.30\\%$  in UF1 and  $9.20\\%$  in UAR, and surpasses LBP-TOP by  $15.17\\%$  in UF1 and  $13.25\\%$  in UAR, highlighting its effectiveness in extracting critical and discriminative features from ME clips. Additionally, compared to recent deep learning methods like FR, our approach yields  $2.94\\%$  and  $1.64\\%$  higher UF1 and UAR, confirming the benefits of incorporating facial topology and structured muscle motion for enhanced performance.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Regarding CAS(ME) $^3$ , the primary challenge lies in its sample complexity. Compared to baseline methods (STST-Net, RCN-A, FR), our proposed method achieves over approximately  $20\\%$  higher UF1 and UAR scores, marking a significant advancement. Our method surpasses three recent SOTA approaches in MER, including HTNet, which employs a hierarchical Transformer for local feature learning via self-attention. Specifically, our approach outperforms HTNet by  $4.54\\%$  in UF1 and  $8.11\\%$  in UAR, leveraging psychological insights and statistical patterns to capture deeper facial muscle dynamics. Additionally, it exceeds Micro-BERT and HSTA by  $6.17\\%$  and  $2.91\\%$  in UF1, and  $1.01\\%$  and  $0.46\\%$  in UAR, respectively. By mining facial movement patterns to better understand topology, our model achieves improved metrics, indicating enhanced accuracy in classifying all emotion categories.",
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+    {
+        "type": "text",
+        "text": "5.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Tab. 3 listed the ablation study results on DFME.",
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+    },
+    {
+        "type": "table",
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+        "table_caption": [
+            "Table 3. Ablation study. L, G, S and D represent Local (upper and lower face), Global, Single stream and Dual Stream, respectively."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Setting</td><td colspan=\"2\">LRM</td><td colspan=\"2\">AFR</td><td colspan=\"2\">InceptionNet</td><td rowspan=\"2\">UF1↑</td><td rowspan=\"2\">UAR↑</td></tr><tr><td>LFE</td><td>SSE</td><td>L</td><td>G</td><td>S</td><td>D</td></tr><tr><td>I</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3249</td><td>0.3404</td></tr><tr><td>II</td><td>✓</td><td></td><td></td><td></td><td></td><td>✓</td><td>0.3362</td><td>0.3517</td></tr><tr><td>III</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>✓</td><td>0.3480</td><td>0.3624</td></tr><tr><td>IV</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>0.3629</td><td>0.3723</td></tr><tr><td>V</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>0.3604</td><td>0.3658</td></tr><tr><td>VI</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>0.3853</td><td>0.3978</td></tr><tr><td>Setting</td><td colspan=\"3\">Without AU Group</td><td colspan=\"3\">With AU Group</td><td>UF1↑</td><td>UAR↑</td></tr><tr><td>VII</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>0.3683</td><td>0.3793</td></tr><tr><td>VIII</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3853</td><td>0.3978</td></tr><tr><td>Setting</td><td colspan=\"3\">Psychological prior</td><td colspan=\"3\">Data-driven Prior</td><td>UF1↑</td><td>UAR↑</td></tr><tr><td>IX</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.3615</td><td>0.3701</td></tr><tr><td>X</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>0.3723</td><td>0.3832</td></tr><tr><td>XI</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3705</td><td>0.3767</td></tr><tr><td>XII</td><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td>0.3853</td><td>0.3978</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Impact of AU Feature: Setting I, which uses only full face OF as input, serves as our baseline for evaluating the role of AU features in MER. In Setting II, integrating AU features into the Dual Stream InceptionNet leads to a  $1.13\\%$  improvement in both UF1 and UAR. This improvement demonstrates that incorporating AU features significantly enhances the model's ability to recognize MEs, and underscores the value of fusing multiple feature types to strengthen model performance.",
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+    {
+        "type": "text",
+        "text": "Impact of ROI Relationship Modeling: The results in Setting III show improvements of  $1.18\\%$  in UF1 and  $1.07\\%$  in UAR compared to Setting II, indicating that the model effectively captures complex dependencies between ROIs and extracts more discriminative feature representations.",
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+    {
+        "type": "text",
+        "text": "Impact of AU grouping: We compared AU feature extraction from the global face with our AU grouping strategy (Setting VII vs. VIII), the performance improvement (UF1:  $1.70\\%$ , UAR:  $1.85\\%$ ), confirming that AU grouping enables the network to learn more representative AU features.",
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+    {
+        "type": "text",
+        "text": "Impact of Modeling the Topological Structure of ME Muscle Movements: Compared to Setting III, Setting IV, including local muscle movement topology modeling, improves UF1 and UAR by  $1.49\\%$  and  $0.99\\%$ , respectively. Setting V, which adds global muscle movement topology modeling, shows gains of  $1.24\\%$  in UF1 and  $0.34\\%$  in UAR over Setting III. Combining both local and global topology modeling yields the best performance on DFME. These results demonstrate that incorporating topological modeling of muscle movements enhances MER.",
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+    {
+        "type": "text",
+        "text": "Impact of Prior Knowledge: Tab. 3 presents the ablation experiments to evaluate the impact of using prior knowledge for constructing facial muscle topology. In particular, compared to Setting IX, Setting X, which uses only psychological knowledge, improves UF1 and UAR by  $1.08\\%$  and",
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+        "text": "14459",
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+        "image_caption": [
+            "(a) UF1 comparison across different clients."
+        ],
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+        "image_caption": [
+            "Figure 5. Compare the performance of different FL frameworks on different clients: UF1 and convergence. See UAR comparison in Suppl."
+        ],
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+        "image_caption": [
+            "(b) Convergence comparison across different clients."
+        ],
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+    {
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+    {
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+        "img_path": "images/5d110c145f2ae6a3be10e74af597573fbc31866014983bc5e3e2f04bef4c399e.jpg",
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+    {
+        "type": "text",
+        "text": "$1.31\\%$ , respectively. Setting XI, incorporating only data-driven knowledge, shows gains of  $0.9\\%$  in UF1 and  $0.66\\%$  in UAR. When both psychological and data-driven knowledge are combined (Setting XII), the improvements reach  $2.38\\%$  in UF1 and  $2.77\\%$  in UAR, proving the effectiveness of the prior knowledge. Constructing a prior adjacency matrix allows the model to capture complex facial muscle topology, while data-driven knowledge directs attention to uncover intrinsic movements patterns of facial muscles.",
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+    },
+    {
+        "type": "text",
+        "text": "5.4. Federated Experiment",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Since FL aims to enhance MER performance on individual clients in scenarios with limited sample sizes and data privacy issue, and given that DFME and  $\\mathrm{CAS}(\\mathrm{ME})^3$  have large sample size, we partition the datasets as mentioned in Section 5.1 and treat the subdivisions as separate clients.",
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+        "type": "text",
+        "text": "While our focus is on application rather than fundamental FL innovation, our experiments confirm the effectiveness of our P-FedProx method, which is tailored for ME data distributions. Benchmarked against several open-source SOTA methods, our approach excels at mitigating small-sample challenges while preserving data privacy. Specifically (Fig. 5), the results show P-FedProx outperforms both the single-client baseline and traditional FL methods (FedAvg, FedProx), with particularly significant gains on clients with more challenging data distributions (Clients 6-7). Compared to recent personalized FL methods, our approach surpasses FedRep and ELLP and achieves performance competitive with the state-of-the-art FedAS, yet with a significantly simpler implementation. These consistent gains demonstrate that our weighted model initialization effectively addresses the data heterogeneity that challenges",
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+    {
+        "type": "text",
+        "text": "traditional FL, thereby mitigating ME sample scarcity while ensuring data privacy.",
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+        "type": "text",
+        "text": "Meantime, we note that all FL methods achieved good performance on the local clients from DFME, which may be due to the fact that these clients have a similar amount of data and slight differences in data distribution, presenting fewer challenges for federated learning.",
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+        "type": "text",
+        "text": "Besides, we analyze the training loss progression of different federated algorithms over communication rounds. We found that P-FedProx demonstrates the smoothest convergence curves with minimal oscillations, particularly evident in Clients 1-5. On the other hand, P-FedProx converges significantly faster than other FL methods. This rapid early convergence suggests that personalized global model assignment provides clients with better initialization states.",
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+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "MER is challenged by limited sample sizes, subtle features, and privacy concerns in real-world applications. To address these issues, we conduct a psychological study to provide structured insights into facial muscle dynamics. We then develop a FED-PsyAU framework that integrates these findings with data-driven patterns for hierarchical learning of dynamic features, enhancing MER performance. Additionally, the FL framework improves MER across clients while preserving data privacy through iterative model updates. The comprehensive experiments validate our approach's effectiveness. In the future, we will integrate additional AUs to build a more comprehensive ME topology information and further advance MER in real-world applications through FL and semi-supervised approaches.",
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+    {
+        "type": "header",
+        "text": "FedAvg(2017) PersonalizedFedProx ELLP(2024) Baseline FedProx(2020) FedRep(2021) FedAS(2024)",
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+        "text": "7. Acknowledgment",
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+        "text": "This research was partially funded by 1) the National Natural Science Foundation of China (62476269, 62276252); 2) the Youth Innovation Promotion Association CAS.",
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+        "type": "text",
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2025/FED-PsyAU_ Privacy-Preserving Micro-Expression Recognition via Psychological AU Coordination and Dynamic Facial Motion Modeling/e27ad4a5-3106-4216-bcea-a95709cd5f65_origin.pdf

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2025/FED-PsyAU_ Privacy-Preserving Micro-Expression Recognition via Psychological AU Coordination and Dynamic Facial Motion Modeling/full.md

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+# FED-PsyAU: Privacy-Preserving Micro-Expression Recognition via Psychological AU Coordination and Dynamic Facial Motion Modeling
+
+Jingting Li $^{1,2}$ , Yu Qian $^{1,3}$ , Lin Zhao $^{1,2}$ , Su-Jing Wang $^{*1,2}$
+
+$^{1}$ State Key Laboratory of Cognitive Science and Mental Health, Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101, China
+
+$^{2}$ Department of Psychology, University of the Chinese Academy of Sciences, Beijing, 100049, China
+
+$^{3}$ School of Computer, Jiangsu University of Science and Technology, Zhenjiang, 212100, China
+
+$^{\dagger}$ Equal contribution, \*Corresponding author (wangsujing@psych.ac.cn)
+
+# Abstract
+
+Micro-expressions (MEs) are brief, low-intensity, often localized facial expressions. They could reveal genuine emotions individuals may attempt to conceal, valuable in contexts like criminal interrogation and psychological counseling. However, ME recognition (MER) faces challenges, such as small sample sizes and subtle features, which hinder efficient modeling. Additionally, real-world applications encounter ME data privacy issues, leaving the task of enhancing recognition across settings under privacy constraints largely unexplored. To address these issues, we propose a FED-PsyAU research framework. We begin with a psychological study on the coordination of upper and lower facial action units (AUs) to provide structured prior knowledge of facial muscle dynamics. We then develop a DPK-GAT network that combines these psychological priors with statistical AU patterns, enabling hierarchical learning of facial motion features from regional to global levels, effectively enhancing MER performance. Additionally, our federated learning (FL) framework advances MER capabilities across multiple clients without data sharing, preserving privacy and alleviating the limited-sample issue for each client. Extensive experiments on commonly-used ME databases demonstrate the effectiveness of our approach. Our implementation is publicly available at https://github.com/MELABIPCAS/FED-PsyAU.git.
+
+# 1. Introduction
+
+Micro-expressions (MEs) [9], resulting from conflicts between voluntary and involuntary expressions, reveal true emotions, making them valuable in non-contact emotion detection applications like criminal interrogation and psychological counseling. MEs are characterized by their brief duration, low intensity, localized occurrence, and occasional
+
+asymmetry [10]. These traits not only restrict large-scale data collection and annotation but also make it challenging for deep learning networks to effectively model their motion characteristics. Some methods focus on regions of interest (ROIs) [4, 21, 31, 49], while others utilize attention mechanisms [3, 14, 33] and transformer-based architectures [24, 50, 57] to capture salient features. Meanwhile, MEs are often complex manifestations involving the combination of multiple AUs. In contrast, individual action units (AUs) correspond to specific, anatomically-based facial muscle movements. Focusing on AUs allows us to model more fundamental and consistent facial appearance changes. Certain approaches use AU labels to construct adjacency matrices for graph convolutional networks (GCNs) [24, 39]. Yet, to the best of our knowledge, these methods often apply AU annotations directly without fully exploiting the anatomical structure and coordinated AU dynamics, limiting the network's understanding on ME.
+
+To address these challenges, we leverage the theory that distinct neural pathways control upper and lower facial movements, resulting in two different motion patterns. Based on this, we conduct a psychological study to investigate upper/lower facial AU coordination, providing crucial prior knowledge on structural motion relationships underpinning MEs. Using both psychological priors and data-driven AU patterns, we design a Graph Attention Network (GAT) [47] based on dynamic prior knowledge, applied separately to the upper and lower regions. A final global GAT captures the topological relationships of muscle movements across the face. The resulting feature, combined with full-face optical flow (OF), is input into a subsequent dual-stream network, effectively integrating structural and dynamic information to enhance ME recognition (MER).
+
+Besides, as mentioned earlier, although MEs have valuable applications in many privacy-sensitive contexts, the sensitivity of biometric data makes it impractical to aggre
+
+gate ME data across clients for training. Meanwhile, the sample size in a single client is often insufficient to train a robust model. Yet, the challenge of enhancing MER performance across diverse clients while preserving privacy remains largely unexplored. To address this, we adopt a federated learning (FL) framework, improving performance by merging and updating model parameters across clients without exchanging local data. This approach preserves data privacy and supports the MER practical deployment.
+
+Overall, our work leverages psychological and data-driven priors to enhance the network's learning of structured ME motion patterns, particularly in limited-sample conditions. Additionally, we introduce FL to advance MER in real-world scenarios. The contributions of this paper are:
+
+- We conduct a psychological experiment to derive AU coordination between the upper and lower facial regions, providing structural priors for ME and facial expression analysis in computer vision.  
+- We design a local-to-global GAT network that integrates psychological priors and data-driven AU patterns in the upper and lower facial regions, improving the network's ability to learn both local and global structural facial dynamics. This feature, combined with global OF feature in a dual-stream network, enhances MER performance.  
+- We employ FL in MER to improve data privacy and overcome small sample size challenges by aggregating features from distributed data-protected sources.
+
+# 2. Related Works
+
+# 2.1. Micro-expression Recognition
+
+In recent years, MER has gained increasing attention from computer vision researchers. Traditional machine learning methods primarily rely on handcrafted feature extraction. For instance, Local Binary Pattern (LBP) [43], effectively utilizes local texture features, has inspired various improvements [18, 49]. Furthermore, OF [26] has been explored for capturing object motion. Liu et al. [38] developed the Main Directional Mean OF (MDMO) method by aligning faces in the OF domain, while Liong et al. [34] added optical strain features for MER. However, traditional approaches depend heavily on manually crafted features, limiting both accuracy and generalizability. Meanwhile, deep learning methods, with robust feature extraction capabilities, can automatically learn multi-level representations to capture subtle ME changes. The availability of several spontaneous ME databases, such as CASME II [51], SAMM [6], CAS(ME) $^{3}$  [27], DFME [59] and others [1, 30, 32, 44, 54], has accelerated deep learning advancements in MER. Inspired by Liong et al.'s work [35] on sequence redundancy, many studies [4, 13, 50] now use keyframes (onset and apex) as input, reducing model parameters while achieving excellent results.
+
+Despite advancements in preprocessing and feature extraction, deep learning alone has yet to achieve high MER accuracy. As MEs stem from physiological muscle activity, incorporating prior knowledge offers meaningful context. FACS [10], which defines expressions through AUs, provides a basic theoretical framework for MER. Recent studies explore AU-ME relationships to enhance MER performance. Lei et al. [24] applied GCN [21] to model AU co-occurrences, especially around the eyebrow and mouth regions. Xie et al. [53] introduced an AU-assisted GCN, with modules for AU feature extraction and ME image generation. Wang et al. [48] used transformers to learn dynamic AU adjacency, boosting model generalization. These networks typically rely on AU labels from databases, without fully integrating structured facial muscle movements, AU interrelations, or their links to expressions. In this work, we refine structured ME feature extraction using a local-to-global GAT network, which integrates priors on facial AU coordination from psychological experiments with data-driven movement patterns.
+
+# 2.2. Federated Learning
+
+To assess MER across databases, ME Grand Challenge (MEGC) 2018 [56] introduced the Holdout-database Evaluation and Composite Database Evaluation tasks, utilizing the CASME II and SAMM databases. MEGC 2019 [45] expanded the CDE task to include the SMIC databases. While research on MEs predominantly utilizes these public datasets, existing methodologies do not address the privacy concerns that arise in practical applications.
+
+FL [41] could addresses ME data scarcity and privacy concerns through collaborative training. It includes two main phases: local training and global aggregation. Many existing FL works for expressions, while insightful, are often not open-source or use highly customized frameworks (e.g., non-random client data allocation [12], specialized parameter aggregation [11]) making standard methods more suitable for implementation and comparisons in our study. For instance, McMahan et al. [41] proposed FedAvg, a basic aggregation method that uses weighted averaging based on each client's data volume. Li et al. [28] introduced FedProx by adding a regularization term to the client loss function, aligning updates more closely with the global model. However, the one-global model-fits-all approach ignores client data diversity. To solve this, our approach extends FedProx by distributing a personalized global model to each client.
+
+# 3. Proposed Psychological Study on AU Incoordination
+
+This study employed a behavioral experiment to investigate individuals' cognitive responses to AU incoordination in the upper and lower facial regions.
+
+![](images/d0be976c39a1a2b1350002c8024a300f5603459bf08e9cad7c5424168a69b569.jpg)  
+(a) AU  $4 + 9$
+
+![](images/6a6758a36e511f40688f624788965fb5f708c901579da499564d7275e17f1144.jpg)  
+(b) AU 6+12
+
+![](images/75bb2e5693552c09e2c1a618dc3ae130c5010e3798a28cb5539630fc5fb61851.jpg)  
+(c) AU 4+12  
+Figure 1. Examples of AU composite images. (a) and (b) are coordinated composites. (c) and (d) are uncoordinated composites.
+
+![](images/c488cf12372e861cf51dcda4ad2396759b6b73ada71b35e9bbaf1e1974f014a9.jpg)  
+(d) AU 6+15
+
+The study included 30 college participants (20 female, Mean= 22.22 years), a sample size considered adequate for statistical reliability under the Central Limit Theorem [23]. All procedures followed the Declaration of Helsinki and were approved by the institutional review board of the Institute of Psychology, Chinese Academy of Sciences.
+
+This behavioral experiment employed a within-subjects design. The independent variable was the type of AU composite image (coordinated vs. uncoordinated AU composites), as shown in Fig. 1. The face images were segmented anatomically. The dividing line was consistently present in all stimuli, serving as a control variable and would not influence the experiment's outcomes. To control for individual facial differences in emotion recognition, the original images used for composites were sourced from the same person [10]. Seventy-two composite images were generated from upper and lower facial AUs across six basic emotions, with each emotion represented by six coordinated and six uncoordinated expressions.
+
+The dependent variables are accuracy rates and scores. Specifically, participants made two judgments for each composite image: whether it was coordinated or uncoordinated, and the degree of coordination or incoordination.
+
+Statistical analysis from this study showed that participants were significantly more accurate in recognizing coordinated AU composite images than uncoordinated ones (Please see Supplementary Materials (Suppl.) for more experimental details and statistical results). The study further highlighted specific AU combinations, such as AU4 and AU12, that participants quickly identified as uncoordinated, whereas combinations like AU6 and AU12 were rapidly recognized as coordinated. This suggests that these uncoordinated AU pairings may inherently convey emotional incoordination. Besides, the coordination patterns between specific AUs reveal systematic facial action structures. These patterns help the network distinguish both coordinated and uncoordinated facial movements, thus enhancing its ability to identify ME features more effectively.
+
+# 4. Our Proposed FED-PsyAU Framework
+
+We propose the FED-PsyAU framework (Fig. 2), which embeds a psychology-driven MER model within a federated aggregation module. The model features a hierarchi
+
+cal structure that learns from local ROIs to AU groups and finally to global facial regions, capturing dynamic topology while minimizing redundancy. It leverages a multiscale InceptionNet to extract and fuse global OF with structural facial features. The federated module enables privacy-preserving collaborative training to boost MER performance on each client.
+
+# 4.1. Localized ROI Modeling
+
+Since MEs are manifested by muscle movements in key facial regions (e.g., eyes, mouth, nose) [10], we refine the standard 68 landmarks from Dlib [20] to precisely capture these changes. As shown in Fig. 3, we discard 10 less informative outer contour landmarks and add 7 new midpoints to better track movements in the cheek and eyebrow regions, resulting in a final set of 65 keypoints.
+
+Then, onset-apex OF inputs  $(128 \times 128$  pixels) are cropped into 65 ROIs, each measuring  $5 \times 5$  pixels, centered on selected facial landmarks  $\mathbf{p}_k = (x_k, y_k)$ , where  $k \in 1, 2, \ldots, 65$ , denotes the landmark index. To enhance robustness to apex annotation, we also compute OF using a small window of frames around the apex. The ROI features input to the Local ROI Feature Extractor (LFE), denoted as  $\Theta_k$ , contain the horizontal and vertical components of OF and optical strain. The LFE module consists of three convolutional layers, each followed by batch normalization and ReLU activation. All kernel sizes were  $3 \times 3$ . The output channels in the first two layers increase from 32 to 64, while the final layer outputs 3 channels. This design helps the LFE capture complex local patterns, with the output features referred to as  $\Phi_k = \mathrm{LFE}(\Theta_k)$ .
+
+Inspired by Vision Transformer [8], we use a Spatial Structure Encoder (SSE), i.e., Transformer Encoder with three attention heads to capture diverse dependencies among ROIs, as MEs result from coordinated muscle movements across multiple areas. Precisely, we convert  $\Phi_k$ , into a token. To retain the positional information of the facial landmarks, a positional embedding  $E_{k}$  is added based on the landmark index to each token, yielding  $X_{k} = \Phi_{k} + E_{k}$ . We add the output of the three head attention module to the input feature  $X_{k}$ , and then normalize the result using LayerNorm. Finally, after passing through a feed-forward neural network and applying LayerNorm, the final output representation is obtained as  $Z_{k}\in \mathbb{R}^{3\times 5\times 5}$ .
+
+# 4.2. Relationship Modeling among AU Features
+
+Our proposed Relationship Modeling among AU Features (AFR) module consists of two components: an AU Feature Extractor (AFE) to derive features from AU-specific facial regions, and a GAT-structure to model the topological relationships between these AUs.
+
+![](images/32a7893b63bbeb533929b4b91016e08a888aebebc0656d7b79a2840f881c5d6b.jpg)  
+Figure 2. The pipeline of our proposed FED-PsyAU framework, including MER network (black block) and the Federated Aggregation (FA) module (orange block). In MER network, the LRM module consists of the local ROI feature extractor (LFE) and the spatial structure encoder (SSE), which preserves spatial structure information while efficiently extracting ROI features; the AFR module includes the AU feature extractor (AFE) and the dynamic prior knowledge-based graph attention network (DPK-GAT) for effective AU feature extraction and capturing AU dynamic relationships, the DSI module use a dual-stream structure to capture multi-scale facial muscle topology and motion information for MER. Then, the FA module integrates the MER network into the FL framework.
+
+![](images/6fff2cada31386a5b011df13bd87f2c5f07231243518331d7ca049c484b4cd7c.jpg)  
+Figure 3. ROI grouping strategy for AU. OF features from each ROI are processed through LFE and SSE to yield high-dimensional representations. ROIs are then grouped by AU movement patterns to create inputs for AFEs, ultimately producing AU node features for the GAT network.
+
+# 4.2.1. AU Feature Extractor
+
+MEs involve dynamic, coordinated interactions across multiple regions [10] and are characterized by subtle movements that differ from typical macro-expressions. Therefore, as shown in Fig. 3, when grouping ROIs for the AFE module, the AU selection and regionalization are based on: 1) AU frequency in MEs; 2) Grouping by primary/secondary muscle activation areas [7]. Notably, not all AUs employed in Section 3 are applied to MER. We specifically retain only the 12 AUs exhibiting the highest relevance to ME dynamics, as listed in Tab. 1. Detailed occurrences are provided in the Suppl.
+
+The first step we construct in AFE is Group Squeeze and
+
+Table 1. Selected AUs and Corresponding Regions (Primary and Secondary/ Coordinate).  $g$ ,  $N_g$  and  $N_{g\_AU}$  represent ROI Group index, corresponding ROI number and AU amount.  
+
+<table><tr><td>g</td><td>AU</td><td>Primary</td><td>Secondary/ Coordinate</td><td>Ng</td><td>Ng-AU</td></tr><tr><td>1</td><td>1,2,4</td><td>Eyebrows</td><td>Eyes</td><td>23</td><td>3</td></tr><tr><td>2</td><td>5,6,7</td><td>Eyes</td><td>Eyebrows, Cheeks, Mouth</td><td>48</td><td>3</td></tr><tr><td>3</td><td>9,10</td><td>Nose, Cheeks</td><td>Mouth, Chin</td><td>38</td><td>2</td></tr><tr><td>4</td><td>12,14,15,17</td><td>Mouth</td><td>Eyes, Eyebrows, Nose</td><td>52</td><td>4</td></tr></table>
+
+Excitation (GSE). It computes the attention for each group of AUs (ROI group), which makes the model pay more attention to the critical ROIs. Specifically, for each ROI group input  $R_{g} = \{Z_{1}, Z_{2}, \ldots, Z_{N_{g}}\}$ ,  $g \in \{1, 2, 3, 4\}$ , the GSE module performs global average pooling on each ROI and computes channel importance through a fully connected (FC) layer. The original features are then preserved through residual concatenation:
+
+$$
+f _ {\mathrm {G S E}} \left(R _ {g}\right) = \left\{W _ {k} ^ {\text {a t t}} \odot Z _ {k} + Z _ {k} \mid Z _ {k} \in R _ {g} \right\} \tag {1}
+$$
+
+where  $W_{k}^{att}$  is the attention weight for each group of ROI,  $\odot$  denotes element-wise multiplication along the channel dimension of  $Z_{k}$ . Next,  $f_{\mathrm{GSE}}(R_g)$  undergoes further feature extraction, reducing from  $N_{g}$  composite features to  $N_{g\_AU}$  representative AU features, yielding the output feature  $F_{g\_AU}$ . Precisely, the process comprises two convolutional layers: a  $3 \times 3$  layer that doubles the input dimensions and a  $1 \times 1$  layer that restores them to the original size. Both layers are followed by Batch Normalization and ReLU activation for improved stability and representation.
+
+# 4.2.2. AU Relationship Modeling
+
+Prior Knowledge: To model AU dynamic relationships, we integrate two forms of prior knowledge: an "intrinsic" prior
+
+from psychological principles and an "extrinsic" prior from data-driven patterns. The intrinsic prior, derived from our psychological findings on AU coordination (Sec. 3), provides structural guidance by defining the initial GAT adjacency matrix  $A$ . The extrinsic prior, based on statistical AU co-occurrence patterns in the data, offers data-driven refinement that theoretical models may overlook. This extrinsic prior forms a prior attention matrix  $D$  to guide weight allocation among AU nodes. By fusing this foundational psychological structure with real-world dynamics, our model achieves superior adaptability and generalization (see Suppl. for matrix details).
+
+Facial Segmentation: As presented in Sec. 3, the upper and lower facial regions, controlled by different neural pathways, exhibit distinct muscle movement patterns. AUs and their associated primary muscles in the upper and lower face can exhibit coordination (potential co-occurrence) or lack of coordination (infrequent simultaneous appearance). Leveraging these intra- and inter-regional interactions, we model AU relationships for the upper face, lower face, and whole face. Consistent with the experimental setup in Sec. 3, we segment the face into upper and lower parts based on the orbicularis oculi muscle. Specifically, following the primary occurrence regions of 12 listed AUs, the AUs in the first two groups from Tab. 1 are classified as upper face AUs, while those in the last two groups are classified as lower face AUs.
+
+$$
+F _ {A U} ^ {U p p e r} = F _ {1 \_ A U} \cup F _ {2 \_ A U}, F _ {A U} ^ {L o w e r} = F _ {3 \_ A U} \cup F _ {4 \_ A U} (2)
+$$
+
+We input the AU features from the upper and lower face:  $F_{AU}^{Upper}$ ,  $F_{AU}^{Lower}$  into our proposed Dynamic Prior Knowledge GATs (DPK-GATs) in parallel (Details are presented in the next part of this subsection). These networks use psychology prior knowledge to build AU adjacency relationships and data-driven priors to guide attention learning, producing outputs  $h^{Upper}$  and  $h^{Lower}$ , which are combined into  $h^{Local}$  for the next stage.
+
+In the whole-face DPK-GAT, we construct the network similarly but set adjacency values within the same region to zero, ignoring intra-regional AU relationships. By learning cross-regional topological structures and statistical patterns, we obtain global AU relationship features, denoted as  $h^{Global}$ , as illustrated in Fig. 4.
+
+DPK-GAT: We model dynamic AU node relationships combing GAT and the prior knowledge. In particular, for the input feature belonging to  $\{F_{AU}^{Upper}, F_{AU}^{Lower}, h^{Local}\}$ , a linear mapping projects it to a higher-dimensional space as  $f$ . The similarity score  $e_{ij}$  between AU nodes  $i$  and  $j$ , is calculated using the attention weight vector  $\vec{a}$  and concatenated node features  $f_{i}$  and  $f_{j}$ :
+
+$$
+e _ {i j} = \left\{ \begin{array}{l l} \text {L e a k y R e L U} \left(\tilde {a} ^ {T} [ f _ {i} | | f _ {j} ]\right), & \text {i f} A _ {i j} > 0 \\ - \infty , & \text {i f} A _ {i j} = 0 \end{array} \right. \tag {3}
+$$
+
+![](images/3934cbe5af16a98d999e3491078e08adc38f6f6edc979040b58195a36422df20.jpg)  
+Figure 4. DPK-GAT from facial segmentations to global face. First, intra-regional AU node relationships are learned within the upper and lower facial regions. Second, cross-regional relationships are modeled to integrate interactions between these regions.
+
+Here, only neighboring nodes defined by the psychology-derived adjacency matrix  $A$  are considered.
+
+The final attention  $\alpha_{ij}$  is calculated by combining the data-driven prior attention  $D_{ij}$  and the self-attention, obtained by the softmax operation applied to  $e_{ij}$ :
+
+$$
+\alpha_ {i j} = (1 - \beta) \cdot \operatorname {s o f t m a x} \left(e _ {i j}\right) + \beta \cdot D _ {i j} \tag {4}
+$$
+
+where,  $\beta$  is the dynamic prior attention weight, updated based on the training rounds. Along with a residual concatenation, the final node representation  $h_i$  is aggregated as:
+
+$$
+h _ {i} = \operatorname {E L U} \left(\sum_ {j \in \mathcal {N} (i)} \alpha_ {i j} \cdot f _ {j}\right) + f _ {i} \tag {5}
+$$
+
+where  $\mathcal{N}(i)$  denotes the neighboring nodes of  $i$ . In our implementation, we employ three attention heads and a two-layer structure, enabling the extraction of complex AU dependencies.
+
+# 4.3. Dual-Stream-InceptionNet
+
+Muscle movements vary widely across facial regions, making multi-scale information essential for the MER task. InceptionNet's core concept is leveraging parallel convolutional kernels to extract multi-scale features, enhancing the network's ability to capture fine details and overall structure [46]. We build on this by using a dual-stream InceptionNet as the ME feature extractor. One stream processes the AU relationship features  $h^{Global}$ , while the other handles global OF features  $\Theta$ . This dual-stream design allows the model to capture the topological relationships of facial muscles through AUs and holistic motion via OF. The output tensors from both streams are flattened, concatenated, and fed into a FC layer for ME prediction.
+
+# 4.4. Federated Aggregation
+
+Traditional centralized learning consolidates all data on a single server, enhancing model accuracy and generalization but neglecting privacy concerns in MER. FL could address this by training models locally and sharing only parameters, protecting data privacy and retaining each client's unique data characteristics.
+
+FedProx [29] is a FL approach designed to address data heterogeneity among clients. It incorporates proximal terms during model aggregation to balance global and client-local learning, improving both performance and convergence speed. We extend FedProx by altering the server's processing and distribution strategy during aggregation, which we call Personalized FedProx (P-FedProx). Specifically, P-FedProx initializes each client's model  $W_{i}^{t}$  in round  $t$  by combining its previous model  $\mathring{W}_{i}^{t-1}$  with models from other clients  $\mathring{W}_{j}^{t-1}$ .
+
+$$
+W _ {i} ^ {t} = \theta \cdot \mathring {W} _ {i} ^ {t - 1} + \sum_ {\substack {j = 1 \\ j \neq i}} ^ {n} \omega_ {j} \cdot \mathring {W} _ {j} ^ {t - 1}, \text {where} \sum_ {\substack {j = 1 \\ j \neq i}} ^ {n} \omega_ {j} = 1 - \theta \tag{6}
+$$
+
+where weight  $\omega_{j}$  is proportional to  $j$ th client's data size. For  $i$ th client,  $\theta$  is set to 0.9 (optimal experimental result, see more detail in the Suppl.)
+
+# 4.5. Loss Function
+
+AU Prediction Loss: To enhance MER, our network models the topological relationships and statistical patterns of AUs, making AU prediction an auxiliary task. The prediction is utilized in two stages: one enhances the AU feature extraction performance of the AFE module, and the other improves the GAT network's ability to learn AU topological structures. AU recognition is formulated as a multi-label classification problem, with the Binary Cross-Entropy Loss for each AU label defined as:
+
+$$
+L _ {\mathrm {A}} = \frac {\sum_ {j = 1} ^ {M} \left[ y _ {j} \cdot \log \left(\sigma \left(\hat {y} _ {j}\right)\right) + \left(1 - y _ {j}\right) \cdot \log \left(1 - \sigma \left(\hat {y} _ {j}\right)\right) \right]}{- M} \tag {7}
+$$
+
+where  $M$  is the total number of AUs,  $y_{j}$ ,  $\sigma (\hat{y}_j)$  and  $\hat{y}_j$  represent respectively the ground truth label (0 or 1), the logit output and prediction after applying the sigmoid function for the  $j$ -th AU. The loss function is consistent for both stages, i.e.,  $L_{\mathrm{A}}^{\mathrm{AFE}}$  and  $L_{\mathrm{A}}^{\mathrm{GAT}}$ .
+
+MER Loss: The Cross-Entropy Loss function is utilized for emotion classification. Thus, our overall MER loss is composed as follows:
+
+$$
+L _ {\text {M E R}} = \alpha_ {1} \cdot \left(- \sum_ {i = 1} ^ {N} y _ {i} \cdot \log (\hat {y} _ {i})\right) + \alpha_ {2} \cdot L _ {\mathrm {A}} ^ {\mathrm {A F E}} + \alpha_ {3} \cdot L _ {\mathrm {A}} ^ {\mathrm {G A T}} \tag {8}
+$$
+
+where,  $N$  represents the number of classes,  $y_{i}$  and  $\hat{y}_i$  are the one-hot encoded ground truth label and the predicted probability for class  $i$ ,  $\alpha_{1}$ ,  $\alpha_{2}$  and  $\alpha_{3}$  are hyperparameters, set to 0.2, 0.8, and 0.8 to prioritize MER loss while balancing AU recognition (See parameter analysis in Suppl.).
+
+Federated Loss: During federated training, the local client's loss function includes the MER loss  $L_{\mathrm{MER}}$  and a proximal term:
+
+$$
+L _ {\mathrm {F L}} = L _ {\mathrm {M E R}} + \frac {\alpha_ {4}}{2} \cdot \left\| W - W _ {t} \right\| ^ {2} \tag {9}
+$$
+
+where  $W_{t}$  denotes the global model in the server's  $t$ -th round of distribution, and  $W$  represents the current model of the client.  $\alpha_{4}$  is the hyperparameter for the weight of the proximal term.
+
+# 5. Experiments
+
+# 5.1. Configuration
+
+Databases: We use two recently published large scale and challenging ME databases: CAS(ME) $^3$  and DFME. CAS(ME) $^3$ -Part A offers 860 samples from 100 participants. DFME includes three subsets with (participants, samples): A (72,1,118), B (92,969), C (492,5,439). For Apex-first-frame scenario, we compute the OF between the apex and mid-frame towards the offset.
+
+Pre-training: To enhance the model's ability to perceive facial motion patterns, we first pre-trained the AU module (LRM+AFR) on the DISFA [40] and CK [19] datasets. The effect of this pre-training is detailed in the Suppl.
+
+MER Experiment Settings: The evaluation follows standard protocols on two datasets. On  $\mathrm{CAS(ME)^3}$ , we perform 3-class classification (positive, negative, surprised) [45] with Leave-One-Subject-Out (LOSO) validation. On DFME, we conduct 7-class classification (Happiness, Surprise, Disgust, Sadness, Anger, Fear, and Contempt) using scale-adapted 10-fold cross-validation [59]. To address class imbalance, performance is measured by the UF1 and UAR. Experiments were implemented in PyTorch 1.13.0 and run on five NVIDIA GeForce RTX 4090 GPUs.
+
+Federated Experiment Settings: The DFME and  $\mathrm{CAS(ME)^3}$  datasets are randomly split into 5 and 2 local clients, respectively, with each client assigned an equal number of subjects. However, variations in microexpression (ME) counts per subject result in differing ME data distributions and quantities across clients, mirroring real-world data heterogeneity (See detailed data distributions in the Suppl.). Traditional LOSO and k-fold cross-validation can leak training samples in a federated setting, so we employ a random partition strategy with  $70\%$  of samples for training and  $30\%$  for testing, averaging results over 10 tests to minimize randomness. Furthermore, we assume an ideal FL scenario with no client dropouts and equal local updates per client. In FedAvg [41] and FedProx [28], the server assigns an identical global model to all clients each round; differently, FedProx adds a proximal term to reduce model bias in local training. Our P-FedProx enhances this by assigning tailored initial models, with  $90\%$  ( $\theta$ ) weight on each client's own model and  $10\%$  on others'. Additionally, we compare against recent personalized FL methods: FedRep [5] uses shared representations with personalized heads, ELLP [61] employs parameter decoupling with Fisher Information weighting, and FedAS [55] applies parameter alignment and client synchronization. Unlike these approaches requiring architectural changes or complex procedures, P-FedProx achieves personalization through simple weighted initialization.
+
+Table 2. SOTA methods comparison on DFME and CAS(ME)  ${}^{3}$  
+
+<table><tr><td rowspan="2">Category</td><td rowspan="2">Method</td><td rowspan="2">Year</td><td colspan="2">DFME</td><td colspan="2">CAS(ME)3</td></tr><tr><td>UF1</td><td>UAR</td><td>UF1</td><td>UAR</td></tr><tr><td rowspan="2">3D-CNN</td><td>I3D [2]</td><td>2017</td><td>0.2923</td><td>0.3058</td><td>-</td><td>-</td></tr><tr><td>R3D [17]</td><td>2018</td><td>0.2164</td><td>0.2313</td><td>-</td><td>-</td></tr><tr><td rowspan="2">Hand-crafted</td><td>LBP-TOP [49]</td><td>2014</td><td>0.2336</td><td>0.2653</td><td>-</td><td>-</td></tr><tr><td>MDMO [37]</td><td>2015</td><td>0.2489</td><td>0.2939</td><td>-</td><td>-</td></tr><tr><td rowspan="13">Deep Learning</td><td>OFF-ApexNet [15]</td><td>2019</td><td>0.2386</td><td>0.2806</td><td>-</td><td>-</td></tr><tr><td>AlexNet [22]</td><td>2012</td><td>-</td><td>-</td><td>0.2570</td><td>0.2634</td></tr><tr><td>STSTNet [36]</td><td>2019</td><td>0.2714</td><td>0.3108</td><td>0.3795</td><td>0.3792</td></tr><tr><td>RCN-A [52]</td><td>2020</td><td>0.2751</td><td>0.3123</td><td>0.3928</td><td>0.3893</td></tr><tr><td>MERSiam [58]</td><td>2021</td><td>0.3184</td><td>0.3532</td><td>0.3184</td><td>0.3532</td></tr><tr><td>FGRL [24]</td><td>2021</td><td>0.0736</td><td>0.1429</td><td>0.3333</td><td>0.2636</td></tr><tr><td>FR [24, 60]</td><td>2022</td><td>0.3559</td><td>0.3814</td><td>0.3493</td><td>0.3413</td></tr><tr><td>MMNet [25]</td><td>2022</td><td>0.2649</td><td>0.2776</td><td>0.3706</td><td>0.3646</td></tr><tr><td>BDCNN [4]</td><td>2022</td><td>0.2975</td><td>0.3314</td><td>0.5050</td><td>0.5164</td></tr><tr><td>Micro-BERT [42]</td><td>2023</td><td>-</td><td>-</td><td>0.5604</td><td>0.6125</td></tr><tr><td>HTNet [50]</td><td>2024</td><td>0.3243</td><td>0.3368</td><td>0.5767</td><td>0.5415</td></tr><tr><td>HSTA [16]</td><td>2024</td><td>-</td><td>-</td><td>0.593</td><td>0.618</td></tr><tr><td>Ours</td><td>-</td><td>0.3853</td><td>0.3978</td><td>0.6221</td><td>0.6226</td></tr></table>
+
+# 5.2. Comparison to State-of-the-art Methods
+
+Tab. 2 list the SOTA comparisons on DFME and CAS(ME) $^3$ . The confusion matrices are shown in the Suppl.
+
+Regarding DFME, classifying ME samples into seven categories poses significant challenges, resulting in relatively low UF1 and UAR scores across all methods. However, our proposed method outperforms all others in every metric. Specifically, Our method outperforms I3D by  $9.30\%$  in UF1 and  $9.20\%$  in UAR, and surpasses LBP-TOP by  $15.17\%$  in UF1 and  $13.25\%$  in UAR, highlighting its effectiveness in extracting critical and discriminative features from ME clips. Additionally, compared to recent deep learning methods like FR, our approach yields  $2.94\%$  and  $1.64\%$  higher UF1 and UAR, confirming the benefits of incorporating facial topology and structured muscle motion for enhanced performance.
+
+Regarding CAS(ME) $^3$ , the primary challenge lies in its sample complexity. Compared to baseline methods (STST-Net, RCN-A, FR), our proposed method achieves over approximately  $20\%$  higher UF1 and UAR scores, marking a significant advancement. Our method surpasses three recent SOTA approaches in MER, including HTNet, which employs a hierarchical Transformer for local feature learning via self-attention. Specifically, our approach outperforms HTNet by  $4.54\%$  in UF1 and  $8.11\%$  in UAR, leveraging psychological insights and statistical patterns to capture deeper facial muscle dynamics. Additionally, it exceeds Micro-BERT and HSTA by  $6.17\%$  and  $2.91\%$  in UF1, and  $1.01\%$  and  $0.46\%$  in UAR, respectively. By mining facial movement patterns to better understand topology, our model achieves improved metrics, indicating enhanced accuracy in classifying all emotion categories.
+
+# 5.3. Ablation Study
+
+Tab. 3 listed the ablation study results on DFME.
+
+Table 3. Ablation study. L, G, S and D represent Local (upper and lower face), Global, Single stream and Dual Stream, respectively.  
+
+<table><tr><td rowspan="2">Setting</td><td colspan="2">LRM</td><td colspan="2">AFR</td><td colspan="2">InceptionNet</td><td rowspan="2">UF1↑</td><td rowspan="2">UAR↑</td></tr><tr><td>LFE</td><td>SSE</td><td>L</td><td>G</td><td>S</td><td>D</td></tr><tr><td>I</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3249</td><td>0.3404</td></tr><tr><td>II</td><td>✓</td><td></td><td></td><td></td><td></td><td>✓</td><td>0.3362</td><td>0.3517</td></tr><tr><td>III</td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>✓</td><td>0.3480</td><td>0.3624</td></tr><tr><td>IV</td><td>✓</td><td>✓</td><td>✓</td><td></td><td></td><td>✓</td><td>0.3629</td><td>0.3723</td></tr><tr><td>V</td><td>✓</td><td>✓</td><td></td><td>✓</td><td></td><td>✓</td><td>0.3604</td><td>0.3658</td></tr><tr><td>VI</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>0.3853</td><td>0.3978</td></tr><tr><td>Setting</td><td colspan="3">Without AU Group</td><td colspan="3">With AU Group</td><td>UF1↑</td><td>UAR↑</td></tr><tr><td>VII</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>0.3683</td><td>0.3793</td></tr><tr><td>VIII</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3853</td><td>0.3978</td></tr><tr><td>Setting</td><td colspan="3">Psychological prior</td><td colspan="3">Data-driven Prior</td><td>UF1↑</td><td>UAR↑</td></tr><tr><td>IX</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.3615</td><td>0.3701</td></tr><tr><td>X</td><td></td><td>✓</td><td></td><td></td><td></td><td></td><td>0.3723</td><td>0.3832</td></tr><tr><td>XI</td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>0.3705</td><td>0.3767</td></tr><tr><td>XII</td><td></td><td>✓</td><td></td><td></td><td>✓</td><td></td><td>0.3853</td><td>0.3978</td></tr></table>
+
+Impact of AU Feature: Setting I, which uses only full face OF as input, serves as our baseline for evaluating the role of AU features in MER. In Setting II, integrating AU features into the Dual Stream InceptionNet leads to a  $1.13\%$  improvement in both UF1 and UAR. This improvement demonstrates that incorporating AU features significantly enhances the model's ability to recognize MEs, and underscores the value of fusing multiple feature types to strengthen model performance.
+
+Impact of ROI Relationship Modeling: The results in Setting III show improvements of  $1.18\%$  in UF1 and  $1.07\%$  in UAR compared to Setting II, indicating that the model effectively captures complex dependencies between ROIs and extracts more discriminative feature representations.
+
+Impact of AU grouping: We compared AU feature extraction from the global face with our AU grouping strategy (Setting VII vs. VIII), the performance improvement (UF1:  $1.70\%$ , UAR:  $1.85\%$ ), confirming that AU grouping enables the network to learn more representative AU features.
+
+Impact of Modeling the Topological Structure of ME Muscle Movements: Compared to Setting III, Setting IV, including local muscle movement topology modeling, improves UF1 and UAR by  $1.49\%$  and  $0.99\%$ , respectively. Setting V, which adds global muscle movement topology modeling, shows gains of  $1.24\%$  in UF1 and  $0.34\%$  in UAR over Setting III. Combining both local and global topology modeling yields the best performance on DFME. These results demonstrate that incorporating topological modeling of muscle movements enhances MER.
+
+Impact of Prior Knowledge: Tab. 3 presents the ablation experiments to evaluate the impact of using prior knowledge for constructing facial muscle topology. In particular, compared to Setting IX, Setting X, which uses only psychological knowledge, improves UF1 and UAR by  $1.08\%$  and
+
+![](images/7d0359ab475a41676321769bfdef60e3582e90475e1d72ee6269ed907c5d0965.jpg)
+
+![](images/a86bcd8e0a2ef30abe66e39830767a2927e9ac24819ae8d569c5be5d4acfe90c.jpg)
+
+![](images/ed619347e1503f8d05331087100313350ff40d9aa809b553fab8d6c994e8edc0.jpg)  
+(a) UF1 comparison across different clients.
+
+![](images/4dca360b1ef279a4b74913e2b235d6d2581047bd809eaacd2dfa43f486177ef5.jpg)
+
+![](images/4d64020bb307952c01cb4203c06cbd5b28c204536d2809b574d8cc0743ca013d.jpg)
+
+![](images/7ce7a4851e79c5bfbe1887a3d439063c725adae50997589753a075c3fe04ae49.jpg)
+
+![](images/d60e9d362a4ca3a84d4fb9c4de393ad2b5ae925c765090503f0a69e38f92bcc4.jpg)
+
+![](images/ca2225a778ac85bbd9856be72ef91346a4870f018b736395c5f8e1ce97c1f509.jpg)  
+Figure 5. Compare the performance of different FL frameworks on different clients: UF1 and convergence. See UAR comparison in Suppl.
+
+![](images/9758b0502f57eb674eb29a4c4cbace84da198af57d5284b0fb0e007d7bf93c9b.jpg)
+
+![](images/d6e5db3f15daf1da9eeb5b183ec476c91b6fe6759cc2c50eeadc434b1fbd0e13.jpg)  
+(b) Convergence comparison across different clients.
+
+![](images/164efcb98172282f2bc845b5954f618bf38f57aef2f9040df21f9014b03d4a75.jpg)
+
+![](images/0278f3eb28b06d6cbecc906342c457ab2c577fc37247aa6ffcea9c6160bebf87.jpg)
+
+![](images/56f21f9e921cc95ebcf6812103c58b7add37417461d1b73fabeea964d84ffd19.jpg)
+
+![](images/5d110c145f2ae6a3be10e74af597573fbc31866014983bc5e3e2f04bef4c399e.jpg)
+
+$1.31\%$ , respectively. Setting XI, incorporating only data-driven knowledge, shows gains of  $0.9\%$  in UF1 and  $0.66\%$  in UAR. When both psychological and data-driven knowledge are combined (Setting XII), the improvements reach  $2.38\%$  in UF1 and  $2.77\%$  in UAR, proving the effectiveness of the prior knowledge. Constructing a prior adjacency matrix allows the model to capture complex facial muscle topology, while data-driven knowledge directs attention to uncover intrinsic movements patterns of facial muscles.
+
+# 5.4. Federated Experiment
+
+Since FL aims to enhance MER performance on individual clients in scenarios with limited sample sizes and data privacy issue, and given that DFME and  $\mathrm{CAS}(\mathrm{ME})^3$  have large sample size, we partition the datasets as mentioned in Section 5.1 and treat the subdivisions as separate clients.
+
+While our focus is on application rather than fundamental FL innovation, our experiments confirm the effectiveness of our P-FedProx method, which is tailored for ME data distributions. Benchmarked against several open-source SOTA methods, our approach excels at mitigating small-sample challenges while preserving data privacy. Specifically (Fig. 5), the results show P-FedProx outperforms both the single-client baseline and traditional FL methods (FedAvg, FedProx), with particularly significant gains on clients with more challenging data distributions (Clients 6-7). Compared to recent personalized FL methods, our approach surpasses FedRep and ELLP and achieves performance competitive with the state-of-the-art FedAS, yet with a significantly simpler implementation. These consistent gains demonstrate that our weighted model initialization effectively addresses the data heterogeneity that challenges
+
+traditional FL, thereby mitigating ME sample scarcity while ensuring data privacy.
+
+Meantime, we note that all FL methods achieved good performance on the local clients from DFME, which may be due to the fact that these clients have a similar amount of data and slight differences in data distribution, presenting fewer challenges for federated learning.
+
+Besides, we analyze the training loss progression of different federated algorithms over communication rounds. We found that P-FedProx demonstrates the smoothest convergence curves with minimal oscillations, particularly evident in Clients 1-5. On the other hand, P-FedProx converges significantly faster than other FL methods. This rapid early convergence suggests that personalized global model assignment provides clients with better initialization states.
+
+# 6. Conclusion
+
+MER is challenged by limited sample sizes, subtle features, and privacy concerns in real-world applications. To address these issues, we conduct a psychological study to provide structured insights into facial muscle dynamics. We then develop a FED-PsyAU framework that integrates these findings with data-driven patterns for hierarchical learning of dynamic features, enhancing MER performance. Additionally, the FL framework improves MER across clients while preserving data privacy through iterative model updates. The comprehensive experiments validate our approach's effectiveness. In the future, we will integrate additional AUs to build a more comprehensive ME topology information and further advance MER in real-world applications through FL and semi-supervised approaches.
+
+# 7. Acknowledgment
+
+This research was partially funded by 1) the National Natural Science Foundation of China (62476269, 62276252); 2) the Youth Innovation Promotion Association CAS.
+
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+        "type": "text",
+        "text": "{brian.k.isaac-medina, yona.f.binti-abd-gaus, toby.breckon}@durham.ac.uk mauricio.adrian.che.moguel@univie.ac.at samet.akcay@intel.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "text": "Modern machine learning models, that excel on computer vision tasks such as classification and object detection, are often overconfident in their predictions for Out-of-Distribution (OOD) examples, resulting in unpredictable behaviour for open-set environments. Recent works have demonstrated that the free energy score is an effective measure of uncertainty for OOD detection given its close relationship to the data distribution. However, despite that free energy-based methods representing a significant empirical advance in OOD detection, our theoretical analysis reveals previously unexplored and inherent vulnerabilities within the free energy score formulation such that in-distribution and OOD instances can have distinct feature representations yet identical free energy scores. This phenomenon occurs when the vector representing the feature space difference between the in-distribution and OOD sample belongs to the null space of the last layer of a neural-based classifier. To mitigate these issues, we explore lower-dimensional feature spaces to reduce the null space footprint and introduce novel regularisation to maximize the least singular value of the final linear layer, hence enhancing intersample free energy separation. We refer to these techniques as Free Energy Vulnerability Elimination for Robust Out-of-Distribution Detection (FEVER-OOD). Extensive experimentation shows that FEVER-OOD improves OOD detection in CIFAR-10 with  $28.22\\%$  FPR95 and 94.78 AUROC vs  $33.66\\%$  FPR95 and 92.15 AUROC of the baseline model, CIFAR-100 with  $42.77\\%$  FPR95 and 89.98 AUROC vs  $50.96\\%$  FPR95 and 88.06 AUROC of the baseline model, and achieves state of the art OOD detection in Imagenet-100, with average OOD FPR95 of  $36.50\\%$  and an AUROC of 92.74 when used with the Dream-OOD model, compared with a  $39.33\\%$  and 91.84 AUROC without FEVER-OOD.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Out-of-distribution (OOD) detection (c.f. anomaly/outlier detection), aims to identify abnormal samples that deviate significantly from a given data distribution. Whilst",
+        "bbox": [
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+        "type": "image",
+        "img_path": "images/848d7e663e2933ff92e896c599e56815165ef8b69813df492dfc4ac6e02b7a86.jpg",
+        "image_caption": [
+            "Free Energy-based OOD (VOS)"
+        ],
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+    {
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+        "img_path": "images/b79fe209468046edba6d570b17932480933ce0e0db970c3334cea190f38ac4df.jpg",
+        "image_caption": [
+            "FEVER-OOD (VOS)",
+            "Figure 1. FEVER-OOD improves baseline Free Energy-based OOD detection methods, where baseline methods predict OOD classes as in-distribution (left, blue), while FEVER-OOD classifies them as OOD (right, green)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "type": "text",
+        "text": "OOD is essential in developing deployable machine learning systems, to ensure valid inference only on data drawn from same distribution used in training [24, 36, 44], real-world deployments often involve scenarios where models encounter unseen OOD classes that could otherwise undermine decision stability and hence wider system robustness.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Methods such as deep ensembles [23], ODIN [27], Mahalanobis distance-based detection [25], and generalized ODIN [16] all utilize softmax() to differentiate indistribution from OOD. Whilst intuitive, such approaches often struggle as deep neural networks commonly yield overly high softmax() scores, even for inputs far from the training data distribution [31]. Given OOD and indistribution samples should have significant spatial separation in any given feature space, Liu et al. [29] developed an alternative scoring function to effectively measure the alignment of a given sample to an a priori learned distribution. Denoted as the free energy scoring function, this formulation demonstrates superior OOD performance across both classification [7-9] and detection tasks [6, 7, 18, 21].",
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+    {
+        "type": "text",
+        "text": "Despite free energy-based methods representing a significant empirical advance in OOD detection, our theoretical analysis reveals previously unexplored and inherent vulnerabilities within the free energy score formulation that could impact their practical reliability. These vulnerabilities reveal that in-distribution and OOD instances can have distinct feature representations yet produce identical free en",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This ICCV 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": "4529",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "ergy scores. This phenomenon occurs in the feature space when the vector direction representing the difference between an in-distribution and an OOD sample lies within the null space of the last layer of neural-based classifier. Such regions, effectively \"blind spots\" in terms of OOD, lead to OOD and in-distribution generating identical or near-identical free energy score values.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To mitigate these issues, we explore lower-dimensional feature spaces to effectively reduce the size of the null space. In addition, we also introduce a novel regulariser to maximize the least singular value of the final linear layer, hence enhancing inter-sample free energy separation to improve OOD robustness. We refer to these techniques as Free energy Vulnerability Elimination for Robust Out-of-Distribution Detection (FEVER-OOD).",
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+    {
+        "type": "text",
+        "text": "In summary, our key contributions in this paper are:",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- The identification of inherent free energy score vulnerabilities, where under null-space conditions, in-distribution and OOD instances will yield similar free energy scores despite differing feature representations. Denoted as Null Space Vulnerabilities (NSV) such conditions readily occur when the feature dimension exceeds the number of classes. Additionally, such free energy similarity can be influenced by the least singular vector (LSV) of the last linear layer of a neural-based classifier, leading to what we denote as Least Singular Value Vulnerabilities (LSVV). Both vulnerabilities negatively impact in-distribution to OOD discrimination.",
+            "- Novel formulations that mitigate the NSV and LSVV impact (Fig. 1). To address NSV, we introduce an additional layer to reduce the null space whilst for LSVV, we develop an LSV Regulariser that maximizes the least singular value, guaranteeing detectable energy variations from small feature-space differences and hence enhancing inter-sample energy scores discrimination. Furthermore, we explore a Condition Number Regulariser to promote balanced energy changes for displacements in all feature-space direction hence ensuring improved uniformity in energy score variations.",
+            "- Comprehensive experiments and ablation studies using established benchmark datasets over both object classification and detection tasks, that demonstrate the effectiveness of FEVER-OOD in improving OOD detection performance. Specifically, Dream-OOD [8] with FEVER-OOD trained on Imagenet-100 [35] as in-distribution decreases the FPR95 from  $39.33\\%$  to  $36.50\\%$  and increases the average AUROC from 91.84 to 92.74, achieving state-of-the-art performance for OOD detection."
+        ],
+        "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": "Identifying OOD samples is a crucial yet inherently challenging problem, as models are not exposed to, and hence cannot reliably differentiate, OOD samples.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "OOD Detection: to overcome this challenge, researchers have begun incorporating additional data during training to establish a more conservative and safe decision boundary against OOD inputs. Some methods [1, 19] have used unlabeled data to regularise model training while still focusing on classifying labeled in-distribution data, while others [2] leverage human assistance to strategically label examples within a novel maximum disambiguation region. Despite its potential, leveraging unlabeled data is non-trivial due to the heterogeneous mix of in-distribution and OOD instances. The absence of a clean OOD set presents significant challenges in designing effective OOD learning algorithms. A different branch of works incorporate post-hoc methods, focusing on designing OOD scoring mechanisms at test time. Hendrycks and Gimpel [15] introduced the maximum predicted softmax() probability as an in-distribution score function, establishing an initial baseline for scoring OOD detection. Similarly, ODIN [27] aims to widen the gap between values in the softmax() score vectors by temperature scaling and gradient-based input perturbation, enhancing the separation between in-distribution and OOD instances. Lee et al. [25] use the Mahalanobis distance between the average softmax() vectors of images and incorporate intermediate features to improve detection performance and robustness. Nonetheless, the misalignment between the softmax() score and the true data density [29, 32] ultimately makes these techniques a suboptimal solution to OOD detection. Closer to our work, Cook et al. [4] identify null space adversarial attacks, proposing that instances with large magnitude of their projection onto the span of the null space of a neural network classifier would likely be an outlier. Similarly, Wang et al. [41] propose that since the features lie in low-dimensional manifolds, outliers are likely to deviate from the principal subspace, i.e. the span of the eigenvectors or the largest eigenvalues, of the in-distribution data. Therefore, OOD instances are detected with respect to the magnitude of the component of the perpendicular subspace to the principal subspace.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Energy-based OOD Detection: to address these limitations, Liu et al. [29] propose to use a free energy-based in-distribution score function instead of the softmax() score to identify OOD instances. This approach regularises the model to produce lower energy values for in-distribution and higher energy values for auxiliary outliers, creating a significant energy gap that enhances the model ability to detect OOD samples. Energy-based OOD modeling has enabled novel outlier synthesis paradigms. For instance, Du et al. [7] propose virtual outlier synthesis (VOS) by sampling outliers from low-likelihood in-distribution regions. VOS has shown to be effective for classification and object-level OOD detection. Further outlier synthesis techniques based on VOS have been proposed, including using normalizing flows [21], sampling based on the in-distribution boundary",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4530",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "instances [39] or extending VOS when class labels are unavailable [18]. In addition, VOS techniques arensuitable for object detection [7, 21]. Whilst VOS and subsequent works synthesize outliers in the feature space, Dream-OOD [8] uses Stable Diffusion [34] to generate outliers in the pixel-space, learning better discriminative free-score values for OOD instances and providing visual examples of outliers. Energy-based methods have shown great performance, becoming state-of-the-art in several benchmarks (e.g., Dream-OOD [8] for ImageNet-100 in-distribution), hence we focus in the properties of these methods. Notwithstanding that the core idea of the energy score is that OOD samples must have a significantly different free energy than in-distribution sample, we examine some inherent vulnerabilities in the energy formulation based on the null space and least singular value of the last linear layer of neural-based classifiers.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Preliminaries: Free Energy Score",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The goal of OOD detection is to detect outliers,  $\\mathbf{v}$ , that have a low probability in the true (unknown) in-distribution density  $p(\\mathbf{x})$ . However, the computation of  $p(\\mathbf{x})$  is usually unfeasible or computationally untractable, so we instead resort to additional information. Now consider that we also have a set of in-distribution categories  $\\{1,\\dots ,K\\}$  such that if we know the joint probability distribution,  $p(\\mathbf{x},k)$ , for  $k\\in \\{1,\\ldots ,K\\}$ , we could marginalize  $p(\\mathbf{x})$ . Nonetheless, since the actual joint probabilities  $p(\\mathbf{x},k)$  might be also untractable, we could instead use non-negative arbitrary potential functions  $\\phi (\\mathbf{x},k)$  that measure the affinity of the states of  $\\mathbf{x}$  and  $k$  [12]. In this sense, we can construct the unnormalized probability:",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {p} (\\mathbf {x}) = \\sum_ {k = 1} ^ {K} \\phi (\\mathbf {x}, k) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            218,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "that gives an idea of the likelihood  $\\mathbf{x}$ . Furthermore, energy-based models enforce the non-negative constraint of  $\\phi$  by:",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\phi (\\mathbf {x}, k) = \\exp (- E (\\mathbf {x}, k)), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            659,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $E$  is an unbounded arbitrary function called the energy. By substituting Eq. (2) into Eq. (1) and taking the negative  $\\log^1$ , we get a value known as the free energy:",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} (\\mathbf {x}) = - \\log \\tilde {p} (\\mathbf {x}) = - \\log \\sum_ {k = 1} ^ {K} \\exp (- E (\\mathbf {x}, k)), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and more recently used as a concept in OOD detection [7, 8, 18, 21, 29]. To get the actual density  $p(\\mathbf{x})$ , we must compute the normalizing partition function of Eq. (1); since we are interested in distinguishing between in-distribution and OOD,  $\\mathcal{F}(\\mathbf{x})$  thus serves well for this purpose.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/bdd060b5b3baf52a609a84f74c4399fcafd9d4e86650030073fdec620e75a556.jpg",
+        "image_caption": [
+            "Figure 2. Vulnerabilities of Free Energy-based OOD detection. Directions in the Null Space do not change the energy, while the LSV direction has minimal change, compared to other directions."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            227
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In a general machine learning context, a classifier  $f(\\mathbf{x};\\theta):\\mathbb{R}^d\\to \\mathbb{R}^K$  with learned parameters  $\\theta$  assigns categorical unnormalized probabilities  $f_{k}(\\mathbf{x};\\theta)$ , called logits, for a given  $\\mathbf{x}\\in \\mathbb{R}^d$ . While the logits are usually normalized using the softmax() function in order to obtain a probability distribution, they can also be used as the energy  $E$  in Eq. (2). This realization enables the use of the free energy (Eq. (3)) as a measure of uncertainty for a classifier:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} (\\mathbf {x}) = - \\log \\sum_ {k = 1} ^ {K} \\exp \\left(f _ {k} (\\mathbf {x}; \\theta)\\right). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Liu et al. [29] demonstrate that Eq. (4) is superior for effective OOD detection when compared to use of softmax() whilst Du et al. [7] explicitly use the free energy score (Eq. (4)) to perform binary classification between indistribution and OOD by training with synthetic outliers.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. Vulnerabilities of the Free Energy Score",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Although the free energy (Eq. (4)) is an effective uncertainty measure for OOD detection [7, 29], here we examine some inherent vulnerabilities when used in conjunction with a neural network based classifier. Firstly, Sec. 4.1 investigates OOD instances that have similar energies as in-distribution samples, whilst Sec. 4.2 discusses minimal changes in free energy, and finally Sec. 4.3 outlines our proposed approach to minimize the impact of these vulnerabilities.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Null Space Vulnerability",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Consider a neural network-based classifier  $f = (g \\circ h)(\\mathbf{x})$  where  $h(\\mathbf{x}): \\mathbb{R}^d \\to \\mathbb{R}^{d'}$  encodes the input into a  $d'$ -dimensional feature vector and  $g: \\mathbb{R}^{d'} \\to \\mathbb{R}^K$  is the last layer of the neural network that transforms the features into unnormalized class probabilities (i.e., the logits). If  $g$  is a linear layer (as for most classifiers [5, 14, 43]), then:",
+        "bbox": [
+            511,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf (\\mathbf {x}) = \\mathrm {W} _ {c l s} ^ {\\top} h (\\mathbf {x}), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            642,
+            840,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathrm{W}_{cls} \\in \\mathbb{R}^{d' \\times K}$  are learnable weights. Hence, the logits  $f_{k}(\\mathbf{x};\\theta)$  correspond to the  $k$ -th index of  $f(\\mathbf{x})$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "$^{1}$ N.B. the signs of the free energy and the argument of the exponent of  $\\phi$  are arbitrarily negative for historical reasons.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4531",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The core idea of energy-based OOD is that outliers  $\\mathbf{v}$  have a significantly different free energy,  $\\mathcal{F}(\\mathbf{v})$ , from in-distribution samples,  $\\mathcal{F}(\\mathbf{x})$ . Since OOD instances should be far from in-distribution samples in the feature space [7, 39], the expected distance from the inlier features  $h(\\mathbf{x})$  and outlier features  $h(\\mathbf{v})$  should be greater than a given boundary distance,  $d_b$ , as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbb {E} \\left[ \\| h (\\mathbf {x}) - h (\\mathbf {v}) \\| \\right] \\geq d _ {b}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            199,
+            205,
+            483,
+            224
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "for a norm  $\\|\\cdot\\|$ . In other words, the inliers remain bounded to a region in the feature space while outliers are unbounded. Therefore, the expected distance between inliers and outliers is greater than a bounding distance  $d_b$ . Subsequently, we can rewrite Eq. (6) as:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh (\\mathbf {v}) = h (\\mathbf {x}) + \\boldsymbol {\\delta}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            222,
+            318,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\delta$  is a vector with  $\\mathbb{E}[\\|\\delta\\|] \\geq d_b$ . By substituting Eq. (7) into Eq. (5) we obtain the following:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf (\\mathbf {v}) = \\mathrm {W} _ {c l s} ^ {\\top} (h (\\mathbf {x}) + \\boldsymbol {\\delta}) = f (\\mathbf {x}) + \\mathrm {W} _ {c l s} ^ {\\top} \\boldsymbol {\\delta}. \\qquad (8)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            404
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "However within this formulation, if  $\\mathrm{W}_{cls}$  has more rows than columns, which occurs when the feature dimension is larger than the number of classes, the size of the null space of  $\\mathrm{W}_{cls}^{\\top}$ , called the nullity, is nullity  $(\\mathrm{W}_{cls}^{\\top}) = d' - \\operatorname{rank}(\\mathrm{W}_{cls})$  due to the rank-nullity theorem. Mathematically, this means that there exists a linear subspace  $\\mathrm{Null}(\\mathrm{W}_{cls}^{\\top}) \\subset \\mathbb{R}^{d'}$  such that if  $\\delta \\in \\mathrm{Null}(\\mathrm{W}_{cls}^{\\top})$  then  $\\mathrm{W}_{cls}^{\\top} \\delta = 0$ . Within our OOD context, if an outlier instance,  $\\mathbf{v}$ , has a feature representation,  $h(\\mathbf{v})$ , such that its difference with respect to the inlier feature representation,  $h(\\mathbf{x})$ , of any inlier instance,  $\\mathbf{x}$ , is in the null space of the last layer of the classifier, then their free energy scores are the same:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nh (\\mathbf {v}) - h (\\mathbf {x}) \\in \\operatorname {N u l l} \\left(\\mathrm {W} _ {c l s} ^ {\\top}\\right) \\Rightarrow \\mathcal {F} (\\mathbf {x}) = \\mathcal {F} (\\mathbf {v}). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            129,
+            616,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Practically, Eq. (9) is telling us that it is possible for in-distribution and OOD instances to have different feature representations (satisfying the condition of Eq. (6)) and yet have the same free energy score, as depicted in Fig. 2. This fundamentally challenges the notion that free energy is an effective mechanism for OOD detection as any approaches reliant on Eq. (3), such as [7, 8, 18, 21, 29], contain inherent \"detection blind-spots\" as per Eq. (9). We denote Eq. (9) as the Null Space Vulnerabilities (NSV) of classifier  $f$  with size nullity  $(\\mathrm{W}_{cls}^{\\top}) = d' - \\mathrm{rank}(\\mathrm{W}_{cls})$ . An approach to minimize this vulnerability is outlined in Sec. 4.3.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As an additional remark, NSV are inherent in energy-based methods; while some post hoc methods use the projection of features onto the null space as a discriminator between in-distribution and OOD [4, 41], energy-based methods use the classification logits for detecting outliers, hence the null space projection does not change the OOD score.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Minimal Change of Free Energy",
+        "text_level": 1,
+        "bbox": [
+            511,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now turn our attention to the case where  $\\delta$  is not in the null space of  $\\mathbf{W}_{cls}^{\\top}$ . Furthermore, we can focus on  $\\delta$  orthogonal to  $\\mathrm{Null}(\\mathbf{W}_{cls}^{\\top})$ , since every vector in the domain of  $\\mathbf{W}_{cls}^{\\top}$  can be decomposed into one component in  $\\mathrm{Null}(\\mathbf{W}_{cls}^{\\top})$  and one component in  $\\mathrm{Null}(\\mathbf{W}_{cls}^{\\top})^{\\perp}$ , and the effect of the component in  $\\mathrm{Null}(\\mathbf{W}_{cls}^{\\top})$  will be dealt with using the null space reduction method (Sec. 4.3).",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In order to create more discriminative OOD detectors based on the free energy score, we investigate cases where the difference in OOD and in-distribution free energy is minimal. We can state our problem formulation to find the case that minimizes the free energy difference:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\min  _ {\\substack {\\boldsymbol {\\delta}: \\| \\boldsymbol {\\delta} \\| \\geq d _ {b}, \\\\ \\boldsymbol {\\delta} \\in \\operatorname {Null} \\left(\\mathrm {W} _ {c l s} ^ {\\top}\\right) ^ {\\perp}}} | \\mathcal {F} (\\mathbf {v}) - \\mathcal {F} (\\mathbf {x}) | \\\\ = \\min  _ {\\substack {\\boldsymbol {\\delta}: \\| \\boldsymbol {\\delta} \\| \\geq d _ {b}, \\\\ \\boldsymbol {\\delta} \\in \\operatorname {Null} \\left(\\mathrm {W} _ {c l s} ^ {\\top}\\right) ^ {\\perp}}} \\left| \\log \\frac {\\sum_ {k} ^ {K} \\exp \\left(f _ {k} (h (\\mathbf {x}))\\right)}{\\sum_ {k} ^ {K} \\exp \\left(f _ {k} (h (\\mathbf {x}) + \\boldsymbol {\\delta})\\right)} \\right|. \\end{array} \\tag{10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            535,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Whilst in Eq. (10) we set  $\\| \\delta \\| \\geq d_b$  instead of  $\\mathbb{E}\\left[\\| \\delta \\| \\right]\\geq$ $d_{b}$ , in reality we are just interested in the case of non-zero  $\\delta$  since otherwise the solution would be trivial. Whilst the solution to Eq. (10) may be challenging to obtain, we note the difference in free-energies tends to 0 if the value inside the  $\\log ()$  function tends to 1. This is equivalent to making  $f_{k}(h(\\mathbf{x}))$  and  $f_{k}(h(\\mathbf{x}) + \\delta)$  similar for all  $k$ . Therefore, considering that  $f_{k}$  is in the form of Eq. (5), our problem consists on finding the following proxy minimum:",
+        "bbox": [
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+            404,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{r l} \\underset {\\delta : \\| \\boldsymbol {\\delta} \\| \\geq d _ {b},} {\\min } & \\| \\mathrm {W} _ {c l s} ^ {\\top} (h (\\mathbf {x}) + \\boldsymbol {\\delta}) - \\mathrm {W} _ {c l s} ^ {\\top} h (\\mathbf {x}) \\| \\\\ & = \\underset {\\substack {\\boldsymbol {\\delta}: \\| \\boldsymbol {\\delta} \\| \\geq d _ {b}, \\\\ \\boldsymbol {\\delta} \\in \\operatorname {Null} \\left(\\mathrm {W} _ {c l s} ^ {\\top}\\right) ^ {\\perp}}} {\\min } \\| \\mathrm {W} _ {c l s} ^ {\\top} \\boldsymbol {\\delta} \\|. \\end{array} \\tag{11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            551,
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+            631
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the  $L^2$ -norm in Eq. (11), we thus obtain:",
+        "bbox": [
+            511,
+            643,
+            810,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\substack {\\boldsymbol {\\delta}: \\| \\boldsymbol {\\delta} \\| _ {2} \\geq d _ {b}, \\\\ \\boldsymbol {\\delta} \\in \\operatorname {Null} \\left(\\mathrm {W} _ {c l s} ^ {\\top}\\right) ^ {\\perp}}} \\| \\mathrm {W} _ {c l s} ^ {\\top} \\boldsymbol {\\delta} \\| _ {2} = d _ {b} \\sigma_ {m i n} \\left(\\mathrm {W} _ {c l s}\\right), \\tag{12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            669,
+            906,
+            707
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma_{\\min}(\\mathrm{W}_{cls})$  is the least singular value of  $\\mathrm{W}_{cls}$  (see further mathematical formulation details in Supp. Mat.).",
+        "bbox": [
+            511,
+            719,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Subsequently, Eq. (12) holds for the case where  $\\delta$  is in the direction corresponding to the least singular value, such that the change in the free energy will be smaller than any other direction for  $\\delta$  (and considering  $\\delta \\in \\mathrm{Null}(\\mathrm{W}_{cls}^{\\top})^{\\perp}$ ). We name this result (from Eq. (12)) the Least Singular Value Vulnerabilities (LSVV) of  $f$ . In our OOD context, it means that there could exist some outliers far from the inlier distribution, in terms of Eq. (6), with similar free energy scores because they may fall in the direction of the least singular value of  $\\mathrm{W}_{cls}$ . Again, this fundamentally challenges",
+        "bbox": [
+            511,
+            750,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4532",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the notion that free energy is an effective mechanism for OOD as free energy has been shown to be non-linear with respect to a given feature representation,  $h(\\cdot)$ .",
+        "bbox": [
+            89,
+            90,
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This analysis is itself inspired by the seminal adversarial attacks analysis of Simon-Gabriel et al. [37], where they instead maximize the change in the classifier response for small input perturbations. Whilst here we are modelling the opposite problem, (i.e., the minimum change in the classifier for perturbations larger than a non-zero value), we could consider this analysis as an effective adversarial attack mechanism for the OOD domain.",
+        "bbox": [
+            89,
+            137,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Null Space Reduction & Regularisation",
+        "text_level": 1,
+        "bbox": [
+            89,
+            267,
+            429,
+            282
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce our Free Energy Vulnerability Elimination for Robust OOD Detection (FEVER-OOD) framework, where we explore readily available methods to minimize the NSV (Sec. 4.1) and LSVV (Sec. 4.2) impact potential within free energy score based OOD approaches.",
+        "bbox": [
+            89,
+            289,
+            483,
+            364
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Null Space Reduction (NSR). For NSV, we propose to reduce the null space by adding an extra linear layer  $g' : \\mathbb{R}^{d'} \\to \\mathbb{R}^r$ , where we choose  $r < d'$  to reduce the size of the NSV (Fig. 3). We denote this method as  $r$ -null space reduction ( $r$ -NSR). Therefore, the new classifier becomes  $f' = g \\circ g' \\circ h$  such that the feature representation of a sample is in  $\\mathbb{R}^r$  and is given instead by  $(g' \\circ h)(\\mathbf{x})$ . Effectively, within an OOD context, we are promoting better discrimination between OOD and in-distribution instances.",
+        "bbox": [
+            89,
+            366,
+            483,
+            500
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Least Singular Value Regulariser (LSVR). To minimize the impact of LSVV, we maximise  $\\sigma_{min}(\\mathrm{W}_{cls})$  by adding an LSVR to the loss function  $\\mathcal{L}$  of a baseline method:",
+        "bbox": [
+            89,
+            501,
+            483,
+            546
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {L S V} := \\mathcal {L} + \\lambda_ {L S V} \\sigma_ {\\min } ^ {- 1} \\left(\\mathrm {W} _ {c l s}\\right), \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            171,
+            558,
+            482,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{LSV}$  is a scalar hyperparameter that controls the contribution of the LSV regulariser. It is additionally noted that alternatively maximizing the LSV might also increase the rest of the singular values, resulting in more significant changes of energy in all directions. In the context of OOD detection, LSVR increases the discriminative capacity for OOD detection of baseline methods.",
+        "bbox": [
+            89,
+            587,
+            483,
+            691
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Condition Number (CN) Regulariser. Whilst the LSV regulariser will increase the change in energy for  $\\delta$  in the LSV direction, there is no constraint with regard to the distribution over all other directions. For this reason, we explore a Condition Number Regulariser (CNR):",
+        "bbox": [
+            89,
+            693,
+            483,
+            768
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {C N} := \\mathcal {L} + \\lambda_ {C N} \\kappa \\left(\\mathrm {W} _ {\\text {c l s}}\\right), \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            191,
+            781,
+            482,
+            797
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\kappa (\\mathrm{W}_{cls})$  is the condition number of the WCLS matrix, i.e., the ratio of the greatest and least singular values. Intuitively, this will encourage equalized energy changes for displacements in all directions where we note that Eq. (14) similarly assumes use of the  $L^2$ -norm as per Eq. (12). A different approach to the CNR is the orthogonal constraint",
+        "bbox": [
+            89,
+            809,
+            483,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/9ce8f5922b4e4211f3267ae349a5be11a44052d8378b0f5c650be308d1177588.jpg",
+        "image_caption": [
+            "Figure 3. Null space reduction. We add an extra layer  $g'$  to create  $r$ -dimensional features, reducing the size of the null space."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            537,
+            88,
+            885,
+            299
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "$\\| W_{cls}W_{cls}^{\\top} - I\\|$ . However, this method adds the additional constraint that the singular values must be close to one, which might be a stronger prior than the CNR, hence we opt for the latter. The gradients for the singular values in Eqs. (13) and (14) are detailed by Lewis and Sendov [26] (Proposition 6.2) and further discussed in the Supp. Mat.",
+        "bbox": [
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+            340,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experimental Details",
+        "text_level": 1,
+        "bbox": [
+            513,
+            443,
+            715,
+            459
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We study the impact of FEVER-OOD on free energy baseline methods (Sec. 5.1) across different standard datasets (Sec. 5.2). Implementation details are given in Sec. 5.3.",
+        "bbox": [
+            511,
+            469,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Baseline Methods and Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            511,
+            529,
+            870,
+            542
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Three free energy baseline methods for image OOD detection that use the free energy score are tested: VOS [7], FFS [21] and Dream-OOD [8]. These baseline methods learn a small MLP  $\\psi : \\mathbb{R} \\to (0,1)$  that uses the free energy in Eq. (4) to predict an uncertainty score. Since OOD data is unavailable during training, these methods use synthetic outliers to train  $\\psi$ . While VOS and FFS synthesize outliers in the feature space  $h(\\mathbf{x})$ , Dream-OOD generates outliers in the pixel space using Stable Diffusion [34]. Additionally, VOS and FFS are also implemented as object detectors for object-level OOD detection, synthesizing outliers before the last layer of the classification head of a Faster RCNN [33].",
+        "bbox": [
+            511,
+            551,
+            905,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We follow standard evaluation metrics, reporting the false positive rate for OOD detection at  $95\\%$  true positive rate of in-distribution detection (FPR95) and the area under the receiver operating characteristic curve (AUROC). We also assess the effect of our proposed techniques into the main in-distribution task (accuracy for classification and MS-COCO [28] mean average precision (mAP) for object detection). FPR95 and AUROC metrics are reported using a single intersection-over-union threshold for object detection, corresponding to the one that maximises the F-1 score, as described by Harakeh and Waslander [13].",
+        "bbox": [
+            511,
+            734,
+            906,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "4533",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/ad272b348d5f821114dc6e272341dc498cbe59becddba24f00ec480376c0be72.jpg",
+        "table_caption": [
+            "Table 1. CIFAR-10 Results (ID Acc. = in-distribution accuracy; Null Space Reduction (NSR) methods = our approach)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td rowspan=\"2\" colspan=\"2\">FEVER-OOD</td><td colspan=\"12\">OOD Datasets</td><td rowspan=\"3\">ID Acc</td></tr><tr><td colspan=\"2\">Textures</td><td colspan=\"2\">SHVN</td><td colspan=\"2\">Places365</td><td colspan=\"2\">LSUN</td><td colspan=\"2\">iSUN</td><td colspan=\"2\">Avg</td></tr><tr><td>r-NSR</td><td>Regularizer</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td></tr><tr><td rowspan=\"7\">VOS</td><td>-</td><td>-</td><td>50.05±5.70</td><td>86.79±1.28</td><td>39.15±10.52</td><td>91.73±2.88</td><td>40.88±1.75</td><td>89.54±0.69</td><td>8.22±1.02</td><td>98.36±0.20</td><td>30.01±4.44</td><td>94.31±0.84</td><td>33.66±2.21</td><td>92.15±0.59</td><td>94.83±0.16</td></tr><tr><td>-</td><td>λLSV=1.0</td><td>55.58±6.35</td><td>86.71±2.35</td><td>43.00±3.16</td><td>92.09±0.94</td><td>38.78±2.51</td><td>91.14±0.56</td><td>7.36±1.59</td><td>98.46±0.32</td><td>21.23±6.95</td><td>96.23±1.17</td><td>33.19±3.20</td><td>92.92±0.85</td><td>94.66±0.18</td></tr><tr><td>-</td><td>λCN=0.1</td><td>50.80±3.06</td><td>85.39±0.79</td><td>30.78±2.95</td><td>94.04±0.58</td><td>41.60±1.40</td><td>88.77±0.74</td><td>8.50±0.82</td><td>98.30±0.10</td><td>30.91±4.54</td><td>93.41±1.68</td><td>32.52±1.25</td><td>91.98±0.46</td><td>94.69±0.16</td></tr><tr><td>96</td><td>λLSV=1.0</td><td>40.86±4.83</td><td>92.12±1.05</td><td>41.92±16.11</td><td>93.20±2.61</td><td>35.69±2.29</td><td>92.61±0.57</td><td>4.95±1.49</td><td>98.93±0.24</td><td>17.68±5.26</td><td>97.04±0.85</td><td>28.22±4.18</td><td>94.78±0.85</td><td>94.74±0.17</td></tr><tr><td>64</td><td>λLSV=1.0</td><td>44.41±5.39</td><td>91.26±1.29</td><td>34.68±10.93</td><td>94.39±1.72</td><td>35.85±2.56</td><td>92.42±0.53</td><td>5.68±0.57</td><td>98.75±0.13</td><td>24.03±5.91</td><td>96.02±0.95</td><td>28.93±3.86</td><td>94.57±0.66</td><td>94.75±0.13</td></tr><tr><td>32</td><td>λLSV=0.001</td><td>46.53±3.77</td><td>89.67±1.09</td><td>27.84±9.47</td><td>95.29±1.08</td><td>37.33±1.63</td><td>91.77±0.39</td><td>5.65±0.77</td><td>98.82±0.11</td><td>24.09±6.77</td><td>95.68±1.35</td><td>28.29±3.33</td><td>94.25±0.55</td><td>94.68±0.07</td></tr><tr><td>10</td><td>-</td><td>53.20±3.90</td><td>88.97±0.73</td><td>35.62±9.66</td><td>94.41±1.28</td><td>45.73±6.29</td><td>89.73±1.69</td><td>11.72±3.39</td><td>97.93±0.46</td><td>41.80±14.35</td><td>92.51±3.03</td><td>37.61±4.00</td><td>92.71±0.97</td><td>91.95±2.32</td></tr><tr><td rowspan=\"7\">FFS</td><td>-</td><td>-</td><td>52.86±4.49</td><td>83.47±1.67</td><td>38.67±11.21</td><td>89.74±5.19</td><td>44.65±1.29</td><td>87.47±0.77</td><td>6.59±0.92</td><td>98.67±0.17</td><td>31.34±1.88</td><td>93.24±0.97</td><td>34.82±2.03</td><td>90.52±0.98</td><td>94.69±0.15</td></tr><tr><td>-</td><td>λLSV=0.001</td><td>50.74±3.98</td><td>84.93±0.75</td><td>32.25±12.16</td><td>92.97±3.60</td><td>42.99±2.30</td><td>88.30±1.10</td><td>5.76±1.23</td><td>98.82±0.27</td><td>28.16±6.45</td><td>94.18±1.98</td><td>31.98±3.10</td><td>91.84±1.28</td><td>94.73±0.12</td></tr><tr><td>-</td><td>λCN=1.0</td><td>50.08±3.86</td><td>84.92±1.85</td><td>30.91±6.19</td><td>92.77±2.33</td><td>45.69±2.59</td><td>87.16±0.75</td><td>6.22±0.65</td><td>98.73±0.11</td><td>26.60±3.64</td><td>94.80±0.64</td><td>31.90±2.51</td><td>91.67±0.94</td><td>94.85±0.20</td></tr><tr><td>96</td><td>λLSV=1.0</td><td>48.11±5.15</td><td>89.84±1.51</td><td>40.65±15.47</td><td>93.32±3.16</td><td>36.37±2.28</td><td>92.29±0.60</td><td>5.22±1.35</td><td>98.89±0.18</td><td>24.84±10.08</td><td>95.82±1.68</td><td>31.04±5.05</td><td>94.03±1.06</td><td>94.71±0.08</td></tr><tr><td>64</td><td>λLSV=1.0</td><td>51.70±5.67</td><td>88.81±1.09</td><td>33.02±14.09</td><td>94.60±2.30</td><td>39.05±3.73</td><td>91.53±1.23</td><td>5.56±1.95</td><td>98.84±0.30</td><td>26.63±7.51</td><td>95.65±1.12</td><td>31.19±4.32</td><td>93.89±0.69</td><td>94.68±0.08</td></tr><tr><td>32</td><td>-</td><td>46.75±3.49</td><td>89.61±1.40</td><td>31.77±8.73</td><td>94.44±1.35</td><td>41.51±3.38</td><td>90.72±1.02</td><td>4.93±1.11</td><td>99.04±0.16</td><td>28.92±11.23</td><td>94.49±2.94</td><td>30.78±3.70</td><td>93.66±0.95</td><td>94.79±0.18</td></tr><tr><td>10</td><td>-</td><td>54.72±5.89</td><td>84.77±3.23</td><td>45.70±12.95</td><td>91.49±2.27</td><td>41.52±3.27</td><td>89.51±1.31</td><td>8.21±3.59</td><td>98.33±0.67</td><td>28.58±7.75</td><td>94.30±1.82</td><td>35.75±5.26</td><td>91.68±1.38</td><td>94.54±0.17</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5.2. Datasets",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We assess FEVER-OOD with standard datasets for both classification and object detection. For image-level OOD detection (i.e., image classification), we train VOS and FFS using the CIFAR-10 and CIFAR-100 [20] datasets as in-distribution while testing OOD detection in five non-overlapping datasets: Textures [3], SVHN [30], Places365 [47], LSUN [45] and iSUN [11]. We also test Dream-OOD with the CIFAR-100 dataset as in-distribution data with the same OOD datasets. Additionally, we also train Dream-OOD with the Imagenet-100 dataset, a 100 classes partition of Imagenet [35], as in-distribution while testing OOD detection in four datasets: Textures [3], Places365 [47], iNaturalist [40] and SUN [42]. We use the PASCAL VOC [10] dataset as in-distribution for object-level OOD detection using VOS and FFS and test for OOD detection on the MS-COCO dataset [28] removing images containing objects with overlapping in-distribution categories [7].",
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+    },
+    {
+        "type": "text",
+        "text": "5.3. Implementation details",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We follow the established architectural choices of prior works. For image-level OOD detection with VOS and FFS, we use a WideResNet-40 [46] with a 128-dimensional feature space. We choose different NSR values ranging from the feature dim to the number of classes, gradually decreasing the nullity. For CIFAR-10, we evaluate the  $\\{96,64,32,10\\}$ -NSR, while for CIFAR-100 we assess  $\\{114,100\\}$ -NSR. With respect to Dream-OOD models, we use a ResNet-34 [14] with 512-dimensional feature space, evaluating  $\\{256,128,100\\}$ -NSR for both CIFAR-100 and Imagenet-100. Similarly, we reduce the feature space of the classification head to 768, 512 and 265 dimensions for VOS and FFS object detection experiments, having an original 1,024-dimensional object-wise feature space (as per Faster RCNN [33]). With regards to the LSVR and CNR, we test with various loss weight values in all the architectures (1, 0.1, 0.01, and 0.001), to evaluate their impact on model performance (except for Imagenet-100, where we use  $\\lambda_{LSV} = 0.001$  and  $\\lambda_{CN} = 0.01$  based on CIFAR-100 experiments). We train all the models using the original",
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+    {
+        "type": "text",
+        "text": "corresponding baseline settings. Details on the hyperparameters and the training regime for each model are given in the Supp. Mat. To obtain reliable comparisons we use deterministic learning via a fixed random seed for all experiments. We run all experiments 5 times and report mean and standard deviation for all metrics.",
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+    {
+        "type": "text",
+        "text": "6. Results",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We discuss the performance of FEVER-OOD against different free energy based OOD detection models in classification and detection. Tabs. 1 to 3 compare the use of FEVER-OOD with the corresponding baseline methods. We report different NSR as well as the best results obtained using  $\\lambda_{LSV}$  (Eq. (13)) or  $\\lambda_{CN}$  (Eq. (14)), and their corresponding value (we show both cases when no NSR is applied). Extensive ablations are available in the Supp. Mat.",
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+    {
+        "type": "text",
+        "text": "CIFAR-10. Tab. 1 shows the results of the VOS and FFS architectures with CIFAR-10 as in-distribution. In general, NSR and LSVR improve OOD detection for both VOS and FFS models. The best performance using the VOS method is achieved using a 96-NSR with LSVR, using a  $\\lambda_{LSV} = 1.0$ , where the average AUROC increases to 94.78 and the average FPR95 reduces to  $28.22\\%$ , compared to an AUROC of 92.15 and  $33.66\\%$  of the baseline VOS model without affecting the in-distribution accuracy. Similarly, the best FFS setting is achieved with a 96-NSR and  $\\lambda_{LSV} = 1.0$ , resulting in 94.03 AUROC and  $31.04\\%$  FPR95, compared to the baseline FFS model, with an AUROC of 90.52 and FPR95 of  $34.82\\%$ , although the best FPR95 is achieved with 32-NSR and no singular value regularization, with an FPR95 of 30.78. In general, it is seen that a large NSR (i.e., 10-NSR) may decrease the AUROC and increase the FPR95. Since VOS and FFS are techniques that synthesize outliers in the feature space, a large reduction of the feature dimension might not allow for proper in-distribution understanding, impacting in the OOD training of these techniques. Additionally, it is also observed that LSVR yields better results than CNR, and a value for  $\\lambda_{LSV} = 1.0$  is adequate for none to moderate NSR, while smaller values for LSVR (or none) are better for large NSR. While LSVR increases the differ",
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+    },
+    {
+        "type": "page_number",
+        "text": "4534",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/d0107b85f7a5a0e33af91b81e5a80311a473c9b260a0ca7d6911b533d953983e.jpg",
+        "table_caption": [
+            "Table 2. CIFAR-100 Results (ID Acc. = in-distribution accuracy; Null Space Reduction (NSR) methods = our approach)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"2\">FEVER-OOD</td><td colspan=\"12\">OOD Datasets</td><td rowspan=\"3\">ID Acc</td></tr><tr><td rowspan=\"2\">r-NSR</td><td rowspan=\"2\">Regularizer</td><td colspan=\"2\">Textures</td><td colspan=\"2\">SHVN</td><td colspan=\"2\">Places365</td><td colspan=\"2\">LSUN</td><td colspan=\"2\">iSUN</td><td colspan=\"2\">Avg</td></tr><tr><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td></tr><tr><td rowspan=\"5\">VOS</td><td>-</td><td>-</td><td>81.24±2.11</td><td>76.01±0.80</td><td>76.09±6.51</td><td>83.18±3.59</td><td>80.53±1.46</td><td>76.25±0.78</td><td>37.86±4.06</td><td>93.21±0.68</td><td>79.34±1.60</td><td>76.43±1.44</td><td>71.01±1.23</td><td>81.02±0.40</td><td>76.04±0.22</td></tr><tr><td>-</td><td>λLSV=0.1</td><td>82.87±1.11</td><td>76.49±0.94</td><td>73.35±2.96</td><td>84.57±1.53</td><td>80.36±1.16</td><td>76.89±0.79</td><td>40.05±3.74</td><td>92.83±0.46</td><td>74.28±4.03</td><td>80.25±3.34</td><td>70.18±0.87</td><td>82.21±0.56</td><td>76.01±0.16</td></tr><tr><td>-</td><td>λCN=0.01</td><td>82.51±2.64</td><td>76.04±1.91</td><td>73.67±3.10</td><td>85.31±1.24</td><td>80.18±1.08</td><td>76.59±0.23</td><td>41.08±3.27</td><td>92.75±0.63</td><td>80.83±4.37</td><td>73.79±5.51</td><td>71.65±0.96</td><td>80.90±1.11</td><td>76.20±0.11</td></tr><tr><td>114</td><td>λLSV=0.01</td><td>80.02±2.75</td><td>78.73±1.83</td><td>83.45±2.59</td><td>82.07±1.36</td><td>78.41±0.96</td><td>77.71±0.93</td><td>28.90±3.61</td><td>95.11±0.58</td><td>72.07±9.07</td><td>80.55±4.70</td><td>68.57±2.28</td><td>82.83±0.91</td><td>75.72±0.16</td></tr><tr><td>100</td><td>-</td><td>80.47±2.32</td><td>78.21±1.14</td><td>79.10±7.42</td><td>83.39±3.91</td><td>79.19±1.04</td><td>77.23±0.50</td><td>28.99±2.59</td><td>95.15±0.39</td><td>75.51±6.68</td><td>79.63±3.70</td><td>68.65±2.29</td><td>82.72±0.57</td><td>75.54±0.19</td></tr><tr><td rowspan=\"5\">FFS</td><td>-</td><td>-</td><td>82.87±1.39</td><td>75.54±0.93</td><td>76.32±6.17</td><td>84.83±2.36</td><td>81.14±1.09</td><td>76.27±0.74</td><td>36.27±4.91</td><td>93.54±1.03</td><td>82.83±2.98</td><td>74.29±3.08</td><td>71.89±1.64</td><td>80.89±1.11</td><td>76.04±0.11</td></tr><tr><td>-</td><td>λLSV=0.01</td><td>80.95±1.34</td><td>76.53±0.70</td><td>83.12±5.59</td><td>81.61±2.92</td><td>80.19±0.84</td><td>76.58±0.49</td><td>32.93±4.05</td><td>94.20±0.51</td><td>79.05±5.16</td><td>77.28±3.23</td><td>71.25±2.11</td><td>81.24±0.72</td><td>76.27±0.28</td></tr><tr><td>-</td><td>λCN=0.001</td><td>80.27±2.76</td><td>76.78±1.53</td><td>78.57±7.32</td><td>82.57±2.95</td><td>80.40±1.09</td><td>76.40±0.53</td><td>32.91±4.90</td><td>94.06±1.02</td><td>80.71±7.90</td><td>74.49±5.57</td><td>70.57±2.41</td><td>80.86±0.88</td><td>76.05±0.16</td></tr><tr><td>114</td><td>λLSV=0.001</td><td>79.26±2.67</td><td>78.16±1.50</td><td>74.28±7.13</td><td>85.37±3.20</td><td>79.45±0.85</td><td>77.25±0.61</td><td>24.10±1.42</td><td>95.94±0.17</td><td>73.61±5.82</td><td>80.61±2.49</td><td>66.14±1.91</td><td>83.47±0.98</td><td>75.45±0.37</td></tr><tr><td>100</td><td>-</td><td>77.69±2.97</td><td>78.62±1.02</td><td>77.84±9.62</td><td>83.40±3.52</td><td>80.41±0.72</td><td>76.58±0.35</td><td>21.91±0.95</td><td>96.25±0.11</td><td>79.60±6.06</td><td>75.79±5.17</td><td>67.49±2.03</td><td>82.13±0.85</td><td>75.48±0.28</td></tr><tr><td rowspan=\"6\">Dream-OOD</td><td>-</td><td>-</td><td>62.20±1.02</td><td>83.84±0.38</td><td>73.05±1.92</td><td>84.56±0.21</td><td>77.95±1.97</td><td>79.43±0.17</td><td>39.90±2.01</td><td>92.87±0.44</td><td>1.70±0.11</td><td>99.58±0.04</td><td>50.96±1.44</td><td>88.06±0.60</td><td>75.61±0.19</td></tr><tr><td>-</td><td>λLSV=0.01</td><td>58.45±2.27</td><td>86.04±0.41</td><td>68.75±1.84</td><td>87.65±0.30</td><td>77.45±2.11</td><td>78.59±0.22</td><td>15.45±2.57</td><td>97.24±0.09</td><td>1.55±0.03</td><td>99.63±0.45</td><td>44.33±3.48</td><td>89.83±0.12</td><td>75.87±0.23</td></tr><tr><td>-</td><td>λCN=0.001</td><td>57.40±1.88</td><td>86.28±0.32</td><td>77.75±1.11</td><td>85.13±0.41</td><td>78.60±1.23</td><td>78.73±0.15</td><td>27.2±1.77</td><td>95.01±0.42</td><td>1.55±0.08</td><td>99.57±0.07</td><td>48.5±1.54</td><td>88.94±0.43</td><td>76.32±0.14</td></tr><tr><td>256</td><td>-</td><td>60.00±3.21</td><td>85.42±0.79</td><td>67.50±2.47</td><td>85.84±0.66</td><td>75.90±1.10</td><td>79.57±0.43</td><td>19.85±1.05</td><td>96.74±0.67</td><td>1.00±0.02</td><td>99.78±0.06</td><td>44.82±2.72</td><td>89.47±0.242</td><td>77.01±0.12</td></tr><tr><td>128</td><td>λLSV=0.1</td><td>56.45±2.39</td><td>87.73±1.01</td><td>67.45±1.12</td><td>87.53±0.44</td><td>78.45±2.46</td><td>77.24±0.61</td><td>29.60±1.73</td><td>94.81±0.40</td><td>1.95±0.10</td><td>99.5±0.10</td><td>46.78±2.72</td><td>89.36±0.83</td><td>76.21±0.35</td></tr><tr><td>100</td><td>-</td><td>57.55±2.48</td><td>86.8±0.44</td><td>54.45±3.02</td><td>88.69±0.59</td><td>75.80±1.21</td><td>78.88±0.69</td><td>24.45±1.57</td><td>95.86±0.52</td><td>1.60±0.07</td><td>99.65±0.21</td><td>42.77±2.10</td><td>89.98±0.15</td><td>76.41±0.32</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/68fa8866a7e13226a215d32b057d741526ad5890366a3a42010a74173933b055.jpg",
+        "table_caption": [
+            "Table 3. ImageNet-100 Results (ID Acc. = in-distribution accuracy; Null Space Reduction (NSR) methods = our approach)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"2\">FEVER-OOD</td><td colspan=\"10\">OOD Datasets</td><td rowspan=\"3\">ID Acc</td></tr><tr><td rowspan=\"2\">r-NSR</td><td rowspan=\"2\">Regularizer</td><td colspan=\"2\">iNaturalist</td><td colspan=\"2\">Places365</td><td colspan=\"2\">SUN</td><td colspan=\"2\">Textures</td><td colspan=\"2\">Avg</td></tr><tr><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td></tr><tr><td>Dream-OOD</td><td>-</td><td>-</td><td>23.98±2.08</td><td>95.94±0.26</td><td>41.75±1.72</td><td>92.48±0.12</td><td>40.85±1.13</td><td>92.76±0.09</td><td>50.73±0.85</td><td>86.21±0.29</td><td>39.33±1.08</td><td>91.84±0.12</td><td>87.76±0.19</td></tr><tr><td></td><td>-</td><td>λLSV=0.01</td><td>59.91±3.09</td><td>90.89±0.48</td><td>66.26±2.17</td><td>88.12±0.47</td><td>74.26±1.52</td><td>84.53±0.33</td><td>60.56±1.21</td><td>83.91±0.42</td><td>65.25±1.50</td><td>86.87±0.25</td><td>87.85±0.11</td></tr><tr><td></td><td>-</td><td>λLSV=0.001</td><td>59.71±3.53</td><td>90.97±0.70</td><td>65.01±1.90</td><td>88.39±0.45</td><td>73.93±1.58</td><td>84.69±0.49</td><td>60.51±1.46</td><td>84.01±0.51</td><td>64.79±1.69</td><td>87.01±0.45</td><td>87.77±0.13</td></tr><tr><td></td><td>256</td><td>-</td><td>23.84±1.73</td><td>95.80±0.30</td><td>44.35±1.71</td><td>92.14±0.30</td><td>42.92±1.98</td><td>92.46±0.33</td><td>44.38±1.81</td><td>88.60±0.54</td><td>38.87±1.29</td><td>92.25±0.23</td><td>87.57±0.24</td></tr><tr><td></td><td>128</td><td>λLSV=0.01</td><td>23.46±2.54</td><td>95.93±0.36</td><td>43.37±1.47</td><td>92.19±0.22</td><td>42.42±1.60</td><td>92.44±0.29</td><td>41.86±1.09</td><td>89.48±0.27</td><td>37.78±1.45</td><td>92.51±0.22</td><td>87.60±0.11</td></tr><tr><td></td><td>100</td><td>λLSV=0.01</td><td>22.24±0.81</td><td>96.16±0.14</td><td>41.08±3.03</td><td>92.59±0.44</td><td>40.39±2.84</td><td>92.91±0.40</td><td>42.31±0.97</td><td>89.30±0.37</td><td>36.50±1.67</td><td>92.74±0.21</td><td>87.42±0.15</td></tr></table>",
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+        "image_caption": [
+            "(a) Dataset: CIFAR-10",
+            "Figure 4. Singular Values Spectrum."
+        ],
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+            "(b) Dataset: CIFAR-100"
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+    {
+        "type": "text",
+        "text": "ence in energy of outliers in or near the least singular vector direction, the CN regulariser makes equalized free energy changes for all directions. Since the latter effect might disable directions with smaller energy changes than others, it might also reduce the free energy change in the direction of the largest singular value. Fig. 4(a) shows the singular value spectrum of the baseline VOS model against the LSVR and CNR versions for the CIFAR-10 dataset. It is seen that the while both regularizers homogenize the singular values, the CNR also reduces the most significant singular value. Finally, our experiments show that VOS achieves better results than FFS in CIFAR-10 OOD detection.",
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+    {
+        "type": "text",
+        "text": "CIFAR-100. Tab. 2 shows the results for VOS, FFS and Dream-OOD trained on the CIFAR-100 dataset as in-distribution. The best models for VOS and FFS are achieved with 114-NSR and LSVR, with a  $68.57\\%$  FPR95  $(-2.44\\%)$  VOS) and 82.83  $(+1.81\\mathrm{VOS})$  AUROC for VOS-114-NSR and  $66.14\\%$  FPR95  $(-5.75\\%)$  FFS) and 83.47  $(+2.58\\mathrm{FFS})$  AUROC for FFS-114-NSR. However, despite these improvements, the performance of virtual outlier synthesis methods is usually poor for several in-distribution classes [44], hence the enhancement of these architectures is still challenging. Regarding Dream-OOD, it is noted that the best results are obtained by Dream-OOD-100-NSR, having an FPR95 of  $42.77\\%$ $(-8.19\\%)$  Dream-OOD) and 89.98",
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+    {
+        "type": "text",
+        "text": "AUROC (+1.9 Dream-OOD). Finally, for the three energy techniques (VOS, FFS and Dream-OOD), we observed that the model does not converge when using 100-NSR and the CNR (see Supp. Mat.), suggesting that the conditioning number penalization does not allow the model to learn the in-distribution task. Fig. 4(b) shows the singular value spectrum for the LSVR and CNR versions of the VOS model. Differently from the CIFAR-10 experiments, it is seen that LSVR keeps the most significant singular values similar to the baseline but homogenizes the least significant singular values, while the CNR keeps all singular values at a low level, hence explaining why it fails for this dataset.",
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+    {
+        "type": "text",
+        "text": "Imagenet-100. We show the results of Dream-OOD with Imagenet-100 as in-distribution in Tab. 3. Similar as with CIFAR-100, the best results are obtained with NSR100, effectively eliminating the null space of the last layer (since it becomes square and is not singular). Contrary to CIFAR-100, LSVR has a negative impact when used alone. Considering that we use the same pre-training scheme as Du et al. [8], adding LSVR and CNR on an already pretrained last linear layer might affect the already formed feature space. Hence, these regularisers benefit untrained NSR modules. The best model, Dream-OOD-100-NSR with LSVR, achieves an average  $36.50\\%$  FPR95 and 92.74 AUROC, compared to the baseline  $39.33\\%$  FPR95 and 91.84 AUROC, becoming the state-of-the-art for Imagenet-100.",
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+    {
+        "type": "text",
+        "text": "PASCAL VOC. We test FEVER-OOD techniques in object detection task, where the goal is to detect object-level OOD instances. Tab. 4 show the result for the baseline VOS and FFS, taking PASCAL VOC [10] as in-distribution dataset. For both tasks, we evaluate on two OOD datasets that contain subset of images from: MS-COCO [28] and OpenImages [22], following the original works [7, 21]. The best-performing model for VOS is VOS-768-NSR with CNR,",
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+        "text": "4535",
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+    {
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+        "image_caption": [
+            "Figure 5. MS-COCO objects detected on OOD images by VOS baseline [7] (first row) and Fever-OOD (second row). Blue: OOD objects detected and mis-classified as being in-distribution. Green: the same OOD objects correctly detected as OOD by FEVER-OOD (ours)."
+        ],
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+    {
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+    {
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+    {
+        "type": "image",
+        "img_path": "images/12c8724f5737873132ceb2e02d3f4dab10f687b8d2e26550db93809d26955762.jpg",
+        "image_caption": [],
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+    {
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+        "img_path": "images/99ec6a99027725d4b081080c4d77dad883791b868892b91ecf0d7d6f85eb605c.jpg",
+        "table_caption": [
+            "Table 4. VOS results with PASCAL VOC as in-distribution (Null Space Reduction (NSR) methods = our approach)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"3\">FEVER-OOD</td><td colspan=\"4\">OOD Datasets</td><td rowspan=\"3\">mAP</td></tr><tr><td rowspan=\"2\">r-NSR</td><td rowspan=\"2\">λLSV</td><td rowspan=\"2\">λCN</td><td colspan=\"2\">MS-COCO</td><td colspan=\"2\">OpenImages</td></tr><tr><td>FPR95</td><td>AUROC</td><td>FPR95</td><td>AUROC</td></tr><tr><td rowspan=\"3\">VOS</td><td>-</td><td>-</td><td>-</td><td>50.29</td><td>87.77</td><td>53.09</td><td>86.58</td><td>0.489</td></tr><tr><td>-</td><td>0.001</td><td>-</td><td>49.96</td><td>88.10</td><td>52.26</td><td>85.80</td><td>0.489</td></tr><tr><td>-</td><td>-</td><td>1</td><td>53.42</td><td>86.66</td><td>52.73</td><td>85.77</td><td>0.490</td></tr><tr><td></td><td>768</td><td>-</td><td>-</td><td>48.94</td><td>87.94</td><td>52.34</td><td>86.33</td><td>0.489</td></tr><tr><td></td><td>768</td><td>0.01</td><td>-</td><td>50.08</td><td>87.78</td><td>51.71</td><td>86.04</td><td>0.493</td></tr><tr><td></td><td>768</td><td>-</td><td>0.01</td><td>47.47</td><td>88.15</td><td>49.36</td><td>86.32</td><td>0.491</td></tr><tr><td></td><td>512</td><td>-</td><td>-</td><td>49.84</td><td>88.42</td><td>55.33</td><td>85.33</td><td>0.486</td></tr><tr><td></td><td>512</td><td>0.001</td><td>-</td><td>49.26</td><td>88.39</td><td>54.32</td><td>85.82</td><td>0.489</td></tr><tr><td></td><td>512</td><td>-</td><td>0.01</td><td>49.59</td><td>87.48</td><td>54.81</td><td>85.48</td><td>0.490</td></tr><tr><td></td><td>256</td><td>-</td><td>-</td><td>47.88</td><td>88.49</td><td>52.41</td><td>86.39</td><td>0.486</td></tr><tr><td></td><td>256</td><td>0.01</td><td>-</td><td>48.51</td><td>88.36</td><td>50.52</td><td>86.12</td><td>0.491</td></tr><tr><td></td><td>256</td><td>-</td><td>0.001</td><td>49.1</td><td>88.27</td><td>51.47</td><td>86.08</td><td>0.489</td></tr><tr><td rowspan=\"3\">FFS</td><td>-</td><td>-</td><td>-</td><td>50.77</td><td>87.18</td><td>53.78</td><td>85.34</td><td>0.487</td></tr><tr><td>-</td><td>0.01</td><td>-</td><td>53.09</td><td>86.75</td><td>53.47</td><td>85.86</td><td>0.490</td></tr><tr><td>-</td><td>-</td><td>0.01</td><td>50.36</td><td>87.65</td><td>51.19</td><td>85.98</td><td>0.485</td></tr><tr><td></td><td>768</td><td>-</td><td>-</td><td>51.50</td><td>87.59</td><td>53.33</td><td>85.84</td><td>0.488</td></tr><tr><td></td><td>768</td><td>0.01</td><td>-</td><td>47.42</td><td>88.36</td><td>52.46</td><td>86.40</td><td>0.489</td></tr><tr><td></td><td>768</td><td>-</td><td>0.01</td><td>51.12</td><td>86.82</td><td>55.44</td><td>84.84</td><td>0.490</td></tr><tr><td></td><td>512</td><td>-</td><td>-</td><td>46.93</td><td>88.82</td><td>53.89</td><td>86.28</td><td>0.491</td></tr><tr><td></td><td>512</td><td>0.01</td><td>-</td><td>47.42</td><td>88.36</td><td>52.46</td><td>86.40</td><td>0.488</td></tr><tr><td></td><td>512</td><td>-</td><td>0.01</td><td>51.42</td><td>87.05</td><td>54.98</td><td>84.55</td><td>0.490</td></tr><tr><td></td><td>256</td><td>-</td><td>-</td><td>51.18</td><td>88.74</td><td>53.67</td><td>86.56</td><td>0.487</td></tr><tr><td></td><td>256</td><td>0.01</td><td>-</td><td>47.93</td><td>88.04</td><td>47.93</td><td>84.95</td><td>0.489</td></tr><tr><td></td><td>256</td><td>-</td><td>0.01</td><td>52.94</td><td>86.62</td><td>52.88</td><td>84.45</td><td>0.489</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "achieving average FPR95 scores of  $47.47\\%$  and  $49.36\\%$  on MS-COCO and OpenImages, respectively, an improvement of nearly  $4\\%$  over the VOS baseline. For FFS, we achieve a minimum FPR95 of  $46.93\\%$  with FFS-512-NSR model and  $47.93\\%$  for the FFS-256-NSR model with the LSVR for both OOD datasets. Additionally, our approach generally delivers higher AUROC scores compared to the FFS baseline across both OOD datasets. Qualitative results are illustrated in Fig. 5, where we visualize the prediction on MS-COCO OOD images, using the baseline VOS (top) and the best Fever-OOD model, i.e., VOS-768-NSR, with the PASCAL-VOC as the in-distribution dataset, showing that out framework outperforms baseline VOS in in detecting outlier objects with a significantly lower false positive rate.",
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+    },
+    {
+        "type": "text",
+        "text": "Computational overhead. The computational overhead introduced by our method is minimal since we only add an extra linear layer. For instance, the ResNet-34 used in Dream-OOD takes  $4.42 \\pm 1.15$  ms/img and has 21.5M",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "params. Adding 256, 128, 100-NSR layers change the inference time to  $3.91 \\pm 0.62$ ,  $4.44 \\pm 1.17$ ,  $4.13 \\pm 1.02$  ms/img, with an extra 105k, 27k, 10k params, which is negligible compared with the total size of ResNet-34.",
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+    },
+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we present FEVER-OOD, a robust approach for addressing critical vulnerabilities found in existing energy-based OOD detection. Our method targets the Null Space Vulnerabilities (NSV), where in-distribution and OOD instances can produce similar free energy scores despite differing feature representations, and Least Singular Value Vulnerabilities (LSVV), where energy score similarities are influenced by the least singular vector of the classifier last linear layer. These vulnerabilities are especially problematic in high-dimensional feature spaces where the feature dimension exceeds the number of classes, impacting the effectiveness of OOD detection. To mitigate these issues, FEVER-OOD incorporates strategies such as reducing the null space through lower-dimensional feature spaces and introducing a Least Singular Value Regularizer to maximize the least singular value, enhancing the distinction between energy scores of different samples. Additionally, we propose a Condition Number Regularizer to promote uniform energy changes for feature-space displacements, fostering consistent energy variation and improving detection robustness. Our comprehensive evaluation on benchmark datasets, including applications to the Dream-OOD framework with ImageNet-100 as the ID dataset, demonstrates the significant effectiveness of FEVER-OOD. Specifically, our approach achieves a  $10.13\\%$  reduction in the average false positive rate and a  $1.6\\%$  increase in AUROC, setting a new state-of-the-art in OOD detection. Furthermore, our results highlight the generalization capability of FEVER-OOD across different detection architectures, showcasing its potential beyond conventional classification settings. Future extensions of FEVER-OOD could include applications to varied domains and integration with other OOD detection frameworks to further validate its versatility and performance in diverse machine learning contexts. This work provides valuable insights into enhancing OOD robustness and sets a foundation for more resilient free energy-based detection methods.",
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+    {
+        "type": "page_number",
+        "text": "4536",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            104,
+            187,
+            119
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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