— on the grill” |\\n| open small drawer | placement | 3 | 3.0 | “open the — drawer” |\\n| stack cups blocks | color | 20 | 10.0 | “Identify the most common color in the block pile, and stack the other cups |\\n| | | | | on the cup that matches that color” |\\n| push button light | color | 20 | 2.0 | “push the button with the same color as the light” |\\n\\nWe provide a detailed description of each novel task below and explain the modifications from the base tasks.\\n\\n#### B.2.1 Meat on Grill\\n\\nTask: Place either a chicken or a steak on the grill depending on the variation.\\nfilename: meat_on_grill.py\\nBase task: meat off grill.\\nModified: The task requires placing meat onto the grill, whereas the base task involves removing it. The cam_over_shoulder_right camera’s position and orientation were modified to better observe the drawer. The camera was repositioned to [0.20,-0.36,1.85] and reoriented to [-0.85*math.pi, 0, math.pi].\\nSuccess Metric: The selected meat (chicken or steak) is successfully placed on the grill and released from the gripper.\\n\\n#### B.2.2 Stack Cups Blocks\\n\\nTask: Identify the most common color in the block pile, and stack the other cups on the cup that matches that color.\\nfilename: stack_cups_blocks.py\\nBase task: Stack cups.\\nModified: The task involves identifying the cup that matches the most common color among the distractor blocks, then stacking the other two cups on top. The base task is simply stacking the cups without considering block colors.\\nSuccess Metric: Success is measured when the correct cup is stacked with the other cups based on the color identification and all cups are within the target area defined by the proximity sensor.\\n\\n#### B.2.3 Close Jar Banana\\n\\nTask: Close the jar that is closer to the banana by screwing on its lid.\\nfilename: close_jar_banana.py\\nBase task: close jar.\\nModified: The task involves identifying the jar closer to the banana and screwing its lid on, while the base task only requires closing a jar without proximity consideration.\\nSuccess Metric: The lid is successfully placed on the jar closest to the banana, confirmed by the proximity sensor.\\n\\n#### B.2.4 Close Jar Distractor\\n\\nTask: Close the jar by screwing on the lid, while distractor objects are present.\\nfilename: close_jar_distractor.py\\nBase task: close jar.\\nModified: The task includes distractor objects, such as a button and block, which are colored and placed near the jars. These objects have been encountered during training, adding complexity compared to the base task.\\nSuccess Metric: The jar lid is successfully placed on the target jar, confirmed by the proximity sensor.\\n\\n#### B.2.5 Close Drawer\\n\\nTask: Close one of the drawers (bottom, middle, or top) by sliding it shut.\\nfilename: close_drawer.py\\nBase task: open drawer.\\nModified: The task involves closing the drawer instead of opening it.\\nSuccess Metric: The selected drawer is closed successfully, confirmed by the joint position of the drawer.\\n\\n#### B.2.6 Open Drawer Small\\n\\nTask: Open one of the smaller drawers (bottom, middle, or top) by sliding it open.\\nfilename: open_drawer_small.py\\nBase task: open drawer.\\nModified: The task involves opening a smaller drawer compared to the base task, with adjusted camera settings for better visibility.\\nSuccess Metric: The selected drawer is opened successfully, verified by the joint position of the drawer.\\n\\n#### B.2.7 Condition Block\\n\\nTask: Stack a specified number of blocks and, if the blue block is present, add it to the stack.\\nfilename: condition_block.py\\nBase task: stack blocks.\\nModified: The task involves stacking a specified number of blocks, with an additional requirement to include the blue block if it is present.\\nSuccess Metric: The correct number of target blocks are stacked, and if the blue block is present, it is also correctly added to the stack.\\n\\n#### B.2.8 Push Button Light\\n\\nTask: Push the button that matches the color of a light bulb on the first attempt.\\nfilename: push_buttons_light.py\\nBase task: push button.\\nModified: The task involves pressing a single button that matches the color of a light bulb. The button must be pressed correctly on the first attempt; repeated attempts are not allowed.\\nSuccess Metric: The correct button matching the light bulb’s color is pressed on the first attempt.\\n\\n### B.3 Failure cases of GravMAD\\n\\nFigure: Figure 9: Failure cause analysis, including (a) visualization of failure examples; (b) comparison of imprecise labels and expected labels.\\nRefer to caption: x10.png\\n\\nIn this section, we analyze why GravMAD underperforms compared to the baseline model 3D Diffuser Actor on certain base tasks, particularly in the “Place Wine” task and drawer-related tasks.\\n\\nAs discussed in the main paper, GravMaps represent spatial relationships in 3D space, but this introduces a challenge: areas close to the sub-goal often share the same cost value, as seen in the value map on the right side of Fig. 9 (a). This uniform cost value can mislead the robot into assuming it should complete the sub-goal within that area. For tasks requiring precise actions, such as the “Open Drawer” task, GravMaps’ coarse guidance may lead to suboptimal performance compared to 3D Diffuser Actor.\\nIn the left schematic of Fig. 9(a), the robot must grasp the center of a small handle to achieve optimal performance in the “Open Drawer” task. This high precision demand on the end-effector results in a lower success rate for GravMAD. This limitation extends to the “Put in Drawer” task, which depends on the successful completion of “Open Drawer”. Similarly, in the “Place Wine” task, insufficient predictive accuracy causes the robot to misalign the bottle with the correct slot by one unit, leading to failure.\\n\\nIn the VLM setting, sub-goal accuracy often suffers, as shown in Fig. 9(b), further reducing model performance. These inaccuracies typically arise from two factors: (1) SAM may fail to accurately identify ideal areas, leading to imprecise contextual information from the Detector module for tasks like “Place Wine”, “Open Drawer”, and “Put in Drawer”; (2) the camera’s positioning may not capture the full scene, leaving some task-relevant objects out of view, as seen in tasks like “Meat off Grill”.\\nTo overcome these VLM limitations, potential solutions include: (1) integrating multi-view information into the Detector for a more comprehensive scene observation; and (2) using a more granular segmentation model to provide GPT-4 with a wider range of labels, improving the quality of the context generated by the Detector.\",\n \"metadata\": {\n \"authors\": [\n \"Yangtao Chen\",\n \", Zixuan Chen\",\n \", Junhui Yin\",\n \", Jing Huo\",\n \", Pinzhuo Tian\",\n \", Jieqi Shi\",\n \", Yang Gao\",\n \"School of Computer Engineering and Science,\",\n \"Shanghai University, Shanghai, China\"\n ],\n \"title\": \"GravMAD : Gr ounded Sp a tial V alue M aps Guided A ction D iffusion for Generalized 3D Manipulation\",\n \"total_chars\": 63952,\n \"total_lines\": 530,\n \"updated_at\": \"2026-01-25T15:02:44.025842\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"Q1mbvzMjqD","initial_rating":5,"confidence":5,"soundness":2,"contribution":2,"presentation":3,"summary":"The paper proposes a pipeline of Grounded Spatial Value Maps-guided Action Diffusion (*GravMAD*), which is a subgoal-driven, language-conditioned action diffusion framework combining VoxPoser (Huang et al., 2023) with subtask imitation learning based on 3D Diffuser Actor (Ke et al., 2024). The idea is essentially to break tasks into sub-goals based on language instructions, allowing auxiliary guidance to help robots conceptually grasp tasks more accurately than directly using pre-trained foundation models.\n\nThe division of subtasks is conducted via Sub-goal Keypose Discovery, which is defined to happen when end effectors make contact or disengage with the objects. The proposed method uses pre-computed keyposes and touch&gripper change detection to segment subtasks for training epochs. During inference, the proposed method uses the LLM-based Planner and Composer from VoxPoser (Huang et al., 2023).\n\nWith the segmented subtasks, the proposed method first uses VoxPoser (Huang et al., 2023) to generate 3D value maps *GravMaps* and then uses 3D Diffuser Actor (Ke et al., 2024) to conduct subtask imitation learning and generate action sequences with the condition of tokens from *GravMaps*.\n\nThe authors test *GravMAD* on 20 RLBench (James et al., 2020) simulated tasks, including 12 original tasks selected from RLBench and 8 modified new tasks. Empirical results show that the proposed framework outperforms both VoxPoser and 3D Diffuser Actor in most seen and novel tasks, which validates GravMAD's superiority in both generalization and preciseness.","strengths":"1. The paper is well-written, easy to follow, and presents its ideas clearly. \n2. The approach of combining VoxPoser's planning and perception ability with precise subtask imitation learning from 3D Diffuser Actor is well-motivated and clever to enhance the model’s long horizon task capability to achieve both VoxPoser's generalization and 3D Diffuser Actor's preciseness.\n3. The reported scores are evaluated across 3 seeds, which are statically robust.","weaknesses":"1. The proposed Sub-goal Keypose Discover method is kind of naive. The proposed method simply uses the change in the gripper’s open/close state and the change in touch force to segment a whole task, which could suit simple tasks like moving the chicken but might not work for tasks with longer horizons. This segmenting requires complex reasoning over the concrete task description and comprehensive understanding. During inference, foundation models like VoxPoser can be better at dividing subtasks due to the reasoning ability of LLM. However, for this proposed pipeline where different segmenting methods are used in training and testing, there could even be a domain shift for the subtasks' distribution itself due to unaligned segmenting.\n2. The comparison and evaluation are limited. The selection strategy of the 12 tasks over 100 language-conditioned tasks from RLBench is not mentioned. The 8 modified tasks are not justified for their novelty, which might cause a doubt on opportunistic choices. \n3. Since both baselines of VoxPoser and 3D Diffuser Actor have conducted real-world evaluations, a real-world comparison for *GravMAD* will be more convincing.\n\nThough conducted in an A+B paradigm on VoxPoser and 3D Diffuser Actor, this work's engineering contribution is solid and the idea of subtask imitation learning is novel. I will raise my score if more validations are provided.","questions":"1. Can you provide more details on the selection strategy of the 12 tasks over 100 language-conditioned tasks from RLBench? Why do you choose 12 and why these 12? The currently designed novel tasks feature scenes and objects similar to those in the training tasks. Can you design more complex novel tasks?\n2. Can you evaluate the performance of the proposed method in a real-world experiment? Most setups should be similar to 3D Diffuser Actor and not that hard."},{"id":"nJjyJQ7KQo","initial_rating":5,"confidence":4,"soundness":2,"contribution":2,"presentation":3,"summary":"This paper introduces GravMAD, a new approach that decomposes 3D manipulation tasks into key sub-goals, generates 3D spatial GravMaps to capture spatial relationships from these sub-goals, and employs an action diffusion policy to learn actions through imitation learning. This design aims to combine the precision of imitation learning with the generalization capabilities of foundation models. Extensive experiments conducted on RLBench show that GravMAD achieves improvements in both training tasks and novel tasks.","strengths":"* The authors conduct extensive experiments, including comparisons with different types of baselines and a detailed ablation study.\n* The authors provide diverse visualization in the paper and on the website, enhancing readers' understanding.\n* The paper is well-organized and easy to comprehend.","weaknesses":"* The novelty of the proposed method is limited, as it resembles a combination of previous works, Voxposer and 3D Diffuser Actor. Specifically, the authors use a similar approach to Voxposer by decomposing tasks and generating 3D spatial heatmaps for each sub-task, which are then integrated into the 3D Diffuser Actor architecture. The primary innovation appears limited to the proposed GravMAD framework.\n* The comparison between GravMAD and 3D Diffuser Actor on training tasks indicates that, although the introduction of GravMap improves performance on most tasks, GravMAD's performance heavily relies on both the Detector and GravMap. If the Detector’s predictions lack precision, it can even degrade the method's performance, potentially compromising its robustness in scenarios where camera capture is unclear or ambiguous.\n* In the ablation study w/o. Cost Map, it is surprising that the method achieves a zero score. Could the authors provide further explanation on why the predicted actions result in non-unit quaternions in this scenario? (This seems to conflict with the statement in Section 3.1, which mentions, \"to avoid quaternion discontinuities, we use the 6D rotation representation.\") Additionally, if the predicted quaternion is not-unit, we can normalize and convert it into a unit quternion. \n* It is advisable to conduct real-world experiments, as many related works, such as Voxposer and 3D Diffuser Actor, also include real-world demonstrations.","questions":"* The use of a foundation model, such as GPT-4o, during inference might be time-consuming and could potentially hinder real-time responsiveness in robotic manipulation. Could the authors provide the average inference time for GravMAD at each sub-task stage?\n* During training, why not generate GravMap in the same way as during inference? (One possible reason may be that the foundation model’s inference time is too lengthy?) The GravMap generated from demonstration ground-truths may differ in distribution from the GravMap produced by the foundation model, which could impact inference performance."},{"id":"zoDnMKT20w","initial_rating":6,"confidence":3,"soundness":2,"contribution":3,"presentation":3,"summary":"This manuscript investigates 3D manipulation tasks through robot learning. Traditional imitation learning excels with familiar tasks but struggles with new, unseen ones. Recent approaches use large foundation models to mitigate this but lack task-specific learning, often leading to failures in 3D environments. To overcome this, the author introduces a novel framework termed Grounded Space Value Map-guided Action Diffusion (GravMAD). Due to its promising results, I am tentatively inclined to accept the paper. However, I find certain aspects unclear, especially the evaluation of design choices and overall performance. I am open to revising my evaluation if the authors can address these concerns comprehensively and convincingly detail the contributions of their work.","strengths":"1. GravMAD shows strong generalization capabilities, achieving at least 13.36% higher success rates than state-of-the-art baselines on 12 base tasks encountered during training and surpassing them by 28.63% on 8 novel tasks.\n 2. The manuscript is well-written with a clear structure, logical flow, detailed technical descriptions, and intuitive chart presentations.","weaknesses":"- Insufficient argumentation\n 1. The manuscript mentions in section 3.2 that different sub-goal keypose discovery rules were designed for different types of manipulation tasks, which seems to lack a reasonable explanation and generalizability.\n 2. The manuscript does not adequately justify the exclusion of GravMap’s guidance in rotation prediction, stating that “rotation actions are difficult to be guided explicitly through value maps.”\n- Inadequate Evaluation: \n 1. Although it is claimed that this method is generalized, all experiments were conducted in the RLBench environment, and there is a lack of validation on other simulation environments or real robots.\n 2. The main evaluation metric used is success rate, overlooking other important dimensions such as completion time, smoothness of action, etc.","questions":"1. What are the specific criteria for “significant changes” in Sub-goal Keypose Discovery?\n2. From Table 2, it is evident that the algorithm exhibits significant differences in performance on similar tasks, such as placing a cup and placing wine. Can you explain the reasons for this?"},{"id":"KUa4VTbtRc","initial_rating":5,"confidence":4,"soundness":3,"contribution":2,"presentation":2,"summary":"This paper proposes a novel method for learning from demonstrations while incorporating knowledge from foundation models to tackle robotic manipulation. It learns to predict robot end-effector actions using a diffusion process and enhances the representation using 3D cost maps introduced in previous work. These cost maps are computed using heuristically extracted sub-goals during training, while foundation models are used instead at inference. In this way, the proposed method is able to combine strong generalisation capabilities from foundation models and learn precise robot actions from available demonstrations. The experiments show strong performance when compared to the considered baselines, while ablation studies provide valuable insights into different components of the method.","strengths":"- The motivation of the paper is strong and well-explained.\n- Figures (both in the main paper and the appendix) are clear and very helpful in understanding the proposed method.\n- The technical challenge of integrating many components together in a unified framework is well-executed and appreciated.\n- Ablation studies are well-executed and provide valuable insights into the method.\n- Overall, utilising foundation models together with some demonstrations to achieve both, task generalisation and high precision seems like a great direction.","weaknesses":"- Novelty and contribution claims are not very clear:\n - 1) Discovering sub-goals and predicting them to guide robot actions has been done before [1,2,3,4]. Is the novelty here mainly the 3D part combined with foundation models? Maybe the difference could be emphasised more.\n - 2) From the paper, it seems that GravMaps are Cost and Gripper openness maps used in VoxPoser, just renamed. Without properly explaining the difference, it shouldn’t be called a novel contribution.\n - 4) Claiming to design two types of tasks (line 124) and then using base tasks from RLBench for one type can come off as being disingenuous about the contribution claims. Rephrasing the 4th contribution to focus more on the evaluation rather than task design would be beneficial.\n- Some parts of the method and design choices need to be better explained:\n - How GravMap tokens are used in the network architecture is not described in the main text of the paper.\n - Explaining in more detail why sub-goals are extracted differently during training and inference would greatly benefit the clarity of the paper. It becomes obvious while reading the paper, but initially, it can cause confusion.\n - It is not clear why rotation maps from VoxPoser are not used. Justifying it would make the overall approach clearer.\n - GravMap Synthesis during Inference is not explained clearly. Lines 305-309 are very dense with information, but it’s very difficult to understand how the sub-goals are actually extracted. If it is done just using existing methods, then contribution claims should be adjusted accordingly. \n- It is not clear if the proposed sub-goal keypose discovery is actually needed. There are no experiments using keyposes, without filtering them. If there are other reasons to filter keyposes, they should be explained.\n- Overall, sub-goal keypose discovery seems very tailored towards specific types of tasks. Limitations of it (and how they could be lifted) are not discussed.\n- What are 3 random seeds used for? Are the models re-trained using different seeds or just to change object poses and the stochastic diffusion process? If it’s the latter, then it is the same as having 3x episodes and the reported statistics don’t hold a lot of value.\n- GravMAD (Manual) seems like an unfair comparison to the baselines. Maybe providing the same ground truth object pose information to other methods would be more valuable for such comparison.\n- Given that the proposed method uses sub-goals to guide the diffusion process, selected baselines are not the most appropriate. Better baselines would be ChainedDiffuser [3] and/or Hierarchical Diffusion Policy [4].\n- There are some contradictory and not complete claims in the paper:\n - Line 144 - Described methods already leverage demonstration data.\n - Line 205 - Quaternions, although they have the double cover property, are continuous unless additional restrictions are imposed (e.g. by requiring that the scalar part w≥0).\n - Line 206 stated that 6D rotation representation is used, but line 510 states that the model can predict non-unit quaternions. How is this possible?\n - What are “3D tasks”? Tasks that involve 3D observations or 6D manipulation? It is not a very clear term.\n- Limitations of the proposed method are only superficially discussed.\n\n[1] Black, Kevin, et al. \"Zero-shot robotic manipulation with pretrained image-editing diffusion models.\" arXiv preprint arXiv:2310.10639 (2023).\n\n[2] Kang, Xuhui, Wenqian Ye, and Yen-Ling Kuo. \"Imagined subgoals for hierarchical goal-conditioned policies.\" CoRL 2023 Workshop on Learning Effective Abstractions for Planning (LEAP). 2023.\n\n[3] Xian, Zhou, et al. \"Chaineddiffuser: Unifying trajectory diffusion and keypose prediction for robotic manipulation.\" 7th Annual Conference on Robot Learning. 2023.\n\n[4] Ma, Xiao, et al. \"Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.","questions":"- Some are raised in the Weaknesses section.\n- What is the difference between GravMaps and the cost maps described in VoxPoser? Is it the downsampling part?\n- Why are rotation maps from VoxPoser not used?\n- Do you have any intuition on how well your proposed method would scale with more data? Would Imitation Learning catch up at some point (with a lot of training data)?\n- Could you expand a bit more about the limitations of your proposed method?\n- GravMaps are just an overparameterization of sub-goals at a high level. The fact that the ablation variant (w/o. GravMap) performs so poorly is not very intuitive. Could you provide more details about this ablation variant and maybe you have some intuition about its performance?"}],"string":"[\n {\n \"id\": \"Q1mbvzMjqD\",\n \"initial_rating\": 5,\n \"confidence\": 5,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"The paper proposes a pipeline of Grounded Spatial Value Maps-guided Action Diffusion (*GravMAD*), which is a subgoal-driven, language-conditioned action diffusion framework combining VoxPoser (Huang et al., 2023) with subtask imitation learning based on 3D Diffuser Actor (Ke et al., 2024). The idea is essentially to break tasks into sub-goals based on language instructions, allowing auxiliary guidance to help robots conceptually grasp tasks more accurately than directly using pre-trained foundation models.\\n\\nThe division of subtasks is conducted via Sub-goal Keypose Discovery, which is defined to happen when end effectors make contact or disengage with the objects. The proposed method uses pre-computed keyposes and touch&gripper change detection to segment subtasks for training epochs. During inference, the proposed method uses the LLM-based Planner and Composer from VoxPoser (Huang et al., 2023).\\n\\nWith the segmented subtasks, the proposed method first uses VoxPoser (Huang et al., 2023) to generate 3D value maps *GravMaps* and then uses 3D Diffuser Actor (Ke et al., 2024) to conduct subtask imitation learning and generate action sequences with the condition of tokens from *GravMaps*.\\n\\nThe authors test *GravMAD* on 20 RLBench (James et al., 2020) simulated tasks, including 12 original tasks selected from RLBench and 8 modified new tasks. Empirical results show that the proposed framework outperforms both VoxPoser and 3D Diffuser Actor in most seen and novel tasks, which validates GravMAD's superiority in both generalization and preciseness.\",\n \"strengths\": \"1. The paper is well-written, easy to follow, and presents its ideas clearly. \\n2. The approach of combining VoxPoser's planning and perception ability with precise subtask imitation learning from 3D Diffuser Actor is well-motivated and clever to enhance the model’s long horizon task capability to achieve both VoxPoser's generalization and 3D Diffuser Actor's preciseness.\\n3. The reported scores are evaluated across 3 seeds, which are statically robust.\",\n \"weaknesses\": \"1. The proposed Sub-goal Keypose Discover method is kind of naive. The proposed method simply uses the change in the gripper’s open/close state and the change in touch force to segment a whole task, which could suit simple tasks like moving the chicken but might not work for tasks with longer horizons. This segmenting requires complex reasoning over the concrete task description and comprehensive understanding. During inference, foundation models like VoxPoser can be better at dividing subtasks due to the reasoning ability of LLM. However, for this proposed pipeline where different segmenting methods are used in training and testing, there could even be a domain shift for the subtasks' distribution itself due to unaligned segmenting.\\n2. The comparison and evaluation are limited. The selection strategy of the 12 tasks over 100 language-conditioned tasks from RLBench is not mentioned. The 8 modified tasks are not justified for their novelty, which might cause a doubt on opportunistic choices. \\n3. Since both baselines of VoxPoser and 3D Diffuser Actor have conducted real-world evaluations, a real-world comparison for *GravMAD* will be more convincing.\\n\\nThough conducted in an A+B paradigm on VoxPoser and 3D Diffuser Actor, this work's engineering contribution is solid and the idea of subtask imitation learning is novel. I will raise my score if more validations are provided.\",\n \"questions\": \"1. Can you provide more details on the selection strategy of the 12 tasks over 100 language-conditioned tasks from RLBench? Why do you choose 12 and why these 12? The currently designed novel tasks feature scenes and objects similar to those in the training tasks. Can you design more complex novel tasks?\\n2. Can you evaluate the performance of the proposed method in a real-world experiment? Most setups should be similar to 3D Diffuser Actor and not that hard.\"\n },\n {\n \"id\": \"nJjyJQ7KQo\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"This paper introduces GravMAD, a new approach that decomposes 3D manipulation tasks into key sub-goals, generates 3D spatial GravMaps to capture spatial relationships from these sub-goals, and employs an action diffusion policy to learn actions through imitation learning. This design aims to combine the precision of imitation learning with the generalization capabilities of foundation models. Extensive experiments conducted on RLBench show that GravMAD achieves improvements in both training tasks and novel tasks.\",\n \"strengths\": \"* The authors conduct extensive experiments, including comparisons with different types of baselines and a detailed ablation study.\\n* The authors provide diverse visualization in the paper and on the website, enhancing readers' understanding.\\n* The paper is well-organized and easy to comprehend.\",\n \"weaknesses\": \"* The novelty of the proposed method is limited, as it resembles a combination of previous works, Voxposer and 3D Diffuser Actor. Specifically, the authors use a similar approach to Voxposer by decomposing tasks and generating 3D spatial heatmaps for each sub-task, which are then integrated into the 3D Diffuser Actor architecture. The primary innovation appears limited to the proposed GravMAD framework.\\n* The comparison between GravMAD and 3D Diffuser Actor on training tasks indicates that, although the introduction of GravMap improves performance on most tasks, GravMAD's performance heavily relies on both the Detector and GravMap. If the Detector’s predictions lack precision, it can even degrade the method's performance, potentially compromising its robustness in scenarios where camera capture is unclear or ambiguous.\\n* In the ablation study w/o. Cost Map, it is surprising that the method achieves a zero score. Could the authors provide further explanation on why the predicted actions result in non-unit quaternions in this scenario? (This seems to conflict with the statement in Section 3.1, which mentions, \\\"to avoid quaternion discontinuities, we use the 6D rotation representation.\\\") Additionally, if the predicted quaternion is not-unit, we can normalize and convert it into a unit quternion. \\n* It is advisable to conduct real-world experiments, as many related works, such as Voxposer and 3D Diffuser Actor, also include real-world demonstrations.\",\n \"questions\": \"* The use of a foundation model, such as GPT-4o, during inference might be time-consuming and could potentially hinder real-time responsiveness in robotic manipulation. Could the authors provide the average inference time for GravMAD at each sub-task stage?\\n* During training, why not generate GravMap in the same way as during inference? (One possible reason may be that the foundation model’s inference time is too lengthy?) The GravMap generated from demonstration ground-truths may differ in distribution from the GravMap produced by the foundation model, which could impact inference performance.\"\n },\n {\n \"id\": \"zoDnMKT20w\",\n \"initial_rating\": 6,\n \"confidence\": 3,\n \"soundness\": 2,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This manuscript investigates 3D manipulation tasks through robot learning. Traditional imitation learning excels with familiar tasks but struggles with new, unseen ones. Recent approaches use large foundation models to mitigate this but lack task-specific learning, often leading to failures in 3D environments. To overcome this, the author introduces a novel framework termed Grounded Space Value Map-guided Action Diffusion (GravMAD). Due to its promising results, I am tentatively inclined to accept the paper. However, I find certain aspects unclear, especially the evaluation of design choices and overall performance. I am open to revising my evaluation if the authors can address these concerns comprehensively and convincingly detail the contributions of their work.\",\n \"strengths\": \"1. GravMAD shows strong generalization capabilities, achieving at least 13.36% higher success rates than state-of-the-art baselines on 12 base tasks encountered during training and surpassing them by 28.63% on 8 novel tasks.\\n 2. The manuscript is well-written with a clear structure, logical flow, detailed technical descriptions, and intuitive chart presentations.\",\n \"weaknesses\": \"- Insufficient argumentation\\n 1. The manuscript mentions in section 3.2 that different sub-goal keypose discovery rules were designed for different types of manipulation tasks, which seems to lack a reasonable explanation and generalizability.\\n 2. The manuscript does not adequately justify the exclusion of GravMap’s guidance in rotation prediction, stating that “rotation actions are difficult to be guided explicitly through value maps.”\\n- Inadequate Evaluation: \\n 1. Although it is claimed that this method is generalized, all experiments were conducted in the RLBench environment, and there is a lack of validation on other simulation environments or real robots.\\n 2. The main evaluation metric used is success rate, overlooking other important dimensions such as completion time, smoothness of action, etc.\",\n \"questions\": \"1. What are the specific criteria for “significant changes” in Sub-goal Keypose Discovery?\\n2. From Table 2, it is evident that the algorithm exhibits significant differences in performance on similar tasks, such as placing a cup and placing wine. Can you explain the reasons for this?\"\n },\n {\n \"id\": \"KUa4VTbtRc\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper proposes a novel method for learning from demonstrations while incorporating knowledge from foundation models to tackle robotic manipulation. It learns to predict robot end-effector actions using a diffusion process and enhances the representation using 3D cost maps introduced in previous work. These cost maps are computed using heuristically extracted sub-goals during training, while foundation models are used instead at inference. In this way, the proposed method is able to combine strong generalisation capabilities from foundation models and learn precise robot actions from available demonstrations. The experiments show strong performance when compared to the considered baselines, while ablation studies provide valuable insights into different components of the method.\",\n \"strengths\": \"- The motivation of the paper is strong and well-explained.\\n- Figures (both in the main paper and the appendix) are clear and very helpful in understanding the proposed method.\\n- The technical challenge of integrating many components together in a unified framework is well-executed and appreciated.\\n- Ablation studies are well-executed and provide valuable insights into the method.\\n- Overall, utilising foundation models together with some demonstrations to achieve both, task generalisation and high precision seems like a great direction.\",\n \"weaknesses\": \"- Novelty and contribution claims are not very clear:\\n - 1) Discovering sub-goals and predicting them to guide robot actions has been done before [1,2,3,4]. Is the novelty here mainly the 3D part combined with foundation models? Maybe the difference could be emphasised more.\\n - 2) From the paper, it seems that GravMaps are Cost and Gripper openness maps used in VoxPoser, just renamed. Without properly explaining the difference, it shouldn’t be called a novel contribution.\\n - 4) Claiming to design two types of tasks (line 124) and then using base tasks from RLBench for one type can come off as being disingenuous about the contribution claims. Rephrasing the 4th contribution to focus more on the evaluation rather than task design would be beneficial.\\n- Some parts of the method and design choices need to be better explained:\\n - How GravMap tokens are used in the network architecture is not described in the main text of the paper.\\n - Explaining in more detail why sub-goals are extracted differently during training and inference would greatly benefit the clarity of the paper. It becomes obvious while reading the paper, but initially, it can cause confusion.\\n - It is not clear why rotation maps from VoxPoser are not used. Justifying it would make the overall approach clearer.\\n - GravMap Synthesis during Inference is not explained clearly. Lines 305-309 are very dense with information, but it’s very difficult to understand how the sub-goals are actually extracted. If it is done just using existing methods, then contribution claims should be adjusted accordingly. \\n- It is not clear if the proposed sub-goal keypose discovery is actually needed. There are no experiments using keyposes, without filtering them. If there are other reasons to filter keyposes, they should be explained.\\n- Overall, sub-goal keypose discovery seems very tailored towards specific types of tasks. Limitations of it (and how they could be lifted) are not discussed.\\n- What are 3 random seeds used for? Are the models re-trained using different seeds or just to change object poses and the stochastic diffusion process? If it’s the latter, then it is the same as having 3x episodes and the reported statistics don’t hold a lot of value.\\n- GravMAD (Manual) seems like an unfair comparison to the baselines. Maybe providing the same ground truth object pose information to other methods would be more valuable for such comparison.\\n- Given that the proposed method uses sub-goals to guide the diffusion process, selected baselines are not the most appropriate. Better baselines would be ChainedDiffuser [3] and/or Hierarchical Diffusion Policy [4].\\n- There are some contradictory and not complete claims in the paper:\\n - Line 144 - Described methods already leverage demonstration data.\\n - Line 205 - Quaternions, although they have the double cover property, are continuous unless additional restrictions are imposed (e.g. by requiring that the scalar part w≥0).\\n - Line 206 stated that 6D rotation representation is used, but line 510 states that the model can predict non-unit quaternions. How is this possible?\\n - What are “3D tasks”? Tasks that involve 3D observations or 6D manipulation? It is not a very clear term.\\n- Limitations of the proposed method are only superficially discussed.\\n\\n[1] Black, Kevin, et al. \\\"Zero-shot robotic manipulation with pretrained image-editing diffusion models.\\\" arXiv preprint arXiv:2310.10639 (2023).\\n\\n[2] Kang, Xuhui, Wenqian Ye, and Yen-Ling Kuo. \\\"Imagined subgoals for hierarchical goal-conditioned policies.\\\" CoRL 2023 Workshop on Learning Effective Abstractions for Planning (LEAP). 2023.\\n\\n[3] Xian, Zhou, et al. \\\"Chaineddiffuser: Unifying trajectory diffusion and keypose prediction for robotic manipulation.\\\" 7th Annual Conference on Robot Learning. 2023.\\n\\n[4] Ma, Xiao, et al. \\\"Hierarchical Diffusion Policy for Kinematics-Aware Multi-Task Robotic Manipulation.\\\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.\",\n \"questions\": \"- Some are raised in the Weaknesses section.\\n- What is the difference between GravMaps and the cost maps described in VoxPoser? Is it the downsampling part?\\n- Why are rotation maps from VoxPoser not used?\\n- Do you have any intuition on how well your proposed method would scale with more data? Would Imitation Learning catch up at some point (with a lot of training data)?\\n- Could you expand a bit more about the limitations of your proposed method?\\n- GravMaps are just an overparameterization of sub-goals at a high level. The fact that the ablation variant (w/o. GravMap) performs so poorly is not very intuitive. Could you provide more details about this ablation variant and maybe you have some intuition about its performance?\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"5;5;5;6\",\n \"rating_avg\": 5.25,\n \"confidence\": \"4;4;5;3\",\n \"confidence_avg\": 4,\n \"soundness\": \"3;2;2;2\",\n \"soundness_avg\": 2.25,\n \"contribution\": \"2;2;2;3\",\n \"contribution_avg\": 2.25,\n \"presentation\": \"2;3;3;3\",\n \"presentation_avg\": 2.75\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"ICLR 2025 Poster\",\n \"venueid\": \"ICLR.cc/2025/Conference\",\n \"processed_at\": \"2026-01-14T22:16:03.710040\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"VYj4MonO4E\",\n \"metareview\": \"The paper presents a framework for robotic manipulation that combines prior work on action diffusion and robotic control with foundation models. The approach demonstrates solid generalization capabilities and outperforms state-of-the-art baselines. \\n\\nStrengths:\\n\\n- Clear motivation and robust experimental design.\\n\\n- Notable performance improvements on training and unseen tasks.\\n\\n- Extensive ablation studies and real-world validations.\\n\\nWeaknesses:\\n\\n- Limited novelty beyond combining existing frameworks.\\n\\n- Challenges with robustness and precision of certain components.\\n\\n- Experiments are limited to RLBench, raising concerns about broader applicability, which was partially addressed by the authors with additional real-world experiments in the rebuttal.\\n\\nWhile the paper has areas that could be improved, such as enhancing methodological contributions and broadening experimental validations, it provides useful insights into robotic manipulation. The authors have addressed most of the reviewers' concerns through detailed rebuttals and revisions, including real-world experiments and clarifications. Therefore, I recommend acceptance.\",\n \"additional_comments\": \"During the discussion, reviewers raised concerns about GravMAD's limited novelty, the simplicity of its Sub-goal Keypose Discovery method, evaluation confined to RLBench, and technical issues like quaternion representation and inference speed. The authors addressed these by mitigating domain shifts through data augmentation, and expanding evaluation with real-world experiments and additional metrics. They clarified technical issues and provided future improvement plans. These efforts resolved most concerns, leading to an overall positive impression and a decision to accept the paper as above the threshold.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Accept (Poster)\"\n}"}}},{"rowIdx":3391,"cells":{"paper_id":{"kind":"string","value":"qQ5djlndm5"},"arxiv_id":{"kind":"string","value":"2312.02252v2"},"title":{"kind":"string","value":"StoryGPT-V: Large Language Models as Consistent Story Visualizers"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract Recent generative models have demonstrated impressive capabilities in generating realistic and visually pleasing images grounded on textual prompts. Nevertheless, a significant challenge remains in applying these models for the more intricate task of story visualization. Since it requires resolving pronouns (he, she, they) in the frame descriptions, i.e., anaphora resolution, and ensuring consistent characters and background synthesis across frames.\\nYet, the emerging Large Language Model (LLM) showcases robust reasoning abilities to navigate through ambiguous references and process extensive sequences. Therefore, we introduce StoryGPT-V , which leverages the merits of the latent diffusion (LDM) and LLM to produce images with consistent and high-quality characters grounded on given story descriptions.\\nFirst, we train a character-aware LDM, which takes character-augmented semantic embedding as input and includes the supervision of the cross-attention map using character segmentation masks, aiming to enhance character generation accuracy and faithfulness.\\nIn the second stage, we enable an alignment between the output of LLM and the character-augmented embedding residing in the input space of the first-stage model. This harnesses the reasoning ability of LLM to address ambiguous references and the comprehension capability to memorize the context. We conduct comprehensive experiments on two visual story visualization benchmarks. Our model reports superior quantitative results and consistently generates accurate characters of remarkable quality with low memory consumption. Our code will be made publicly available 1 1 1 Please refer to the webpage for qualitative results. .\\n\\n## 1 Introduction\\n\\nImage generation algorithms have made significant strides and are on the verge of matching human-level proficiency.\\nDespite this progress, even a powerful image generator suffers from story visualization task, which involves generating a series of frames that maintain semantic coherence based on narrative descriptions [, , , ]. This challenge arises from the fact that captions for a single image are typically self-sufficient, lacking the continuity needed to capture the narrative of object interactions that unfold through multiple sentences over a sequence of frames. This poses a promising avenue for further research and exploration of story visualization. Such a task demands a model capable of producing high-quality characters and detailed environmental objects grounded on given text descriptions. Moreover, it requires the ability to disambiguate referential pronouns in the subsequent frame descriptions, e.g., “she, he, they”.\\n\\nPrior studies [, , , , ] explore the realm of story visualization but do not take reference resolution [] (i.e., anaphora resolution in the context of natural language processing [, ]) into consideration. Story-LDM [] first extended story visualization benchmarks with referential text and devises an attention memory module that retains visual context throughout the series of generated frames. However, it still struggles to generate precise characters for referential text since the interaction between current descriptions and contextual information occurs within the CLIP [] semantic space, causing a loss in fine-grained language understanding and hindering referencing capabilities. Furthermore, the attention memory module requires maintaining all previous images in latent pixel space for attention calculations, significantly increasing memory demands with each additional frame in autoregressive generation.\\n\\nThe limitation of previous works leads us to rethink how to achieve accurate and efficient reference resolution toward consistent story visualization. Large Language Models (LLMs) [, , , ], trained on extensive text corpora, have exhibited impressive capabilities in deciphering contextual references in natural language descriptions. Prior works [, ] have demonstrated the effectiveness of harnessing LLMs for tasks involving image comprehension and generation, where the visual features are adapted within LLM’s token space rather than the pixel space. Hence, such a model could be utilized to efficiently address ambiguous references for story visualization tasks.\\n\\nIn this work, we aim at story visualization grounded on given co-referential frame descriptions, focusing on delivering high-quality and coherent portrayals of characters.\\nTo achieve this, we leverage a powerful text-to-image model [] to generate high-quality characters and environmental objects grounded on given frame descriptions, coupled with the reasoning ability of Large Language Models (LLMs) to resolve ambiguous references and improve the cohesiveness of the context. To improve the generation of highly faithful characters, we enhance the pre-trained Latent Diffusion (LDM) towards character-aware training in the first stage. We first augment the token feature by incorporating the visual representation of the corresponding character. Additionally, we regulate the cross-attention map of the character token to highlight the interaction between the conditional token and specific latent pixels.\\n\\nIn addressing the challenge of ambiguous reference, which cannot be effectively handled by a robust text-to-image model alone, we leverage an LLM that takes interleaved images and co-referential frame descriptions as input, and aligns its visual output with the character-augmented embedding encoded by first-stage model. Such semantic guidance, along with LLM’s casual modeling, enables effective reference resolution and consistent generation. Furthermore, our approach efficiently preserves context by processing images as sequences of tokens in the LLM input space with low memory consumption.\\n\\nContributions. Our contributions are as follows:\\n\\n- •\\nWe first enhance the text representation by integrating the visual features of the corresponding characters, then refine a character-aware LDM for better character generation by directing cross-attention maps with character segmentation mask guidance.\\n- •\\nWe adapt LLM by interlacing text and image inputs, empowering it to implicitly deduce references from previous contexts and produce visual responses that align with the input space of the first-stage Char-LDM. This leverages the LLM’s reasoning capacity for reference resolution and the synthesis of coherent characters and scenes.\\n- •\\nOur model is capable of visualizing stories featuring precise and coherent characters and backgrounds on story visualization benchmarks. Furthermore, we showcase the model’s proficiency in producing extensive (longer than 40 frames) visual stories with low memory consumption.\\n\\n## 2 Related Work\\n\\nText-to-image synthesis. Numerous works [, , ] have demonstrated unprecedented performance on semantic generation. Recently, diffusion-based text-to-image models [, , , ] have shown significant advancements in enhancing image quality and diversity through the utilization of diffusion models. However, these text-to-image approaches primarily concentrate on aligning individual-generated images grounded on text descriptions and do not take into account the crucial aspects of character and scene consistency across multiple frames in the story visualization task. Additionally, they lack the capability to effectively resolve co-reference issues within a narrative description.\\n\\nMulti-modal Large Language Models. Large Language Models (LLMs) wield an extensive repository of human knowledge and exhibit impressive reasoning capabilities. Recent studies [, , , ] utilize pre-trained language models to tackle vision-language tasks, and subsequent studies [, , , , , ] further enhance multi-modal abilities by aligning vision models with LLM input space. In addition to multi-modal comprehension, several works are dedicated to more challenging multi-modal generation tasks. FROMAGe [] appends a special retrieval token to LLM and maps the hidden representation of this token into a vector space for retrieving images. Several current works [, , ] learn a mapping from hidden embeddings of an LLM represents for additional visual outputs into the input space of a frozen pre-trained text-to-image generation model []. In this work, we fed multi-modal LLM with interleaved image and referential text descriptions as input and aligned the output with a character-aware fused embedding from our first-stage Char-LDM, guiding the LLM in implicitly deducing the references.\\n\\nStory Visualization. StoryGAN [] pioneers the story generation task, which proposes a sequential conditional GAN framework with dual frame and story level discriminators to improve image quality and narrative coherence. DuCoStoryGAN [] introduces a dual-learning framework that utilizes video captioning to enhance semantic alignment between descriptions and generated images. VLCStoryGAN [] used video captioning for semantic alignment between text and frames. Recently, StoryDALL-E [] retrofits the cross-attention layers of the pre-trained text-to-image model to promote generalizability to unseen visual attributes of the generated story. These methods do not consider ambiguous references in text descriptions. Story-LDM [] first introduced reference resolution in story visualization tasks and proposed an autoregressive diffusion-based framework with a memory-attention module to resolve ambiguous references. Nevertheless, it struggled with accurately resolving references and was memory-intensive, as it required retaining all previous context in pixel space. In our work, we employ a powerful causal inference LLM for reference resolution, and it efficiently maintains context by mapping visual features into several token embeddings as LLM inputs rather than operating in latent pixel space.\\n\\nFigure: Figure 2: (a) In the first stage, a fused embedding is created by integrating character visuals with text embeddings, serving as the Char-LDM’s conditional input, and the cross-attention maps of Char-LDM will be guided by corresponding character segmentation mask for accurate and high-quality character generation (Section [3.2](#S3.SS2)). (b) In the second stage, the LLM takes the interleaved image and text context as input and generates $R$ [IMG] tokens. These tokens are then projected by LDM Mapper into an intermediate output, which will be encouraged to align with fused embedding as Char-LDM’s input. The figure intuitively shows how the character-augmented fused embedding and the casual language modeling aid LLM for reference resolution (Section [3.3](#S3.SS3)).\\nRefer to caption: /html/2312.02252/assets/x2.png\\n\\n## 3 Methods\\n\\nThe objective of story visualization is to transform a textual narrative, composed of a series of $N$ descriptions ${S_{1},...S_{N}}$, into a sequence of corresponding visual frames ${I_{1},...,I_{N}}$ that illustrate the story. We’ve developed a two-stage method aimed at generating temporally consistent visual stories with accurate and high-quality characters. First, we augment text representation with characters’ visual features and refine a character-aware LDM [] (Char-LDM) towards high-quality character generation. This is achieved by directing the cross-attention maps of specific tokens associated with the corresponding characters, using character segmentation mask supervision (Section [3.2](#S3.SS2)). Then, we leverage the reasoning ability of LLM to resolve ambiguous references by aligning the output of LLM with Char-LDM input space for temporal consistent story visualization (Section [3.3](#S3.SS3)).\\n\\n### 3.1 Preliminaries\\n\\nCross-attention in text-conditioned Diffusion Models. In diffusion models [, ], each diffusion step $t$ involves predicting noise $\\\\epsilon$ from the noise code $z_{t}\\\\in\\\\mathbb{R}^{(h\\\\times w)\\\\times d_{v}}$ conditioned on text embedding $\\\\psi(S)\\\\in\\\\mathbb{R}^{L\\\\times d_{c}}$ via U-shaped Network [], where $\\\\psi$ is the text encoder, $h$ and $w$ are the latent spatial dimensions and $L$ is the sequence length. Within U-Net, the cross-attention layer accepts the spatial latent code $z$ and the text embeddings ${\\\\psi}(S)$ as inputs, then projects them into $Q=W^{q}z$, $K=W^{k}{\\\\psi}(S)$ and $V=W^{v}{\\\\psi}(S)$, where $W^{q}\\\\in\\\\mathbb{R}^{d_{v}\\\\times d^{\\\\prime}}$, $W^{k},W^{v}\\\\in\\\\mathbb{R}^{d_{c}\\\\times d^{\\\\prime}}$. The attention scores is computed as $A=\\\\mathrm{Softmax}(\\\\frac{QK^{T}}{\\\\sqrt{d^{\\\\prime}}})\\\\in\\\\mathbb{R}^{(h\\\\times w)\\\\times L}$, where $A[i,j,k]$ represents the attention of $k$-th text token to the $(i,j)$ latent pixel. In this context, each entry $A[i,j,k]$ within the cross-attention map $A$ quantifies the magnitude of information propagation from the $k$-th text token to the latent pixel at position $(i,j)$. This feature of the interaction between semantic representation and latent pixels is harnessed in various tasks such as image editing [, ], video editing [], and fast adaptation [, , , ].\\n\\n### 3.2 Character-aware LDM with attention control\\n\\nIntegrate visual features with text conditions. To achieve accurate and high-quality characters in story visualization, we augment text descriptions with visual features of corresponding characters and guide the attention of text conditions to focus more on corresponding character synthesis. Given a text description $S$, suppose there are $K$ characters that should be generated in image $I$, images of those characters {$I_{c}^{1},...,I_{c}^{K}$}, a list of token indices indicating each character name located in the description, denoted as $\\\\{i_{c}^{1},...i_{c}^{K}\\\\}$. Inspired by [, , ], we first utilize CLIP [] text encoder ${\\\\psi}$ and image encoder $\\\\phi$ to obtain text embedding and visual features of the characters appear in the image respectively. Then, we augment the text embedding if the token represents a character name. More specifically, we concatenate the token embedding and the visual features of the corresponding character and feed them into an MLP to obtain the augmented text embedding. Each augmented token embedding in the augmented embedding $c$ is formulated as below:\\n\\n$$ $c^{k}=\\\\textrm{MLP}\\\\left(\\\\mathrm{concat}\\\\left(({\\\\psi}(S[i_{c}^{k}]),\\\\phi(I_{c}^{k})\\\\right)\\\\right)$ (1) $$\\n\\nwhere $i_{c}^{k}$ refers to the index of the text token for character $k$, and $I_{c}^{k}$ the image corresponding to character $k$. The embeddings for tokens in $c$ that are unrelated to the character remain identical to the vanilla CLIP token embeddings. The enhanced embedding $c$ is then employed as supervision for the second-stage training, which will be further detailed in Section [3.3](#S3.SS3), where $c_{1},...c_{N}$ are the corresponding augmented embeddings for $S_{1},...,S_{N}$.\\n\\nControlling attention of text tokens. Previous work [] has demonstrated that the visual characteristics of generated images are influenced by the intricate interplay between latent pixels and text embedding through the diffusion process of LDM []. However, in vanilla LDM [], a single latent pixel can unrestrictedly engage with all text tokens. Therefore, we introduce a constraint to refine this behavior and strengthen the impact of the token representing the character’s name on certain pixels in the denoising process, as illustrated in Figure [2](#S2.F2) (a). First, we obtain an offline segmentation mask of corresponding characters denoted as $\\\\{M_{1},...M_{K}\\\\}$ as supervision signals via SAM []. We then encourage the cross-attention map $A_{k}$ for each character $k$ at the token index position $i_{c}^{k}$, to align with the binary segmentation mask $M_{k}$, whereas diverging from irrelevant regions $\\\\bar{M}_{k}$, formulated as follows:\\n\\n$$ $\\\\mathcal{L}_{\\\\textrm{reg}}=\\\\frac{1}{K}\\\\sum_{k=1}^{K}(A_{k}^{-}-A_{k}^{+})$ (2) $$\\n\\nwhere\\n\\n$$ $A_{k}^{-}=\\\\frac{A_{k}\\\\odot\\\\bar{M}_{k}}{\\\\sum_{i,j}(\\\\bar{M}_{k})_{ij}},\\\\,\\\\,A_{k}^{+}=\\\\frac{A_{k}\\\\odot M_{k}}{\\\\sum_{i,j}(M_{k})_{ij}}$ (3) $$\\n\\nwhere $K$ is the number of characters to be generated in the image, $i_{c}^{k}$ is the index of text token representing character $k$ and $\\\\odot$ is the Hadamard product.\\nBy reducing the loss, it increases the attention of character tokens to the relevant pixels of their respective characters, while reducing their attention to irrelevant areas. Moreover, as the token embeddings are enriched with the visual features of the corresponding character, this attention control serves to deepen the connection between the augmented semantic space and latent pixel denoising, which can consequently enhance the quality of synthesized characters.\\n\\nOur first stage Char-LDM focuses solely on the quality of image generation grounded on a single caption. Yet, there remain challenges that surpass the abilities of text-to-image generators in visualizing a sequence of stories. Firstly, story visualization demands character and background consistency, an aspect not covered by our first-stage enhancements. Moreover, the inherent nature of lengthy descriptions includes referential terms like he, she, or they, which presents a significant challenge for LDM in achieving accurate inference. In contrast, LLMs can adeptly infer the intended character to which the ambiguous text refers. Therefore, to address this issue, we harness the formidable reasoning capabilities of LLM to disambiguate such references.\\n\\n### 3.3 Aligning LLM for reference resolution\\n\\nTo enable an LLM to autoregressively generate images conditioned on prior context and resolve ambiguous references, the model must be capable of (i) processing images; (ii) producing images; and (iii) implicitly deducing the subject of reference. The model could understand the image by learning a linear mapping from the visual feature to the LLM input space, and generate images by aligning the hidden states with conditional input required by LDM, which is the fused embedding encoded by first-stage Char-LDM’s text and visual encoder. It integrates the visual features of characters into the text embedding. This character-augmented embedding, along with the causal language modeling (CLM) [, , ] will direct the LLM to implicitly deduce and generate the correct character for the referential input, as depicted in Figure [2](#S2.F2) (b).\\n\\nMore specifically, the LLM input consists of interleaved co-referential text descriptions and story frames with flexible frame length $n$, in the order of $(I_{1},S_{1},...,I_{n-1},S_{n-1},S_{n})$, where $2\\\\leq n\\\\leq N$. We first extract visual embeddings $\\\\phi(I_{i})\\\\in\\\\mathbb{R}^{d_{i}}$ with CLIP [] visual backbone, where $i\\\\in[2,n]$, and learn $\\\\texttt{Mapper}_{LLM}$ with trainable matrix $\\\\mathbf{W}_{v2t}\\\\in\\\\mathbb{R}^{d_{i}\\\\times me}$ which maps $\\\\phi(I_{i})$ into $m$ $k$-dimensional embeddings reside within LLM input space [, , ], where $e$ is the dimension of LLM embedding space. Additionally, like recent works [, , ] in enabling LLM to generate images, we add additional $R$ tokens, denoted as [IMG1], …, [IMGR] to represent visual outputs and incorporate trainable matrix $\\\\mathbf{W}_{gen}\\\\in\\\\mathbb{R}^{R\\\\times e}$ into frozen LLM. The training objective is to minimize the negative log-likelihood of producing [IMG] tokens conditioned on previously interleaved image/text tokens $\\\\mathcal{T}_{prev}$:\\n\\n$$ $\\\\mathcal{L}_{gen}=-\\\\sum_{r=1}^{R}\\\\log p(\\\\texttt{[IMG${}_{r}$]}|\\\\mathcal{T}_{prev},\\\\texttt{[IMG${}_{<r}$]})$ (4) $$\\n\\nwhere\\n\\n$$ $\\\\mathcal{T}_{prev}=\\\\{\\\\phi(I_{<i})^{T}\\\\mathbf{W}_{v2t},\\\\psi(S_{1:i})\\\\}$ (5) $$\\n\\nwhere $i\\\\in[2,n]$ is the number of text descriptions of the current step.\\nTo align [IMG] produced by LLM with LDM input space, we utilize a Transformer-based $\\\\texttt{Mapper}_{LDM}$ to project [IMG] tokens to the input space of first-stage finetuned LDM with $L$ learnable query embeddings $(q_{1},...,q_{L})\\\\in\\\\mathbb{R}^{L\\\\times d}$, where $L$ is the maximum input sequence length of the LDM, similar to BLIP-2 Q-Former []. The training objective is to minimize the distance between $\\\\mathrm{Mapper}$’s output Gen Emb and the augmented conditional text representations of LDM, i.e., Fuse Emb introduced in Section [3.2](#S3.SS2), formulated as:\\n\\n$$ $\\\\mathcal{L}_{\\\\textrm{align}}=||\\\\texttt{Mapper}_{LDM}\\\\left(h_{\\\\texttt{[IMG${}_{1:R}$]}},q_{1},...q_{L}\\\\right)-c_{i}||_{2}^{2}$ (6) $$\\n\\nwhere $h_{[\\\\texttt{IMG}_{1:R}]}$ denotes the last hidden states of LLM’s [IMG] tokens. Suppose we can get access to the original text without reference $S_{i}^{{}^{\\\\prime}}$. Then, $c_{i}$ is the augmented text embedding of caption $S_{i}^{{}^{\\\\prime}}$ encoded by the first-stage model’s text and visual encoder. For instance, if $S_{i}$ is ”They are talking to each other,” then $S_{i}^{{}^{\\\\prime}}$ would be ”Fred and Wilma are talking to each other.” This non-referential text, augmented with character visual features, assists LLM in efficiently disambiguating references using casual language modeling.\\n\\nInference. During the inference process, the model sequentially visualizes stories grounded on text descriptions. It begins by processing the text description of the initial frame $S_{1}$. Focusing exclusively on frame generation, we constrain the LLM to generate only $R$ specific [IMG] tokens and then feed these token embeddings into the first-stage Char-LDM, resulting in the generation of the first frame $I_{1}^{gen}$. Subsequently, the LLM takes a contextual history that includes the text description of the first frame $S_{1}$, the generated first frame $I_{1}^{gen}$, and the text description of the second frame $S_{2}$ as input. This process is repeated to visualize the entire story progressively.\\n\\nTable: Table 1: Main experiments on FlintStonesSV []. The top portion is evaluated on the dataset w/o extended referential text. The bottom half displays the results on the extended dataset with co-reference. ^†StoryDALL-E [] takes the source frame as additional input.\\n\\n## 4 Experiments\\n\\n### 4.1 Experimental Setups\\n\\nDatasets.\\nOur experiments are conducted using two story visualization datasets: FlintstonesSV [] and PororoSV []. FlintstonesSV [] contains 20132-training, 2071-validation, and 2309-test stories with 7 main characters and 323 backgrounds, while PororoSV [] consists of 10,191 training samples, 2,334 for validation, and 2,208 for testing with 9 main characters. We follow [] to extend the datasets with referential text, by replacing the character names with references, i.e., he, she, or they, wherever applicable. Please refer to the supplementary for details.\\n\\nEvaluation metrics.\\nTo measure the accuracy of the characters and background in the generated stories, we consider the following evaluation metrics the same as previous story visualization literature [, , ]: Following [], we finetune Inception-v3 to measure the classification accuracy and F1-score of characters (Char-Acc, Char-F1) and background (BG-Acc, BG-F1) respectively. In addition, we consider the Frechet Inception Distance (FID) score, which compares the distribution between feature vectors from real and generated images for quality assessment.\\n\\nWhen assessing text-image alignment, the CLIP [] score falls short in reliability since it cannot capture fine-grained details. Therefore we choose the powerful captioning model BLIP2 [] as the evaluation model and fine-tune it on the corresponding datasets. We then employ it as a captioner to predict 5 captions for generated images and 5 captions for ground truth images as a comparison to report the average BLEU4 [] and CIDEr [] score to assess text-image alignment.\\n\\nComparison Approaches. We compare our model with state-of-the-art approaches: VLCStoryGAN [], StoryDALL-E [], LDM [] and Story-LDM []. Following previous research [, ], we use 4 consecutive frames for evaluation. For StoryDALL-E [], which takes both story descriptions and the initial frame as input, we use the first frame of a 5-frame story and evaluate using the generated 4 frames. We finetune vanilla Stable Diffusion (LDM) on FlintStonesSV [] and PororoSV [] as a baseline. Since Story-LDM [] does not provide pre-trained checkpoint or cleaned training code, we initiate training from pre-trained LDM(^2^22[https://ommer-lab.com/files/latent-diffusion/nitro/txt2img-f8-large](https://ommer-lab.com/files/latent-diffusion/nitro/txt2img-f8-large)).\\n\\nImplementation Details. For the first stage training, we freeze CLIP [] text encoder and fine-tune the remaining modules for 25k steps with a learning rate of 1e-5 and batch size of 32 on original non-referential text. To enhance inference time robustness and flexibility, we adopt a training strategy that includes $10\\\\%$ unconditional training, i.e., classifier-free guidance [], $10\\\\%$ text-only training, and $80\\\\%$ character-augmented fuse training (Section [3.2](#S3.SS2)).\\n\\nFor the second stage training, we use OPT-6.7B(^3^33[https://huggingface.co/facebook/opt-6.7b](https://huggingface.co/facebook/opt-6.7b)) model as the LLM backbone. To expedite the second stage alignment training, we first pre-compute non-referential fused embeddings residing in the input space of the first-stage Char-LDM. We map visual features into $m=4$ token embeddings as LLM input, set the max sequence length as 160 and the number of additional [IMG] tokens represents for LLM’s visual output as $R=8$, batch size as 64 training for 20k steps. Please refer to the supplementary for more details.\\n\\n### 4.2 Visual Story Generation\\n\\nFigure: Figure 3: Qualitative comparison on FlintStonesSV [] (left) and PororoSV [] (right) with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x3.png\\n\\nQuantitative Results. (i) Generation with original descriptions. The upper half of Table [1](#S3.T1) shows the comparison results on original FlintStonesSV [] without referential text descriptions. Our first-stage Char-LDM exhibits superior performance in generating accurate characters (Char-Acc, Char-F1) and background scenes (BG-Acc, BG-F1), achieving high fidelity (FID), and exhibiting better alignment with given text descriptions (BLEU4 [], CIDEr []).\\n(ii) Generation with co-referenced descriptions. Table [1](#S3.T1) (bottom) and Table [2](#S4.T2) show the results on extended FlintStonesSV [] and PororoSV [] with co-referential text descriptions [] respectively. By harnessing the merit of reasoning and comprehension abilities of LLM, our model substantially boosts performance in reference resolution compared to baselines, while maintaining a strong text-image alignment grounded in the provided text descriptions.\\n\\nTable: Table 2: Performance comparison on PororoSV [] with co-referenced descriptions. ^†StoryDALL-E [] takes the source frame as additional input.\\n\\nFigure: Figure 4: Human evaluation results on FlintStonesSV [] w.r.t visual quality, text-image alignment, character accuracy and temporal consistency.\\nRefer to caption: /html/2312.02252/assets/x4.png\\n\\nQualitative Results. Figure [3](#S4.F3) demonstrates qualitative comparison on FlintStonesSV [] and PororoSV [] with co-reference descriptions. LDM [] could generate high-quality images but struggles to produce correct characters in the presence of reference in the captions. Story-LDM [], despite incorporating an attention-memory module to handle context, fails to produce accurate characters in some frames. In comparison, our model excels at generating frames with pleasing visuals, accurate characters, and maintaining temporal consistency in the background scenes.\\n\\nHuman Evaluation. In addition, we use Mechanical Turk to assess the quality of 100 stories produced by our methods or Story-LDM [] on FlintStonesSV []. Given a pair of stories generated by Story-LDM [] and our model, MTurkers are asked to decide which generated four-frame story is better w.r.t visual quality, text-image alignment, character accuracy, and temporal consistency. Each pair is evaluated by 3 unique workers. In Figure [4](#S4.F4), our model demonstrates significantly better story visualization quality with accurate and temporally coherent synthesis.\\n\\n### 4.3 Ablation Studies\\n\\nFirst stage ablation. We conducted an ablation study for the first stage and presented results in Table [3](#S4.T3). w/o $\\\\mathcal{L}_{reg}$ indicates that we disabled the $\\\\mathcal{L}_{reg}$ loss (Equation [2](#S3.E2)), i.e., the model underwent training without the influence of segmentation masks to direct the cross-attention maps. w/o augmented text signifies that the model’s conditional input during its training phase was the standard CLIP [] text embedding, rather than the fused embedding incorporating the character’s visual attributes as discussed in Section [3.2](#S3.SS2). freeze vis denotes the visual encoder remained frozen during training. Unless specified, the last two layers of the visual encoder are made adjustable. The final two rows employ our default training strategy and the only distinction lies in the inference phase. Default (w/o img) takes vanilla CLIP [] text embedding as input condition, whereas Default (w/ img) employs the fused embedding. As indicated by Table [3](#S4.T3), integrating character visual features during training significantly enhances the generation performance and the additional cross-attention control propels the model to achieve its peak on accurate character generation. Note that the FID score of Default (w/ img) is slightly higher than Default (w/o img). This is because, during inference, the reference images for corresponding characters in Default (w/ img) are obtained online, introducing a slight deviation from the original distribution.\\n\\nTable: Table 3: Ablation study for the first stage finetuning LDM with cross-attention control.\\n\\nSecond stage ablation. As shown in Table [4](#S4.T4), we conducted an ablation study on (i) whether to align with the text embedding (Embtext) or the fused embedding (Embfuse) of our first stage model; (ii) whether the model’s input consists of a sequence of captions (Caption-) or utilizes interleaved training with both images and captions (Interleave-) (Equation [5](#S3.E5)). Experimental results shown in Table [4](#S4.T4) indicate that image-text interleave training can significantly enhance performance. It is intuitive that taking both images and corresponding captions as input provides a more profound comprehension of the characters and their interactions within the image than when provided with sole captions. This, in turn, amplifies its generative capabilities.\\n\\nTable: Table 4: Second stage training strategy ablation. Input only caption or interleaved text and image. The output of LLM is aligned with our Char-LDM text embedding (Embtext) or character-augmented fused embedding (Embfuse).\\n\\n### 4.4 Analysis\\n\\nWe further investigate the impact of first-stage finetuning with cross-attention control by visualizing averaged cross-attention maps in U-Net latent pixel space and interpolating them to match the size of the generated images. As illustrated in Figure [5](#S4.F5), vanilla LDM (top) finetune on FlintStonesSV [] w/o $\\\\mathcal{L}_{reg}$ (Section [3.2](#S3.SS2)) fails to accurately focus on the corresponding characters for character tokens. Our model (bottom), which incorporates cross-attention guidance, is able to precisely direct attention to generated characters given corresponding character tokens.\\n\\nFigure: Figure 5: Visualization of cross attention maps of corresponding character tokens.\\nRefer to caption: /html/2312.02252/assets/x5.png\\n\\n### 4.5 Properties\\n\\nOur model could generate longer stories featuring accurate characters, at a faster speed and with lower computational consumption. Our architecture allows our model to retain an extensive context requiring minimal computational resources by efficiently mapping visual features into tokens instead of operating in pixel space. Figure [6](#S4.F6) shows the comparison between our model and Story-LDM [] w.r.t GPU memory consumption and inference speed for longer-frames story generation. Our model is capable of producing sequences exceeding 50 frames with low memory usage, whereas Story-LDM [] encounters GPU memory limitations (80G A100) when generating 42 frames. This is because Story-LDM [] requires the retention of the entire context, e.g., $n$ frames in latent pixel space ($n\\\\times h\\\\times w\\\\times d$), whereas our model processes visual features as four token embedding ($n\\\\times 4\\\\times d$) with the same dimensions as the text tokens in LLM. Table [5](#S4.T5) compares the accuracy of generated characters and FID score for long story visualizations between our model and Story-LDM []. The performance of Story-LDM [] significantly decreases when generating longer stories and reaches the memory limit before 50 frames. In contrast, by utilizing the capacity of LLM to retain extensive context, our model upholds accurate character consistency in visualizing lengthy narratives with co-referential text descriptions.\\n\\nFigure: Figure 6: Compare inference speed and GPU memory consumption between our method and Story-LDM []. Story-LDM encounters the 80GB GPU limit when generating sequences exceeding 40 frames.\\nRefer to caption: /html/2312.02252/assets/x6.png\\n\\nTable: Table 5: Longer-frames story visualization comparison on FlintStonesSV [] with referential text. Story-LDM reaches maximum GPU capacity when generating 50 frames.\\n\\nOur design could be easily adapted to any LLMs. In our work, we experimented with OPT-6.7b(^4^44[https://huggingface.co/facebook/opt-6.7b](https://huggingface.co/facebook/opt-6.7b)) and Llama2-7b-chat(^5^55[https://huggingface.co/meta-llama/Llama-2-7b-chat](https://huggingface.co/meta-llama/Llama-2-7b-chat)) models. Our findings, as illustrated in Table [9](#A2.T9), indicate an improvement when changing from OPT [] to a more powerful model, Llama2 [].\\n\\nTable: Table 6: Performance on FlintstonesSV [] dataset with referential text using different LLMs.\\n\\nOur model, StoryGPT-V, is capable for multi-model generation. Owing to StoryGPT-V design leveraging the advanced capabilities of Large Language Models (LLMs), it exhibits a unique proficiency in that it can extend visual stories. StoryGPT-V is not merely limited to visualizing stories based on provided textual descriptions. Unlike existing models, it also possesses the innovative capacity to extend these narratives through continuous text generation. Concurrently, it progressively synthesizes images that align with the newly generated text segments.\\n\\nOur model represents a notable advancement in story visualization, being the first of its kind to consistently produce both high-quality images and coherent narrative descriptions. This innovation opens avenues for AI-assisted technologies to accelerate visual storytelling creation experiences by exploring various visualized plot extensions as the story builds.\\n\\n## 5 Conclusion\\n\\nIn this paper, we aim at high-quality and consistent character synthesis for story visualization grounded on co-referential text descriptions. To accomplish this, we utilize the strengths of the LDM for generating high-quality images, combined with the reasoning capability of LLM to comprehend extended contexts, resolve ambiguities, and ensure semantic consistency in the generation process. We first finetune LDM by guiding the cross-attention map of LDM with character segmentation masks, which improves the accuracy and faithfulness of character generation. Next, we facilitate a mapping from the output of LLM to align with the input space of the first stage LDM, thus allowing Multi-modal LLM to both process and produce images. This process leverages the LLM’s logical reasoning to clarify ambiguous references and its capacity to retain contextual information. Our model reports superior quantitative results and consistently generates characters with remarkable quality.\\n\\n## Appendix\\n\\nFigure: Figure 7: Our model StoryGPT-V extending stories in both language and vision: Gray part represents the text descriptions from datasets. Blue part corresponds to the frames and the continued written stories based on the previous captions generated by our model StoryGPT-V. This is the first model capable of story visualization and multi-modal story generation (continuation) by leveraging an LLM.\\nRefer to caption: /html/2312.02252/assets/x7.png\\n\\n## Appendix A Multi-modal Story Generation\\n\\nOwing to StoryGPT-V design leveraging the advanced capabilities of Large Language Models (LLMs), it exhibits a unique proficiency in that it can extend visual stories. StoryGPT-V is not merely limited to visualizing stories based on provided textual descriptions. Unlike existing models, it also possesses the innovative capacity to extend these narratives through continuous text generation. Concurrently, it progressively synthesizes images that align with the newly generated text segments.\\n\\nFigure [7](#Ax1.F7) presents an example of a multi-modal story generation. Initially, the first four frames are created according to the text descriptions from the FlintstonesSV [] dataset (gray part). Subsequently, the model proceeds to write the description for the next frame (blue part), taking into account the captions provided earlier, and then creates a frame based on this new description (blue part). This method is employed iteratively to generate successive text descriptions and their corresponding frames.\\n\\nOur model represents a notable advancement in story visualization, being the first of its kind to consistently produce both high-quality images and coherent narrative descriptions. This innovation opens avenues for AI-assisted technologies to accelerate visual storytelling creation experiences by exploring various visualized plot extensions as the story builds.\\n\\n## Appendix B Ablation Studies\\n\\n### B.1 Effect of first-stage design.\\n\\nIn Table [7](#A2.T7) lower half, we conducted an ablation study on how the stage-1 design contributes to the final performance. In the first line, the stage-2 LLM is aligned with vanilla LDM fine-tuned on FlintstonesSV []. The second line aligns the LLM output with our Char-LDM’s text embedding (Embtext), while the last line aligns with character-augmented fused embedding (Embfuse) of our Char-LDM. The first two lines align to the same text embedding encoded by the CLIP [] text encoder, however, our Char-LDM enhanced with cross-attention control ($\\\\mathcal{L}_{reg}$) produces more precise characters. Different from Embtext, the last line is aligned with Embfuse, which is augmented with characters’ visual features. This visual guidance helps LLM to interpret references more effectively by linking “he, she, they” to the previous language and image context.\\n\\nTable: Table 7: The output of our stage-2 model is aligned with conditional input of vanilla LDM [] (finetuned on FlintstonesSV []), our Char-LDM text embedding (Embtext) or character-augmented fused embedding (Embfuse).\\n\\n### B.2 Number of [IMG] Tokens\\n\\nWe further examined the impact of the number of added [IMG] tokens. As indicated in Table [8](#A2.T8), aligning with the fused embedding and setting $R=8$ yields the best performance.\\n\\nTable: Table 8: StoryGPT-V Ablations: Impact of $R$, the number of added [IMG] tokens. Embtext: the output of LLM is aligned with text embedding extracted from the text encoder; Embfuse: aligned with fused embedding Embfuse of first stage model.\\n\\n### B.3 Different LLMs (OPT vs Llama2)\\n\\nTable: Table 9: Performance on FlintstonesSV [] dataset with referential text using different LLMs.\\n\\nOur primary contribution lies in leveraging Large Language Models (LLMs) for reference resolution for consistent story visualization. In our work, we experimented with OPT-6.7b(^6^66[https://huggingface.co/facebook/opt-6.7b](https://huggingface.co/facebook/opt-6.7b)) and Llama2-7b-chat(^7^77[https://huggingface.co/meta-llama/Llama-2-7b-chat](https://huggingface.co/meta-llama/Llama-2-7b-chat)) models. It’s important to note that the utilization of Llama2 was specifically to demonstrate its additional capability for multi-modal generation. The ablation study of different LLMs was not the main focus of our research.\\n\\nOur findings, as illustrated in Table [9](#A2.T9), indicate only a slight improvement when changing from OPT [] to Llama2 []. This marginal difference is attributed to the evaluation metric’s emphasis on image-generation capabilities, which assesses whether the model’s visual output aligns well with first-stage Char-LDM’s conditional input space.\\n\\n## Appendix C Evaluation\\n\\n### C.1 Text-image alignment.\\n\\nCLIP [] is trained on large-scale image-caption pairs to align visual and semantic space. However, a domain gap exists between pre-train data and the story visualization benchmark. Therefore, we finetune CLIP [] on the story visualization datasets. However, we found it still hard to capture fine-grained semantics, either text-image (T-I) similarity or image-image similarity (I-I), i.e., the similarity between visual features of generated images and corresponding ground truth images.\\n\\nUpon this observation, we choose the powerful captioning model BLIP2 [] as the evaluation model. We finetune BLIP2 on FlintstonesSV [] and PororoSV [], respectively, and employ it as an image captioner for generated visual stories. We avoided direct comparisons to bridge the gap between BLIP2’s predictions and the actual ground truth captions. Instead, we used the fine-tuned BLIP2 to generate five captions for each ground truth image and one caption for each generated image. and report average BLEU4 [] or CIDEr [] score based on these comparisons.\\n\\nTable: Table 10: Text-image alignment score for FlintstonesSV [] with referential text descriptions in terms of CLIP [] similarity, BLEU4 [] and CIDEr [].\\n\\n### C.2 Human evaluation.\\n\\nWe use Mechanical Turk to assess the quality of 100 stories produced by our methods or Story-LDM [] on FlintStonesSV []. Given a pair of stories generated by Story-LDM [] and our model, people are asked to decide which generated four-frame story is better w.r.t visual quality, text-image alignment, character accuracy and temporal consistency. Each pair is evaluated by 3 unique workers. The human study interface is illustrated in Figure [8](#A3.F8).\\n\\nFigure: Figure 8: Human study interface.\\nRefer to caption: /html/2312.02252/assets/x8.png\\n\\n## Appendix D Implementation Details\\n\\n### D.1 Data preparation\\n\\nFlintstonesSV [] provides the bounding box location of each character in the image. We fed the bounding boxes into SAM [] to obtain the segmentation map of corresponding characters. This offline supervision from SAM [] is efficiently obtained without the need for manual labeling efforts. Furthermore, we enhance the original datasets from resolution of 128x128 to 512x512 via a super-resolution model(^8^88[https://huggingface.co/CompVis/ldm-super-resolution-4x-openimages](https://huggingface.co/CompVis/ldm-super-resolution-4x-openimages)) and then we proceed to train and evaluate all models on this enhanced dataset.\\n\\n### D.2 Extending dataset with referential text\\n\\nWe follow Story-LDM [] to extend the datasets with referential text by replacing the character names with references, i.e., he, she, or they, wherever applicable as shown in Algorithm [1](#alg1). The statistics before and after the referentail extension are shown in Table [11](#A4.T11). Please refer to Story-LDM [] implementation(^9^99[https://github.com/ubc-vision/Make-A-Story/blob/main/ldm/data](https://github.com/ubc-vision/Make-A-Story/blob/main/ldm/data)) for more details on how the referential dataset is extended.\\n\\nTable: Table 11: Dataset statistics of FlintstonesSV [] and PororoSV []\\n\\n### D.3 First stage training\\n\\nWe built upon pre-trained Stable Diffusion [] v1-5(^10^1010[https://huggingface.co/runwayml/stable-diffusion-v1-5](https://huggingface.co/runwayml/stable-diffusion-v1-5)) and use CLIP [] ViT-L to extract characters’ visual features. We freeze the CLIP text encoder and fine-tune the remaining modules for 25,000 steps with a learning rate of 1e-5 and batch size of 32. The first stage utilizes solely the original text description without extended referential text. To enhance inference time robustness and flexibility, with or without reference images, we adopt a training strategy that includes $10\\\\%$ unconditional training, i.e., classifier-free guidance [], $10\\\\%$ text-only training, and $80\\\\%$ augmented text training, which integrates visual features of characters with their corresponding token embeddings.\\n\\n### D.4 Second stage training\\n\\nWe use OPT-6.7B(^11^1111[https://huggingface.co/facebook/opt-6.7b](https://huggingface.co/facebook/opt-6.7b)) model as the LLM backbone in all experiments in the main paper. To expedite the second stage alignment training, we first pre-compute non-referential fused embeddings residing in the input space of the first-stage Char-LDM. We map visual features into $m=4$ token embeddings as LLM input, set the max sequence length as 160 and the number of additional [IMG] tokens as $R=8$, batch size as 64 training for 20k steps. Llama2 is only trained for the experiments highlighted in the supplementary materials, demonstrating its capability for multi-modal generation and the ablation of different LLMs. The training configuration is almost the same as OPT, except for batch size 32. All experiments are executed on a single A100 GPU.\\n\\nPlease refer to all the details at the [source code](https://github.com/xiaoqian-shen/StoryGPT-V).\\n\\nFigure: Algorithm 1 Character Replacement Algorithm\\n\\nFigure: Figure 9: DALL-E 3 [] zero-shot inference on FlintstonesSV [] dataset.\\n\\n## Appendix E Limitations\\n\\nOur method demonstrates proficiency in resolving references and ensuring consistent character and background conditions in the context provided by guiding the output of a multi-modal Large Language Model (LLM) with character-augmented semantic embedding. However, several limitations remain. The process involves feeding the previously generated frame into the LLM to produce a visual output that aligns with the Latent Diffusion Model (LDM) input conditional space. This approach guarantees semantic consistency, enabling the generation of characters and environmental objects that resemble their originals. Nonetheless, there are minor discrepancies in detail. This is because the visual output from the Large Language Model (LLM) is aligned with the semantic embedding space rather than the pixel space, which hinders the complete reconstruction of all elements in the input image. However, the current most powerful multi-modal LLM, i.e., DALL-E 3 [], could not solve this exact appearance replication in the multi-round image generation task (Figure [9](#A4.F9)), indicating an area ripe for further exploration and research.\\n\\n## Appendix F Qualitative Results\\n\\nWe provide more generated samples on FlintstonesSV [] and PororoSV [] with referential text as Figure [11](#A6.F11)-[19](#A6.F19) show.\\n\\nFigure: Figure 10: Qualitative comparison on FlintstonesSV [] with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x10.png\\n\\nFigure: Figure 12: Qualitative comparison on FlintstonesSV [] with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x12.png\\n\\nFigure: Figure 14: Qualitative comparison on FlintstonesSV [] with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x14.png\\n\\nFigure: Figure 16: Qualitative comparison on FlintstonesSV [] with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x16.png\\n\\nFigure: Figure 18: Qualitative comparison on PororoSV [] with co-reference descriptions.\\nRefer to caption: /html/2312.02252/assets/x18.png\",\n \"metadata\": {\n \"authors\": [\n \"Xiaoqian Shen\",\n \"KAUST\",\n \"Mohamed Elhoseiny\"\n ],\n \"title\": \"StoryGPT-V: Large Language Models as Consistent Story Visualizers\",\n \"total_chars\": 47429,\n \"total_lines\": 266,\n \"updated_at\": \"2026-01-25T15:02:54.061920\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"NIh9KZr1zS","initial_rating":5,"confidence":4,"soundness":3,"contribution":2,"presentation":3,"summary":"This paper focuses on the task of story visualization and proposes combining the advantages of LLMs and LDMs to generate a consistent story from a given long narrative. To achieve this, the proposed model consists of two stages: the first stage introduces visual features into the text embedding to produce a fused embedding, which is then used in the second stage to generate results. Experimental results demonstrate that the proposed method effectively generates high-quality, consistent outputs.","strengths":"1. The paper proposes combining two powerful models, LLMs and LDMs, for the story visualization task, and experiments show promising results from this combination.\n\n2. Experiments indicate that fusing visual features into text embeddings to refine an LDM can improve the quality of the output results.\n\n3. Autoregressive generation, which continuously utilizes visual features from the previous frame, helps maintain consistency across different frames in a story and enables the model to generate longer narratives.","weaknesses":"1. The strong performance of the proposed method primarily relies on the powerful capabilities of both LLMs and LDMs. Although the authors have introduced a way to combine both models for the story visualization task, the technical novelty may be limited.\n\n2. I have concerns about the diversity of the proposed model. In the first stage, the authors incorporate visual features into text embeddings and use segmentation masks to supervise LDM training. In this setup, the output results of the refined LDMs for a given story may be constrained by the infused visual features. Based on this, I am curious about the diversity of outputs when the same story is provided as input.\n\n3. The paper emphasizes that the proposed method can effectively address consistency issues, such as resolving pronouns in frame descriptions; however, the authors provide only qualitative results for this claim. Including quantitative results could better support the effectiveness of the approach.\n\n4. It may be beneficial to include recent works such as StoryGen and StoryDiffusion, as well as more complex datasets like the StorySalon dataset.\n\nStoryGen, StorySalon dataset: Chang Liu, Haoning Wu, Yujie Zhong, Xiaoyun Zhang, Yanfeng Wang, and Weidi Xie. Intelli- gent grimm-open-ended visual storytelling via latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 6190–6200, 2024.\n\nStory-Diffusion: Yupeng Zhou, Daquan Zhou, Ming-Ming Cheng, Jiashi Feng, and Qibin Hou. Storydiffusion: Con- sistent self-attention for long-range image and video generation. NeurIPS 2024, 2024.","questions":"See above weaknesses."},{"id":"KY6TH6b3hA","initial_rating":6,"confidence":4,"soundness":3,"contribution":2,"presentation":2,"summary":"This paper proposes StoryGPT-V, a novel framework that integrates LLMs with LDMs to enhance the ability to resolve pronouns and consistent generation. It employs a two-stage training process: first, it trains a character-aware LDM to take character embeddings as input; second, it aligns the output of LLM with the input space of LDM. Results show that LLMs significantly enhance the model's ability to understand pronouns, and StoryGPT-V shows good capability to generate consistent stories.","strengths":"- Pronoun resolution is an interesting topic in storytelling. Introducing LLMs to address this problem is a very reasonable approach. The cross-attention map visualized on the anonymous webpage demonstrates that it can effectively assist LDMs in associating pronouns with characters.\n\n- This paper conducts comprehensive ablation experiments to demonstrate the effectiveness of the proposed training strategy in the two-stage training process. Additionally, it shows better competitiveness across various metrics compared to the methods listed on the FlintStonesSV Benchmark.","weaknesses":"My main concern is that the paper does not sufficiently discuss the latest methods.\n\n- Before this paper, there were various storytelling papers(e.g., TaleCrafter[1] in SIGGRAPH Asia 2023, AR-LDM[2] in CVPR 2024) that integrated LLMs into diffusion models, and some works(ConsiStory[3] in TOG 2024) also manipulate attention modules for consistent story generation. A concurrent work, SEED-Story[4], also shares a similar idea that utilizes an LLM for multimodal story generation, and the diffusion model serves as a visual decoder. These works are highly relevant and deserve discussion. \n- Furthermore, some works have also conducted experiments on FlintStonesSV, such as AR-LDM and TaleCrafter. Adding comparisons with these works could potentially enhance the paper's credibility, if possible.\n\n[1] Talecrafter: Interactive story visualization with multiple characters\n[2] Synthesizing coherent story with auto-regressive latent diffusion models\n[3] Training-free consistent text-to-image generation\n[4] SEED-Story: Multimodal Long Story Generation with Large Language Model","questions":"Please check out the Weaknesses part."},{"id":"HccMq4HlwV","initial_rating":3,"confidence":5,"soundness":1,"contribution":2,"presentation":2,"summary":"This work targets to tackle the ambiguous subject reference challenge in text-to-image visual storytelling. The core idea is to leverage the comprehension and reasoning ability of Large Language Model. First, the authors train a character-aware Latent Diffusion Model. Then, the character-aware semantic embeddings from LDM and LLM output are aligned. Experiments are conducted on two story visualization benchmarks and show more consistent character generation.","strengths":"The work addresses an important problem in visual storytelling for enhanced multiple character consistency, leveraging LLM's comprehension and reasoning ability.","weaknesses":"1. The paper writing needs improvements. For example, (1) the sentence \"Since it requires resolving pronouns (he, she, they) in\nthe frame descriptions, i.e., anaphora resolution, and ensuring consistent characters and background synthesis across frames.\" is incomplete in the abstract L14. (2) The core contribution and benefit over previous MLLM alignment approaches is unclear. Suggest to elaborate the advantage of the proposed ''implicitly deduced reference'' explicitly (L109, L139).\n2. Incomprehensive related work. For instance, StoryGen (CVPR'24), StoryDiffusion (NeurIPS'24), and SeedStory ('24) are recent work towards subject consistency in story visualization. In particular, SeedStory ('24) also leverages LLM's reasoning ability and aligns text-image.\n3. Incomplete experiments. It misses important comparisons to the published StoryGen (CVPR'24) and StoryDiffusion (NeurIPS'24). Suggest to include in Table 1 and 2.","questions":"1. What is the benefit of the proposed multimodal alignment over previous methods? It'd make the work more solid by conducting an ablation study comparing the proposed alignment method to counterpart alignment approaches (Table 3), measuring performance on key metrics like character consistency or reference resolution accuracy."},{"id":"7cgwhrBTnV","initial_rating":3,"confidence":3,"soundness":2,"contribution":2,"presentation":2,"summary":"This paper tackles the story visualization task and propose a two-stage approach. First, the authors propose Char-LDM, a finetuned LDM by guiding the cross-attention map of LDM with character segmentation mask. Second, they utilize Multi-modal LLM for retaining contexts and reference resolution by mapping from the output of LLM to align with the input space of the first stage LDM. In the experimental results, it is shown that the proposed approach outperforms baselines including Story-LDM with lower computational resources such as GPU memory for longer image frames and inference speed.","strengths":"- The proposed idea of using segmentation mask for guiding the cross-attention map of LDM makes sense, and using LLM for retaining contexts and reference resolution is interesting.\n- In experimental results, it is shown that the proposed model outperforms the baselines in both quantitative and qualitative evaluations.","weaknesses":"- Novelty seems somewhat incremental as using segmentation mask of characters for generating them is not new (e.g., [1]), and also for LLM to understand and generate images, it uses the similar idea from prior work such as [2].\n- In the experiments, there are points to raise concerns regarding the technical soundness of them. First, it is said: \"Story-LDM (Rahman et al., 2023) does not provide pre-trained checkpoint or cleaned training code\" (line #368), so it was not clear how it was implemented even though it is written: \"we initiate training from pre-trained LDM\". Furthermore, in Table 1 (bottom), the reported Char-acc and Char-F1 (77.23 & 88.26) in the paper are different from what are reported in Story-LDM paper (69.19 & 86.59). Second, in human evaluation, only three judges were used and it seems too few. \n- Writing needs to be clearer. e.g., it is not clear whether only first stage (Char-LDM) was used or both stages were used for the result in Table 1 (upper half) as it is written: \"Our first-stage Char-LDM exhibits superior performance in generating accurate characters\" (line #414). \n- The claim of using less GPU memory is questionable. My understanding is 2nd stage needs to load LLM to memory, so it seems more expensive compared to the baseline, i.e., Story-LDM, especially for the typical scenario for story visualization of generating five image sequence. This seems also confirmed in Figure 6(b) when the number of frames to generate is less than 10. \n- It lacks an important ablation study: using only first stage without second stage to see the effectiveness of LLM.\n\nReferences\n\n[1] Song et al., Character-Preserving Coherent Story Visualization, ECCV 2020\n\n[2] Koh et al., Generating Images with Multimodal Language Models, NeurIPS 2023","questions":"- Notation: what is m in line #282? Also is k the same as e in line #282-283?\n- In Figure 6(b), how did you use longer stories? Did you extend existing stories with LLM?\n- Please address weaknesses mentioned above.\n\nTypo:\nLine #014: visualization. Since -> visualization since"}],"string":"[\n {\n \"id\": \"NIh9KZr1zS\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"This paper focuses on the task of story visualization and proposes combining the advantages of LLMs and LDMs to generate a consistent story from a given long narrative. To achieve this, the proposed model consists of two stages: the first stage introduces visual features into the text embedding to produce a fused embedding, which is then used in the second stage to generate results. Experimental results demonstrate that the proposed method effectively generates high-quality, consistent outputs.\",\n \"strengths\": \"1. The paper proposes combining two powerful models, LLMs and LDMs, for the story visualization task, and experiments show promising results from this combination.\\n\\n2. Experiments indicate that fusing visual features into text embeddings to refine an LDM can improve the quality of the output results.\\n\\n3. Autoregressive generation, which continuously utilizes visual features from the previous frame, helps maintain consistency across different frames in a story and enables the model to generate longer narratives.\",\n \"weaknesses\": \"1. The strong performance of the proposed method primarily relies on the powerful capabilities of both LLMs and LDMs. Although the authors have introduced a way to combine both models for the story visualization task, the technical novelty may be limited.\\n\\n2. I have concerns about the diversity of the proposed model. In the first stage, the authors incorporate visual features into text embeddings and use segmentation masks to supervise LDM training. In this setup, the output results of the refined LDMs for a given story may be constrained by the infused visual features. Based on this, I am curious about the diversity of outputs when the same story is provided as input.\\n\\n3. The paper emphasizes that the proposed method can effectively address consistency issues, such as resolving pronouns in frame descriptions; however, the authors provide only qualitative results for this claim. Including quantitative results could better support the effectiveness of the approach.\\n\\n4. It may be beneficial to include recent works such as StoryGen and StoryDiffusion, as well as more complex datasets like the StorySalon dataset.\\n\\nStoryGen, StorySalon dataset: Chang Liu, Haoning Wu, Yujie Zhong, Xiaoyun Zhang, Yanfeng Wang, and Weidi Xie. Intelli- gent grimm-open-ended visual storytelling via latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 6190–6200, 2024.\\n\\nStory-Diffusion: Yupeng Zhou, Daquan Zhou, Ming-Ming Cheng, Jiashi Feng, and Qibin Hou. Storydiffusion: Con- sistent self-attention for long-range image and video generation. NeurIPS 2024, 2024.\",\n \"questions\": \"See above weaknesses.\"\n },\n {\n \"id\": \"KY6TH6b3hA\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper proposes StoryGPT-V, a novel framework that integrates LLMs with LDMs to enhance the ability to resolve pronouns and consistent generation. It employs a two-stage training process: first, it trains a character-aware LDM to take character embeddings as input; second, it aligns the output of LLM with the input space of LDM. Results show that LLMs significantly enhance the model's ability to understand pronouns, and StoryGPT-V shows good capability to generate consistent stories.\",\n \"strengths\": \"- Pronoun resolution is an interesting topic in storytelling. Introducing LLMs to address this problem is a very reasonable approach. The cross-attention map visualized on the anonymous webpage demonstrates that it can effectively assist LDMs in associating pronouns with characters.\\n\\n- This paper conducts comprehensive ablation experiments to demonstrate the effectiveness of the proposed training strategy in the two-stage training process. Additionally, it shows better competitiveness across various metrics compared to the methods listed on the FlintStonesSV Benchmark.\",\n \"weaknesses\": \"My main concern is that the paper does not sufficiently discuss the latest methods.\\n\\n- Before this paper, there were various storytelling papers(e.g., TaleCrafter[1] in SIGGRAPH Asia 2023, AR-LDM[2] in CVPR 2024) that integrated LLMs into diffusion models, and some works(ConsiStory[3] in TOG 2024) also manipulate attention modules for consistent story generation. A concurrent work, SEED-Story[4], also shares a similar idea that utilizes an LLM for multimodal story generation, and the diffusion model serves as a visual decoder. These works are highly relevant and deserve discussion. \\n- Furthermore, some works have also conducted experiments on FlintStonesSV, such as AR-LDM and TaleCrafter. Adding comparisons with these works could potentially enhance the paper's credibility, if possible.\\n\\n[1] Talecrafter: Interactive story visualization with multiple characters\\n[2] Synthesizing coherent story with auto-regressive latent diffusion models\\n[3] Training-free consistent text-to-image generation\\n[4] SEED-Story: Multimodal Long Story Generation with Large Language Model\",\n \"questions\": \"Please check out the Weaknesses part.\"\n },\n {\n \"id\": \"HccMq4HlwV\",\n \"initial_rating\": 3,\n \"confidence\": 5,\n \"soundness\": 1,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This work targets to tackle the ambiguous subject reference challenge in text-to-image visual storytelling. The core idea is to leverage the comprehension and reasoning ability of Large Language Model. First, the authors train a character-aware Latent Diffusion Model. Then, the character-aware semantic embeddings from LDM and LLM output are aligned. Experiments are conducted on two story visualization benchmarks and show more consistent character generation.\",\n \"strengths\": \"The work addresses an important problem in visual storytelling for enhanced multiple character consistency, leveraging LLM's comprehension and reasoning ability.\",\n \"weaknesses\": \"1. The paper writing needs improvements. For example, (1) the sentence \\\"Since it requires resolving pronouns (he, she, they) in\\nthe frame descriptions, i.e., anaphora resolution, and ensuring consistent characters and background synthesis across frames.\\\" is incomplete in the abstract L14. (2) The core contribution and benefit over previous MLLM alignment approaches is unclear. Suggest to elaborate the advantage of the proposed ''implicitly deduced reference'' explicitly (L109, L139).\\n2. Incomprehensive related work. For instance, StoryGen (CVPR'24), StoryDiffusion (NeurIPS'24), and SeedStory ('24) are recent work towards subject consistency in story visualization. In particular, SeedStory ('24) also leverages LLM's reasoning ability and aligns text-image.\\n3. Incomplete experiments. It misses important comparisons to the published StoryGen (CVPR'24) and StoryDiffusion (NeurIPS'24). Suggest to include in Table 1 and 2.\",\n \"questions\": \"1. What is the benefit of the proposed multimodal alignment over previous methods? It'd make the work more solid by conducting an ablation study comparing the proposed alignment method to counterpart alignment approaches (Table 3), measuring performance on key metrics like character consistency or reference resolution accuracy.\"\n },\n {\n \"id\": \"7cgwhrBTnV\",\n \"initial_rating\": 3,\n \"confidence\": 3,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper tackles the story visualization task and propose a two-stage approach. First, the authors propose Char-LDM, a finetuned LDM by guiding the cross-attention map of LDM with character segmentation mask. Second, they utilize Multi-modal LLM for retaining contexts and reference resolution by mapping from the output of LLM to align with the input space of the first stage LDM. In the experimental results, it is shown that the proposed approach outperforms baselines including Story-LDM with lower computational resources such as GPU memory for longer image frames and inference speed.\",\n \"strengths\": \"- The proposed idea of using segmentation mask for guiding the cross-attention map of LDM makes sense, and using LLM for retaining contexts and reference resolution is interesting.\\n- In experimental results, it is shown that the proposed model outperforms the baselines in both quantitative and qualitative evaluations.\",\n \"weaknesses\": \"- Novelty seems somewhat incremental as using segmentation mask of characters for generating them is not new (e.g., [1]), and also for LLM to understand and generate images, it uses the similar idea from prior work such as [2].\\n- In the experiments, there are points to raise concerns regarding the technical soundness of them. First, it is said: \\\"Story-LDM (Rahman et al., 2023) does not provide pre-trained checkpoint or cleaned training code\\\" (line #368), so it was not clear how it was implemented even though it is written: \\\"we initiate training from pre-trained LDM\\\". Furthermore, in Table 1 (bottom), the reported Char-acc and Char-F1 (77.23 & 88.26) in the paper are different from what are reported in Story-LDM paper (69.19 & 86.59). Second, in human evaluation, only three judges were used and it seems too few. \\n- Writing needs to be clearer. e.g., it is not clear whether only first stage (Char-LDM) was used or both stages were used for the result in Table 1 (upper half) as it is written: \\\"Our first-stage Char-LDM exhibits superior performance in generating accurate characters\\\" (line #414). \\n- The claim of using less GPU memory is questionable. My understanding is 2nd stage needs to load LLM to memory, so it seems more expensive compared to the baseline, i.e., Story-LDM, especially for the typical scenario for story visualization of generating five image sequence. This seems also confirmed in Figure 6(b) when the number of frames to generate is less than 10. \\n- It lacks an important ablation study: using only first stage without second stage to see the effectiveness of LLM.\\n\\nReferences\\n\\n[1] Song et al., Character-Preserving Coherent Story Visualization, ECCV 2020\\n\\n[2] Koh et al., Generating Images with Multimodal Language Models, NeurIPS 2023\",\n \"questions\": \"- Notation: what is m in line #282? Also is k the same as e in line #282-283?\\n- In Figure 6(b), how did you use longer stories? Did you extend existing stories with LLM?\\n- Please address weaknesses mentioned above.\\n\\nTypo:\\nLine #014: visualization. Since -> visualization since\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;3;5;6\",\n \"rating_avg\": 4.25,\n \"confidence\": \"3;5;4;4\",\n \"confidence_avg\": 4,\n \"soundness\": \"2;1;3;3\",\n \"soundness_avg\": 2.25,\n \"contribution\": \"2;2;2;2\",\n \"contribution_avg\": 2,\n \"presentation\": \"2;2;3;2\",\n \"presentation_avg\": 2.25\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"ICLR 2025 Conference Withdrawn Submission\",\n \"venueid\": \"ICLR.cc/2025/Conference/Withdrawn_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.710991\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"\",\n \"metareview\": \"\",\n \"additional_comments\": \"\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"\"\n}"}}},{"rowIdx":3392,"cells":{"paper_id":{"kind":"string","value":"qTWDpbF47t"},"arxiv_id":{"kind":"string","value":"2407.06182v1"},"title":{"kind":"string","value":"Compositional Video Generation as Flow Equalization"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract Large-scale Text-to-Video (T2V) diffusion models\\nhave recently demonstrated unprecedented\\ncapability to transform natural language descriptions into stunning and photorealistic videos.\\nDespite the promising results, a significant challenge remains:\\nthese models struggle to fully grasp complex compositional\\ninteractions between multiple concepts and actions. This issue arises when some words dominantly influence the final video, overshadowing other concepts.\\nTo tackle this problem,\\nwe introduce Vico , a generic framework for compositional video generation\\nthat explicitly ensures all concepts are represented properly.\\nAt its core, Vico analyzes how input tokens influence the generated video,\\nand adjusts the model to prevent any single concept from dominating.\\nSpecifically, Vico extracts attention weights from all layers to build a spatial-temporal attention graph, and then estimates the influence\\nas the max-flow from the source text token to the video target token.\\nAlthough the direct computation of attention flow in diffusion models is typically infeasible,\\nwe devise an efficient approximation based on\\nsubgraph flows and employ\\na fast and vectorized implementation,\\nwhich in turn makes the flow computation\\nmanageable and differentiable.\\nBy updating the noisy latent to balance these flows, Vico captures complex interactions and consequently produces videos that closely adhere to textual descriptions. We apply our method to multiple diffusion-based video models for compositional T2V and video editing. Empirical results demonstrate that our framework significantly enhances the compositional richness and accuracy of the generated videos. Visit our website at https://adamdad.github.io/vico/ .\\n\\n## 1 Introduction\\n\\nHumans recognize the world compositionally. That is to say, we perceive and understand the world by identifying parts of objects and assembling them into a whole. This ability to recognize and recombine elements—making “infinite use of finite mean”—is crucial for understanding and modeling our environment. Similarly, in the realm of generative AI, particularly in video generation, it is crucial to replicate this compositional approach.\\n\\nDespite advancements in generative models, current diffusion models fail to capture the true compositional nature of inputs. Typically, some words disproportionately influence the generative process, leading to visual content that does not reflect the intended composition of elements. While the compositional text-to-image sythesis [, , , , ] has been more studied, the challenge of compositional video generation has received less attention. This oversight is largely due to the high-dimensional nature of video and the complex interplay between concepts and motion.\\n\\nAs an illustration, we highlight some failure cases in Figure 1 (Left), where *certain words dominate* while others are underrepresented. Common issues include *missing subject* and *spatial confusion*, where some concepts do not appear in the video. Even with all concepts present, *semantic leakage* can occur, causing attributes amplified incorrectly, for example, *a bird looks like a cat*. A challenge specific to T2V is *Motion Mixing*, where the action intended for one object mistakenly interacts with another, such as generating a flying wale instead of flying balloon.\\n\\nTo address these challenges, we present Vico, a novel framework for compositional video generation\\nthat ensures all concepts are represented equally.\\nVico operates on the principle that,\\neach textual token should have an equal opportunity\\nto influence the final video output. At our core,\\nVico first assesses and then rebalances the influence of these tokens.\\nThis is achieved through test-time optimization, where we assess and adjust the impact of each token at every reverse time step of our video diffusion model. As shown in 1, Vico resolves the above questions and provides better results.\\n\\nOne significant challenge\\nis accurately attributing text influence.\\nWhile cross-attention [, , , ] provides faithful attribution\\nin text-to-image diffusion models, it is not well-suited for video models. It is because such cross-attention\\nis only applied on spatial modules along,\\ntreating each frame independently,\\nwithout directly influencing temporal dynamics.\\n\\nTo surmount this, we develop\\na new attribution method for T2V model, termed *Spatial-Temporal Attention Flow* (ST-flow). ST-flow considers all attention layers of the diffusion model, and views it as a spatiotemporal flow graph. Using the maximum flow algorithm, it computes the flow values, from input tokens (sources) to video tokens (target). These values serve as our estimated contributions.\\n\\nUnfortunately, this naive attention max-flow computation is, in fact, both computationally expensive and non-differentiable.\\nWe thus derive an efficient and differentiable approximation for the ST-Flow. Rather than computing flow values on the full graph,\\nwe instead compute the flow on all subgraphs.\\nThe ST-Flow is then\\nestimated as the maximum subgraph flow.\\nAdditionally, we have develop a special matrix operation to compute this subgraph flow in a fully vectorized manner, making it approximately 100$\\\\times$ faster than the exact ST-flow.\\n\\nOnce we obtain these attribution scores, we proceed to optimize the model to balance such contributions. We do this as a min-max optimization, where we update the latent code, in the direct that, the least represented token should increase its influence.\\n\\nWe implement Vico on multiple video applications, including text-to-video generation and video editing. These applications highlight the framework’s flexibility and effectiveness in managing complex prompt compositions, demonstrating significant improvements\\nover traditional methods in both the accuracy of generated video. Our contributions can be summarized below:\\n\\n- •\\nWe introduce Vico, a framework for compositional video generation.\\nIt optimizes the model to ensure each input token fairly influences the final video output.\\n- •\\nWe develop ST-flow, a new attribution method that uses attention max-flow to evaluate the influence of each input token in video diffusion models.\\n- •\\nWe derive a differentiable method to approximate ST-flow by calculating flows within subgraphs. It greatly speed up computations with a fully vectorized implementation.\\n- •\\nExtensive evaluation of Vico in diverse settings has proven its robust capability, with substantial improvements in video quality and semantic accuracy.\\n\\n## 2 Preliminaries\\n\\nDenoising Diffusion Probabilistic Models. Diffusion model reverses a progressive noise process based on latent variables. Given data $\\\\mathbf{x}_{0}\\\\sim q(\\\\mathbf{x}_{0})$ sampled from the real distribution, we consider perturbing data with Gaussian noise of zero mean and $\\\\beta_{t}$ variance for $T$ steps/\\nAt the end of day, $\\\\mathbf{x}_{T}\\\\to\\\\mathcal{N}(0,\\\\mathbf{I})$ converge to isometric Gaussian noise. The choice of Gaussian provides a close-form solution to generate arbitrary time-step $\\\\mathbf{x}_{t}$ through\\n\\n$$ $\\\\displaystyle\\\\mathbf{x}_{t}=\\\\sqrt{\\\\bar{\\\\alpha}_{t}}\\\\mathbf{x}_{0}+\\\\sqrt{1-\\\\bar {\\\\alpha}_{t}}\\\\bm{\\\\epsilon},\\\\quad\\\\text{where}\\\\quad\\\\bm{\\\\epsilon}\\\\sim\\\\mathcal{N}( 0,\\\\mathbf{I})$ (1) $$\\n\\nwhere $\\\\alpha_{t}=1-\\\\beta_{t}$ and $\\\\bar{\\\\alpha}_{t}=\\\\prod_{s=1}^{t}\\\\alpha_{s}$. A variational Markov chain in the reverse process is parameterized as a time-conditioned denoising neural network $\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta}}(\\\\mathbf{x},t)$ with $p_{\\\\bm{\\\\theta}}(\\\\mathbf{x}_{t-1}|\\\\mathbf{x}_{t})=\\\\mathcal{N}(\\\\mathbf{x}_{t-1};\\n\\\\frac{1}{\\\\sqrt{1-\\\\beta_{t}}}(\\\\mathbf{x}_{t}+\\\\beta_{t}\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta\\n}}(\\\\mathbf{x},t)),\\\\beta_{t}\\\\mathbf{I})$. The denoiser is trained to minimize a re-weighted evidence lower bound (ELBO) that fits the noise\\n\\n$$ $\\\\displaystyle\\\\mathcal{L}_{\\\\text{DDPM}}$ $\\\\displaystyle=\\\\mathbb{E}_{t,\\\\mathbf{x}_{0},\\\\bm{\\\\epsilon}}\\\\Big{[}||\\\\bm{\\\\epsilon }+\\\\sqrt{1-\\\\bar{\\\\alpha}_{t}}\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta}}(\\\\mathbf{x},t)||_{2}^{2} \\\\Big{]}$ (2) $$\\n\\nTraining with denoising loss, $\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta}}$ equivalently learns to recover the derivative that maximize the data log-likelihood [, , ].\\nWith a trained $\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta}^{*}}(\\\\mathbf{x},t)\\\\approx\\\\nabla_{\\\\mathbf{x}_{t}}\\n\\\\log p(\\\\mathbf{x}_{t})$, we generate the data by reversing the Markov chain\\n\\n$$ $\\\\displaystyle\\\\mathbf{x}_{t-1}\\\\leftarrow\\\\frac{1}{\\\\sqrt{1-\\\\beta_{t}}}(\\\\mathbf{x} _{t}+\\\\beta_{t}\\\\bm{\\\\epsilon}_{\\\\bm{\\\\theta}^{*}}(\\\\mathbf{x},t))+\\\\sqrt{\\\\beta_{t}} \\\\bm{\\\\epsilon}_{t};$ (3) $$\\n\\nThe reverse process could be understood as going along $\\\\nabla_{\\\\mathbf{x}_{t}}\\\\log p(\\\\mathbf{x}_{t})$ to maximize the likelihood.\\n\\nText-to-Video (T2V) Diffusion Models. Given a text prompt $y$, T2V diffusion models progressively generate a video from Gaussian noise. This generation typically occurs within the latent space of an autoencoder [] to reduce the complexity. The architecture design of T2V models often follows either a 3D-UNet [, , , , ] or diffusion transformer [, , ]. For computational efficiency, these architectures commonly utilize separate self-attention [] for spatial and temporal tokens. Moreover, cross-attentions is applied on each frame separately, thereby injecting conditions into the model. More related work is in Appendix C.\\n\\nMaximum-Flow Problem. [, , ] Consider a directed graph $G(V,E)$ with a source node $s$ and a target node $t$. A flow is function on edge $f:E\\\\to\\\\mathbb{R}$ that satisfies both *conservation constraint* and *capacity constraint* at every vertex $v\\\\in V\\\\backslash\\\\{s,t\\\\}$. This means the total inflow into any node $v$ must equals its total outflow, and the flow on any edge cannot exceed its capacity. The flow value $|f|=\\\\sum_{e_{s,v}\\\\in E}f(s,u)$ is defined as the total flow out of the source $s$, which is equal to the total inflow into the target $t$, $|f|=\\\\sum_{e_{u,t}\\\\in E}f(u,t)$. The maximum flow problem is to find a flow $f^{*}$ that maximizes this value.\\n\\n## 3 Vico: Compositional Video Generation as Flow Equalization\\n\\nIn this paper, we solve the problem of compositional video generation by equalizing influence among tokens. We calculate this influence using max-flow within the attention graph of the T2V model and ensure efficient computation. We define our problem and optimization scheme in Sec 3.1. The definition of ST-Flow and its efficient computation are discussed in Sections 3.2 and 3.3.\\n\\nFigure: Figure 2: Overall pipeline of our Vico. Before each denoising step, Vico extracts attention maps from each layer to build a spatiotemporal graph. We calculate the attribution scores as max-flow in the graph and adjust the noisy latent code to balance this flows.\\nRefer to caption: x2.png\\n\\n### 3.1 Overall Pipeline and Optimization\\n\\nOur objective is to generate a video from an input prompt $P$, with $K$ text tokens of interest $\\\\mathcal{V}=\\\\{v_{1},\\\\dots,v_{K}\\\\}$. We aim to ensure that each token fairly contributes to the final video. This process is detailed in Figure 2.\\n\\nObjectives. To achieve this, we define an attribution function $A_{i}=A(v_{i})\\\\in\\\\mathbb{R}$ for each token $v_{i}$, quantifying its impact on the video. We optimize the attribution scores to ensure fairness:\\n\\n$$ $\\\\displaystyle\\\\max_{\\\\mathbf{x}_{t}}\\\\mathcal{L}_{\\\\text{fair}}(A_{1},\\\\dots,A_{K}) =\\\\max_{\\\\mathbf{x}_{t}}\\\\min_{v_{i}}\\\\{A_{1},\\\\dots,A_{K}\\\\};$ (4) $$\\n\\nHere, $\\\\mathcal{L}_{\\\\text{fair}}=\\\\min_{v_{i}}\\\\{A_{1},\\\\dots,A_{K}\\\\}$ serves as the fairness function, focusing on the least represented token. By updating the noisy latent $\\\\mathbf{x}_{t}$ to maximize $\\\\mathcal{L}_{\\\\text{fair}}$, we ensure equal contributions across all tokens. Specifically, we estimate $A_{i}$ as flow in attention graph, which will be discussed later.\\n\\nOptimization. To implement Eq 4, we perform test-time optimization. Before each denoising step, we first feed $\\\\mathbf{x}_{t}$ into the model, extract the $A_{i}$, and update $\\\\mathbf{x}_{t}$ through gradient ascent: $\\\\hat{\\\\mathbf{x}}_{t}\\\\leftarrow\\\\mathbf{x}_{t}+\\\\eta\\\\nabla_{\\\\mathbf{x}_{t}}\\n\\\\mathcal{L}_{\\\\text{fair}}(A_{1},\\\\dots,A_{K})$. $\\\\eta$ is the step size. Then, $\\\\hat{\\\\mathbf{x}}_{t}$ is going through a denoising step to get $\\\\mathbf{x}_{t-1}$ according to Eq 3. We repeat these steps until the video is generated.\\n\\n### 3.2 Attention Flow Across Space and Time\\n\\nWith above formulation, our focus is to develop an efficient and precise attribution $A_{i}$. Recognizing issues with cross-attention, we instead calculate $A_{i}$ as the flow through the entire attention graph.\\n\\nFlawed Cross-Attention in Text-to-Video Models. Cross-attention score has been instrumental in attributing [] and controlling layout and concept composition in text-to-image models [, , ]. However, applying it to T2V diffusion model introduces new problem.\\n\\nThis problem arises because T2V models typically employ cross-attention on spatial tokens only [, , ]. It treats the video as a sequence of independent images, and temporal self-attention mixes tokens across different frames. Consequently, this separation hinders cross-attention’s ability to capture video dynamics, making it challenging to manage actions across frames.\\n\\nFor example, applying the cross-attention-based DAAM attribution [] on VideoCrafterv2 reveals significant issues in visualization. As shown in Figure 3 (Left), cross-attention leads to a flickering pattern in the attention maps, failing to consistently highlight the target object across frames.\\n\\nRecognizing these limitations, we propose a new measurement termed *Spatial-Temporal Flow (ST-Flow)*, which estimates the influence throughout the entire spatiotemporal attention graph in the video diffusion model. As seen in Figure 3 (Right), ST-Flow gets heatmap with improved consistency.\\n\\nFigure: Figure 3: Attribution heatmap comparison between DAAM and ST-Flow.\\nRefer to caption: x3.png\\n\\nAttention as a Graph Over Space and Time. In our approach, we conceptualize the stacked attention layers as a directed graph $G=(V,E)$, where nodes represent tokens and edges weighted by the influence between tokens. A 4-layer example is illustrated in Figure 2 (Right).\\n\\nIts adjacency matrix is built using attention weights and skip connections []. Suppose $w^{att}_{i,j}$ is the $i$-th row $j$-th column element of attention matrix averaged across heads.\\nFor self-attention, the edge weight $e_{i,j}$ between any two tokens, $i$ and $j$, is $e_{i,j}=w^{att}_{i,j}+1$ if $i=j$, indicating a skip-connection, and $e_{i,j}=w^{att}_{i,j}$ if $i\\\\neq j$. In the case of cross-attention, edge $e_{i,j}=w^{att}_{i,j}$ connects text to video, and $e_{i,i}=1$ for connections within video tokens due to skip connections. Given that connections only exist from one layer to the next, the resulting matrix exhibits block-wise sparsity pattern. This is expressed as $\\\\bm{W}=\\\\begin{bmatrix}\\\\bm{0}&E_{t,1}&\\\\bm{0}&\\\\dots&E_{t,l}\\\\\\\\\\n\\\\bm{0}&\\\\bm{0}&E_{2}&\\\\dots&\\\\bm{0}\\\\\\\\\\n\\\\bm{0}&\\\\bm{0}&\\\\bm{0}&\\\\dots&\\\\vdots\\\\\\\\\\n\\\\bm{0}&\\\\bm{0}&\\\\bm{0}&\\\\dots&E_{l}\\\\\\\\\\n\\\\end{bmatrix}$. Here, $E_{i}$ denotes the edge weights within video, and $E_{t,i}$ indicates the influence from text to video at each cross-attention layer.\\n\\nAttribution as Flow on Graph. Given graph $G$, we compute the attribution $A_{i}$ by analyzing all paths from a text token $v_{i}$ to video tokens at the output layer. As such, we formulate it as a *max-flow problem* with capacity matrix $\\\\bm{W}$. To facilitate this, we add an auxiliary target node $\\\\bm{v}_{t}$ to $G$, connecting it to all output video tokens with inflow edges $e_{\\\\bm{v}_{t}^{+}}=1$(^1^11The maximum inflow is 1 for each node due to softmax normalization in the attention.). We treat each text token $v_{i}$ as the source, and $\\\\bm{v}_{t}$ as the sink. The max-flow from source to sink quantifies the influence of $v_{i}$, termed *ST-Flow*.\\n\\nDefinition 1 (ST-Flow). In attention graph $G$ with capacity matrix $\\\\bm{W}$, a input token $v_{i}$ as source and sink node $\\\\bm{v}_{t}$, the attribution value of $A_{i}=|f|^{*}$ is computed as the maximum flow from $v_{i}$ to $\\\\bm{v}_{t}$.\\n\\nOur ST-Flow can be considered as an extension of Attention Flow [], incorporating all attention layers in diffusion model. It is proved to be a kind of Shapley Value [], which is an ideal contribution allocation in game theory [, , ] and interpretable AI model [, ].\\n\\nExact ST-Flow Computation is infeasible. While theoretically possible, calculating the ST-Flow in T2V diffusion models faces practical issues that render it infeasible:\\n\\n- •\\nNon-Differentiable. The max-flow algorithm, by its nature, is non-differentiable. This is a problem when we do gradient-based optimization in Eq 4.\\n- •\\nEfficiency Issue. Solving max-flow for each input token is slow. Even with the Dinic’s algorithm [] (^2^22Given that the attentions has more edge than tokens, Dinic is best choice in theory. However, our implementation shows that max-flow on each token takes $\\\\sim$8s.), the time complexity is $O(K|V|^{2}|E|)$ for large attention graphs extracted from video diffusion model.\\n\\nDespite these obstacles, in Sec 3.3, we derive a min-max approximation to circumvent these issues.\\n\\n### 3.3 Differentiable ST-Flow with Min-Max Path Flow\\n\\nAs discussed above, exact computation of ST-Flow is challenging.\\nInstead of directly estimating the ST-Flow, we approach this by focusing on approximating its lower bound, which is computationally feasible. This is made possible, since any sub-graph has max-flow smaller than that of full graph.\\n\\nTheorem 1 (Sub-Graph Flow)(^3^33Proof in Appendix A). For any sub-graph $g$ of a graph $G$, $g\\\\subseteq G$, the maximum flow $f^{*}_{g}$ in $g$ is less than or equal to the maximum flow $f^{*}_{G}$ in $G$, $|f^{*}_{g}|\\\\leq|f^{*}_{G}|$.\\n\\nBased on this theorem, we need not compute the ST-Flow directly. Instead, we sample multiple subgraphs $g$ from $G$, calculate the maximum flow for each, and take the highest value among these:\\n\\n$$ $\\\\displaystyle|f_{G}|\\\\geq A_{i}=\\\\max_{\\\\forall g\\\\subseteq G}|f_{g}|;$ (5) $$\\n\\nThis approach allows for a more efficient calculation by focusing on a manageable number of subgraphs, solving the max-flow for each, and identifying the maximum flow.\\n\\nIn this work, we focus on the simplest type of subgraph in graph $G$: a path from a $v_{i}$ to target $\\\\bm{v}_{t}$. We efficiently approximate the ST-Flow by computing the *max path flow* for each path. We propose two min-max strategies to achieve this:\\n\\n- •\\nHard Flow Strategy. For each text token $v$, we sample all paths $v_{i}$ to $v_{t}$. The max-flow on each path is calculated as the minimum edge capacity along the path, $|f|=\\\\min_{j}e_{j}$. And the best approximated $A_{i}=\\\\max|f|$ is the maximum of these minimums across all paths.\\n- •\\nSoft Flow Strategy. Instead of get the hard min-max flow, we use *soft-min* and *soft-max* operations using the log-sum-exp trick. This approach provides a smoother approximation of flow values, which can be especially useful in our gradients-based optimization. The soft-min/max is computed as below, with $\\\\tau$ as a temperature\\n$\\\\displaystyle\\\\text{softmax}(e_{1},e_{2},\\\\dots;\\\\tau)=\\\\tau\\\\log\\\\Big{(}\\\\sum_{j}\\n\\\\exp{(\\\\frac{e_{j}}{\\\\tau})}\\\\Big{)};$\\n(6)\\n$\\\\displaystyle\\\\text{softmin}(e_{1},e_{2},\\\\dots;\\\\tau)=-\\\\text{softmax}(-e_{1},-e_\\n{2},\\\\dots;\\\\tau),$\\n(7)\\n\\nVectorized Path Flow Computation. While depth-first and breadth-first searches can identify all paths for above min-max optimization, these methods are slow and cannot be parallelized.\\nInstead, we define a special operation called *min-max multiplication* on the capacity matrix to calculate the maximum flow for each path in a vectorized manner.\\n\\nDefinition 2 (Min-max Multiplication). Given two matrices $A\\\\in\\\\mathbb{R}^{m\\\\times k}$ and $B\\\\in\\\\mathbb{R}^{k\\\\times n}$, min-max multiplication $C=A\\\\odot B\\\\in\\\\mathbb{R}^{m\\\\times n}$ is defined where each element $C_{i,j}=\\\\max_{r}(\\\\min(A_{i,r},B_{r,j}))$.\\n\\nThis operation computes the minimum value across all $r$ for the $i$-th row of $A$ and the $j$-th column of $B$, and $\\\\max_{r}$ selects the maximum of these minimum values for each $C_{i,j}$.\\nWe call it a *multiplication* because it resembles matrix multiplication but replaces element-wise multiplication with a minimum operation and summation with maximization.\\n\\nA very good property is that, the min-max multiplication of capacity matrix $\\\\bm{W}^{k}=\\\\bm{W}^{k-1}\\\\odot\\\\bm{W}$ can be interpreted as the max path flow for all $k$-hop paths.\\n\\nProposition 1 (Max Path Flow using Min-max Multiplication)(^4^44Proof in Appendix B). For min-max power of capacity $\\\\bm{W}^{k}=\\\\bm{W}^{k-1}\\\\odot\\\\bm{W}$, element $\\\\bm{W}^{k}_{i,j}$ equals the max path flow for all $k$-hop path from $v_{i}$ to $v_{j}$.\\n\\nFor attention graph that current layer’s node is only connect to the next layer, all path from text token to output video token has exactly the length of $l$. In this way, what we do is just to extract the attention graph $G$, do $l$ times Min-max Multiplication on its flow matrix, and we consider the value as a approximation of ST-Flow. A tine complexity analysis is prepared in Appendix F.\\n\\nIn this way, we get all pieces to build Vico. We first compute attribution using the approximated ST-Flow, then using Eq 4 to update the latent to equalize such flow.\\n\\n## 4 Experiments\\n\\nIn our experiments section, we evaluate Vico through a series of tests. We start by assessing its performance on generating videos from compositional text prompts. Next, we demonstrate ST-Flow accurately attributes token influence through video segmentation and human study. We also conduct an ablation study to validate our key designs. More application results are provide in Appendix D.\\n\\n### 4.1 Experiment Setup\\n\\nBaselines. We build our method on several open-sourced video diffusion model, including VideoCrafterv2 [], AnimateDiff [] and Zeroscopev2 (^5^55[https://huggingface.co/cerspense/zeroscope_v2_576w](https://huggingface.co/cerspense/zeroscope_v2_576w)). Since no current video diffusion models specifically focus on generation with compositional conditions, we re-implement several methods designed for text-to-image diffusion models and compare with them. These methods include:\\n\\n- •\\nOriginal Model. We directly ask the original base model to produce video based on prompts.\\n- •\\nToken Re-weight. We use the compel (^6^66[https://github.com/damian0815/compel](https://github.com/damian0815/compel)) package to directly up-lift the weight of specific concept token, with a fixed weight of 1.5.\\n- •\\nCompositional Diffusion []. This method directly make multiple noise predictions on different text, and sum the noise prediction as the compositional direction for latent update. In our paper, given a prompt, we first split into short phrases. For example “a dog and a cat” is splitted into “a dog” and “a cat”, make individual denoising, and added up.\\n- •\\nAttend-and-Excite []. A&E refines the noisy latents to excite cross-attention units to attend to all subject tokens in the text prompt.\\n\\n**Table 1: Quantitative results for different methods on compositional text-to-video generation.**\\n| Name | Spatial Relation$\\\\uparrow$ | Multiple Object$\\\\uparrow$ | Motion Composition$\\\\uparrow$ | Overall Consistency$\\\\uparrow$ |\\n| --- | --- | --- | --- | --- |\\n| AnimateDiff [] | 24.80% | 33.44% | 33.90% | 27.75% |\\n| +Compositional Diffusion [] | 19.43% | 7.27% | 23.58% | 24.07% |\\n| +Attend-and-Excite [] | 20.88% | 31.25% | 34.78% | 28.05% |\\n| +Token-Reweight | 28.11% | 36.89% | 37.45% | 26.77% |\\n| +Vico (hard) | 24.22% | 29.95% | 37.23% | 28.85% |\\n| +Vico (soft) | 31.47% | 37.20% | 37.95% | 28.89% |\\n| ZeroScopev2 | 59.52% | 52.52% | 45.51% | 25.83% |\\n| +Compositional Diffusion [] | 31.77% | 8.23% | 33.13% | 23.02% |\\n| +Token-Reweight | 57.48% | 50.00% | 40.42% | 25.74% |\\n| +Attend-and-Excite [] | 59.02% | 62.27% | 45.82% | 25.84% |\\n| +Vico (hard) | 63.60% | 63.34% | 46.32% | 24.89% |\\n| +Vico (soft) | 62.28% | 69.05% | 45.31% | 26.15% |\\n| VideoCrafterv2 [] | 35.86% | 40.66% | 43.82% | 28.06% |\\n| +Compositional Diffusion [] | 23.61% | 10.59% | 35.49% | 24.49% |\\n| +Token-Reweight | 46.08% | 49.16% | 44.33% | 28.29% |\\n| +Attend-and-Excite [] | 48.11% | 66.62% | 43.48% | 28.33% |\\n| +Vico (hard) | 49.85% | 67.84% | 44.46% | 28.41% |\\n| +Vico (soft) | 50.40% | 73.55% | 44.98% | 28.52% |\\n\\nEvaluation and Metrics. We evaluate compositional generation using VBench []. Specifically, we focus on evaluating compositional quality in terms of *Spatial Relation*, *Multiple Object Composition*. For both metrics, the model processes text containing multiple concepts, generates a video. Then a caption model verifies the accuracy of the concept representations within the generated video.\\n\\nAdditionally, we design a new metric, *Motion Composition*. This metric evaluates the generated video based on the presence and accuracy of multiple objects performing different motions. We collect 70 prompts of the form \\\"obj1 is motion1 and obj2 is motion2\\\". Using GRiT [], we generate dense captions on video for each object and verify if each (object, motion) pair appears in the captions. The score is computed as $\\\\frac{\\\\sum_{1,2}(\\\\mathbb{I}(\\\\texttt{obj}_{i})+\\\\mathbb{I}(\\\\texttt{obj}_{i},\\n\\\\texttt{motion}_{i}))}{4}$. Here, $\\\\mathbb{I}(x)$ is an indicator function that returns 1 if $x$ is present in the generated captions, and 0 otherwise.\\n\\nThe overall video quality is measured using ViCLIP [] to compute a score based on text and video alignment, denoted as *Overall Consistency*.\\n\\nImplementation Details. We use the implementations on diffusers for video generation. All videos are generated by a A6000 GPU. We sample videos from Zeroscopev2 and VideoCrafterv2 using 50-step DPM-Solver++ []. AnimateDiff is sampled with 50-step DDIM []. We optimize the latent at each sampling steps, and update the latent with Adam [] optimizer at the learning rate of $1e-5$. We test both the soft and hard-min/max versions of Vico, setting the temperature $\\\\tau=0.01$ for the soft version. The NLTK package identify all nouns and verbs for equalization.\\n\\n### 4.2 Compositional Video Generation\\n\\nQuantitative Results. In Table 1, we present the scores achieved by Vico compared to other methods across various base models on compositional text-to-video generation. Vico consistently surpasses all baselines on every metric. Notably, our ST-flow based method surpasses cross-attention based techniques like Attend&Excite, thanks to its ability to incorporating influences across full attention graph. Additionally, the soft min-max version of Vico generally achieves better fidelity than the hard version, as it is better suited for gradient optimization.\\n\\nSpecifically, Vico demonstrates its most significant improvements in multi-subject generation tasks. For instance, on VideoCrafterv2, it shows a remarkable increase, improving scores from $40.66\\\\%\\\\to 73.55\\\\%$. This suggests that our attention mechanism in T2V is more adept at managing object arrangement. In contrast, compositional diffusion models [] often fail, as they assume conditions to be independent, which is problematic for realistic condition compositions.\\n\\nQualitative Results. We compare the videos generated by different methods in Figure 4. Attend&Excite receive slightly improvements, but still mixes semantics of different subject. For example, on the “a dog and a horse” example (Top Left), both Attend&Excite and the baseline incorrectly combine a dog’s face with a horse’s body. Vico addresses this issue by ensuring each token contributes equally, effectively separating their relationships.\\n\\nAdditionally, cross-attention often leads to temporal inconsistencies in the modified videos. For instance, in the “spider panda” case (Bottom Left), Attend&Excite initially displays a Spider-Man logo but it disappears abruptly in subsequent frames. In contrast, Vico captures dynamics across both spatial and temporal attention, leading to better results. More results is in Appendix D and E.\\n\\nFigure: Figure 4: Qualitative comparison of the videos generated by VideoCrafterv2 baseline, Attribute&Excite and our Vico with compositional textual descriptions.\\nRefer to caption: x4.png\\n\\n### 4.3 Attribution on Video Diffusion Model\\n\\nIn this section, we aim to demonstrate that our ST-Flow (hard) provides a more accurate measure of token contribution compared to other attention-based indicators.\\n\\nObjective Evaluation: Zero-shot Video Segmentation. We test several attribution methods using the VideoCrafterv2 model for zero-shot video segmentation on the Ref-DAVIS2017 [] dataset. To create these maps, we first performed a 25-step DDIM inversion [] to extract noise patterns, followed by sampling to generate the attribution maps. We specifically use maps from from *end of text* ([EOT]) token [] for segmentation. We used the mean value of the map as a threshold for binary segmentation. We compare with cross-attention [] and Attention Rollout []. The more accurate the segmentation is, the attribution is more reasonable for human.\\n\\nResults are presented in Table 5. Our method outperform others, providing the highest segmentation metrics in zero-shot setting. As visualized in Figure 5, cross-attention maps show inconsistent highlighting and flickering. Attention Rollout also conciders the full attention graph, but overly smoothed weights, resulting in less precise object focus.\\n\\nSubjective Evaluation: User Study. Besides, segmentation-based validation, we conducted a subjective user study to evaluate the quality of attribution maps generated by various methods. 20 participants rated maps from three different approaches across ten video clips. The evaluation focused on *Temporal Consistency*, assessing the presence of flickering, and *Reasonability*, determining alignment with human interpretations. Ratings ranged from 1 to 5, with 5 as the highest. As summarized in Table 5, Our ST-Flow outperforms other attention-based explanation, achieving the highest scores in both Temporal Consistency (4.19) and Reasonability (3.78).\\n\\n**Table 2: User study on attribution method.**\\n| Attribution Method | Temporal Consistency$\\\\uparrow$ | Reasonability$\\\\uparrow$ |\\n| --- | --- | --- |\\n| Cross-Attention [] | 2.56 | 2.84 |\\n| Attention Rollout [] | 3.88 | 3.45 |\\n| ST-Flow (Ours) | 4.19 | 3.78 |\\n\\n### 4.4 Ablation Study\\n\\nIn this section, we ablate our two key designs: the loss function and the proposed ST-Flow. We do experiments on VideoCrafterv2 and compare the performance.\\n\\nLoss Function. We modify the loss function used, from using the “min” as a fairness indicator (as described in Sec 3.1) to a variance loss, defined as $\\\\mathcal{L}_{\\\\text{fair}}=-\\\\sum_{i}(A_{i}-\\\\bar{A})^{2}$. It minimizes the differences between each $A_{i}$ and the average attribution value $\\\\bar{A}$, making it fair. The results are shown in Table 5, row 3 and 4. We notice while the variance loss ensures uniformity across all tokens, it overly restricts them, often degrading video quality. Conversely, our min-loss focuses on the least represented token, enhancing object composition accuracy without significantly affecting overall quality.\\n\\nST-Flow $v.s.$ Cross-Attention. A major contribution of our work is the development of ST-Flow and its efficient computation. We compare it against a variant using cross-attention as attribution. In this method, cross-attention maps are extracted and a mean score is computed for each token as $A_{i}$. As demostrated in Table 5, row 2 and 4, using ST-Flow (soft) largely outperforms cross-attention. We also provide the running speed analysis in Appendix F, confirming the efficiency of our approach.\\n\\n## 5 Conclusion\\n\\nIn this paper, we present Vico, a framework designed for compositional video generation. Vico starts by analyzing how input tokens influence the generated video. It then adjusts the model to ensure that no single concept dominates. To implement Vico practically, we calculate each text token’s contribution to the video token using max flow. This computation is made feasible by approximating the subgraph flow with a vectorized implementation. We have applied our method across various diffusion-based video models, which has enhanced both the visual fidelity and semantic accuracy of the generated videos.\\n\\n## Appendix A Proof of Theorem 1: Sub-graph Flow\\n\\nIn a network $G=(V,E)$ with a capacity function $c:E\\\\rightarrow\\\\mathbb{R}^{+}$, and a subgraph $g$ of $G$, the maximum flow $f_{g}$ in $g$ is less than or equal to the maximum flow $f_{G}$ in $G$.\\n\\n### Proof\\n\\n- 1.\\nDefinition of a Subgraph: A subgraph $g$ of $G$ can be defined as $g=(V^{\\\\prime},E^{\\\\prime})$ where $V^{\\\\prime}\\\\subseteq V$ and $E^{\\\\prime}\\\\subseteq E$. All capacities in $g$ are inherited from $G$, i.e., $c^{\\\\prime}(e)=c(e)$ for all $e\\\\in E^{\\\\prime}$.\\n- 2.\\nFlow Conservation: Both $G$ and $g$ must satisfy the flow conservation law at all intermediate nodes. That is, the sum of the flow entering any node must equal the sum of the flow exiting that node, except for the source (where flow is generated) and the sink (where flow is absorbed).\\n- 3.\\nReduced Set of Paths: Since $E^{\\\\prime}\\\\subseteq E$, every path through $g$ is also a path through $G$, but not every path through $G$ is necessarily a path through $g$. This reduction in the number of paths (or edges) in $g$ implies that some routes available for flow in $G$ are not available in $g$.\\n- 4.\\nCapacity Limitations: For any edge $e$ in $E^{\\\\prime}$, the capacity in $g$ (i.e., $c^{\\\\prime}(e)$) equals the capacity in $G$ (i.e., $c(e)$). Therefore, no edge in $g$ can support more flow than it can in $G$. Additionally, since some edges might be missing in $g$, the overall capacity of pathways from the source to the sink might be less in $g$ than in $G$.\\n- 5.\\nMaximum Flow Reduction: Given the reduction in paths and capacities, any flow that is feasible in $g$ is also feasible in $G$, but not vice versa. Hence, the maximum flow $f_{g}$ that can be pushed from the source to the sink in $g$ must be less than or equal to the maximum flow $f_{G}$ that can be pushed in $G$.\\n\\nConclusion: From these points, it follows directly that the maximum flow in a subgraph $g$ cannot exceed the maximum flow in the original graph $G$. This proves that $f_{g}\\\\leq f_{G}$.\\n\\n## Appendix B Proof of Proposition 1: Max Path Flow using Min-max Multiplication\\n\\nDefinitions and Proposition:\\nLet $\\\\mathbf{W}$ be a capacity matrix of a graph where $\\\\mathbf{W}_{i,j}$ is the capacity of the edge from vertex $i$ to vertex $j$. If there is no edge between $i$ and $j$, $\\\\mathbf{W}_{i,j}=0$ or some representation of non-connectivity. A $k$-hop path between two vertices $i$ and $j$ is a path that uses exactly $k$ edges.\\n\\nProposition: The $k$-th min-max power of $\\\\mathbf{W}$, denoted $\\\\mathbf{W}^{k}$, calculated as $\\\\mathbf{W}^{k}=\\\\mathbf{W}^{k-1}\\\\odot\\\\mathbf{W}$, has elements $\\\\mathbf{W}^{k}_{i,j}$ that represent the maximum flow possible on any $k$-hop path from vertex $i$ to $j$.\\n\\nMin-max Multiplication:\\nGiven matrices $\\\\mathbf{A}$ and $\\\\mathbf{B}$, $\\\\mathbf{C}=\\\\mathbf{A}\\\\odot\\\\mathbf{B}$ is defined such that:\\n\\n$$ $\\\\mathbf{C}_{i,j}=\\\\max_{r}(\\\\min(\\\\mathbf{A}_{i,r},\\\\mathbf{B}_{r,j}))$ $$\\n\\nProof by Induction:\\n\\nBase Case ($k=1$):\\n\\n- •\\nClaim: $\\\\mathbf{W}^{1}_{i,j}$ represents the capacity of the edge from $i$ to $j$, which is the maximum flow on a 1-hop path.\\n- •\\nProof: By definition, $\\\\mathbf{W}^{1}=\\\\mathbf{W}$, and $\\\\mathbf{W}^{1}_{i,j}=\\\\mathbf{W}_{i,j}$, which directly corresponds to the edge capacity between $i$ and $j$. Hence, the base case holds.\\n\\nInductive Step:\\n\\n- •\\nAssumption: Assume that for $k-1$, $\\\\mathbf{W}^{k-1}_{i,j}$ correctly represents the maximum flow on any $k-1$-hop path from $i$ to $j$.\\n- •\\nTo Prove: $\\\\mathbf{W}^{k}_{i,j}$ represents the maximum flow on any $k$-hop path from $i$ to $j$.\\n\\nProof:\\nFrom the definition of min-max multiplication,\\n\\n$$ $\\\\mathbf{W}^{k}_{i,j}=\\\\max_{r}(\\\\min(\\\\mathbf{W}^{k-1}_{i,r},\\\\mathbf{W}_{r,j}))$ $$\\n\\n- •\\n$\\\\mathbf{W}^{k-1}_{i,r}$ is the maximum flow from $i$ to $r$ using $k-1$ hops.\\n- •\\n$\\\\mathbf{W}_{r,j}$ is the capacity of the edge from $r$ to $j$ (1-hop).\\n\\nInterpretation: $\\\\min(\\\\mathbf{W}^{k-1}_{i,r},\\\\mathbf{W}_{r,j})$ finds the bottleneck flow for the path from $i$ to $j$ through $r$ using $k$ hops. The minimum function ensures the path’s flow is constrained by its weakest segment.\\n\\nMaximization Step: $\\\\max_{r}$ over all possible intermediate vertices $r$ selects the path with the highest bottleneck value, thus ensuring the selected path is the most capable among all possible $k$-hop paths.\\n\\nConclusion:\\nThe inductive step confirms that the flow represented by $\\\\mathbf{W}^{k}_{i,j}$ is indeed the maximum possible flow across any $k$-hop path from $i$ to $j$. Hence, by induction, the proposition holds for all $k$.\\n\\n## Appendix C Related Work\\n\\nVideo Diffusion Models. Video diffusion models generate video frames by gradually denoising a noisy latent space []. One of the main challenges with these models is their high computational complexity. Typically, the denoising process is performed in the latent space [, , ]. The architectural commonly adopt either a 3D-UNet [, , , , ] or diffusion transformer [, , ]. To enhance computational efficiency, these architectures often employ separate self-attention mechanisms for managing spatial and temporal tokens. Conventionally, training these models involves fine-tuning an image-based model for video data [, , ]. This process includes adding a temporal module while striving to preserve the original visual quality.\\n\\nDespite their ability to generate photorealistic videos, these models frequently struggle with understanding the complex interactions between elements in a scene. This shortcoming can result in the generation of nonsensical videos when responding to complex prompts.\\n\\nCompositional Generation. Current generative models often face challenges in creating data from a combination of conditions, with most developments primarily in the image domain. Energy-based models [, , ], for example, are mathematically inclined to be compositionally friendly, yet they require the conditions to be independent.\\nIn practice, many image-based methods utilize cross-attention to effectively manage the composition of concepts [, , , ]. However, when it comes to video, compositional generation introduces additional complexities. Some video-focused approaches concentrate specific form of composition, including object-motion composition [], subject-composition [], utilize explicit graphs to control content elements [], or integrate multi-modal conditions []. Despite these efforts, a generic solution for accurately generating videos from text descriptions involving multiple concepts is still lacking. We present the first solution for compositional video generation using complex text prompts, an area that remains largely underexplored.\\n\\nAttribution Methods. Attribution methods clarify how specific input features influence a model’s decisions. gradient-based methods [, , ] identify influential image regions by back-propagating gradients to the input. Attention-based methods [, ] that utilize attention scores to emphasize important inputs. Ablation methods[, ] modify data parts to assess their impact. Shapley values [] distribute the contribution of each feature based on cooperative game theory. In our paper, we extend existing techniques of attention flow to video diffusion models. We develop an efficient approximation to solve the max-flow problem. This improvement helps us more accurately identify and balance the impact of each textual elements on synthesized video.\\n\\n## Appendix D Compositional Video Editing\\n\\nOur system, Vico, can be integrated into video editing workflows to accommodate text prompts that describe a composition of concepts.\\n\\nSetup. We begin by performing a 50-step DDIM inversion on the input video. Following this, we generate a new video based on the given prompt.\\n\\nResults. An example of this process is illustrated in Figure 5. The original video demonstrates a strong bias towards a single presented object, making editing with a composition of concepts challenging. However, by applying Vico, we successfully enhance the video to accurately represent the intended compositional concepts.\\n\\nFigure: Figure 5: Video edit results with compositional prompts.\\nRefer to caption: x6.png\\n\\n## Appendix E More Visualizations\\n\\nHere we provide more example for compositional T2V in Figure 6\\n\\nFigure: Figure 6: Video visualization for compositional video generation\\nRefer to caption: x7.png\\n\\n## Appendix F Speed Analysis\\n\\nAttribution Speed. In this section, we assess the running speed of our ST-flow. To assess its computational efficiency, we compare ST-flow with cross-attention and Attention Rollout [] computation, by reporting the theoretical complexity and empirical running time. We assume we have 1 cross attention map of $mxn$ and $L$ self-attention map of $n\\\\times n$, and demonstrated the theoretical results. Specifically, we measure the average running time required for each diffusion model inference, focusing solely on the time taken for attribution computation, excluding the overall model inference time. We use the VideoCrafterv2 as the base model.\\n\\nAs detailed in Table 6, the cross-attention computation is fast, as it processes only a single layer. Both Attention Rollout and our approximated ST-Flow involve matrix multiplications and consequently share a similar time complexity. However, our ST-Flow approximation benefits from the relatively faster speed of element-wise min-max operations compared to the floating-point multiplications used in Attention Rollout, leading to slightly quicker execution times.\\n\\nIn contrast, the exact ST-Flow method is much slower. This is because it requires independently estimating the flow for each sink-source pair, a process that takes considerable time.\\n\\n**Table 6: Speed comparison for attribution method.**\\n| Method | Complexity | sec/inference |\\n| --- | --- | --- |\\n| Cross-Attn. | O(1) | 0.002s |\\n| Attention Rollout | $O(Lmn^{2})$ | 0.042s |\\n| Exact-ST-Flow | $O(L^{3}mn^{4})$ | 8s |\\n| ST-Flow (soft) | $O(Lmn^{2})$ | 0.037s |\\n\\nDiffusion Inference Speed. Our Vico framework includes a iterative optimization process alongside with the denoising. As expected, it should results in longer inference time. We evaluated this using a 50-step DPM denoising process on the VideoCrafterv2 model, at a resolution of $512\\\\times 320$ for 16 frames, on a single A6000 GPU.\\n\\nThe results, shown in Table 7, reveal that the baseline VideoCrafterv2 completed in 23 seconds. Adding the Attend&Excite increased the duration to 48 seconds. In comparison, our Vico framework finished in a comparable time of 50 seconds. Despite its additional complexity, Vico’s efficient design keeps the inference time within a reasonable range.\\n\\n**Table 7: Text-to video model inference time comparison.**\\n| Method | Time |\\n| --- | --- |\\n| VideoCrafterv2 | 23s |\\n| + Attend&Excite | 48s |\\n| + Vico (soft&hard) | 45s |\\n\\n## Appendix G Implementation details of Vico\\n\\nST-Flow Computation. To compute the ST-Flow, we begin by extracting attention weights from all layers. These weights are averaged across all heads and then upscaled to the image size using bicubic interpolation. Due to the block-wise sparse pattern of the connections, min-max matrix multiplication is applied to the capacity matrix for connected layers. Furthermore, given that cross-attention layers include skip connections from previous layers, we divide the network into multiple groups. Within each group, min-max matrix Multiplication is performed. Finally, we aggregate the scores across all groups to obtain the results. The pseudocode for the min-max multiplication is in Algorithm 1.\\n\\nFigure: Algorithm 1 Batched Min-Max Matrix Multiplication\\n\\nLatent Step. During the first half of the sampling process, we update the latent variables. We establish a loss threshold of 0.2; once this threshold is reached, no further updates are made.\\n\\n## Appendix H Limitations\\n\\nAlthough Vico effectively allocates attribution across different tokens, it does not explicitly bind attributes to subjects. Moreover, there is a critical balance to maintain between latent updates and semantic coherence. Excessive updating can lead to the generation of nonsensical videos.\\n\\n## Appendix I Broader Applications\\n\\nTechnically, the computation of attention flow proposed in our system is versatile and can be efficiently applied to a variety of other applications like erase certain concept in diffusion models. Additionally, the principle of fairly distributing the contribution of different input parts can be extended to other domains, such as language modeling.\",\n \"metadata\": {\n \"authors\": [\n \"Xingyi Yang Xinchao Wang\",\n \"National University of Singapore\",\n \"Corresponding Author\"\n ],\n \"title\": \"Compositional Video Generation as Flow Equalization\",\n \"total_chars\": 44547,\n \"total_lines\": 423,\n \"updated_at\": \"2026-01-25T15:02:50.738900\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"TUJxAnaNhm","initial_rating":8,"confidence":3,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper introduces a novel approach for compositional video generation. The proposed method begins by analyzing the impact of input tokens on the video output, ensuring that no single concept predominates the generated content. The core concept involves computing each text token's contribution to the video generation process through maximum flow. The paper introduces an efficient computational technique by approximating the subgraph flow with a vectorized implementation.Finally, the method has been tested across various diffusion-based video models, and the experimental results confirm its effectiveness in enhancing both visual fidelity and semantic accuracy.","strengths":"1. The proposed method is innovative and can be integrated with existing video generation techniques. The experiments demonstrate the effectiveness of applying the \"Vico\" method on current models such as AnimaDiff, ZeroScore V2, and VideoCrafter V2, showing notable improvements in results.\n\n2. The paper is well-articulated, featuring thorough theoretical analysis and proof.","weaknesses":"1. The user study (Table 2) is limited to only ten video clips, which is insufficient to conclusively prove the effectiveness of the method.","questions":"n/a"},{"id":"tg0z4UKIXt","initial_rating":8,"confidence":4,"soundness":3,"contribution":3,"presentation":2,"summary":"This manuscript tackles the problem of video generation, focusing on improving the compositional and complex interactions in the final output. The proposed approach utilizes a flow equalization formulation to ensure that different tokens of input get a fair amount of attention throughout the self-attention layers.","strengths":"Capturing compositional relationships in the final generated output is a very important problem and, to the best of my knowledge, is one of the biggest issues with current SOA in GenAI.\nThis paper correctly identifies one of the main issues throughout the attention mechanism and tries to improve the contribution of different tokens in attention layers as a test-time optimization. The authors model the information flow of the generative model as a graph, which is a smart and (semi-)novel strategy (for the videos) in my opinion.","weaknesses":"The biggest weakness of the solution is the readability of this paper. It was very hard for me to read through the text and jump from text to mathematical notations and back. I will ask for a few clarifications in the questions block.","questions":"1- In line 247, the capacity matrix W, what are each row and column? Why does the first row have the `t` index while other rows don't?\n2- Lines 241, and 243. What is the difference between e_(i,j), i=j and e_(i,i) difference?\n3- Section 3.1: At first glance, it is not clear what is x_t (definition) and how A_i is extracted out of it. \n4- What is token-reweight in Table 1? \n5- There are some valid categories of issues in Video Generation shown in Figure 1. My question is if the lack of fair attribution and attention is the only problem that causes these issues. If not, what are the other factors?"},{"id":"HbbNhx9ZTa","initial_rating":3,"confidence":5,"soundness":3,"contribution":2,"presentation":2,"summary":"This paper introduces Vico, a novel framework specifically designed for compositional video generation. Vico employs a maximum flow approach to ensure fair contributions from each input token, integrating sub-graphs, a soft flow strategy, and vectorized path flow computation for efficient inference. Extensive experiments demonstrate that Vico significantly surpasses existing baselines in compositional generation tasks.","strengths":"1. This paper presents a highly innovative solution to the problem, utilizing traditional max flow to address token-level response balancing, thereby achieving effective compositional generation.\n2. I appreciate that extensive effort has been put into designing feasible experiments. The authors introduce practical techniques such as subgraph, soft min, and vectorized flow strategies, which significantly enhance inference speed.\n3. The experiments are thorough and well-executed, including comprehensive comparative studies and a detailed user study, which provides strong validation for the proposed approach.\n4. The visual quality of the generated videos is satisfying, despite the limited number of examples presented.","weaknesses":"1. The primary concern is the lack of comparisons or discussions involving recent text-to-video (T2V) methods. The baseline model, VideoCrafter2, was released over a year ago. To convincingly demonstrate the relevance of the compositional generation problem, the paper should ideally compare against more advanced, recent baselines like OpenSora[1], CogVideoX[2], or more.\n2. Additionally, the paper lacks comparisons to existing compositional video generation models. For instance, methods like LVD[3], which uses LLMs for prompt decomposition with gradient-based layout optimization during inference, VideoTetris[4], which employs spatiotemporal diffusion for multi-object generation, and VideoDirectorGPT[5], which combines an LLM director with spatial convolutions for layout learning, are not discussed. Including comparative studies with these related works would strengthen the evaluation and clarify the advantages of the proposed approach.\n3. The paper lacks a theoretical justification for the assumption that each token should have an equal impact on the generated result. In typical prompts, not all tokens necessarily require equal influence; for instance, non-descriptive tokens or function words might logically play a reduced role in the attention process. Given the strength of this assumption, a more rigorous rationale or proof would help validate its applicability.\n4. Another strong assumption is made regarding cross-attention in T2V models. The paper’s approach relies on cross-attention being embedded uniformly across all layers and frames, yet many contemporary T2V models, such as CogVideoX[2], Mochi-1[6], and commercial models like Kling[7], utilize 3D attention mechanisms similar to MMDiT. This raises concerns about the applicability of the paper’s assumptions to modern architectures, which may limit its generalizability.\n5. The paper contains a few typographical errors that affect readability. For example, in the introduction, the prompt \"a bird looks like a cat\" is used as an example, but the actual effect of this prompt is not demonstrated.\n\n[1] Open-Sora: Democratizing Efficient Video Production for All, https://github.com/hpcaitech/Open-Sora\n\n[2] Yang, Zhuoyi, et al. \"Cogvideox: Text-to-video diffusion models with an expert transformer.\" arXiv preprint arXiv:2408.06072 (2024).\n\n[3] Lian, Long, et al. \"Llm-grounded video diffusion models.\" arXiv preprint arXiv:2309.17444 (2023).\n\n[4] Tian, Ye, et al. \"VideoTetris: Towards Compositional Text-to-Video Generation.\" arXiv preprint arXiv:2406.04277 (2024).\n\n[5] Lin, Han, et al. \"Videodirectorgpt: Consistent multi-scene video generation via llm-guided planning.\" arXiv preprint arXiv:2309.15091 (2023).\n\n[6] Mochi-1: https://www.genmo.ai/blog\n\n[7] Kling: https://www.klingai.com/","questions":"1. My primary question is, do the paper's assumptions hold true for modern 3D attention models, such as the open-source CogVideoX. Can the proposed method balance token contributions effectively when applied to an attention graph in such models?\n2. In the case of 3D attention, how much additional computational overhead does the proposed approach introduce? Cross-attention calculations are relatively lightweight, but if full attention is employed, as in MMDiT, would the method’s computations lead to significant cost increases?\n3. The paper mainly showcases relatively short prompts. I would like to ask if the proposed method can handle modern, highly descriptive prompts that may reach up to 100 words. Would the method remain feasible for inference, and what would be the associated computational cost in such cases?\n4. As a fair comparison, could the paper utilize T2V CompBench[1], a benchmark specifically designed to evaluate compositional video generation, to better assess and compare the performance of the proposed model against other existing models? I wonder how well this method performs under a more comprehensive benchmark.\n\n[1] Sun, Kaiyue, et al. \"T2V-CompBench: A Comprehensive Benchmark for Compositional Text-to-video Generation.\" arXiv preprint arXiv:2407.14505 (2024)."},{"id":"PsW5BG85rD","initial_rating":5,"confidence":4,"soundness":3,"contribution":2,"presentation":2,"summary":"This paper presented a new method named Vico, a framework designed for compositional video generation. Different from existing methods that may not reflect the intended composition of elements, the proposed Vico tries to adjust the model to ensure that no single concept dominates. Specifically, Vico calculate the contribution of each text token using max-flow and leverage a sub-graph flow to propagate information. The proposed method can be implemented by inserting into diffusion-based methods. Extensive experimental results verify the effectiveness of the proposed method.","strengths":"1.\tA new method named Vico for compositional video generation is proposed.\n2.\tThe proposed Vico leverage max-flow to ensure that no single concept dominates.\n3.\tExtensive results verify the effectiveness of the proposed method in generation high-quality videos.","weaknesses":"1.\tThis paper argues that the proposed method explicitly constrains the contribution of each token to be the equal, but in fact there are some words with no contribution or words with outstanding contribution in a sentence, that is, the importance of each word should be different. For example, \"On a certain day, a boy is running\", where \"On a certain day\" is not informative, only the following \"the boy is running\" is informative. The authors should discuss the problem.\n2.\tThe proposed method needs to be optimized at test time, and the resource consumption of optimization such as time and computational overhead should be discussed.\n3.\tThis paper said “While the compositional text-to-image sythesis Liu et al. (2022); Chefer et al. (2023); Kumari et al. (2023); Feng et al. (2023); Huang et al. (2023) has been more studied, the challenge of compositional video generation has received less attention.” My question is that whether these image methods can be extended to compositional video generation task? If not, the authors should give a explanation. If yes, please give a comparison with them.\n4.\tCan Vico be used in compositional motion scenarios? Such as \"In a room, a cat is running from left to right, a dog is running from right to left\", this complex movement scene is very interesting.\n\n--------------------------------\nPost review:\nThank the authors for the responses. Given ICLR's high standards, I decided to keep the score at 5. The motivation of this paper is good, but in the current version, the different processing of prompt words may ignore some cases, such as when some words other than verbs and nouns have a certain amount of information. And the proposed method requires test-time optimization, which greatly increases the inference cost, considering that the model is getting larger and larger now.","questions":"Please refer to Weaknesses for more details."}],"string":"[\n {\n \"id\": \"TUJxAnaNhm\",\n \"initial_rating\": 8,\n \"confidence\": 3,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper introduces a novel approach for compositional video generation. The proposed method begins by analyzing the impact of input tokens on the video output, ensuring that no single concept predominates the generated content. The core concept involves computing each text token's contribution to the video generation process through maximum flow. The paper introduces an efficient computational technique by approximating the subgraph flow with a vectorized implementation.Finally, the method has been tested across various diffusion-based video models, and the experimental results confirm its effectiveness in enhancing both visual fidelity and semantic accuracy.\",\n \"strengths\": \"1. The proposed method is innovative and can be integrated with existing video generation techniques. The experiments demonstrate the effectiveness of applying the \\\"Vico\\\" method on current models such as AnimaDiff, ZeroScore V2, and VideoCrafter V2, showing notable improvements in results.\\n\\n2. The paper is well-articulated, featuring thorough theoretical analysis and proof.\",\n \"weaknesses\": \"1. The user study (Table 2) is limited to only ten video clips, which is insufficient to conclusively prove the effectiveness of the method.\",\n \"questions\": \"n/a\"\n },\n {\n \"id\": \"tg0z4UKIXt\",\n \"initial_rating\": 8,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"This manuscript tackles the problem of video generation, focusing on improving the compositional and complex interactions in the final output. The proposed approach utilizes a flow equalization formulation to ensure that different tokens of input get a fair amount of attention throughout the self-attention layers.\",\n \"strengths\": \"Capturing compositional relationships in the final generated output is a very important problem and, to the best of my knowledge, is one of the biggest issues with current SOA in GenAI.\\nThis paper correctly identifies one of the main issues throughout the attention mechanism and tries to improve the contribution of different tokens in attention layers as a test-time optimization. The authors model the information flow of the generative model as a graph, which is a smart and (semi-)novel strategy (for the videos) in my opinion.\",\n \"weaknesses\": \"The biggest weakness of the solution is the readability of this paper. It was very hard for me to read through the text and jump from text to mathematical notations and back. I will ask for a few clarifications in the questions block.\",\n \"questions\": \"1- In line 247, the capacity matrix W, what are each row and column? Why does the first row have the `t` index while other rows don't?\\n2- Lines 241, and 243. What is the difference between e_(i,j), i=j and e_(i,i) difference?\\n3- Section 3.1: At first glance, it is not clear what is x_t (definition) and how A_i is extracted out of it. \\n4- What is token-reweight in Table 1? \\n5- There are some valid categories of issues in Video Generation shown in Figure 1. My question is if the lack of fair attribution and attention is the only problem that causes these issues. If not, what are the other factors?\"\n },\n {\n \"id\": \"HbbNhx9ZTa\",\n \"initial_rating\": 3,\n \"confidence\": 5,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper introduces Vico, a novel framework specifically designed for compositional video generation. Vico employs a maximum flow approach to ensure fair contributions from each input token, integrating sub-graphs, a soft flow strategy, and vectorized path flow computation for efficient inference. Extensive experiments demonstrate that Vico significantly surpasses existing baselines in compositional generation tasks.\",\n \"strengths\": \"1. This paper presents a highly innovative solution to the problem, utilizing traditional max flow to address token-level response balancing, thereby achieving effective compositional generation.\\n2. I appreciate that extensive effort has been put into designing feasible experiments. The authors introduce practical techniques such as subgraph, soft min, and vectorized flow strategies, which significantly enhance inference speed.\\n3. The experiments are thorough and well-executed, including comprehensive comparative studies and a detailed user study, which provides strong validation for the proposed approach.\\n4. The visual quality of the generated videos is satisfying, despite the limited number of examples presented.\",\n \"weaknesses\": \"1. The primary concern is the lack of comparisons or discussions involving recent text-to-video (T2V) methods. The baseline model, VideoCrafter2, was released over a year ago. To convincingly demonstrate the relevance of the compositional generation problem, the paper should ideally compare against more advanced, recent baselines like OpenSora[1], CogVideoX[2], or more.\\n2. Additionally, the paper lacks comparisons to existing compositional video generation models. For instance, methods like LVD[3], which uses LLMs for prompt decomposition with gradient-based layout optimization during inference, VideoTetris[4], which employs spatiotemporal diffusion for multi-object generation, and VideoDirectorGPT[5], which combines an LLM director with spatial convolutions for layout learning, are not discussed. Including comparative studies with these related works would strengthen the evaluation and clarify the advantages of the proposed approach.\\n3. The paper lacks a theoretical justification for the assumption that each token should have an equal impact on the generated result. In typical prompts, not all tokens necessarily require equal influence; for instance, non-descriptive tokens or function words might logically play a reduced role in the attention process. Given the strength of this assumption, a more rigorous rationale or proof would help validate its applicability.\\n4. Another strong assumption is made regarding cross-attention in T2V models. The paper’s approach relies on cross-attention being embedded uniformly across all layers and frames, yet many contemporary T2V models, such as CogVideoX[2], Mochi-1[6], and commercial models like Kling[7], utilize 3D attention mechanisms similar to MMDiT. This raises concerns about the applicability of the paper’s assumptions to modern architectures, which may limit its generalizability.\\n5. The paper contains a few typographical errors that affect readability. For example, in the introduction, the prompt \\\"a bird looks like a cat\\\" is used as an example, but the actual effect of this prompt is not demonstrated.\\n\\n[1] Open-Sora: Democratizing Efficient Video Production for All, https://github.com/hpcaitech/Open-Sora\\n\\n[2] Yang, Zhuoyi, et al. \\\"Cogvideox: Text-to-video diffusion models with an expert transformer.\\\" arXiv preprint arXiv:2408.06072 (2024).\\n\\n[3] Lian, Long, et al. \\\"Llm-grounded video diffusion models.\\\" arXiv preprint arXiv:2309.17444 (2023).\\n\\n[4] Tian, Ye, et al. \\\"VideoTetris: Towards Compositional Text-to-Video Generation.\\\" arXiv preprint arXiv:2406.04277 (2024).\\n\\n[5] Lin, Han, et al. \\\"Videodirectorgpt: Consistent multi-scene video generation via llm-guided planning.\\\" arXiv preprint arXiv:2309.15091 (2023).\\n\\n[6] Mochi-1: https://www.genmo.ai/blog\\n\\n[7] Kling: https://www.klingai.com/\",\n \"questions\": \"1. My primary question is, do the paper's assumptions hold true for modern 3D attention models, such as the open-source CogVideoX. Can the proposed method balance token contributions effectively when applied to an attention graph in such models?\\n2. In the case of 3D attention, how much additional computational overhead does the proposed approach introduce? Cross-attention calculations are relatively lightweight, but if full attention is employed, as in MMDiT, would the method’s computations lead to significant cost increases?\\n3. The paper mainly showcases relatively short prompts. I would like to ask if the proposed method can handle modern, highly descriptive prompts that may reach up to 100 words. Would the method remain feasible for inference, and what would be the associated computational cost in such cases?\\n4. As a fair comparison, could the paper utilize T2V CompBench[1], a benchmark specifically designed to evaluate compositional video generation, to better assess and compare the performance of the proposed model against other existing models? I wonder how well this method performs under a more comprehensive benchmark.\\n\\n[1] Sun, Kaiyue, et al. \\\"T2V-CompBench: A Comprehensive Benchmark for Compositional Text-to-video Generation.\\\" arXiv preprint arXiv:2407.14505 (2024).\"\n },\n {\n \"id\": \"PsW5BG85rD\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper presented a new method named Vico, a framework designed for compositional video generation. Different from existing methods that may not reflect the intended composition of elements, the proposed Vico tries to adjust the model to ensure that no single concept dominates. Specifically, Vico calculate the contribution of each text token using max-flow and leverage a sub-graph flow to propagate information. The proposed method can be implemented by inserting into diffusion-based methods. Extensive experimental results verify the effectiveness of the proposed method.\",\n \"strengths\": \"1.\\tA new method named Vico for compositional video generation is proposed.\\n2.\\tThe proposed Vico leverage max-flow to ensure that no single concept dominates.\\n3.\\tExtensive results verify the effectiveness of the proposed method in generation high-quality videos.\",\n \"weaknesses\": \"1.\\tThis paper argues that the proposed method explicitly constrains the contribution of each token to be the equal, but in fact there are some words with no contribution or words with outstanding contribution in a sentence, that is, the importance of each word should be different. For example, \\\"On a certain day, a boy is running\\\", where \\\"On a certain day\\\" is not informative, only the following \\\"the boy is running\\\" is informative. The authors should discuss the problem.\\n2.\\tThe proposed method needs to be optimized at test time, and the resource consumption of optimization such as time and computational overhead should be discussed.\\n3.\\tThis paper said “While the compositional text-to-image sythesis Liu et al. (2022); Chefer et al. (2023); Kumari et al. (2023); Feng et al. (2023); Huang et al. (2023) has been more studied, the challenge of compositional video generation has received less attention.” My question is that whether these image methods can be extended to compositional video generation task? If not, the authors should give a explanation. If yes, please give a comparison with them.\\n4.\\tCan Vico be used in compositional motion scenarios? Such as \\\"In a room, a cat is running from left to right, a dog is running from right to left\\\", this complex movement scene is very interesting.\\n\\n--------------------------------\\nPost review:\\nThank the authors for the responses. Given ICLR's high standards, I decided to keep the score at 5. The motivation of this paper is good, but in the current version, the different processing of prompt words may ignore some cases, such as when some words other than verbs and nouns have a certain amount of information. And the proposed method requires test-time optimization, which greatly increases the inference cost, considering that the model is getting larger and larger now.\",\n \"questions\": \"Please refer to Weaknesses for more details.\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;5;8;8\",\n \"rating_avg\": 6,\n \"confidence\": \"5;4;4;3\",\n \"confidence_avg\": 4,\n \"soundness\": \"3;3;3;3\",\n \"soundness_avg\": 3,\n \"contribution\": \"2;2;3;3\",\n \"contribution_avg\": 2.5,\n \"presentation\": \"2;2;2;3\",\n \"presentation_avg\": 2.25\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"Submitted to ICLR 2025\",\n \"venueid\": \"ICLR.cc/2025/Conference/Rejected_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.712093\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"ly1iMA9YDP\",\n \"metareview\": \"This paper introduces Vico, an inference-time method designed to enhance compositional video generation. Vico ensures equal influence for each textual token (verbs and nouns only) on the final video output through test-time optimization, dynamically assessing and rebalancing token impacts at each diffusion step. The reviewers recognize the significance of the problem, the (semi-)novel approach, and the extensive results that demonstrate the method's effectiveness.\\n\\nHowever, the reviewers also highlight several weaknesses. While many concerns were addressed following the rebuttal, the remaining issues are:\\n\\n* Test-time optimization overhead: Two reviewers raised concerns about the significant increase in computation time. For instance, Vico requires 200 seconds for CogVideoX-2B, more than doubling the 90 seconds needed by the baseline CogVideoX. The authors responded by outlining plans to integrate the Vico framework into the training phase to mitigate this overhead.\\n\\n* Balancing strategy: Reviewer kAsb questioned the approach of equalizing only nouns and verbs, suggesting it may oversimplify the process. \\n\\nFinally, this paper receives mixed evaluations: accept (low confidence), marginally above the acceptance threshold, and marginally below the acceptance threshold. The opposing Reviewer kAsb remains unwilling to adjust their score after reading the rebuttal, making it a borderline case.\\n\\nThe AC finds Reviewer kAsb's arguments persuasive and agrees with their concerns. While this work shows potential for improvement, the significant overhead introduced by test-time optimization diminishes its practical significance. Regarding the technical design, the AC agrees with Reviewer kAsb's critique that balancing only nouns and verbs may overlook other important word types. This limitation could hinder the model's ability to effectively handle long and complex prompts. This limitation is particularly relevant as recent video generation models often use rephrasers to expand short user prompts into complex structures, incorporating multiple nouns, verbs, and other word types (e.g., attributes, geometric details, relationships) that convey subtle yet essential information.\\n\\nIn light of the above, the AC recommends that accepting this submission may be premature until the concerns are fully resolved.\",\n \"additional_comments\": \"Two reviewers responded to the rebuttal: one increased their score to 6, while the other remained unwilling to change their score of 5. The points raised by the reviewers, along with the AC's assessment, are detailed above in the metareview.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Reject\"\n}"}}},{"rowIdx":3393,"cells":{"paper_id":{"kind":"string","value":"qUJsX3XMBH"},"arxiv_id":{"kind":"string","value":"2410.09335v1"},"title":{"kind":"string","value":"Rethinking Data Selection at Scale: Random Selection is Almost All You Need"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract Supervised fine-tuning (SFT) is crucial for aligning Large Language Models (LLMs) with human instructions. The primary goal during SFT is to select a small yet representative subset of training data from the larger pool, such that fine-tuning with this subset achieves results comparable to or even exceeding those obtained using the entire dataset. However, most existing data selection techniques are designed for small-scale data pools, which fail to meet the demands of real-world SFT scenarios. In this paper, we replicated several self-scoring methods—those that do not rely on external model assistance—on two million-scale datasets, and found that nearly all methods struggled to significantly outperform random selection when dealing with such large-scale data pools. Moreover, our comparisons suggest that, during SFT, diversity in data selection is more critical than simply focusing on high-quality data. We also analyzed the limitations of several current approaches, explaining why they perform poorly on large-scale datasets and why they are unsuitable for such contexts. Finally, we found that filtering data by token length offers a stable and efficient method for improving results. This approach, particularly when training on long-text data, proves highly beneficial for relatively weaker base models, such as Llama3. The code is available at https://github.com/xiatingyu/SFT-DataSelection-at-scale .\\n\\n## 1 Introduction\\n\\nWith the advent of large language models (LLMs) such as ChatGPT, we have observed significant advancements in tasks involving instruction following (Wang et al., ), intent comprehension (Lu et al., ), and text generation (Zhao et al., ).\\nOne of the primary objectives of developing LLMs is to harness their potential\\nfor generalizing to unseen natural language\\nprocessing (NLP) tasks. To achieve this aim, many LLMs focus on precisely aligning with human instructions.\\n\\nRecent studies indicate that supervised fine-tuning (SFT) can customize LLMs for specific domains, tasks, or applications by utilizing well-crafted data. According to the study in Zhou et al. (), it is feasible to fine-tune a pre-trained language model with a relatively small set of examples. Building on this insight, several papers have explored data selection strategies for SFT of LLMs (Wang et al., ; Qin et al., ), emphasizing the importance of enhancing the quality of instruction tuning (IT) data or increasing data diversity. These strategies can be classified into two primary categories: (1) Extenral-scoring methods, which require support from more sophisticated external models like GPT-4 to score the data for the subsequent selection (Lu et al., ; Chen et al., ; Du et al., ; Liu et al., ; Zhou et al., ); (2) Self-scoring methods, which leverage LLMs themselves as data scorers (Zhou et al., ; Li et al., ; ; Liu et al., ; Xia et al., ; Yin et al., ).\\n\\nFigure: Figure 1: The discrepancy between each methods and random selection on BBH benchmark. The Y-axis represents the differential score, which is computed by subtracting the random selection score from the scores obtained using various methods.\\nRefer to caption: x1.png\\n\\nExisting SFT data selection methodologies, both external-scoring and self-scoring, are primarily assessed using several widely recognized IT datasets, such as alpaca-GPT4 (Peng et al., ), Dolly (Conover et al., ), FLAN (Longpre et al., ), WizardLM (Xu et al., ), and ShareGPT (Chiang et al., ). These datasets are limited in size and originate from a single source. Meanwhile, in practical applications, to fully leverage the inherent knowledge of LLMs, the SFT process frequently necessitates a substantial volume of varied data, ideally in the range of millions or more. This discrepancy creates a gap between the present SFT data selection strategies and real-world applications. In order to observe the impact brought by the dataset size on the performance of different selection strategies, we analyze the difference in outcomes between existing SFT data selection methods and random selection within source datasets ranging from 10K-30K to 1M on Llama3-8B (AI@Meta, ). As shown in Figure 1, when the scale of the datasets increases to 1M, these data selection methods yield suboptimal performance compared with random selection.\\n\\nInspired by this finding, we rethink whether SFT data selection methods can work when they are required to handle large-scale IT datasets. For external-scoring approaches, it is impractical to apply them to tackle vast amounts of IT data due to the substantial costs (Liu et al., ), we hence focus on the self-scoring methods. For self-scoring approaches, we refer to the article Qin et al. () to categorize the techniques into two types: data quality-based methods and data diversity-based methods. To explore how self-scoring methods influence LLMs’ performance when dealing with large-scale IT data, we evaluate several recent methods on two benchmarks that contain millions of instances. The findings from our experiments reveal three main points:\\n\\n- •\\nMost self-scoring data selection techniques do not significantly outperform random selection on large-scale datasets. Even though these self-scoring methods can achieve significant gains on small-scale datasets, their effectiveness will be greatly reduced when the data size increases and the data sources become complex.\\n- •\\nData diversity holds more significance than data quality during the SFT phase. Data quality-based selection methods are more effective than data diversity-based methods when dealing with a small-scale dataset from a single source. However, when tackling multi-source data, only considering data quality is far from enough.\\n- •\\nThrough a comparative empirical analysis of two IT datasets, we find that it is useful to utilize token length as a criterion to conduct data filtering, yielding stable and efficient results for SFT when dealing with large-scale IT data. Previous work (Liu et al., ) has demonstrated the benefit of long texts training for models on subjective evaluation tasks such as MTbench (Zheng et al., ) and AlpacaEval (Li et al., ), we have further confirmed the positive effect of long texts training on objective evaluation tasks, such as Big-Bench-Hard (Suzgun et al., ). While utilizing token length in SFT may not yield optimal outcomes on every language model, it is highly beneficial for applying it in training with long texts, especially on a relatively weak BASE language model, like Llama3-8B.\\n\\n## 2 Related Work\\n\\nExternal-scoring Method.\\nLu et al. () introduced an open-set instruction tagging method called INSTAG, which employed ChatGPT to generate detailed tags to measure and examine the variety and intricacy of human instructions for LLMs during SFT. Chen et al. () presented the ALPAGASUS model that used ChatGPT to evaluate each instruction and then selected various data based on a certain threshold. Du et al. () suggested a model-oriented instruction selection approach that not only considered the quality and coverage of instruction data but also incorporated the necessity of instructions according to the capabilities of specific LLMs. Liu et al. () introduced DEITA, it used ChatGPT to iteratively enhance the complexity or quality of each data sample across relevant dimensions and then requested ChatGPT to evaluate these samples for their complexity or quality. These models exceed the performance of the basic foundation models trained on complete datasets. However, they heavily depend on high-performing external LLMs to score data.\\n\\nSelf-scoring Method.\\nLi et al. () put forward an autonomously guided method enabling LLMs to discern relevant instruction pairs from open-source data. An Instruction-Following Difficulty (IFD) metric was introduced to highlight inconsistencies between a language model’s anticipated responses and its self-generated outputs.\\nWu et al. () came up with DiverseEvol, which enabled the model to progressively select training subsets to enhance performance, without external oversight from humans or more advanced LLMs. This approach focused on maintaining high diversity within the selected subsets, as the model opted for new data points that are most distinct from existing ones based on its current embedding space.\\nXia et al. () suggested LESS, designed to pick out relevant instruction tuning data for a specific application. It utilized a gradient datastore with low-dimensional gradient features, selecting examples based on their resemblance to few-shot examples that represent a particular capability.\\nYin et al. () observed that model performance is inversely related to the compression ratio of training data. They introduced a universal data selection method named ZIP aimed at prioritizing data subsets with low compression ratios for training LLMs.\\nLiu et al. () developed SelectIT, which leveraged the inherent uncertainty in LLMs at various levels—grain, token, sentence, and model—to more effectively identify high-quality instruction tuning data, eliminating the need for additional resources.\\nLi et al. () introduced Nuggets, which employs one-shot learning to choose high-quality instruction data. It used a scoring system based on the influence of candidate examples on the perplexity of a diverse anchor set, thereby facilitating the selection of the most beneficial data for instruction tuning.\\n\\n## 3 Self-scoring strategies\\n\\nIn this paper, we focus on self-scoring methods that do not rely on external advanced LLMs to score data. We refer Qin et al. ()’s work and categorize existing resourceful data selection methods into two main perspectives: data quality-based methods and data diversity-based methods.\\n\\n### 3.1 Quality-based Selections\\n\\nIn this section, we introduce 4 methods based on data quality assessment and selection.\\n“Quality” here refers primarily to the complexity, completeness, score, and influence of the datapoints. Different from Qin et al. (), we believe that the influence of a datapoint in the target dataset is also a reflection of data quality, especially in practical scenarios, where we are required to deal with diverse tasks rather than a single task. We thus regard the influence as a quality category as well.\\n\\nLESS Xia et al. () instroduced low-rank gradient similarity search to select influential data for the target application. Concretely, a model was trained with LoRA (Hu et al., ) for a warmup period on a small subset $\\\\mathcal{D}_{\\\\mathrm{warmup}}\\\\subset\\\\mathcal{D}$. Then, the Adam LoRA gradient features for each data point were computed and stored in a gradient database.\\n\\nNext, a gradient datastore of projected low-dimensional gradient features was constructed\\nwhich can be reused for different target tasks. For training datapoints $\\\\bm{z}$, they computed d-dimensional\\nprojection of the LoRA gradient $\\\\tilde{\\\\nabla}\\\\ell(\\\\bm{z};\\\\bm{\\\\theta}_{i})=\\\\Pi^{\\\\top}\\\\hat{\\\\nabla}\\\\ell(\\\\bm{z};\\n\\\\bm{\\\\theta}_{i})$, where $\\\\Pi^{\\\\top}$ is computed and applied by memory-efficient online implementation of random projections proposed by Park et al. (). For validation datapoint $\\\\bm{z}^{\\\\prime}$, they computed $\\\\tilde{\\\\Gamma}(\\\\bm{z}^{\\\\prime},\\\\cdot)=\\\\Pi^{\\\\top}\\\\hat{\\\\Gamma}(\\\\bm{z}^{\\\\prime},\\\\cdot)$.\\n\\nFinally, LESS computed $\\\\max_{j}\\\\mathrm{Inf}_{\\\\mathrm{Adam}}(\\\\bm{z},\\\\mathcal{D}_{\\\\mathrm{val}}^{(j)})$ for the training set $\\\\bm{z}$ across all sub-validation sets $\\\\mathcal{D}_{val}$. Then it selected the highest score examples to construct $\\\\mathcal{D}_{train}$.\\n\\n$$ $\\\\displaystyle\\\\mathrm{Inf}_{\\\\mathrm{Adam}}(\\\\bm{z},\\\\mathcal{D}_{\\\\mathrm{val}}^{( j)})=\\\\sum_{i=1}^{N}\\\\bar{\\\\eta}_{i}\\\\frac{\\\\langle\\\\bar{\\\\nabla}\\\\ell(\\\\mathcal{D}_{ \\\\mathrm{val}}^{(j)};\\\\bm{\\\\theta}_{i}),\\\\tilde{\\\\Gamma}(\\\\bm{z},\\\\bm{\\\\theta}_{i}) \\\\rangle}{\\\\|\\\\bar{\\\\nabla}\\\\ell(\\\\mathcal{D}_{\\\\mathrm{val}}^{(j)};\\\\bm{\\\\theta}_{i}) \\\\|\\\\|\\\\tilde{\\\\Gamma}(\\\\bm{z},\\\\bm{\\\\theta}_{i})\\\\|}$ (1) $$\\n\\nIFD introduced the Instruction-Following Difficulty\\n(IFD) score, a metric devised to evaluate the challenge each instructional sample presents (Li et al., ). Given a $(Q,A)$ pair, they calculated the ratio between $s(A)$ and $s(A|Q)$:\\n\\n$$ $\\\\displaystyle\\\\mathrm{IFD}(Q,A)=\\\\frac{s(A|Q)}{s(A)}=\\\\frac{-\\\\frac{1}{N}\\\\sum_{i=1 }^{N}\\\\log P(x_{i}^{A}|Q,x_{1}^{A},x_{2}^{A},\\\\ldots,x_{i-1}^{A})}{-\\\\frac{1}{N} \\\\sum_{i=1}^{N}\\\\log P(x_{i}^{A}|x_{1}^{A},\\\\ldots,x_{i-1}^{A})}$ (2) $$\\n\\nwhere $s(A)$ means Direct Answer\\nScore, which measures LLM’s ability to generate the answer alone.\\n$s(A|Q)$ means Conditioned Answer Score, which is calculated by continuously\\npredicting the next tokens given the instruction $Q$\\nand their proceeding words.\\n\\nIn this paper, the authors first generated 100 clusters on instruction embeddings and sampled 10 instances in each cluster based on IFD score on pre-trained base LLM. Then they trained that LLM for 1 epoch by using the selected datapoints. After training, they calculated the IFD score of each datapoint of the whole training set $\\\\mathcal{D}$ and finally selected the highest IFD score data as $\\\\mathcal{D}_{train}$.\\n\\nSelectIT selected high-quality\\nIT data based on the intrinsic uncertainty reflected by\\nLLMs (Liu et al., ). It included three grains of sample evaluation modules: token, sentence, and model level self-reflections.\\n\\nFor token level, SelectIT calculated the\\nprobability of the next token (from $1$ to $K$) based on the rating prompt $RP$ and query-response pair $E$. The score token with the highest probability was then considered as the quality of the sample. The higher $P^{{}^{\\\\prime}}_{E^{base}}$, the more confidence\\nof LLMs\\n\\n$$ $\\\\displaystyle E^{base}=\\\\text{ arg max }P_{k}^{\\\\prime},P_{k}^{\\\\prime}=\\\\left( \\\\frac{e^{P_{k}}}{\\\\sum_{j=1}^{K}e^{P_{j}}}\\\\right)$ (3) $$\\n\\nwhere $P_{k}$ and $P_{k}^{{}^{\\\\prime}}$ mean the probability and softmax probability of token $k$. K means the number of scores to be considered. In that paper, the score token ranged from $1$ to $5$. To enhance the credibility of quality assessment, SelectIT assessed the average disparity between the predicted token $E^{base}$ and the other, where the greater the disparity, the greater the confidence of the LLM.\\n\\n$$ $\\\\displaystyle E^{token}=E^{base}\\\\times\\\\frac{1}{K-1}\\\\sum_{i=1}^{K}|P_{i}^{ \\\\prime}-P_{E^{base}}^{\\\\prime}|$ (4) $$\\n\\nFor sentence level, since different prompts can significantly affect outputs of LLMs, it designed $K$ semantically similar rating prompts $\\\\{RP_{0},RP_{1},\\\\ldots,RP_{K}\\\\}$ and obtained a series of quality scores $\\\\{E_{0}^{token},E_{1}^{token},\\\\ldots,E_{K}^{token}\\\\}$, respectively.\\n\\n$$ $\\\\displaystyle E^{sent}=\\\\frac{\\\\mathbf{Avg}\\\\{E_{i}^{token}\\\\}_{i=1}^{K}}{1+\\\\alpha \\\\times\\\\mathbf{Std}\\\\{E_{i}^{token}\\\\}_{i=1}^{K}}$ (5) $$\\n\\nwhere $\\\\mathbf{Avg\\\\{\\\\cdot\\\\}}$ and $\\\\mathbf{Std\\\\{\\\\cdot\\\\}}$ denote the\\nmean and standard deviation of $E_{i}^{token}$, respectively. $K$ means the number of rating prompts $RP$.\\n\\nFor model level, SelectIT used $N$ foundation models with parameter counts $\\\\{\\\\beta_{1},\\\\beta_{2},\\\\ldots,\\\\beta_{N}\\\\}$ and their respective sentence-level scores for a sample E being\\n$\\\\{E_{0}^{sent},E_{1}^{sent},\\\\ldots,E_{N}^{sent}\\\\}$, then the model-level\\nscore $E_{model}$ was computed as follows.\\n\\n$$ $\\\\displaystyle E^{model}=\\\\sum_{i=1}^{N}\\\\left(\\\\frac{\\\\beta_{i}}{\\\\sum_{j=1}^{N} \\\\beta_{j}}\\\\times E_{i}^{sent}\\\\right)$ (6) $$\\n\\nwhere $N$ means the number of the foundation models.\\nIt used $E_{model}$ as the final evaluation of sample $E$ in SelectIT.\\n\\nCross-entropy: Language models can be considered a form of compression, with LLMs showing strong capabilities in data compression empirically (Delétang et al., ).\\nCompression efficiency is a stable and reliable assessment that is linearly related to the model’s capabilities. It reflects the model’s ability to extract relevant information and eliminate unnecessary elements, providing insight into the intrinsic capability of the language model (Huang et al., ; Wei et al., ).\\n\\nThe cross-entropy loss employed in the training of LLMs establishes a coherent relationship between LLMs and information compression of each query-response pair $E$.\\n\\n$$ $\\\\displaystyle\\\\mathbb{E}_{x^{E}\\\\sim\\\\rho}[-\\\\sum_{i=1}^{n}\\\\log_{2}\\\\rho_{model}(x^ {E}_{i}|x^{E}_{1:i-1})]$ (7) $$\\n\\nInspired by this foundational insight, we select data based on the cross-entropy of each datapoint, where the higher value of cross-entropy means the better quality.\\n\\n### 3.2 Diversity-based Selections\\n\\nIn this section, we introduce methods that emphasize\\nthe diversity of instruction datasets, where diversity refers to the overall diversity of the entire training dataset.\\n\\nDiverseEvol iteratively sampled training subsets to improve its own performance (Wu et al., ). It selected new data points most distinct from any existing ones according to its current embedding space in each iteration phase.\\n\\nGiven a training set $\\\\mathcal{D}$, DiverseEvol first randomly selected a data pool $P_{0}$ and trained an initial model $M_{0}$. In each iteration, it consisted of two operations: 1. Deduce new data points $\\\\mathcal{D}_{t}$ to merge into $P_{t+1}$, informed by the previously trained model $M_{t}$. 2.\\nTrain the subsequent chat model $M_{t+1}$, with the\\nupdated data pool $P_{t+1}$.\\n\\nDiverseEvol used K-Center-Sampling to select data.\\nFrom a candidate pool, it chose $k$ data points in such a way that the distances to their respective nearest existing training data points were maximized.\\n\\n$$ $\\\\displaystyle\\\\arg\\\\max_{i\\\\in N_{t}}\\\\min_{j\\\\in P_{t}}\\\\Delta\\\\left(\\\\mathbf{n}_{i}, \\\\mathbf{p}_{j}\\\\right)$ (8) $$\\n\\nAt each step, the input parameters to K-Center-Sampling were the model $M_{t}$, the current training pool $P_{t}$, and $\\\\mathcal{D}_{t}$. The selection function K-Center-Sampling then outputs the new data point $N_{t}$, which was added to the training pool for the next iteration $P_{t+1}$.\\n\\nZIP presented that model performance is negatively correlated to the compression ratio of training data, which usually yields a lower\\ntraining loss. Yin et al. () proposed a quite efficient and universal data selection method named ZIP for training LLMs, which aimed to\\nprioritize data subsets exhibiting a low compression ratio.\\n\\nZIP is initialized by calculating the\\nsample-level compression ratio for the entire dataset $\\\\mathcal{D}$, where $\\\\pi_{\\\\mathcal{D}}$ shows the information redundancy state of $\\\\mathcal{D}$.\\nIn each iteration, it selected $K_{1}$ samples with the lowest $\\\\pi_{\\\\mathcal{D}_{1}}$ to form an initial candidate pool $\\\\mathcal{D}_{K_{1}}$.\\nThen, it calculated the compression ratio of a merged set that adds each sample in $\\\\mathcal{D}_{K_{1}}$ to the selected set $\\\\mathcal{D}_{train}$, to update the redundancy state of the information $\\\\pi_{\\\\mathcal{D}_{1}}$.\\n\\nBased on the scores of the samples in $\\\\mathcal{D}_{K_{1}}$, ZIP selected $\\\\mathcal{D}_{K_{2}}$ samples with the lowest scores.\\nAfter that, it initialized an empty selected set $\\\\mathcal{D}_{K_{3}}$, and computed the compression ratio of the union of $\\\\mathcal{D}_{K_{3}}$ and each sample in $\\\\mathcal{D}_{K_{2}}$. Then, the sample with the lowest compression ratio was added to $\\\\mathcal{D}_{K_{3}}$, and removed from $\\\\mathcal{D}_{K_{2}}$.\\nFinally, each sample in $\\\\mathcal{D}_{K_{3}}$ was added to the selected set $\\\\mathcal{D}_{train}$. In ZIP, the compression ratio calculation $g(\\\\mathcal{C}(D))$ is defined as:\\n\\n$$ $\\\\displaystyle g(\\\\mathcal{C}(D))=\\\\frac{\\\\mathrm{Bits}(D)}{\\\\mathrm{Bits}(\\\\mathcal {C}(D))}$ (9) $$\\n\\n## 4 Experiment\\n\\n### 4.1 Datasets\\n\\nIn practical applications, researchers frequently encounter extensive datasets from various sources during SFT, which may also contain imperfections. Thus, in this study, rather than using the typically employed IT datasets such as alpaca (Taori et al., ), we select two large-scale IT datasets at the million-record level, Openhermes2.5 (Teknium, ) and WildChat-1M (Zhao et al., ), to examine the efficiency of existing data selection techniques in handling large datasets and to assess their performance in real-world scenarios.\\n\\nOpenhermes2.5 is presented by Teknium (), which comprises over 1 million data points. It is significantly more comprehensive and of higher quality, predominantly consisting of generated guides and chats. The dataset’s information is sourced from 16 distinct origins, including metamath (Yu et al., ), CamelAI (Li et al., ), among others. It encompasses a wide variety of subjects such as mathematics, programming, and authentic user dialogues.\\n\\nWildChat-1M is introduced by Zhao et al. () and features solely non-toxic user inputs and ChatGPT responses. The dataset comprises 1 million dialogues between human users and ChatGPT, with 25.53% of the interactions stemming from the GPT-4 model, and the remainder from GPT-3.5. It encompasses a diverse range of user-chatbot exchanges, including ambiguous user inquiries, code-switching, topic-switching, and political discussions. In this study, we extract English dialogues from the WildChat dataset, resulting in over 440k interactions.\\n\\n### 4.2 Benchmarks\\n\\nTo thoroughly evaluate the capabilities of LLM, we explored various approaches across different downstream tasks.\\nWe assess the reasoning abilities of LLMs using two commonly used datasets: the Grade School Math dataset (GSM) (Cobbe et al., ) and Big-Bench-Hard (BBH) (Suzgun et al., ) within the CoT setting (Wei et al., ).\\nWe evaluate the code generation capability with the HumanEval dataset (Chen et al., ) and report pass@1 results.\\nTo determine the factual knowledge of LLMs, we use the Massive Multitask Language Understanding dataset (MMLU) (Hendrycks et al., ) and provide 5-shot results.\\nWe also assess instruction-following ability using the IFEval (Zhou et al., ) dataset and report both strictly and loosely followed scores. Additionally, we utilize scripts from OpenInstruct, which includes a collection of standard benchmarks focusing on core capabilities (Wang et al., ; Ivison et al., ; ).\\n\\n### 4.3 Implementation Details\\n\\nSpecifically, we leverage the widely-used LLaMA3-8B (AI@Meta, ) and Qwen2-7B (qwe, ) as our base models, and fine-tune them using the Llama-Factory framework (Zheng et al., ). We train these models for 3 epochs with a batch size of 128. Our training process employs a cosine learning rate scheduler beginning at $7e-6$, which decays to 0.1, warms to 0.01, and utilizes an input length of 4096. To replicate our baseline methods on Openhermes and WildChat, we adjust some original parameters and implementations to fit the large-scale datasets.\\n\\nIn term of LESS, individual models are built and trained on specific tasks. However, in practical applications, our goal is to train a model that enhances performance across various scenarios. Thus, given that the two datasets we select are both extensive and diverse, we randomly select 1000 data points from each dataset as $\\\\mathcal{D}_{val}$. Additionally, due to the volume of our data, we randomly pick 10,000 data points for warm-up training, differing from the method described in (Xia et al., ).\\n\\nAs for IFD, we initially generate 1000 clusters on instruction embeddings, which differs from the settings given in Li et al. (). For SelectIT, we adopt model-level selection as the final strategy for the Qwen2 model and evaluate the model-level score on Qwen2-1.5B and Qwen2-7B. While for Llama3, we employ sentence-level selection as the final approach. Considering that the Llama3 family only has two public variants, Llama3-8B and Llama3-70B, and to mitigate time costs, we compute the score based solely on Llama3-8B.\\n\\nWithin DiverseEvol, during each iteration’s K-Center-Sampling stage, data points are selected based on maximizing their distance to the nearest existing training data points, one at a time, until the desired count is reached. Consequently, it is essential to maintain a $n\\\\times n$ float-type matrix for the entire computation, where $n$ represents the dataset size. Given that our OpenHermes dataset exceeds 1 million entries, the matrix calculation would require more than 1 terabyte of memory. Therefore, we revised this part to select all required data points once for each iteration, which significantly reduces the memory requirement.\\n\\n## 5 Discussion\\n\\n### 5.1 Baseline Methods vs Random\\n\\nIn this section, we reproduce all baseline methods in experiments involving LLaMA3-8B and Qwen2-7B on OpenHermes2.5, the experimental results are presented in Table 1, and results on WildChat are detailed in Table 2. We assess LLaMA3-8B and Qwen2-7B with and without fine-tuning on the entire dataset. All mentioned SFT data selection methods are employed to select 10,000 samples as described in Section 4.3. We randomly run 5 times and all of the results are provided in the tables. Furthermore, 50,000 samples obtained through various methods are also shown in the Appendix Table 5, 6.\\n\\nAs indicated in Table 1 and 2, it is evident that when dealing with extensive and diverse IT datasets, no data selection techniques consistently outperform random sampling by a substantial margin, which implies that the average score exceeds the random score by more than 1%.\\nIn most cases, the results of the baseline method are within the range of the results obtained by 5 random runs, and a few methods are even worse than the worst random result, For instance, when evaluating Cross-Entropy on Qwen2-7B using Openhermes2.5, the average result is a mere 54.02, significantly below the lowest score of 57.04 obtained in the 5 random trials.\\n\\nBased on the experimental results, when dealing with an extensive SFT dataset, it is more efficient to randomly select training data instead of spending significant time and resources to meticulously choose seemingly optimal training data. Random selection reduces costs and yields superior training results.\\n\\n**Table 1: The overall results(%) on a variety of downstream tasks based on Openhermes2.5 dataset. CODE means HumanEval, Random $n$ denotes the $n$th random selection. Except for fine-tuning with the entire Openhermes dataset, the bold numbers indicate the best score of each part, and the underlined numbers indicate the suboptimal score.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| Base | 59.07 | 72.40 | 55.67 | 70.20 | 28.84 | 31.24 | 52.90 | 60.93 | 55.12 | 37.59 | 65.30 | 19.41 | 21.07 | 43.24 |\\n| all data | 61.39 | 80.12 | 63.32 | 68.50 | 40.85 | 44.18 | 59.73 | 63.33 | 73.24 | 46.43 | 63.90 | 46.40 | 49.72 | 57.17 |\\n| Random 1 | 59.72 | 82.41 | 62.10 | 68.30 | 33.27 | 36.41 | 57.04 | 64.72 | 53.90 | 45.21 | 63.20 | 39.19 | 43.62 | 51.64 |\\n| Random 2 | 61.48 | 83.47 | 64.33 | 67.90 | 38.08 | 40.30 | 59.26 | 60.83 | 56.86 | 48.99 | 62.70 | 41.77 | 45.47 | 52.77 |\\n| Random 3 | 61.85 | 81.65 | 62.90 | 68.10 | 36.78 | 38.45 | 58.29 | 63.43 | 59.74 | 46.83 | 62.70 | 43.25 | 46.21 | 53.69 |\\n| Random 4 | 61.20 | 82.71 | 59.27 | 68.00 | 36.60 | 39.19 | 57.83 | 63.98 | 59.59 | 45.18 | 63.80 | 44.36 | 47.13 | 54.01 |\\n| Random 5 | 61.30 | 82.71 | 62.23 | 68.90 | 35.86 | 37.71 | 58.12 | 62.31 | 56.10 | 42.07 | 63.50 | 44.55 | 48.80 | 52.89 |\\n| LESS | 61.20 | 81.65 | 53.26 | 67.60 | 32.16 | 37.15 | 55.50 | 61.39 | 57.70 | 41.43 | 64.20 | 38.08 | 41.96 | 50.79 |\\n| IFD | 57.96 | 79.23 | 68.48 | 56.70 | 33.27 | 35.12 | 55.13 | 57.41 | 53.53 | 32.41 | 59.90 | 43.07 | 45.84 | 48.69 |\\n| SelectIT | 59.17 | 80.44 | 66.46 | 67.20 | 35.86 | 38.82 | 57.99 | 62.59 | 61.56 | 42.38 | 63.60 | 38.45 | 42.14 | 51.79 |\\n| Entropy | 61.30 | 55.04 | 61.04 | 68.90 | 37.34 | 40.48 | 54.02 | 58.61 | 50.72 | 44.02 | 61.40 | 32.90 | 37.89 | 47.59 |\\n| Diverse | 61.11 | 81.73 | 61.71 | 68.65 | 40.85 | 43.44 | 59.58 | 65.00 | 56.25 | 44.51 | 63.84 | 43.99 | 47.13 | 53.45 |\\n| ZIP | 60.65 | 80.52 | 66.10 | 68.60 | 37.15 | 39.56 | 58.76 | 63.98 | 59.67 | 40.70 | 62.60 | 43.81 | 46.58 | 52.89 |\\n\\n**Table 2: The overall results(%) on a variety of downstream tasks based on WildChat dataset. CODE means HumanEval, Random $n$ denotes the $n$th random selection. Except for fine-tuning with the entire Openhermes dataset, the bold numbers indicate the best score of each part, and the underlined numbers indicate the suboptimal score.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| Base | 59.07 | 72.40 | 55.67 | 70.20 | 28.84 | 31.24 | 52.90 | 60.93 | 55.12 | 37.59 | 65.30 | 19.41 | 21.07 | 43.24 |\\n| all data | 62.87 | 80.82 | 62.84 | 68.70 | 45.84 | 48.80 | 61.65 | 63.70 | 56.94 | 47.44 | 63.30 | 46.40 | 49.72 | 54.58 |\\n| Random 1 | 61.30 | 82.64 | 61.98 | 68.10 | 40.30 | 42.33 | 59.44 | 63.70 | 56.48 | 51.92 | 63.30 | 39.37 | 41.95 | 52.79 |\\n| Random 2 | 60.93 | 81.96 | 61.43 | 67.50 | 38.63 | 40.67 | 58.52 | 62.41 | 52.62 | 49.33 | 64.00 | 44.18 | 46.77 | 53.22 |\\n| Random 3 | 60.28 | 82.64 | 62.07 | 68.30 | 41.04 | 42.88 | 59.54 | 63.52 | 58.38 | 43.90 | 64.10 | 42.33 | 45.29 | 52.92 |\\n| Random 4 | 61.11 | 80.36 | 65.46 | 67.50 | 37.34 | 40.67 | 58.74 | 63.33 | 55.42 | 51.10 | 64.50 | 41.96 | 44.55 | 53.48 |\\n| Random 5 | 61.57 | 81.50 | 60.27 | 68.20 | 41.77 | 43.99 | 59.55 | 64.91 | 60.27 | 48.66 | 64.30 | 42.14 | 45.84 | 54.35 |\\n| LESS | 52.59 | 60.50 | 61.19 | 68.00 | 38.82 | 41.77 | 53.81 | 63.43 | 57.01 | 50.43 | 64.50 | 40.85 | 44.92 | 53.52 |\\n| IFD | 60.56 | 76.27 | 65.24 | 68.00 | 36.23 | 38.26 | 57.43 | 63.33 | 59.29 | 47.16 | 64.60 | 40.30 | 43.81 | 53.08 |\\n| SelectIT | 60.37 | 82.34 | 64.97 | 68.50 | 36.97 | 39.19 | 58.72 | 61.48 | 53.22 | 46.01 | 63.20 | 40.11 | 42.88 | 51.15 |\\n| Entropy | 60.37 | 81.96 | 62.90 | 68.40 | 42.51 | 46.21 | 60.39 | 63.15 | 56.10 | 47.71 | 63.00 | 45.10 | 49.54 | 54.10 |\\n| Diverse | 61.02 | 80.82 | 65.09 | 67.33 | 41.04 | 42.88 | 59.70 | 62.59 | 53.30 | 33.48 | 64.46 | 47.87 | 50.65 | 52.06 |\\n| ZIP | 62.59 | 81.80 | 68.17 | 68.00 | 40.11 | 42.33 | 60.50 | 62.31 | 60.96 | 46.58 | 64.50 | 45.10 | 48.06 | 54.59 |\\n\\n**Table 3: The overall results (%) of token length selection.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| OpenHermes | 60.65 | 80.74 | 60.18 | 68.33 | 37.89 | 41.40 | 58.20 | 64.63 | 61.33 | 45.70 | 64.41 | 48.43 | 52.87 | 56.23 |\\n| WildChat | 61.67 | 81.05 | 59.21 | 67.82 | 39.56 | 42.14 | 58.58 | 66.11 | 60.35 | 51.16 | 63.91 | 43.81 | 47.69 | 55.51 |\\n\\n### 5.2 Quality vs Diversity\\n\\nTables 1 and 2 demonstrate that the diversity-based selection strategy outperforms the quality-based one. To examine whether prioritizing diversity over data quality improves data selection, we designed a supplementary experiment by incorporating a K-means clustering process on the OpenHermes dataset. Instead of selecting data based solely on method scores, we choose higher-scoring data within each cluster to boost the final training set’s diversity.\\n\\nTable 4 illustrates that integrating the K-means clustering with quality-based selection methods enhances the effectiveness for most approaches. Notably, Cross Entropy on both Llama3 and Qwen2 models shows improvement over 5% and 3%, respectively, when K-means is used to diversify the data. This suggests that for a large-scale IT dataset, data diversity holds more significance than data quality. This also clarifies why random selection often outperforms most SFT data selection methods, as the random process preserves the dataset’s original distribution and diversity to the greatest possible extent.\\n\\n**Table 4: The overall results (%) on a variety of downstream tasks based on Openhermes2.5 dataset. Methodkm means method with kmeans process. The bold number indicates the avg performance increase after add K-means phase.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| LESS | 61.20 | 81.65 | 53.26 | 67.60 | 32.16 | 37.15 | 55.50 | 61.39 | 57.70 | 41.43 | 64.20 | 38.08 | 41.96 | 50.79 |\\n| IFD | 57.96 | 79.23 | 68.48 | 56.70 | 33.27 | 35.12 | 55.13 | 57.41 | 53.53 | 32.41 | 59.90 | 43.07 | 45.84 | 48.69 |\\n| SelectIT | 59.17 | 80.44 | 66.46 | 67.20 | 35.86 | 38.82 | 57.99 | 62.59 | 61.56 | 42.38 | 63.60 | 38.45 | 42.14 | 51.79 |\\n| Entropy | 61.30 | 55.04 | 61.04 | 68.90 | 37.34 | 40.48 | 54.02 | 58.61 | 50.72 | 44.02 | 61.40 | 32.90 | 37.89 | 47.59 |\\n| LESSkm | 61.30 | 81.96 | 54.63 | 67.79 | 34.38 | 38.26 | 56.39 | 60.93 | 50.27 | 48.11 | 63.97 | 39.74 | 44.55 | 51.26 |\\n| IFDkm | 60.19 | 78.77 | 59.70 | 66.81 | 30.31 | 31.79 | 54.60 | 60.74 | 58.98 | 40.37 | 62.95 | 40.67 | 42.70 | 51.07 |\\n| SelectITkm | 60.93 | 82.34 | 61.04 | 67.85 | 36.78 | 39.19 | 58.02 | 62.96 | 59.36 | 40.85 | 63.43 | 39.74 | 43.07 | 51.57 |\\n| Entropykm | 60.37 | 81.12 | 59.27 | 68.55 | 35.67 | 38.45 | 57.24 | 61.02 | 61.64 | 48.32 | 61.12 | 39.00 | 43.99 | 52.52 |\\n\\nFigure: Figure 2: The average score(%) of each methods on Llama3 and Qwen2.\\nRefer to caption: x2.png\\n\\n### 5.3 Baseline Analysis\\n\\nIn this part, we mainly analyze several methods and try to find the reasons why these methods fail in large-scale data sets and why these methods are not applicable to practical applications.\\n\\nThe lack of availability of Less is primarily evident in how its influence score is calculated. Since it requires computing the score for the final data point in the target task, it is essential to meticulously design a target set for each task to filter the data. However, in practical applications, we face a variety of training tasks that require our target data to be comprehensive and diverse. Hence, the effectiveness of LESS is strongly related to the quality of $\\\\mathcal{D}_{val}$.\\n\\nThe IFD approach determines the ultimate IFD score by evaluating the perplexity (ppl) of the response. However, the length of the data significantly affects the ppl value. In particular, shorter data tend to produce excessively high ppl values, which contradicts with our expected results. Ultimately, we note that the IT data instructions selected by the IFD approach are quite brief, averaging merely 42 tokens on Openhermes, which aligns with the findings reported by Liu et al. ().\\n\\nSelectIT can perform well at the model level, but it necessitates combining LLMs with various sizes to score the data. As IT datasets become larger, the computational cost required for LLMs with more parameters tends to increase exponentially, which limits their applicability to extensive datasets.\\n\\nCross-entropy is influenced by the length of responses. Typically, cross-entropy favors data with lengthy responses, whereas it shows no specific preference towards instructions. Consequently, the training samples will include simple instructions but extensive responses.\\n\\nIn addition, in this article, we do not use NUGGETS (Li et al., ) as our baseline method. During our experimentation, we discover that the computational time for NUGGETS is significantly higher compared to other methods. Even with 40 A100 80G GPUs, it requires over 2,000 hours to perform the calculations. Given this high time cost, we decide to abandon this method.\\n\\nThe diversity-based approach usually outperforms the quality-based selection methods, however, one main issue with the diversity-based approach is its time and memory consumption.\\n\\nTo reproduce DiverseEvol, we utilized 8 A100 80G resources and consistently performed 3 iterations. However, each iteration requires 1-2 days, totaling 5-7 days to choose the final training subset. When dealing with large-scale data sets, the results often fall within the random range, though optimal results occur sporadically. This may be due to modifications in our implementation to address memory constraints during replication (see Section 4.3), which may have slightly diminished the method’s performance.\\n\\nIn contrast, ZIP does not need GPU resources, but the computing process is greedy. It incrementally adds 100 data at a time to the final training subset. For large data scales, it takes approximately 7 days to select 50,000 data. In addition, ZIP serves as a data selection method that operates independently of the model, meaning that the selected data cannot be adaptively tuned on the basis of the model. As illustrated in Tables 1 and 2, the data chosen by ZIP in OpenHermes perform poorly in both Llama3-8B and Qwen2-7B, whereas the data selected in WildChat exhibit the best performance across these models.\\n\\nMoreover, we attempt to utilize DQ (Zhou et al., ) as our baseline method. However, DQ uses a submodular strategy to choose a subset by optimizing submodular gains within the feature space. When dealing with millions of data points, it requires more than 1TB memory resources. Eventually, we decide to forgo this approach.\\n\\n### 5.4 Which method is the best?\\n\\nBy examining the average results of all methods, we notice that the majority of methods perform better with WildChat as the data source compared to OpenHermes, as illustrated in Figure 2, which is rather unexpected. Nonetheless, from a quality perspective, WildChat’s conversation data tends to be noisy, particularly since the context of multiple conversation rounds is sometimes unrelated, while OpenHermes’s data quality should be substantially higher than WildChat. However, the performance of the same data selection methods on these two types of data contradicts with our expectations. It is observed that the average token length for WildChat data is 1142, whereas for OpenHermes data, it is 354. Drawing inspiration from the work of Shen (), we devise a new experiment concentrating on data selection by token length. Initially, we obtain $N$ clusters through the K-Means process and subsequently select a certain amount of data based on the token length from each cluster proportional to its size. The results are presented in Table 3.\\n\\nBased on Table 3, it is evident that using token length as the criterion for data selection generally yields optimal results. Specifically, for Llama3, regardless of whether the data source is OpenHermes or WildChat, the results are significantly superior to those achieved by other methods. In addition, the average score on WildChat ($55.51$) surpasses that obtained by fine-tuning with the entire dataset ($54.58$).\\n\\nSelecting data by token length can stably obtain a relatively high training benefit, reduce the uncertainty caused by randomness, and reduce costs. This approach is particularly beneficial for BASE language models which generally have limited capabilities, as they tend to derive the most significant benefits from training on longer texts.\\n\\n## 6 Conclusion\\n\\nIn this study, we observe that many SFT data selection methods depend on small-scale data sets, which do not meet the actual needs in real-world scenarios. This finding makes us rethink whether SFT data selection methods can work when they are required to handle large-scale IT datasets. We reproduce some existing self-scoring data selection approaches that do not need external LLMs’ support on two million-scale datasets and find that almost all present methods do not significantly surpass random selection when dealing with large-scale datasets. Moreover, our analyses show that during the SFT phase, data diversity in data selection plays a more significant role than data quality. In addition, using token length as the quality metric is more appropriate for SFT data selection compared to other carefully crafted quality metrics.\\n\\n## Appendix A Appendix\\n\\nIn this section, table 5, 6 includes training results of various methodologies with a training dataset comprising 50,000 entries 5, 6.\\n\\n**Table 5: The comprehensive results (%) on various downstream tasks using OpenHermes. Mention that CODE means Humaneval. Algorithmkm means the algorithm has a Kmeans process, and Randomx denotes the xth random selection. The bold numbers indicate the best avg score of each part, and the underlined numbers indicate the suboptimal score.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| Base | 59.07 | 72.40 | 55.67 | 70.20 | 28.84 | 31.24 | 52.90 | 60.93 | 55.12 | 37.59 | 65.30 | 19.41 | 21.07 | 43.24 |\\n| all data | 61.39 | 80.12 | 63.32 | 68.50 | 40.85 | 44.18 | 59.73 | 63.33 | 73.24 | 46.43 | 63.90 | 46.40 | 49.72 | 57.17 |\\n| Random1 | 62.87 | 80.67 | 62.44 | 68.33 | 34.75 | 38.08 | 57.86 | 63.89 | 64.37 | 46.19 | 62.75 | 45.10 | 49.72 | 55.34 |\\n| Random2 | 61.11 | 80.82 | 65.76 | 68.12 | 38.08 | 40.67 | 59.09 | 62.13 | 66.57 | 47.32 | 61.57 | 46.58 | 49.54 | 55.62 |\\n| Random3 | 61.02 | 81.35 | 60.15 | 68.54 | 38.63 | 40.85 | 58.42 | 65.65 | 63.53 | 44.05 | 61.96 | 42.51 | 46.21 | 53.99 |\\n| Random4 | 60.37 | 80.06 | 55.98 | 68.95 | 37.34 | 40.30 | 57.17 | 62.78 | 62.40 | 45.12 | 62.41 | 47.87 | 50.83 | 55.24 |\\n| Random5 | 60.19 | 80.14 | 63.29 | 69.16 | 38.08 | 40.85 | 58.62 | 64.72 | 65.13 | 45.18 | 62.51 | 45.47 | 49.17 | 55.36 |\\n| LESS | 60.46 | 80.29 | 58.66 | 67.40 | 39.00 | 43.25 | 58.18 | 61.02 | 57.85 | 17.01 | 63.01 | 40.30 | 46.40 | 47.60 |\\n| IFD | 57.50 | 80.52 | 67.13 | 66.79 | 35.86 | 38.08 | 57.65 | 61.94 | 52.84 | 44.63 | 63.36 | 41.04 | 43.99 | 51.30 |\\n| SelectIT | 60.56 | 79.98 | 62.77 | 67.96 | 36.04 | 39.00 | 57.72 | 61.20 | 64.22 | 40.03 | 62.40 | 41.96 | 44.92 | 52.46 |\\n| Entropy | 60.83 | 77.56 | 59.24 | 69.02 | 36.78 | 39.56 | 57.17 | 60.65 | 55.50 | 49.02 | 57.51 | 47.13 | 51.02 | 53.47 |\\n| Diverse | 61.67 | 81.35 | 61.89 | 68.60 | 44.55 | 46.40 | 60.74 | 63.33 | 61.11 | 48.75 | 63.62 | 46.21 | 49.17 | 55.37 |\\n| zip | 59.81 | 82.03 | 68.48 | 68.08 | 35.67 | 38.26 | 58.72 | 63.89 | 57.92 | 42.65 | 62.58 | 43.25 | 46.95 | 52.87 |\\n| LESSkm | 61.20 | 81.88 | 54.51 | 67.77 | 32.90 | 36.60 | 55.81 | 61.02 | 59.44 | 47.04 | 63.35 | 42.14 | 47.32 | 53.39 |\\n| IFDkm | 59.81 | 78.92 | 60.55 | 67.09 | 28.65 | 31.24 | 54.38 | 63.43 | 63.23 | 43.41 | 61.19 | 40.11 | 43.81 | 52.53 |\\n| SelectITkm | 61.20 | 81.20 | 66.52 | 69.10 | 34.57 | 38.45 | 58.51 | 61.85 | 61.49 | 45.76 | 61.64 | 43.44 | 48.43 | 53.77 |\\n| Entropykm | 61.02 | 80.82 | 66.04 | 68.25 | 36.78 | 39.37 | 58.71 | 61.85 | 64.22 | 48.66 | 61.85 | 42.70 | 46.58 | 54.31 |\\n| Lengthkm | 60.46 | 83.62 | 63.35 | 68.79 | 38.26 | 41.59 | 59.35 | 65.09 | 62.70 | 47.29 | 62.73 | 45.10 | 49.17 | 55.35 |\\n\\n**Table 6: The comprehensive results (%) on various downstream tasks using WildChat. Mention that CODE means Humaneval. Algorithmkm means the algorithm has a Kmeans process, and Randomx denotes the xth random selection. The bold numbers indicate the best avg score of each part, and the underlined numbers indicate the suboptimal score.**\\n| | Qwen2-7B | Llama3-8B | | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | BBH | GSM | CODE | MMLU | IFEVAL | AVG | BBH | GSM | CODE | MMLU | IFEVAL | AVG | | |\\n| | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | 3 shot | 8 shot | pass 1 | 5 shot | strict | loose | | |\\n| Base | 59.07 | 72.40 | 55.67 | 70.20 | 28.84 | 31.24 | 52.90 | 60.93 | 55.12 | 37.59 | 65.30 | 19.41 | 21.07 | 43.24 |\\n| all data | 62.87 | 80.82 | 62.84 | 68.70 | 45.84 | 48.80 | 61.65 | 63.70 | 56.94 | 47.44 | 63.30 | 46.40 | 49.72 | 54.58 |\\n| Random1 | 61.85 | 81.50 | 60.55 | 68.02 | 40.48 | 42.70 | 59.18 | 63.61 | 55.72 | 48.90 | 64.07 | 42.51 | 45.66 | 53.41 |\\n| Random2 | 60.74 | 82.03 | 58.72 | 68.05 | 40.67 | 44.36 | 59.10 | 61.76 | 54.66 | 50.95 | 63.38 | 42.88 | 46.03 | 53.28 |\\n| Random3 | 59.07 | 81.35 | 64.45 | 67.63 | 41.77 | 44.92 | 59.87 | 63.98 | 55.42 | 53.11 | 63.33 | 43.81 | 46.77 | 54.40 |\\n| Random4 | 62.41 | 82.34 | 60.95 | 68.43 | 42.51 | 45.10 | 60.29 | 63.70 | 58.91 | 50.09 | 63.84 | 43.62 | 46.03 | 54.37 |\\n| Random5 | 61.30 | 82.49 | 59.05 | 67.60 | 42.70 | 44.92 | 59.68 | 64.54 | 55.65 | 49.91 | 64.16 | 42.70 | 45.84 | 53.80 |\\n| LESS | 58.80 | 81.35 | 66.95 | 68.10 | 41.04 | 43.99 | 60.04 | 63.43 | 57.01 | 50.43 | 64.50 | 40.85 | 44.92 | 53.52 |\\n| IFD | 59.44 | 81.50 | 66.46 | 67.90 | 38.45 | 40.85 | 59.10 | 63.33 | 59.29 | 47.16 | 64.60 | 40.30 | 43.81 | 53.08 |\\n| SelectIT | 60.74 | 84.23 | 60.49 | 69.24 | 41.04 | 44.36 | 60.02 | 61.48 | 53.22 | 46.01 | 63.20 | 40.11 | 42.88 | 51.15 |\\n| Entropy | 61.02 | 81.96 | 60.88 | 68.40 | 43.07 | 46.58 | 60.32 | 61.48 | 55.34 | 48.90 | 64.02 | 47.50 | 51.02 | 54.71 |\\n| Diverse | 59.81 | 82.03 | 67.10 | 68.00 | 41.77 | 44.36 | 60.51 | 65.09 | 56.18 | 38.81 | 63.03 | 44.36 | 47.13 | 52.43 |\\n| zip | 59.91 | 79.83 | 71.04 | 67.97 | 42.88 | 45.84 | 61.25 | 64.72 | 57.16 | 41.49 | 61.54 | 45.84 | 48.43 | 53.20 |\\n| LESSkm | 59.54 | 80.89 | 67.84 | 68.20 | 43.62 | 46.95 | 61.17 | 61.94 | 54.74 | 48.99 | 64.10 | 43.99 | 46.95 | 53.45 |\\n| IFDkm | 59.26 | 80.67 | 68.41 | 68.13 | 41.77 | 43.99 | 60.37 | 62.69 | 56.10 | 48.63 | 63.02 | 40.85 | 42.70 | 52.33 |\\n| SelectITkm | 60.46 | 83.17 | 59.39 | 68.79 | 39.93 | 43.07 | 59.14 | 61.20 | 54.89 | 45.88 | 63.50 | 43.99 | 48.06 | 52.92 |\\n| Entropykm | 60.93 | 82.79 | 59.82 | 67.01 | 39.19 | 42.14 | 58.65 | 63.06 | 58.45 | 45.73 | 63.85 | 41.04 | 45.10 | 52.87 |\\n| Lengthkm | 61.30 | 79.76 | 59.76 | 68.19 | 42.88 | 45.29 | 59.53 | 62.41 | 60.05 | 49.82 | 64.23 | 45.47 | 48.80 | 55.13 |\",\n \"metadata\": {\n \"authors\": [\n \"Yi Chang\",\n \"Junyang Lin\"\n ],\n \"title\": \"Rethinking Data Selection at Scale: Random Selection is Almost All You Need\",\n \"total_chars\": 46249,\n \"total_lines\": 338,\n \"updated_at\": \"2026-01-25T15:02:51.622451\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"Cc2sPQljz6","initial_rating":6,"confidence":3,"soundness":3,"contribution":2,"presentation":3,"summary":"In this paper authors proposed a data filtration technique for the SFT (supervised fine-tuning phase) of LLM training.\nRigorously testing existing SOTA methods that were proven to work on the small scale datasets, authors found that \nfiltering data by token length offers an efficient way for improving downstream results further. In addition to that authors demonstrated that SOTA methods fall short in quality when handling large-scale 1T datasets. Authors demonstrated that data diversity plays the most important role in the SFT phase, thus quality filtering is suboptimal.","strengths":"Constructing a high-quality multi-corpora dataset that is useful for training LLMs is a hard and important task. Input data is crucial for making a high-quality reliable and safe LLM at scale. Authors explore the topic of improving the dataset construction process and suggest a simplified framework that does not require rigorous data cleaning at scale. Considering that developing and using filtration techniques at scale might present computational challenges, this paper makes a significant contribution to the field with their simplified proposal.","weaknesses":"One of the challenges with assessing the quality of LLMs is the quality and generalizability of the downstream tasks. Majority of the times that amount of the overlap between training and downstream data can cause skewed assessments in the quality of data processing techniques. I could not find any statistics reported by the authors for the amount of the overlap present in their training corpuses and the downstream tasks. It is important to understand that before drawing any conclusions with regards to the data filtration techniques. \nIt might be the case that some of the filtration strategies are heavily biased towards the examples present in the downstream tasks, and not necessarily improve model's generazability qualities.","questions":"I would like to see the stats on the overlap present in the tokens from your SFT datasets and downstream tasks. It would also be useful to know whether any deduplication method was applied on top of the SFT datasets to eliminate the effect of model's memorization."},{"id":"4twc1auQh0","initial_rating":3,"confidence":4,"soundness":2,"contribution":3,"presentation":2,"summary":"This paper investigates the effectiveness of data selection methods for supervised fine-tuning (SFT) of Large Language Models (LLMs) at scale. Through extensive experimentation on million-scale datasets, the research reveals that most existing self-scoring data selection methods, which don't require external model assistance, fail to significantly outperform random selection when applied to large-scale data pools.","strengths":"1. This paper studies an interesting yet important task of selecting training data for supervised fine-tuning (SFT) in large language models.\n\n2. The experimental results reveal that various data selection methods struggle to significantly outperform random selection, a finding that will likely be beneficial to practitioners.","weaknesses":"1. Some of the conclusions presented are already established in existing literature. For instance, paper [1] has previously demonstrated the importance of data diversity in SFT data selection with large-scale datasets, while paper [2] has shown the effectiveness of selecting longer answers for data selection. It appears the authors overlooked these references, which limits the novelty and contribution of this work.\n\n2. Although the paper identifies that certain data selection methods fail to outperform random selection, it lacks a thorough analysis—either theoretical or empirical—explaining why these approaches underperform. This absence of deeper exploration reduces the overall depth and insight provided by the study, which is required by top-tier ML conferences.\n\n3. The paper does not provide a clear definition of what is an \"extensive SFT dataset.\" In practical applications, it remains unclear how to determine whether a dataset qualifies as \"extensive,\" which could lead to ambiguity in interpreting the paper's findings and recommendations.\n\n\n[1] Bukharin, Alexander, and Tuo Zhao. \"Data diversity matters for robust instruction tuning.\" arXiv preprint arXiv:2311.14736 (2023).\n\n[2] Zhao, Hao, et al. \"Long Is More for Alignment: A Simple but Tough-to-Beat Baseline for Instruction Fine-Tuning.\" Forty-first International Conference on Machine Learning.","questions":"See above."},{"id":"thiE3wsuYV","initial_rating":5,"confidence":4,"soundness":2,"contribution":3,"presentation":2,"summary":"This paper studies the efficacy of various data filtering strategies when applied to large-scale SFT datasets (i.e.., OpenHermes2.5, WildChat). While these same strategies often outperform random selection on smaller-scale SFT datasets they are shown to be surprisingly less impactful when applied to these larger-scale (state-of-the-art) open-source datasets. On these datasets, approaches that target diversity seem to be more effective than those that target quality. Finally, the authors test their own length-based filtering strategy, which outperforms the other methods when the base model is Llama3-8B.","strengths":"**Originality and Significance.** This paper performs a valuable and novel (to the best of my knowledge) empirical study to see whether existing SFT data selection methods remain effective when applied on larger SFT datasets. Because these larger SFT datasets are generally better than the smaller datasets these methods were previously tested on, it is important to see whether filtering works in this more state of the art regime. The main findings that (i) many of these methods no longer are as impactful; (ii) diversity is more important than quality-filtering are therefore quite significant and potentially highly-relevant to future SFT data curation efforts.\n\n**Quality.** This paper implements a good number of baselines and also is thorough about trying multiple base models and dataset sizes (post data selection). These variations are nice to test the robustness of the main takeaways.\n\n**Clarity.** Overall, most of the paper is easy to follow with the exception of the description of baseline methods (see W3).","weaknesses":"**(W1) Isolating dataset size.** A central claim in the paper is that dataset size is what causes differences in the behavior of the baselines. However, there are also other differences between OH2.5/WildChat and older datasets besides data quantity; e.g., quality-based selection may be less impactful simply because these larger datasets are already the result of more careful curation and thus higher-quality compared to older ones. An experiment that would better isolate data quantity (and control for quality) would be to run the existing experiments on progressively smaller random subsets of OH2.5/WildChat (e.g., what happens when the starting pool is 10K/100K examples of OH2.5 v.s. 1M?)\n\n**(W2) Understanding run-to-run variance / Fairness of comparison to random.** The stated takeaway from the results is that *\"it is more efficient to randomly select training data...random selection reduces costs and yields superior training results\"* but I don't know if that's fully borne out by the results.\n- For the Qwen2 results (which achieve highest overall perforamnce), in the 50K regime, the best average results are achieved by non-random curation methods (Diverse and ZIP each score 1% higher than the max over the random runs in Tables 5 and 6 respectively). In the 10K regime, this is also almost true with the exception of 1/5 of the random runs.\n- In general, I'm not sure its fair to compare the max over 5 random runs to a single run of a selection method. if only 1 of 5 runs ends up doing better, then in practice you'd likely have to try multiple times when randomly sampling a subset that outperforms non-random selection, increasing costs. \n- Ideally, it would be nice to show the average and stdev across the 5 random runs and to also get a sense of run-to-run variation for the non-random methods (though I acknowledge this might be costly). \n\n**(W3) Clarity when describing existing methods.** I currently found Sec 3. a bit hard to follow. It may be helpful to define up front unified notation for variables that appear in multiple methods instead of using the differing notation from each of the original papers (e.g. whether a sample is given by $z$ or $x$ or $n$). Also, in some places, symbols are currently used without an explicit definition (e.g. $\\hat{\\Gamma}$ in LESS, $\\mathcal{C}$ in ZIP). \n\n**Miscellaneous Notes**\n- In captions for Tables 1 and 2, \"the suboptimal score\" is confusing terminology, I believe you meant \"second highest score\"? \n- Given that originally LESS is a targeted selection method, I'm not sure it's completely aligned with the spirit of the original method to set the target as a subset of the overall data pool? I suspect what might be leading to bad performance is that this may actually result in selecting a less diverse dataset (by prioritizing examples that represent the majority).","questions":"(Q1) Could you share more details about Figure 1, given that the difference between small/large regimes is a key aspect of the paper? In particular, which datasets were used for the 10K-300K scale in Figure 1? Are these already random subsets of OH2.5/WildChat (basically what i suggested in W1) or are they some other datasets (e.g. Dolly, ShareGPT)?\n\n(Q2) What is the cost of the fine-tuning runs in your experiment setup? It would be helpful to know this relative to the costs of running the various data curation algorithms (when discussing them in 5.3)."},{"id":"NG18D9Ims8","initial_rating":5,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"In this paper, the authors study the effectiveness of data selection methods on large-scale datasets, which is largely unexplored. With experiments on large-scale datasets, the authors find that nearly existing data selection methods do not significantly outperform random selection on large-scale datasets. This paper also tries to explain the reason that leads to inferior performance of existing methods on a larger data pool. Ultimately, the authors propose a more effective data selection method based on token length. This paper offers researchers a new perspective on data selection in large language models.","strengths":"The authors study the effectiveness of data selection methods on large-scale datasets, and find the inferior performance of existing methods when dealing with large-scale data pools. At the same time, the authors try to analyze the reason that leads to inferior performance of existing methods on a larger data pool.","weaknesses":"1. **Title Reflecting Content**: The title of this paper suggests that ”random\nselection is almost all you need”, while results show that the diversity-based\nselection method achieves superior performance with an average score of\n59.58 under Qwen2-7B in Table 1. The result does not indicate that random\nselection is a better method. In this paper, it seems to show that\ndiversity plays an important role in data selection for large-scale datasets. A more representative title improves clarity\nand helps set readers’ expectations.\n\n2. **Insufficient experiments**: This paper’s results show that existing data\nselection methods do not significantly outperform random selection on large-scale datasets. However, the authors only perform experiments on two models. Are there similar outcomes for different LLMs (e.g., different-sized models)?","questions":"**Questions**: This paper proposes a data selection method by token\nlength to achieve optimal results. However, as shown in Table 3, does the Qwen2-7B model not get better results with this method compared with\nexisting methods? By the way, why is this selection method beneficial? In\nother words, what is the motivation for this approach? Moreover, what\ndoes it mean to ”reduce the uncertainty caused by randomness”?"},{"id":"zRVyZCD4V7","initial_rating":3,"confidence":4,"soundness":2,"contribution":2,"presentation":2,"summary":"This paper investigates supervised fine-tuning (SFT) for large language models (LLMs), specifically focusing on selecting a representative subset of training data that performs as well as or better than using the full dataset. It reveals that existing data selection methods, particularly self-scoring techniques, struggle to outperform random selection on million-scale datasets and highlights the importance of diversity over mere data quality in large-scale scenarios. Additionally, the authors find that filtering data by token length enhances SFT, especially for weaker base models like Llama3, offering a stable and efficient improvement method.","strengths":"The finding that \"Most self-scoring data selection techniques do not significantly outperform random selection on large-scale datasets\" could contribute novel insights to the community.","weaknesses":"- The motivation for this research is unclear. The authors claim that \"This discrepancy creates a gap between the present SFT data selection strategies and real-world applications,\" yet it remains unclear what these real-world applications are.\n\n- Finding 2, namely, \"Data quality-based selection methods are more effective than data diversity-based methods when dealing with a small-scale dataset from a single source,\" is interesting, but exploring why this discrepancy occurs would be more valuable.\n\n- Finding 3, that \"token length could be used for data filtering,\" does not fit well within the overall narrative. In general, while the paper presents three findings, they are neither well-motivated nor well-connected. As an exploratory paper, its contribution feels limited.\n\n- When using the term “significantly better,” please provide a p-value to substantiate the statistical significance of the results.\n\n- Clarification:\n\n - The introduction should clarify what “scoring” means in this context and better motivate the need for scoring. Additionally, for the self-scoring approaches, the authors further categorise their techniques into two types: data quality-based methods and data diversity-based methods, but this distinction needs clearer explanation in the context.\n\n Although further detail is provided in Section 3, the introduction is challenging to follow.\n\n - In Figure 1, \"BBH benchmark\" requires a reference.\n\n - Line 58: \"in practical applications\" needs clarification.\n\n- Typos:\n\n - Line 39: missing a space before the citation.\n - Table 1: some of the best numbers are not in bold.\n - Line 324: missing a space before the bracket.","questions":"- What real-world applications could benefit from the outcomes of this research?\n- What is the difference between data quality-based methods and data diversity-based approaches?\n- Why is utilising token length in SFT beneficial for weaker base language models, like Llama3-8B?"}],"string":"[\n {\n \"id\": \"Cc2sPQljz6\",\n \"initial_rating\": 6,\n \"confidence\": 3,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"In this paper authors proposed a data filtration technique for the SFT (supervised fine-tuning phase) of LLM training.\\nRigorously testing existing SOTA methods that were proven to work on the small scale datasets, authors found that \\nfiltering data by token length offers an efficient way for improving downstream results further. In addition to that authors demonstrated that SOTA methods fall short in quality when handling large-scale 1T datasets. Authors demonstrated that data diversity plays the most important role in the SFT phase, thus quality filtering is suboptimal.\",\n \"strengths\": \"Constructing a high-quality multi-corpora dataset that is useful for training LLMs is a hard and important task. Input data is crucial for making a high-quality reliable and safe LLM at scale. Authors explore the topic of improving the dataset construction process and suggest a simplified framework that does not require rigorous data cleaning at scale. Considering that developing and using filtration techniques at scale might present computational challenges, this paper makes a significant contribution to the field with their simplified proposal.\",\n \"weaknesses\": \"One of the challenges with assessing the quality of LLMs is the quality and generalizability of the downstream tasks. Majority of the times that amount of the overlap between training and downstream data can cause skewed assessments in the quality of data processing techniques. I could not find any statistics reported by the authors for the amount of the overlap present in their training corpuses and the downstream tasks. It is important to understand that before drawing any conclusions with regards to the data filtration techniques. \\nIt might be the case that some of the filtration strategies are heavily biased towards the examples present in the downstream tasks, and not necessarily improve model's generazability qualities.\",\n \"questions\": \"I would like to see the stats on the overlap present in the tokens from your SFT datasets and downstream tasks. It would also be useful to know whether any deduplication method was applied on top of the SFT datasets to eliminate the effect of model's memorization.\"\n },\n {\n \"id\": \"4twc1auQh0\",\n \"initial_rating\": 3,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"This paper investigates the effectiveness of data selection methods for supervised fine-tuning (SFT) of Large Language Models (LLMs) at scale. Through extensive experimentation on million-scale datasets, the research reveals that most existing self-scoring data selection methods, which don't require external model assistance, fail to significantly outperform random selection when applied to large-scale data pools.\",\n \"strengths\": \"1. This paper studies an interesting yet important task of selecting training data for supervised fine-tuning (SFT) in large language models.\\n\\n2. The experimental results reveal that various data selection methods struggle to significantly outperform random selection, a finding that will likely be beneficial to practitioners.\",\n \"weaknesses\": \"1. Some of the conclusions presented are already established in existing literature. For instance, paper [1] has previously demonstrated the importance of data diversity in SFT data selection with large-scale datasets, while paper [2] has shown the effectiveness of selecting longer answers for data selection. It appears the authors overlooked these references, which limits the novelty and contribution of this work.\\n\\n2. Although the paper identifies that certain data selection methods fail to outperform random selection, it lacks a thorough analysis—either theoretical or empirical—explaining why these approaches underperform. This absence of deeper exploration reduces the overall depth and insight provided by the study, which is required by top-tier ML conferences.\\n\\n3. The paper does not provide a clear definition of what is an \\\"extensive SFT dataset.\\\" In practical applications, it remains unclear how to determine whether a dataset qualifies as \\\"extensive,\\\" which could lead to ambiguity in interpreting the paper's findings and recommendations.\\n\\n\\n[1] Bukharin, Alexander, and Tuo Zhao. \\\"Data diversity matters for robust instruction tuning.\\\" arXiv preprint arXiv:2311.14736 (2023).\\n\\n[2] Zhao, Hao, et al. \\\"Long Is More for Alignment: A Simple but Tough-to-Beat Baseline for Instruction Fine-Tuning.\\\" Forty-first International Conference on Machine Learning.\",\n \"questions\": \"See above.\"\n },\n {\n \"id\": \"thiE3wsuYV\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"This paper studies the efficacy of various data filtering strategies when applied to large-scale SFT datasets (i.e.., OpenHermes2.5, WildChat). While these same strategies often outperform random selection on smaller-scale SFT datasets they are shown to be surprisingly less impactful when applied to these larger-scale (state-of-the-art) open-source datasets. On these datasets, approaches that target diversity seem to be more effective than those that target quality. Finally, the authors test their own length-based filtering strategy, which outperforms the other methods when the base model is Llama3-8B.\",\n \"strengths\": \"**Originality and Significance.** This paper performs a valuable and novel (to the best of my knowledge) empirical study to see whether existing SFT data selection methods remain effective when applied on larger SFT datasets. Because these larger SFT datasets are generally better than the smaller datasets these methods were previously tested on, it is important to see whether filtering works in this more state of the art regime. The main findings that (i) many of these methods no longer are as impactful; (ii) diversity is more important than quality-filtering are therefore quite significant and potentially highly-relevant to future SFT data curation efforts.\\n\\n**Quality.** This paper implements a good number of baselines and also is thorough about trying multiple base models and dataset sizes (post data selection). These variations are nice to test the robustness of the main takeaways.\\n\\n**Clarity.** Overall, most of the paper is easy to follow with the exception of the description of baseline methods (see W3).\",\n \"weaknesses\": \"**(W1) Isolating dataset size.** A central claim in the paper is that dataset size is what causes differences in the behavior of the baselines. However, there are also other differences between OH2.5/WildChat and older datasets besides data quantity; e.g., quality-based selection may be less impactful simply because these larger datasets are already the result of more careful curation and thus higher-quality compared to older ones. An experiment that would better isolate data quantity (and control for quality) would be to run the existing experiments on progressively smaller random subsets of OH2.5/WildChat (e.g., what happens when the starting pool is 10K/100K examples of OH2.5 v.s. 1M?)\\n\\n**(W2) Understanding run-to-run variance / Fairness of comparison to random.** The stated takeaway from the results is that *\\\"it is more efficient to randomly select training data...random selection reduces costs and yields superior training results\\\"* but I don't know if that's fully borne out by the results.\\n- For the Qwen2 results (which achieve highest overall perforamnce), in the 50K regime, the best average results are achieved by non-random curation methods (Diverse and ZIP each score 1% higher than the max over the random runs in Tables 5 and 6 respectively). In the 10K regime, this is also almost true with the exception of 1/5 of the random runs.\\n- In general, I'm not sure its fair to compare the max over 5 random runs to a single run of a selection method. if only 1 of 5 runs ends up doing better, then in practice you'd likely have to try multiple times when randomly sampling a subset that outperforms non-random selection, increasing costs. \\n- Ideally, it would be nice to show the average and stdev across the 5 random runs and to also get a sense of run-to-run variation for the non-random methods (though I acknowledge this might be costly). \\n\\n**(W3) Clarity when describing existing methods.** I currently found Sec 3. a bit hard to follow. It may be helpful to define up front unified notation for variables that appear in multiple methods instead of using the differing notation from each of the original papers (e.g. whether a sample is given by $z$ or $x$ or $n$). Also, in some places, symbols are currently used without an explicit definition (e.g. $\\\\hat{\\\\Gamma}$ in LESS, $\\\\mathcal{C}$ in ZIP). \\n\\n**Miscellaneous Notes**\\n- In captions for Tables 1 and 2, \\\"the suboptimal score\\\" is confusing terminology, I believe you meant \\\"second highest score\\\"? \\n- Given that originally LESS is a targeted selection method, I'm not sure it's completely aligned with the spirit of the original method to set the target as a subset of the overall data pool? I suspect what might be leading to bad performance is that this may actually result in selecting a less diverse dataset (by prioritizing examples that represent the majority).\",\n \"questions\": \"(Q1) Could you share more details about Figure 1, given that the difference between small/large regimes is a key aspect of the paper? In particular, which datasets were used for the 10K-300K scale in Figure 1? Are these already random subsets of OH2.5/WildChat (basically what i suggested in W1) or are they some other datasets (e.g. Dolly, ShareGPT)?\\n\\n(Q2) What is the cost of the fine-tuning runs in your experiment setup? It would be helpful to know this relative to the costs of running the various data curation algorithms (when discussing them in 5.3).\"\n },\n {\n \"id\": \"NG18D9Ims8\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"In this paper, the authors study the effectiveness of data selection methods on large-scale datasets, which is largely unexplored. With experiments on large-scale datasets, the authors find that nearly existing data selection methods do not significantly outperform random selection on large-scale datasets. This paper also tries to explain the reason that leads to inferior performance of existing methods on a larger data pool. Ultimately, the authors propose a more effective data selection method based on token length. This paper offers researchers a new perspective on data selection in large language models.\",\n \"strengths\": \"The authors study the effectiveness of data selection methods on large-scale datasets, and find the inferior performance of existing methods when dealing with large-scale data pools. At the same time, the authors try to analyze the reason that leads to inferior performance of existing methods on a larger data pool.\",\n \"weaknesses\": \"1. **Title Reflecting Content**: The title of this paper suggests that ”random\\nselection is almost all you need”, while results show that the diversity-based\\nselection method achieves superior performance with an average score of\\n59.58 under Qwen2-7B in Table 1. The result does not indicate that random\\nselection is a better method. In this paper, it seems to show that\\ndiversity plays an important role in data selection for large-scale datasets. A more representative title improves clarity\\nand helps set readers’ expectations.\\n\\n2. **Insufficient experiments**: This paper’s results show that existing data\\nselection methods do not significantly outperform random selection on large-scale datasets. However, the authors only perform experiments on two models. Are there similar outcomes for different LLMs (e.g., different-sized models)?\",\n \"questions\": \"**Questions**: This paper proposes a data selection method by token\\nlength to achieve optimal results. However, as shown in Table 3, does the Qwen2-7B model not get better results with this method compared with\\nexisting methods? By the way, why is this selection method beneficial? In\\nother words, what is the motivation for this approach? Moreover, what\\ndoes it mean to ”reduce the uncertainty caused by randomness”?\"\n },\n {\n \"id\": \"zRVyZCD4V7\",\n \"initial_rating\": 3,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper investigates supervised fine-tuning (SFT) for large language models (LLMs), specifically focusing on selecting a representative subset of training data that performs as well as or better than using the full dataset. It reveals that existing data selection methods, particularly self-scoring techniques, struggle to outperform random selection on million-scale datasets and highlights the importance of diversity over mere data quality in large-scale scenarios. Additionally, the authors find that filtering data by token length enhances SFT, especially for weaker base models like Llama3, offering a stable and efficient improvement method.\",\n \"strengths\": \"The finding that \\\"Most self-scoring data selection techniques do not significantly outperform random selection on large-scale datasets\\\" could contribute novel insights to the community.\",\n \"weaknesses\": \"- The motivation for this research is unclear. The authors claim that \\\"This discrepancy creates a gap between the present SFT data selection strategies and real-world applications,\\\" yet it remains unclear what these real-world applications are.\\n\\n- Finding 2, namely, \\\"Data quality-based selection methods are more effective than data diversity-based methods when dealing with a small-scale dataset from a single source,\\\" is interesting, but exploring why this discrepancy occurs would be more valuable.\\n\\n- Finding 3, that \\\"token length could be used for data filtering,\\\" does not fit well within the overall narrative. In general, while the paper presents three findings, they are neither well-motivated nor well-connected. As an exploratory paper, its contribution feels limited.\\n\\n- When using the term “significantly better,” please provide a p-value to substantiate the statistical significance of the results.\\n\\n- Clarification:\\n\\n - The introduction should clarify what “scoring” means in this context and better motivate the need for scoring. Additionally, for the self-scoring approaches, the authors further categorise their techniques into two types: data quality-based methods and data diversity-based methods, but this distinction needs clearer explanation in the context.\\n\\n Although further detail is provided in Section 3, the introduction is challenging to follow.\\n\\n - In Figure 1, \\\"BBH benchmark\\\" requires a reference.\\n\\n - Line 58: \\\"in practical applications\\\" needs clarification.\\n\\n- Typos:\\n\\n - Line 39: missing a space before the citation.\\n - Table 1: some of the best numbers are not in bold.\\n - Line 324: missing a space before the bracket.\",\n \"questions\": \"- What real-world applications could benefit from the outcomes of this research?\\n- What is the difference between data quality-based methods and data diversity-based approaches?\\n- Why is utilising token length in SFT beneficial for weaker base language models, like Llama3-8B?\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;3;5;5;6\",\n \"rating_avg\": 4.4,\n \"confidence\": \"4;4;4;4;3\",\n \"confidence_avg\": 3.8,\n \"soundness\": \"2;2;3;2;3\",\n \"soundness_avg\": 2.4,\n \"contribution\": \"2;3;3;3;2\",\n \"contribution_avg\": 2.6,\n \"presentation\": \"2;2;3;2;3\",\n \"presentation_avg\": 2.4\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"Submitted to ICLR 2025\",\n \"venueid\": \"ICLR.cc/2025/Conference/Rejected_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.712910\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"DWQjqrz6vB\",\n \"metareview\": \"The paper analyzes methods for selecting a high quality dataset for LLM supervised fine tuning (SFT). This task is highly motivated given that many papers show the crucial role of data quality in LLM training. An additional strength mentioned by the reviewers is the insights provided in the paper, showing that many of the existing methods for data selection are in fact no better than random selection. \\n\\nThe authors provide additional insights and some supporting experiments, but according to the reviews, these require additional and deeper analysis to meet the bar of ICLR. The authors provided some clarifications and additional data in the rebuttal stage, but the reviews did not find it to be sufficient, and this key issue remains. Other than the need for a deeper analysis, some concerns were raised regarding the novelty compared to previous works (yhuK, MLme). This issue might be mitigated given a deeper analysis addressing the points raised in the reviews. \\n\\nConcluding, the paper deals with an important problem and has potential, but it requires more work.\",\n \"additional_comments\": \"see meta review\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Reject\"\n}"}}},{"rowIdx":3394,"cells":{"paper_id":{"kind":"string","value":"qUZY7ymDPr"},"arxiv_id":{"kind":"string","value":"2411.02327v2"},"title":{"kind":"string","value":"PPLLaVA: Varied Video Sequence Understanding With Prompt Guidance"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract The past year has witnessed the significant advancement of video-based large language models. However, the challenge of developing a unified model for both short and long video understanding remains unresolved. Most existing video LLMs cannot handle hour-long videos, while methods custom for long videos tend to be ineffective for shorter videos and images. In this paper, we identify the key issue as the redundant content in videos. To address this, we propose a novel pooling strategy that simultaneously achieves token compression and instruction-aware visual feature aggregation. Our model is termed Prompt-guided Pooling LLaVA, or PPLLaVA for short. Specifically, PPLLaVA consists of three core components: the CLIP-based visual-prompt alignment that extracts visual information relevant to the user’s instructions, the prompt-guided pooling that compresses the visual sequence to arbitrary scales using convolution-style pooling, and the clip context extension designed for lengthy prompt common in visual dialogue. Moreover, our codebase also integrates the most advanced video Direct Preference Optimization (DPO) and visual interleave training. Extensive experiments have validated the performance of our model. With superior throughput and only 1024 visual context, PPLLaVA achieves better results on image benchmarks as a video LLM, while achieving state-of-the-art performance across various video benchmarks, excelling in tasks ranging from caption generation to multiple-choice questions, and handling video lengths from seconds to hours. Codes have been available at https://github.com/farewellthree/PPLLaVA .\\n\\n## 1 Introduction\\n\\nVideo Large Language Models (Video LLMs) have made significant advancements over the past year. Given the extensive resources and the scarcity of high-quality video-text data required for video pretraining, performing Image-to-Video transfer on powerful Image-domain Large Language Models has become a more practical approach for most Video LLMs. Building on the most advanced image LLMs (Liu et al., ; ; Dai et al., ), existing video LLMs typically address the modal differences between images and videos by video instruction data production (Maaz et al., ; Li et al., ; Luo et al., ; Zhang et al., ), temporal modeling (Liu et al., ; ; Li et al., ; Huang et al., ), or video token aggregation (Jin et al., ; Li et al., ; Xu et al., ). Meanwhile, a wide range of video benchmarks and test tasks offer diverse perspectives and options for evaluating the capabilities of video LLMs, including video question answering (Maaz et al., ; Xu et al., ; Caba Heilbron et al., ; Wu et al., ), video dense captioning (Ren et al., ), multiple-choice questions (Li et al., ; Fu et al., ), and long video assessment (Fu et al., ; Song et al., ; Zhang et al., ).\\n\\nFigure: Figure 1: (a) An instance from VideoMME (Fu et al., ). The crucial information pertains to only a small portion of the video for different questions. (b) Performance comparison of PPLLaVA with recent strong Video LLM among video benchmarks, image benchmarks, and efficiency. All the models are based on Vicuna-7B.\\nRefer to caption: x1.png\\n\\nFor temporal modeling, an intuitive approach is to directly input tokens from each frame into the LLM, a method proven effective in several studies (Liu et al., ; ; Li et al., ). However, while this method leverages the LLM’s sequence modeling capabilities, it leads to an excessively long visual context. This not only increases computational resource consumption and processing time but also limits the model’s ability to handle extended videos. To address this issue, several alternative approaches exist. A commonly adopted method is average pooling across the temporal dimension, frequently seen in early video LLMs (Li et al., ; Maaz et al., ; Luo et al., ; Liu et al., ). While this approach maintains a constant context length, it significantly diminishes the model’s ability to capture temporal dynamics. Models designed specifically for long videos often incorporate unique structures, such as memory mechanisms (Ren et al., ; Zhang et al., ; Zhou et al., ). Although these designs enable the models to handle hour-long videos, they offer limited utility for short videos or images.\\nAnother approach is the use of conditional token pooling or aggregation (Li et al., ; Xu et al., ; Jin et al., ). Unlike global average pooling, this method reduces the context length while preserving some spatiotemporal structure, enabling more effective spatiotemporal modeling.\\n\\nHowever, pooling inevitably leads to performance loss compared to using the full set. So, how can we reduce the number of tokens while preserving the spatiotemporal modeling capabilities? We believe the solution lies in the inherent characteristics of the video. As proven by many previous works (Han et al., ; Liu et al., ; Ma et al., ), videos contain significant redundancy, with key information often concentrated in just a few frames, which is particularly true for long videos. For video LLMs, this issue can be more pronounced. As shown in Fig. 1(a), the user’s instruction may pertain to only a small portion of the video, with the rest being redundant for correctly answering the question. Therefore, if we can extract crucial video information while compressing tokens, we can maintain or even enhance performance. In this context, Image LLMs have offered valuable inspiration. The BLIP series (Li et al., ; Dai et al., ; Xue et al., ) and the LLaVA series (Liu et al., ; ; ; Li et al., ) are the two most popular structures in multimodal LLM. BLIP uses a Q-Former for image-to-text mapping, while the LLaVA series employs simple linear projection or MLP. Recently, LLaVA-based models have demonstrated that simple mapping can achieve better results with less training (Liu et al., ). However, despite requiring more computation resources and training stages, the Q-Former offers two key advantages: first, it significantly reduces visual tokens by converting them into fewer query tokens; second, through the interaction between text and visual tokens within the Q-Former, it enables more targeted extraction of video features relevant to the user’s instructions (Dai et al., ). Hence, can we develop a pooling method that retains LLaVA’s simple structure and powerful weights while reducing the number of tokens and enabling prompt-aware feature extraction?\\n\\nTo this end, we propose Prompt-guided Pooling LLaVA (PPLLaVA), a novel method that combines visual pooling with instruction-aware visual feature extraction. Specifically, PPLLaVA first identifies prompt-relevant visual representations through fine-grained vision-prompt alignment. Then, using the prompt-vision relevance as a 3D convolutional kernel, PPLLaVA can compress the visual tokens to any desired three-dimensional size based on the specified output size or stride. Finally, recognizing that CLIP pretraining provides a limited context length and that training video LLMs—particularly for multi-turn dialogues—requires long text contexts, PPLLaVA also employs asymmetric positional embedding extensions to expand the text encoding capacity. As a result, PPLLaVA effectively extracts relevant visual features from both long texts and short phrases while compressing video tokens. PPLLaVA achieves over an 80% compression rate, supports ultra-long video inputs, and simultaneously improves performance on short videos.\\nIn fact, PPLLaVA functions similarly to a Q-Former within LLaVA, but it offers several advantages over directly training a Q-Former: (1) PPLLaVA introduces far fewer additional parameters and computational overhead, amounting to less than one-tenth of a Q-Former. (2) While a Q-Former requires a three-stage pretraining process—contrastive learning, alignment training, and instruction tuning—PPLLaVA can be utilized solely during instruction tuning, allowing for seamless transfer from image-domain LLMs. (3) PPLLaVA supports flexible output sizes for different modalities, whereas the number of queries in a Q-Former is fixed once set. As a result, different Q-Formers typically need to be trained separately for images and videos (Zhang et al., ; Li et al., ).\\n\\nExtensive experiments on the latest multimodal LLM benchmarks have validated the superiority of PPLLaVA: with superior throughput, PPLLaVA has achieved top results across a wide range of test sets, including MSRVTT (Xu et al., ), MSVD (Wu et al., ), ActivityNet (Caba Heilbron et al., ), VCG Bench (Maaz et al., ), MVBench (Li et al., ), and Video-MME (Fu et al., ). These benchmarks encompass tasks such as video question answering, detailed video captioning, and video multiple-choice questions, with video lengths ranging from seconds to hours. Furthermore, our codebase has integrated cutting-edge video LLM techniques, including video Direct Preference Optimization and video-image-multiple image interleave training. As shown in Fig. 1(b), compared to recent top Video LLMs, PPLLaVA demonstrates clear advantages across both video and image benchmarks, while responding 7x faster than LLaVA-Next-Video-7B.\\n\\n## 2 Related Works\\n\\nImage-domain LLMs.\\nImage-domain pretrained models have long served as the foundation for video understanding (Carreira & Zisserman, ; Luo et al., ; Liu et al., ). This is partly due to the inherent similarities between image and video modalities and partly because image pretraining datasets offer a level of quality, quantity, and diversity that video datasets often lack. In the field of multimodal LLMs, the BLIP and LLaVA series have consistently served as the foundation for various video LLMs. The BLIP series is particularly notable for its Q-Former (Li et al., ), which acts as an intermediary between the vision encoder and the LLM. The Q-Former not only enhances visual encoding but also compresses the number of visual tokens. Building on this foundation, InstructBLIP further developed the Q-Former’s capability to extract instruction-aware visual features, making it a preferred choice for some video LLMs (Zhang et al., ; Li et al., ; Liu et al., ; Ren et al., ). LLaVA, a pioneer in visual instruction tuning (Liu et al., ), accomplished the mapping from the visual encoder to the LLM using simple linear layers or MLPs. The LLaVA series has been continually updated (Liu et al., ; ; Li et al., ), with later versions showing that this straightforward mapping approach can achieve superior results with less data. This simplicity and effectiveness inspired us to use LLaVA as the foundation for our model. Alongside this, we introduced the pooling module that retains LLaVA’s efficient structure while also enabling the compression of visual tokens and the extraction of prompt-specific visual features.\\n\\nVideo LLMs.\\nIn the past year, Video LLMs have experienced rapid development since their inception.\\nFor video LLMs, updating video instruction data and benchmarks is essential. Video-ChatGPT (Maaz et al., ) was the first to introduce a high-quality video instruction training dataset and test set, establishing a benchmark for GPT-assisted evaluation. MVBench (Li et al., ) provides a multiple-choice benchmark that assesses video performance across 20 different tasks. Video-MME (Fu et al., ) extends video duration significantly, reaching up to several hours, and serves as a comprehensive multiple-choice video QA benchmark. On the other hand, early Video LLMs (Li et al., ; Zhang et al., ; Luo et al., ; Maaz et al., ; Liu et al., ) typically used average pooling to process video sequences with Image LLMs while employing modality perceivers to model temporal sequences. However, this approach significantly limited the model’s ability to fully understand video sequences. Alternatively, some models (Liu et al., ; ; Xu et al., ) rely on the LLM itself to model video sequences, achieving good video understanding results. Nonetheless, this method is limited to handling a small number of frames and does not support the comprehension of long videos.\\n\\nUnderstanding long videos is also a hot topic in video LLMs. MovieChat (Song et al., ) and Flash-VStream (Zhang et al., ) use memory structures to process streaming videos, while Chat-UniVi (Jin et al., ) adopts a clustering approach for token aggregation. LLaMA-VID (Li et al., ) compresses each video frame into two tokens, capturing both local and global information. Most similar to our work, PLLaVA (Xu et al., ) employs a non-parametric AdaptiveAvgPool3d function to compress visual tokens. In contrast, our method supports not only token compression but also the extraction of visual features pertinent to user prompts. Furthermore, our convolution-style pooling method enables flexible output sizes. Notably, compared to the aforementioned methods, our approach has achieved state-of-the-art results on both long and short video benchmarks, whereas the other methods may exhibit slightly lower performance on videos of certain lengths.\\n\\nThe diversification of data modalities and formats has also become a prominent direction in research. Beyond the classic image-video instruction tuning, CAT (Ye et al., ) introduced mixed training with video and audio, while VideoMME (Fu et al., ) emphasized the importance of subtitles. VILA (Lin et al., ) and LLaVA-Interleave underscored the value of interleaved training. Besides instruction tuning, Reinforcement Learning from Human Feedback (RLHF) has also been proven to be particularly effective for video LMM. Specifically, VLM-RLAIF (Ahn et al., ) and LLaVA-Hound (Zhang et al., ) demonstrated the effectiveness of Proximal Policy Optimization (PPO) and Direct Preference Optimization (DPO), respectively. We have also integrated these cutting-edge techniques into our codebase and demonstrated that they can operate in parallel with PPLLaVA.\\n\\nFigure: Figure 2: The overview of PPLLaVA for compressing the video based on user prompts and generating responses on the input video and instructions.\\nRefer to caption: x2.png\\n\\n## 3 Methodology\\n\\n### 3.1 Motivation and Analysis\\n\\nIn the previous section, we discussed that the videos are redundant in both length and content. Vista-LLaMA (Ma et al., ) demonstrated that the extensive number of tokens in long videos makes it difficult for LLMs to capture video content. In this section, we further examine whether redundant video content impacts the performance of video LLMs and whether extracting key video content can enhance performance. Inspired by EgoSchema (Mangalam et al., ), we adopt the certificate length to measure the redundancy.\\nThe certificate length of a video-QA pair is determined by the shortest video sub-clip that can answer the question. Instead of using manual annotation, we employed an automated method to determine the certificate. Specifically, frames are sampled at 2 fps, and then the similarity between each frame and the question-answer text is calculated using CLIP-L-336 (Radford et al., ). If the similarity exceeds 0.5, the frame is considered relevant to the text. Finally, the proportion of relevant frames to the entire video is calculated as the certificate.\\n\\n**Table 1: The study on the impact of video redundancy, we used the Vicuna-7B version for all models. ”Average” and ”Manual” refer to the default average frame sampling and manual frame selection, respectively.**\\n| Model | Frames | Tokens | Video-MME-full | Video-MME-redund | |\\n| --- | --- | --- | --- | --- | --- |\\n| average | average | manual | | | |\\n| InstructBLIP | 32 | 1024 | 39.2 | 36.1 (-3.1) | 39.5 (+0.3) |\\n| LLaVA-Next | 32 | 4608 | 41.1 | 36.9 (-4.2) | 42.0 (+0.9) |\\n| LLaVA-Next-Video | 8 | 1152 | 42.9 | 39.0 (-3.9) | 43.5 (+0.6) |\\n| LLaVA-Next-Video | 32 | 4608 | 45.0 | 41.5 (-3.5) | 46.1 (+1.1) |\\n| PPLLaVA (ours) | 32 | 1024 | 49.8 | 47.6 (-2.2) | 50.5 (+0.7) |\\n\\nBased on the Video-MME dataset, we selected the 100 video-QA pairs with the shortest certificate lengths termed Video-MME-redund. We then evaluated the performance of various models on both the full Video-MME dataset and these selected samples. Additionally, for these 100 samples, we manually selected the frames most relevant to the questions, alongside the default frame sampling method. This approach was used to test whether extracting key information enhances video understanding. As shown in Table 1, all models experienced a decline in performance on high-redundancy videos. As an earlier model, InstructBLIP performed as expected, not matching the overall performance of the more advanced LLaVA-Next. However, on high-redundancy videos, InstructBLIP, which has instruction-aware video feature extraction capabilities, declined slower than LLaVA-Next. Furthermore, when manually selected frames were used, all models showed significant performance improvements, highlighting the importance of extracting key video information for enhancing video understanding. Additionally, we clearly observed the importance of including more frames for long videos, such as those in the Video-MME dataset. These findings motivated us to explore token compression to accommodate more video frames while effectively extracting key information.\\n\\n### 3.2 PPLLaVA\\n\\nAs shown in Fig. 2, PPLLaVA, like most video LLMs, includes a vision encoder, a mapping layer, and a LLM. It also features an additional text encoder paired with the visual encoder. Given a $T$-frame video, we first pass it through the CLIP-ViT visual encoder, obtaining the visual feature $V\\\\in\\\\mathbb{R}^{T\\\\times W\\\\times H\\\\times D}$. This feature is then fed into the Prompt-guided Pooling module, where it is compressed by over 90%, resulting in $V^{\\\\prime}\\\\in\\\\mathbb{R}^{T^{\\\\prime}\\\\times W^{\\\\prime}\\\\times H^{\\\\prime}\\\\times D}$. $V^{\\\\prime}$ is fed into the MLP mapping layer as the final visual input. Importantly, $V^{\\\\prime}$ not only contains significantly fewer tokens but also condenses information more relevant to the user’s instructions. This ensures improved performance while efficiently processing the video input.\\nNext, we will detail how $V^{\\\\prime}$ is obtained.\\n\\nFine-grained Vision-Prompt Alignment.\\nTo extract video features relevant to the prompt, we first utilize the original CLIP dual encoders to identify which video features are related to the text. Specifically, we input the user’s question into the CLIP text encoder to obtain the text feature $c\\\\in\\\\mathbb{R}^{D}$. Following the CLIP training pipeline, we only use the CLS token of the text. The attention score of the $(t^{th},w^{th},h^{th})$ video token relative to the text feature is then calculated as:\\n\\n$$ $s_{(t,w,h)}=\\\\frac{\\\\mathrm{exp}(\\\\tau c\\\\cdot f_{clipv}(v_{(t,w,h)}))}{\\\\sum_{t=1} ^{T}\\\\sum_{w=1}^{W}\\\\sum_{h=1}^{H}{\\\\mathrm{exp}(\\\\tau c\\\\cdot f_{clipv}(v_{(t,w,h) }))}},$ (1) $$\\n\\nwhere $v_{(t,w,h)}$ represents the token at the $(t,w,h)$ position in $V$, $\\\\tau$ is the CLIP temperature scale, and $f_{clipv}$ is the CLIP visual projection, which is typically not used in multimodal LLMs. Note that $v_{(t,w,h)}$ typically refers to the patch token from the penultimate layer of CLIP, rather than the CLS token from the final layer used during CLIP training. However, since the spatial representations in CLIP’s final layers are similar, applying $f_{clipv}$ still allows the patch tokens to be mapped into the interaction space with the text.\\n\\nPrompt-Guided Pooling.\\nIn the previous section, we obtained token-level weights corresponding to the user’s prompt, which we use as guidance for pooling the video. Unlike traditional tasks that require only a D-dimensional feature for contrastive learning (Ma et al., ; Wang et al., ), our approach aims to preserve a certain 3-dimensional structure to enable the LLM to perform temporal modeling.\\nTo achieve this, we perform pooling with $S=\\\\{s_{(t,w,h)}\\\\}$ in a manner similar to 3D convolution. Specifically, we define the spatiotemporal 3D convolution kernel and stride as $(k_{t},k_{w},k_{h})$ and $(d_{t},d_{w},d_{h})$, respectively. The output dimension of $V^{\\\\prime}$ can then be expressed as:\\n\\n$$ $T^{\\\\prime}=(\\\\frac{T-k_{t}}{d_{t}})+1,~{}~{}~{}W^{\\\\prime}=(\\\\frac{W-k_{w}}{d_{w} })+1,~{}~{}~{}H^{\\\\prime}=(\\\\frac{H-k_{h}}{d_{h}})+1.\\\\\\\\$ (2) $$\\n\\nUnlike conventional convolution kernels, our kernel parameters are derived from $S$. Moreover, the parameters of the kernel are dynamic; as the kernel slides over different positions in $V$, its parameters are taken from the corresponding positions in $S$. Finally, the feature at position $(t,w,h)$ in the output $V^{\\\\prime}$ is calculated as:\\n\\n$$ $v^{\\\\prime}_{(t,w,h)}=\\\\sum_{i=0}^{k_{t}-1}\\\\sum_{j=0}^{k_{w}-1}\\\\sum_{k=0}^{k_{h} -1}v_{(t*d_{t}+i,w*d_{w}+j,h*d_{h}+k)}s_{(t*d_{t}+i,w*d_{w}+j,h*d_{h}+k)}.$ (3) $$\\n\\nBy flexibly adjusting the stride and kernel size, we can control the output dimensions. This approach allows us to better accommodate videos of varying lengths and facilitates joint training with images, compared to fixed-output methods.\\n\\nCLIP Context Extension.\\nIn our method, CLIP-text is the only additional parameter used. Despite having significantly fewer parameters than Qformer, it achieves better performance. However, CLIP-text has a major limitation: its context length is too short (default is 77). While this length is sufficient for objects or simple descriptions, it is inadequate for long prompts or multi-turn dialogues in multimodal LLMs. To address this performance bottleneck, we propose extending the context length of CLIP-text using asymmetric positional embedding extensions. In most cases, extending the positional embedding involves randomly initializing new embeddings at the end. A more theoretically sound approach is to perform linear interpolation on the original positional embedding at a rate of $r$. Assuming the original and target positional embeddings are $P$ and $P^{\\\\prime}$, respectively, the $i^{th}$ position of $P^{\\\\prime}$ can be represented as:\\n\\n$$ $P^{\\\\prime}_{i}=P_{\\\\lfloor j\\\\rfloor}+(j-\\\\lfloor j\\\\rfloor)\\\\cdot(P_{\\\\lfloor j \\\\rfloor+1}-P_{\\\\lfloor j\\\\rfloor}),~{}~{}j=i\\\\cdot r,$ (4) $$\\n\\nwhere $\\\\lfloor j\\\\rfloor$ means taking the floor of $j$. However, we found linear interpolation yielded inferior results to randomly initializing embeddings at the end. We believe this is because CLIP’s positional embeddings are well-trained, and globally averaged interpolation disrupts the well-pre-trained information. Given that short sentences dominate CLIP’s training data, the earlier parts of positional embeddings are more thoroughly trained. Hence, we adopted asymmetric interpolation, applying different interpolation rates at different positions. In the early part of the new positional embedding, we use a large $r$ value to shorten the interpolation distance, while in the later part, we use a smaller $r$ value to extend the interpolation distance. This asymmetric approach allows us to effectively extend the context length of CLIP-text while preserving as much of the pre-trained information as possible.\\n\\n### 3.3 Training\\n\\nInterleave Instruction Tuning.\\nPPLLaVA enables plug-and-play transfer of image-domain LLMs to the video domain. As a result, initialized from well-pretrained image LLM, we can bypass expensive contrastive or alignment pretraining and proceed directly to instruction tuning. In this stage, we fully fine-tune the LLM, the projection MLP, and the CLIP text encoder. Our instruction datasets include multi-turn and single-turn conversations presented in a conversational format, along with various forms of visual input such as images, videos, and multiple images. For different types of data, we employed an interleaving training approach. Rather than using batches composed of a single data type, we mixed various data types within the same batch. Numerous studies (Li et al., ; Laurençon et al., ; Xue et al., ) have demonstrated that this method is the most natural approach for handling multimodal data. Additionally, this training method enables the model to simultaneously process both long videos with many frames and single-frame images, greatly enhancing its adaptability to visual sequences of varying lengths.\\n\\nDirect Preference Optimization. (DPO)\\nVideo, especially long video-based dialogue, is more prone to hallucinations compared to images. As a result, Reinforcement Learning from Human Feedback (RLHF) (Zhang et al., ; Ahn et al., ) has proven particularly effective for video. Therefore, we also implemented this method based on our model. Following LLaVA-Hound (Zhang et al., ). We used detailed video captions as proxies for video content and performed DPO with feedback from the language model serving as a reward. In this stage, all parameters except the LLM were frozen, and only video data was used. This additional phase significantly reduced the occurrence of hallucinations during video-based dialogue.\\n\\n## 4 Experiments\\n\\nIn this section, we have performed comprehensive experimental evaluations of PPLLaVA, covering crucial settings, comparisons, and ablations, while more ablation studies, visualizations, and limitations analysis can be found the appendix.\\n\\n### 4.1 Experiment Setup\\n\\nImplementation Details.\\nPPLLaVA is built upon the advanced image-domain LLaVA-Next models (Liu et al., ). To ensure a fair comparison with most models, we chose the Vicuna-7B version. For image and multiple-image inputs, the pooling kernel and strides are set to $(1,3,3)$. For video inputs, we uniformly sample 32 frames and set the pooling kernel and strides to $(2,3,3)$, compressing the video tokens by over 15 times. During training, both questions and answers are fed into the CLIP text encoder to better capture prompt-vision relevance. For CLIP context extension, when $i<20$, $r$ is set to 1, and when $i\\\\geq 20$, $r$ is set to 0.25. We train for one epoch using a learning rate of $2e-5$ and a batch size of 256. We provid both GPU and NPU versions, and the full training takes 24 hours on 16 A100 GPUs or 32 910B NPUs.\\n\\n**Table 2: The results of open-ended QA with GPT-based evaluation, including MSVD-QA, MSRVTT-QA, ActivityNet-QA(ANet), and VCG Bench. All the models are based on the Vicuna-7B. † means using DPO or PPO.**\\n| Method | MSVD | MSRVTT | ANet | VCG Bench | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| Acc. | Sco. | Acc. | Sco. | Acc. | Sco. | CI | DO | CU | TU | CO | Avg. | |\\n| VideoChat (Li et al., ) | 56.3 | 2.8 | 45.0 | 2.5 | 26.5 | 2.2 | 2.23 | 2.50 | 2.53 | 1.94 | 2.24 | 2.29 |\\n| Video-ChatGPT (Maaz et al., ) | 64.9 | 3.3 | 49.3 | 2.8 | 35.2 | 2.7 | 2.50 | 2.57 | 2.69 | 2.16 | 2.20 | 2.42 |\\n| BT-Adapter (Liu et al., ) | 67.5 | 3.7 | 57.0 | 3.2 | 45.7 | 3.2 | 2.68 | 2.69 | 3.27 | 2.34 | 2.46 | 2.69 |\\n| Video-LLaVA (Lin et al., ) | 70.7 | 3.9 | 59.2 | 3.5 | 45.3 | 3.3 | - | - | - | - | - | - |\\n| MovieChat (Song et al., ) | 75.2 | 3.8 | 52.7 | 2.6 | 45.7 | 3.4 | 2.76 | 2.93 | 3.01 | 2.24 | 2.42 | 2.67 |\\n| Chat-UniVi (Jin et al., ) | 65.0 | 3.6 | 54.6 | 3.1 | 45.8 | 3.2 | 2.89 | 2.91 | 3.46 | 2.89 | 2.81 | 2.99 |\\n| VideoChat2 (Li et al., ) | 70.0 | 3.9 | 54.1 | 3.3 | 49.1 | 3.3 | 3.02 | 2.88 | 3.51 | 2.66 | 2.81 | 2.98 |\\n| Vista-LLaMA (Ma et al., ) | 65.3 | 3.6 | 60.5 | 3.3 | 48.3 | 3.3 | 2.44 | 2.64 | 3.18 | 2.26 | 2.31 | 2.57 |\\n| LLaMA-VID (Li et al., ) | 69.7 | 3.7 | 57.7 | 3.2 | 47.4 | 3.3 | 2.96 | 3.00 | 3.53 | 2.46 | 2.51 | 2.89 |\\n| ST-LLM (Liu et al., ) | 74.6 | 3.9 | 63.2 | 3.4 | 50.9 | 3.3 | 3.23 | 3.05 | 3.74 | 2.93 | 2.81 | 3.15 |\\n| PLLaVA (Xu et al., ) | 76.6 | 4.1 | 62.0 | 3.5 | 56.3 | 3.5 | 3.21 | 2.86 | 3.62 | 2.33 | 2.93 | 2.99 |\\n| CAT (Ye et al., ) | - | - | 62.1 | 3.5 | 50.2 | 3.5 | 3.08 | 2.95 | 3.49 | 2.81 | 2.89 | 3.07 |\\n| VLM-RLAIF † (Ahn et al., ) | 76.4 | 4.0 | 63.0 | 3.4 | 57.3 | 3.5 | 3.85 | 3.45 | 3.84 | 3.63 | 2.8 | 3.49 |\\n| LLaVA-Next-Video (Liu et al., ) | - | - | - | - | 53.5 | 3.2 | 3.39 | 3.29 | 3.92 | 2.60 | 3.12 | 3.26 |\\n| LLaVA-Next-Video † | - | - | - | - | 60.2 | 3.5 | 3.64 | 3.45 | 4.17 | 2.95 | 4.08 | 3.66 |\\n| PPLLaVA | 75.8 | 3.9 | 61.9 | 3.3 | 56.1 | 3.4 | 3.32 | 3.20 | 3.88 | 3.00 | 3.20 | 3.32 |\\n| PPLLaVA † | 77.1 | 4.0 | 64.3 | 3.5 | 60.7 | 3.6 | 3.85 | 3.56 | 4.21 | 3.21 | 3.81 | 3.73 |\\n\\n**Table 3: Performance on Video-MME with short, medium, and long durations, under the settings of “without subtitles” and “with subtitles”. * means using multi-images during training.**\\n| Models | LLM | Short (%) | Medium (%) | Long (%) | Overall (%) | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| Params | w/o subs | w/ subs | w/o subs | w/ subs | w/o subs | w/ subs | w/o subs | w/ subs | |\\n| Qwen-VL-Chat (Bai et al., ) | 7B | 46.9 | 47.3 | 38.7 | 40.4 | 37.8 | 37.9 | 41.4 | 41.9 |\\n| Qwen-VL-Max (Bai et al., ) | - | 55.8 | 57.6 | 49.2 | 48.9 | 48.9 | 47.0 | 51.3 | 51.2 |\\n| InternVL-V1.5 (Chen et al., ) | 20B | 60.2 | 61.7 | 46.4 | 49.1 | 45.6 | 46.6 | 50.7 | 52.4 |\\n| Video-LLaVA | 7B | 45.3 | 46.1 | 38.0 | 40.7 | 36.2 | 38.1 | 39.9 | 41.6 |\\n| ST-LLM | 7B | 45.7 | 48.4 | 36.8 | 41.4 | 31.3 | 36.9 | 37.9 | 42.3 |\\n| VideoChat2-Mistral | 7B | 48.3 | 52.8 | 37.0 | 39.4 | 33.2 | 39.2 | 39.5 | 43.8 |\\n| Chat-UniVi-V1.5 | 7B | 45.7 | 51.2 | 40.3 | 44.6 | 35.8 | 41.8 | 40.6 | 45.9 |\\n| LLaVA-NeXT-Video | 7B | 45.9 | 49.8 | 40.3 | 44.3 | 36.6 | 41.0 | 40.9 | 45.0 |\\n| LLaVA-NeXT-Video | 34B | 61.7 | 65.1 | 50.1 | 52.2 | 44.3 | 47.2 | 52.0 | 54.9 |\\n| PPLLaVA | 7B | 56.1 | 59.7 | 43.9 | 48.6 | 38.4 | 44.0 | 46.1 | 50.0 |\\n| PPLLaVA* | 7B | 58.7 | 62.8 | 45.6 | 50.4 | 42.2 | 47.4 | 48.8 | 53.6 |\\n\\nData Details.\\nThe instruction tuning data includes diverse modalities and sources. We randomly sampled 300k image data from the LLAVA-1.5 training set (Liu et al., ) and used 594k multiple-image data from LLAVA-Interleave (Liu et al., ). The video data includes Kinetics (Kay et al., ), SthSth-V2 (Goyal et al., ), Next-QA (Xiao et al., ), CLEVRER (Yi et al., ), and LLAVA-Interleave-300k, resulting in a total of 1.36M multimodal training samples. Notably, to ensure fairness in the comparison experiments, we excluded multi-image data and used only 760k image-video data, comparable to the training volume of most video LLMs.\\n\\nWe evaluate our model on six video LLM benchmarks, categorized into two types based on the evaluation method: GPT-based evaluation and multiple-choice questions. The GPT evaluation mainly involves open-ended QA, including the Video-based Generative Performance Benchmark (VCG Bench) (Maaz et al., ), MSVD-QA (Wu et al., ), MSRVTT-QA (Xu et al., ), and ActivityQA (Caba Heilbron et al., ). Consistent with most models, we used the GPT-3.5-turbo-0613 version for testing. The multiple-choice question benchmarks include MVBench (Li et al., ) and Video-MME (Fu et al., ). This evaluation method is more objective by eliminating the potential disturbances of GPT. For medium-to-long videos in Video-MME, we sampled 64 frames instead of the 32 frames used in other datasets. Our test corpus encompasses videos of various genres and lengths, offering a comprehensive evaluation of PPLLaVA’s performance.\\n\\n**Table 4: Results on MVBench. Models without additional annotation are 7B by default. * means using multi-images during training.**\\n| Method | AS | AP | AA | FA | UA | OE | OI | OS | MD | AL | ST | AC | MC | MA | SC | FP | CO | EN | ER | CI | Avg. |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| Video-LLaMA | 27.5 | 25.5 | 51.0 | 29.0 | 39.0 | 48.0 | 40.5 | 38.0 | 22.5 | 22.5 | 43.0 | 34.0 | 22.5 | 32.5 | 45.5 | 32.5 | 40.0 | 30.0 | 21.0 | 37.0 | 34.1 |\\n| LLaMA-Adapter | 23.0 | 28.0 | 51.0 | 30.0 | 33.0 | 53.5 | 32.5 | 33.5 | 25.5 | 21.5 | 30.5 | 29.0 | 22.5 | 41.5 | 39.5 | 25.0 | 31.5 | 22.5 | 28.0 | 32.0 | 31.7 |\\n| Video-ChatGPT | 23.5 | 26.0 | 62.0 | 22.5 | 26.5 | 54.0 | 28.0 | 40.0 | 23.0 | 20.0 | 31.0 | 30.5 | 25.5 | 39.5 | 48.5 | 29.0 | 33.0 | 29.5 | 26.0 | 35.5 | 32.7 |\\n| VideoChat | 33.5 | 26.5 | 56.0 | 33.5 | 40.5 | 53.0 | 40.5 | 30.0 | 25.5 | 27.0 | 48.5 | 35.0 | 20.5 | 42.5 | 46.0 | 26.5 | 41.0 | 23.5 | 23.5 | 36.0 | 35.5 |\\n| VideoChat2 | 66.0 | 47.5 | 83.5 | 49.5 | 60.0 | 58.0 | 71.5 | 42.5 | 23.0 | 23.0 | 88.5 | 39.0 | 42.0 | 58.5 | 44.0 | 49.0 | 36.5 | 35.0 | 40.5 | 65.5 | 51.1 |\\n| ST-LLM | 66.0 | 53.5 | 84.0 | 44.0 | 58.5 | 80.5 | 73.5 | 38.5 | 42.5 | 31.0 | 86.5 | 36.5 | 56.5 | 78.5 | 43.0 | 44.5 | 46.5 | 34.5 | 41.5 | 58.5 | 54.9 |\\n| PLLaVA-7B | 58.0 | 49.0 | 55.5 | 41.0 | 61.0 | 56.0 | 61.0 | 36.0 | 23.5 | 26.0 | 82.0 | 39.5 | 42.0 | 52.0 | 45.0 | 42.0 | 53.5 | 30.5 | 48.0 | 31.0 | 46.6 |\\n| PLLaVA-13B | 66.0 | 53.0 | 65.5 | 45.0 | 65.0 | 58.0 | 64.5 | 35.5 | 23.5 | 30.0 | 85.0 | 39.5 | 45.5 | 57.0 | 47.5 | 49.5 | 49.0 | 33.0 | 53.0 | 37.0 | 50.1 |\\n| PLLaVA-34B | 67.5 | 53.0 | 82.0 | 47.0 | 79.0 | 68.5 | 67.5 | 36.5 | 37.5 | 49.5 | 91.0 | 40.5 | 43.0 | 70.0 | 51.5 | 50.0 | 66.5 | 39.5 | 63.5 | 59.0 | 58.1 |\\n| GPT-4V | 55.5 | 63.5 | 72.0 | 46.5 | 73.5 | 18.5 | 59.0 | 29.5 | 12.0 | 40.5 | 83.5 | 39.0 | 12.0 | 22.5 | 45.0 | 47.5 | 52.0 | 31.0 | 59.0 | 11.0 | 43.5 |\\n| PPLLaVA-7B | 69.0 | 54.4 | 69.5 | 50.5 | 69.0 | 87.0 | 67.0 | 38.0 | 35.0 | 33.0 | 69.5 | 37.5 | 63.5 | 91.0 | 47.5 | 47.5 | 51.5 | 27.0 | 47.5 | 57.5 | 57.1 |\\n| PPLLaVA-7B* | 73.5 | 61.0 | 83.5 | 45.5 | 68.0 | 87.5 | 75.5 | 33.0 | 37.5 | 40.0 | 83.0 | 37.0 | 67 | 96.5 | 50.5 | 43.5 | 59.0 | 35.5 | 44.5 | 63.0 | 59.2 |\\n\\n**Table 5: The ablation study on model components. TP means throughput (seconds/video).**\\n| Model | Context | VCG Bench | Video-MME (w/ subs) | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| Length | CI | DO | CU | TU | CO | Avg | TP | Short | Medium | Long | Overall | TP | |\\n| LLaVA-Next (Average Pooing) | 576 | 3.05 | 3.07 | 3.71 | 2.62 | 3.01 | 3.09 | 2.9 | 53.1 | 41.3 | 36.0 | 43.4 | 3.1 |\\n| LLaVA-Next (w/o Pooing) | 4608 | 3.23 | 3.08 | 3.82 | 2.75 | 3.11 | 3.20 | 15.0 | 58.4 | 45.1 | 38.8 | 47.4 | 15.2 |\\n| +Prompt-guided Pooling | 1024 | 3.21 | 3.15 | 3.80 | 2.88 | 3.02 | 3.21 | 4.6 | 59.0 | 45.6 | 42.2 | 48.9 | 5.3 |\\n| +CLIP Context Extension | 1024 | 3.32 | 3.20 | 3.88 | 3.00 | 3.20 | 3.32 | 4.6 | 59.7 | 48.6 | 44.0 | 50.0 | 5.3 |\\n\\n### 4.2 Quantitative Result\\n\\nGPT-Based Evaluation.\\nTable 2 presents the quantitative results for open-ended question-answering, showing that PPLLaVA achieves top performance across all datasets. It also demonstrates a significant performance gap compared to models other than LLaVA-Next-Video, demonstrating the strong text generation capability of our model. Despite using lower-quality data (as LLaVA 1.6 data is not publicly available), PPLLaVA outperforms LLaVA-Next-Video. More importantly, PPLLaVA uses significantly fewer visual contexts (1024 vs. 4096), resulting in higher throughput. After applying DPO, PPLLaVA also shows consistent improvements and outperforms other models that use DPO or PPO, further proving the adaptability of the PPLLaVA architecture across different training stages.\\n\\nVideo-MME.\\nAlthough Video-MME is a new benchmark, it offers high quality and data diversity. Its inclusion of hour-long videos makes it particularly effective for evaluating models’ long video understanding capabilities. As shown in Table 3, PPLLaVA achieves the best results on Video-MME, with a notably significant advantage on videos of different lengths compared to other models. The 7B model’s long video comprehension already surpasses the 34B LLaVA-Next-Video, as PPLLaVA efficiently compresses video tokens, enabling support for a much higher number of frames than LLaVA-Next-Video, thereby enhancing long video understanding capabilities.\\n\\nMVBench.\\nMVBench is a multiple-choice benchmark offering a comprehensive set of evaluation tasks, including Action Sequence (AS), Action Prediction (AP), Action Antonym (AA), Fine-grained Action (FA), Unexpected Action (UA), Object Existence (OE), Object Interaction (OI), Object Shuffle (OS), Moving Direction (MD), Action Localization (AL), Scene Transition (ST), Action Count (AC), Moving Count (MC), Moving Attribute (MA), State Change (SC), Fine-grained Pose (FP), Character Order (CO), Egocentric Navigation (EN), Episodic Reasoning (ER), Counterfactual Inference (CI), and the average across all 20 metrics (Avg). PPLLaVA achieves the best average results among models, demonstrating a clear advantage and strong adaptability in video understanding across diverse scenarios, especially for moving and action tasks.\\n\\n### 4.3 Ablations and Analysis\\n\\nModel Components.\\nThe core of PPLLaVA is its prompt-guided token compression, which enhances both video understanding efficiency and performance. To assess the impact of this feature, we conducted ablation experiments on the overall model components. As shown in Table 5, while the LLaVA-Next Baseline’s direct averaging method is the most efficient, its performance is subpar. Directly feeding all tokens into the LLM yields reasonable results but suffers from extremely low throughput. Our Pooling module substantially improves both efficiency and performance. Extending the CLIP context further enhances results, particularly in long video understanding. The simultaneous improvement in efficiency and effectiveness underscores the superiority of our model.\\n\\nFigure: Figure 3: Spatial pooling effects. We set $T=16$ and $k_{t}=d_{t}=1$, varying the spatial kernel size and stride.\\nRefer to caption: x3.png\\n\\n**Table 6: The image results. $\\\\star$ means self-implementation.**\\n| Model | Resolution | MMMU(val) | MathVista | MMB-ENG | MMB-CN | MM-Vet | SEED-IMG | MME | POPE |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| LLaVA-1.5-13B | 336*336 | 36.4 | 27.6 | 67.8 | 63.3 | 36.3 | 68.2 | 1531/295 | 85.93 |\\n| LLaVA-Next-7B | 672*672 | 35.8 | 34.6 | 67.4 | 60.6 | 43.9 | 70.2 | 1519/332 | 86.53 |\\n| VideoLLaVA | 336*336 | - | - | 60.9 | - | 32.0 | - | - | 84.40 |\\n| Chat-Univ-1.5 | 336*336 | - | - | 62.7 | - | 28.3 | - | - | 85.40 |\\n| LLaVA-Next-Video $\\\\star$ | 336*336 | 34.2 | 28.9 | 64.7 | 56.7 | 44.0 | 64.6 | 1501/351 | 83.10 |\\n| PPLLaVA | 336*336 | 37.9 | 34.6 | 68.9 | 62.0 | 44.7 | 70.7 | 1539/277 | 88.46 |\\n\\nFigure: Table 7: The ablation study on the Pooling Approach. We report the overall performance of VideoMME (w/ subs).\\n\\nPooling Size.\\nPPLLaVA can flexibly implement pooling at any scale. However, as the pooling kernel and stride increase, while efficiency improves, there will inevitably be performance degradation. Therefore, it’s crucial to find a pooling size that balances both efficiency and performance. As illustrated in Fig. 4, we first explore the impact of pooling in the spatial dimension. It is evident that when the pooling kernel and stride are small, increasing them significantly improves efficiency, and thanks to the prompt-guided approach, the performance remains almost unaffected. In contrast, as shown in Fig. 4, pooling in the temporal dimension yields smaller efficiency gains compared to spatial scaling, with more noticeable performance degradation as the kernel and stride sizes increase. When the pooling kernel and stride are large, the efficiency gains tend to plateau, but the decline in effectiveness becomes significantly pronounced, particularly in spatial pooling, where the performance drop is more severe. Considering all factors, for video input, we ultimately selected a pooling kernel and stride of (2, 3, 3) to ensure a substantial improvement in efficiency while maintaining stable model performance.\\n\\n**Table 9: The study on multimodal data with interleave training and DPO training.**\\n| Model | Video | Image | Multi-Image | Interleave | DPO | VcgBench | MvBench | VideoMME |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| LLaVA-Next-Video | $\\\\checkmark$ | $\\\\checkmark$ | | $\\\\checkmark$ | | 3.26 | - | - |\\n| $\\\\checkmark$ | $\\\\checkmark$ | | $\\\\checkmark$ | $\\\\checkmark$ | 3.66 | - | - | |\\n| PPLLaVA | $\\\\checkmark$ | | | | | 3.20 | 55.0 | 48.9 |\\n| $\\\\checkmark$ | $\\\\checkmark$ | | | | 3.09 | 49.8 | 44.1 | |\\n| $\\\\checkmark$ | $\\\\checkmark$ | | $\\\\checkmark$ | | 3.32 | 57.1 | 50.0 | |\\n| $\\\\checkmark$ | $\\\\checkmark$ | $\\\\checkmark$ | $\\\\checkmark$ | | 3.21 | 59.2 | 53.6 | |\\n| $\\\\checkmark$ | $\\\\checkmark$ | | $\\\\checkmark$ | $\\\\checkmark$ | 3.73 | 55.8 | 49.3 | |\\n\\nFigure: Figure 5: The visualization of the attention weights used to guide video pooling.\\nRefer to caption: x5.png\\n\\nImage Performance.\\nTheoretically, further video tuning on top of an image-domain LLM could lead to catastrophic forgetting of pre-trained knowledge and image understanding. The PPLLaVA method can also be seamlessly applied to images. Although images do not have the same need for token compression as videos, and compression may lead to performance loss, the guidance from user prompts can still similarly enhance performance.\\nIn Table 6, we present PPLLaVA’s results on various popular image LLM benchmarks. Since PPLLaVA was trained on LLaVA-1.5 image data based on LLaVA-Next, we compared the results of these two models. We also compare the image performance with LLaVA-Next-Video and other image-video unified models. As shown, PPLLaVA shows a significant advantage in image performance compared to video models, indicating that PPLLaVA has effectively retained pre-trained knowledge. Compared to image models, despite using a smaller LLM or lower image resolution, PPLLaVA, as a video model, still achieved better results on most benchmarks.\\nNotably, our pooling method reduced the visual tokens to one-ninth of the original count at the same resolution. This demonstrates that PPLLaVA can achieve both performance and efficiency improvements even on image-based tasks, highlighting its potential for lightweight multimodal LLM.\\n\\nPrompt-Guided Pooling Approach.\\nBeyond the weighted average pooling detailed in the main text, we experimented with several alternative pooling methods guided by the prompt. First, we applied separate spatiotemporal pooling, conducting pooling operations independently on the temporal and spatial dimensions before concatenation. We also explored combinations of different pooling sizes to assess their impact. Lastly, we implemented max pooling using weights derived from the prompt as guidance. As shown in Table 7, spatiotemporal separate pooling demonstrates the worst performance, underscoring the importance of maintaining the 3-dimensional spatiotemporal structure during pooling. Max pooling, though slightly better, still falls short, suggesting that a few prominent features are insufficient to represent the entirety of the video. The combination of various pooling kernels performs similarly to direct weighted averaging when the context length is comparable. Consequently, we opted for weighted averaging, as it provides optimal results while maintaining a simpler structure.\\n\\nIs PPLLaVA Really Helpful for Long Video?\\nToken compression is a key feature of PPLLaVA, primarily aimed at enhancing the understanding of long videos. To validate PPLLaVA’s effectiveness in this regard, we conducted an additional ablation experiment. As shown in Table 8, we first experimented with larger pooling kernels to accommodate more frames. The results indicate that even with some discrepancies between training and testing, using a greater number of frames still improves long video comprehension. When fewer frames are used during training, the disadvantage in long video understanding becomes even more pronounced. In the most extreme case, when no pooling is applied, even with significantly longer context lengths, the understanding of long videos is the weakest due to the limited number of frames that can be accommodated.\\n\\nInterleave training and DPO.\\nMultimodal data interleaved training and DPO are two key techniques utilized in this work. We conducted an analysis of their effects and compatibility with PPLLaVA. As shown in Table 9, when different data modalities are not mixed within a batch, adding image or multi-image modalities leads to performance degradation compared to pure video training. This aligns with the conclusions of LLaVA-Next-Video. When data modalities are mixed within the same batch, the additional images enhance performance. However, we found that when further adding multi-image data, the performance on the multiple-choice benchmark improved, but the performance on the caption generation benchmark declined. This indicates that multi-image data can enhance the model’s visual knowledge but may reduce its capability in video-based dialogue.\\nIn contrast, DPO training has a minimal side effect on multiple-choice benchmarks but significantly improves results in GPT-based evaluation. This highlights DPO’s ability to effectively reduce hallucinations in LLM outputs, leading to higher-quality dialogues. Moreover, when compared to the baseline and LLaVA-Next-Video, the combination of DPO and PPLLaVA yields similar improvements. This emphasizes the strong compatibility between PPLLaVA and DPO.\\n\\nFigure: Figure 6: Qualitative result of video summary and detailed video description.\\nRefer to caption: x6.png\\n\\n## 5 Qualitative Results\\n\\nIn Fig. 5, we visualize the attention weights used to guide video pooling based on the user prompts. For the same video, we tried different questions. It can be clearly observed that the model’s attention shifts noticeably depending on the question. For example, when the user asks about the girl’s feelings, the attention is significantly focused on her face. Conversely, when asked about the number\\n\\nFigure: Figure 7: Qualitative result of multi-turn video conversation and reasoning.\\nRefer to caption: x7.png\\n\\nof 3D objects in the video, the attention shifts more toward the 3D objects. These visualizations demonstrate that while reducing the visual context, PPLLaVA effectively captures the key information in the video. In Fig. 6 and 7, we further present some examples of video dialogue. As shown in Fig. 6, for the famous Sora video, PPLLaVA can accurately and intricately describe details about the protagonist and the environment. For the more complex scene changes in the trailer for Black Myth Wu Kong, PPLLaVA remarkably captures the details of each scene and character. In Fig. 7, PPLLaVA maintains accuracy and consistency across multiple rounds of dialogue and is capable of making reasonable inferences on open-ended questions.\\n\\n## 6 Limitation\\n\\nAlthough the 7B PPLLaVA has demonstrated impressive performance, even rivaling that of 34B video LLMs, our biggest regret is that, due to a lack of computational resources, we were unable to train larger-scale LLMs to uncover the limits of this architecture. Additionally, the conflict between the enhanced understanding capabilities brought by multi-image data and the decline in dialogue abilities remains unsolved in this work; a reasonable data allocation ratio might address this issue. We leave these problems for future work.\\n\\n## 7 Conclusion\\n\\nIn this paper, we propose Prompt-guided Pooling LLaVA (PPLLaVA), a novel pooling method that achieves token compression and prompt-aware feature extraction simultaneously. We first observed that current video LLMs struggle to balance performance on both long and short videos. Further analysis revealed that redundant tokens in videos negatively impact video understanding performance. To address this, our model incorporates three key modules: Fine-grained Vision-Prompt Alignment, Prompt-Guided Convolution-Style Pooling, and CLIP Context Extension. These modules significantly reduce the visual context while effectively extracting essential visual features. Extensive experiments have demonstrated the effectiveness of PPLLaVA on both images and videos, as it achieves the best results across benchmarks of various tasks and video lengths, ensuring excellent efficiency, with particularly outstanding performance on long videos.\",\n \"metadata\": {\n \"authors\": [\n \"Ruyang Liu\",\n \"Haoran Tang\",\n \"Haibo Lu\",\n \"Yixiao Ge\",\n \"Ying Shan\",\n \"Chen Li ✉\",\n \"Jiankun Yang ✉\",\n \"Peking University\",\n \"Applied Research Center (ARC), Tencent PCG\",\n \"Peng Cheng Laboratory\",\n \"{palchenli,yixiaoge,yingsshan}@tencent.com\"\n ],\n \"title\": \"PPLLaVA: Varied Video Sequence Understanding With Prompt Guidance\",\n \"total_chars\": 47737,\n \"total_lines\": 254,\n \"updated_at\": \"2026-01-25T15:02:51.431437\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"PYoXbUjM1T","initial_rating":6,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"The paper proposes a new model that can handle short and long videos with state-of-the-art performance under comparable model sizes. By using DPO's fine-tuning strategy, the proposed PPLLaVA is able to outperform selected baseline models. This is achieved by incorporating three components: the CLIP-based visual-prompt alignment that extracts visual information relevant to the user’s instructions, the prompt-guided pooling that compresses the visual sequence to arbitrary scales using convolution-style pooling, and the clip context extension designed for lengthy prompt common in visual dialogue.","strengths":"1. The paper's motivation is interesting: applying pooling based on the text-frame similarity is reasonable. This is effective on removing redundant video frames conditioned on the user prompt input.\n2. The author also proposes methods to handle long user inputs.\n3. The final results are promising.","weaknesses":"1. How the capability of CLIP affects the model performance is not discussed. Since the method relay on CLIP to remove redundant video frames, its accuracy could be the bottleneck of the method. Will a stronger text-image matching encoder further improve the model's performance? I believe adding this type pf discussion to the paper will make it stronger.","questions":"Please refer to the weakness section: Will a stronger text-image matching encoder further improve the model's performance?"},{"id":"lNhtzSmEh5","initial_rating":6,"confidence":5,"soundness":3,"contribution":4,"presentation":3,"summary":"This paper proposes a novel pooling method to enhance video large language models (LLMs) by enabling token compression and prompt-aware feature extraction. The approach can be summarized as follows:\n- Prompt-Relevant Visual Feature Extraction: The method begins by identifying visual features relevant to the prompt through a fine-grained visual-prompt alignment.\n- 3D Token Compression: Leveraging prompt-vision alignment, the authors employ a 3D convolutional kernel to compress tokens to a specified 3D size, adjusting the output stride accordingly.\n- Asymmetric Positional Embedding: To further enhance the model's capabilities, the authors introduce asymmetric positional embedding extensions to expand the capacity of text encoding.\n\nThe proposed method achieves a significant compression rate and supports both short and long token inputs. In comparison to Q-Former, the authors argue that their approach offers greater flexibility and adaptability.\n\nExtensive experiments across a variety of datasets demonstrate promising performance improvements with this method.","strengths":"- This paper begins with a clear analysis of video LLMs and highlights limitations in existing pooling techniques, effectively motivating the proposed approach.\n- The proposed method, which comprises three key components, is technically sound and well-justified, addressing the identified challenges.\n- The training strategy is particularly interesting, utilizing detailed video captions as proxies for video content and performing DPO with feedback from the language model serving as a reward signal.\n- Experimental results demonstrate substantial performance improvements, supporting the effectiveness of the proposed approach.\n- The paper includes detailed analysis, providing insights into the efficiency and performance gains of the model, with evidence suggesting that DPO plays a critical role in achieving the final results.\n- The paper is well-written and easy to understand.","weaknesses":"- The diagrams could benefit from more detailed captions to enhance clarity. For example, Figure 2 requires additional context to quickly convey the relationship between [TOK] and the 3D blue rectangle, as this took some time to interpret.\n- The fairness of the comparisons is questionable, as many previous works do not utilize DPO in their training. This difference may give the proposed method an advantage, making it challenging to assess its improvements solely based on the new pooling technique.","questions":"- Since the proposed method builds on the image-domain LLaVA, would it be feasible to adapt this approach to existing video LLMs directly? It would be interesting to understand any potential challenges or modifications required for integration with current video-specific models."},{"id":"Ipl6mLVhGq","initial_rating":3,"confidence":5,"soundness":3,"contribution":3,"presentation":3,"summary":"The paper proposes a novel method named PPLLAVA, which is based on Video LLM. my concerns are as below.\n1. The authors claim that the method is for long video, however, I cannot see the comparison of performances when applying the method to long/short videos. Also, how to define \"long video\"? 1 hour long?\n2. I think LLAVA is for images, instead of video. While if the authors want to apply LLAVA to videos, why not do like this: a. locate the related frames; b. VQA on frames. I cannot see the necessity of the three steps way.\n3. The authors seems want to satisfy the user's needs/reply to user's questions. What if the questions are open-ended questions without an answer?\n4. why we need \"Prompt-Guided Pooling\"? I cannot see the necessity of prompt here.","strengths":"The paper is well-written, with clear pipeline, framework, and experimental results.","weaknesses":"As can be found in the summary. I cannot see why the approach should be applied to videos instead of image-level applications.","questions":"Will the method also be applied to image-level applications? is video necessary?"},{"id":"z97QpYzXlO","initial_rating":5,"confidence":4,"soundness":3,"contribution":2,"presentation":2,"summary":"This paper proposed PPLLAVA, a video-LLM based on a prompt-guide pooling strategy. The core idea is to conduct text query/prompt-dependent pooling for video features before putting them into LLM. The authors conduct extensive experiments to show the effectiveness of the proposed method. The proposed PPLLAVA outperforms other training-free/training-based video-LLM at a similar model scale.","strengths":"(1) this paper conducts extensive experiments to show the effectiveness of the proposed methods.\n\n(2) pooling redundant tokens based on visual-text similarity is an efficient solution to capture query-related information in a video with large redundancy.\n\n(3) The design of extending the CLIP content window is smart enough to adapt CLIP to a longer context with minimal modification.","weaknesses":"(1) one thing I'm a bit confused about is the video captioning setting when adapting this prompt-guided pooling strategy. As the caption prompts are not as diverse as that question answering, holistic captioning should be affected unless the user is querying a specific object-related caption. I would suggest some experiments on video caption benchmarks, e.g. activitynet caption or newer DREAM-1K, to further support the strong video understanding ability claim.\n\n(2) it seems the paper missed some related baseline methods, see LongVA [1], and Kangaroo [2]. It should be helpful to include a more comprehensive analysis and comparison with those methods, even if some of them achieve better performance on some datasets. \n\n(3) My other big concern is the novelty side. While I understand this paper did a good job of validating their idea/design with extensive experiments and ablations, comparing some zero-shot baseline like PLLAVA/LLaVA-NeXT-Video, the big boost of the performance might come from fine-tuning on 1.3M multimodal data and the prompt-guided pooling seems a bit incremental from my personal perspective. So I am a bit worried that if we conduct the same level of training with a stronger LLM backbone that has a long content window, the model can learn this query-related attention itself, so the proposed core idea, prompt-guided pooling, seems sub-optimal. \n\n(4) A potential solution might be to fine-tune zero methods that conduct their token merging idea with the same data and show the performance difference.\n\n[1] Long Context Transfer from Language to Vision\n[2] Kangaroo: A powerful video-language model supporting long-context video input","questions":"Please see the weaknesses."},{"id":"DbXjUMw9uV","initial_rating":3,"confidence":4,"soundness":3,"contribution":2,"presentation":3,"summary":"The paper introduces a novel approach to video understanding by leveraging prompt guidance to enhance the performance of video language models (VLMs). The methodology focuses on reducing video redundancy and extracting key content to enhance the performance of VLMs. It uses CLIP-based visual-prompt alignment to extract relevant visual information and compresses visual sequences using convolution-style pooling. Direct Preference Optimization (DPO) was also used to improve its performance. In experiments, PPLLaVA demonstrated good results on both long and short video benchmarks, and achieves over an 80% compression rate.","strengths":"1. The paper introduces methods for video understanding by leveraging prompt guidance through the use of CLIP-based visual-prompt alignment and convolution-style pooling.\n2. PPLLaVA shows versatility by performing well on both long and short video benchmarks, demonstrating robust performance for varied video sequence understanding. This adaptability is crucial for handling diverse video lengths and complexities, making it a robust solution for varied video sequence understanding5.\n3. PPLLaVA uses Direct Preference Optimization (DPO) to reduce hallucinations in video-based dialogue and also applies CLIP Context Extension to expand text encoding capacity.","weaknesses":"1. PPLLaVA does not show leading results compared to some training-free compression methods like SLOWFAST-LLAVA[1], on benchmarks such as MSVD and MSRVTT.\n2. The use of Direct Preference Optimization (DPO) and Proximal Policy Optimization (PPO) lacks innovation. Also, LLaVA-Next-Video also achieve great accuracy improvements using above methods, but this paper does not highlight any unique advantages of these methods within PPLLaVA. \n\n[1] SlowFast-LLaVA: A Strong Training-Free Baseline for Video Large Language Models","questions":"1. The method seems similar to the involution kernel[1]. What are the differences between the two? \n2. Have any ablation studies been conducted using regular 3D convolution for pooling instead of prompt-guided methods? \n3. In Table 5, why is the context length for average pooling set to 576 instead of 1024?\n4. Can PPLLaVA extend to multimodal **generative** models?\n\n[1] Involution: Inverting the Inherence of Convolution for Visual Recognition"}],"string":"[\n {\n \"id\": \"PYoXbUjM1T\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"The paper proposes a new model that can handle short and long videos with state-of-the-art performance under comparable model sizes. By using DPO's fine-tuning strategy, the proposed PPLLaVA is able to outperform selected baseline models. This is achieved by incorporating three components: the CLIP-based visual-prompt alignment that extracts visual information relevant to the user’s instructions, the prompt-guided pooling that compresses the visual sequence to arbitrary scales using convolution-style pooling, and the clip context extension designed for lengthy prompt common in visual dialogue.\",\n \"strengths\": \"1. The paper's motivation is interesting: applying pooling based on the text-frame similarity is reasonable. This is effective on removing redundant video frames conditioned on the user prompt input.\\n2. The author also proposes methods to handle long user inputs.\\n3. The final results are promising.\",\n \"weaknesses\": \"1. How the capability of CLIP affects the model performance is not discussed. Since the method relay on CLIP to remove redundant video frames, its accuracy could be the bottleneck of the method. Will a stronger text-image matching encoder further improve the model's performance? I believe adding this type pf discussion to the paper will make it stronger.\",\n \"questions\": \"Please refer to the weakness section: Will a stronger text-image matching encoder further improve the model's performance?\"\n },\n {\n \"id\": \"lNhtzSmEh5\",\n \"initial_rating\": 6,\n \"confidence\": 5,\n \"soundness\": 3,\n \"contribution\": 4,\n \"presentation\": 3,\n \"summary\": \"This paper proposes a novel pooling method to enhance video large language models (LLMs) by enabling token compression and prompt-aware feature extraction. The approach can be summarized as follows:\\n- Prompt-Relevant Visual Feature Extraction: The method begins by identifying visual features relevant to the prompt through a fine-grained visual-prompt alignment.\\n- 3D Token Compression: Leveraging prompt-vision alignment, the authors employ a 3D convolutional kernel to compress tokens to a specified 3D size, adjusting the output stride accordingly.\\n- Asymmetric Positional Embedding: To further enhance the model's capabilities, the authors introduce asymmetric positional embedding extensions to expand the capacity of text encoding.\\n\\nThe proposed method achieves a significant compression rate and supports both short and long token inputs. In comparison to Q-Former, the authors argue that their approach offers greater flexibility and adaptability.\\n\\nExtensive experiments across a variety of datasets demonstrate promising performance improvements with this method.\",\n \"strengths\": \"- This paper begins with a clear analysis of video LLMs and highlights limitations in existing pooling techniques, effectively motivating the proposed approach.\\n- The proposed method, which comprises three key components, is technically sound and well-justified, addressing the identified challenges.\\n- The training strategy is particularly interesting, utilizing detailed video captions as proxies for video content and performing DPO with feedback from the language model serving as a reward signal.\\n- Experimental results demonstrate substantial performance improvements, supporting the effectiveness of the proposed approach.\\n- The paper includes detailed analysis, providing insights into the efficiency and performance gains of the model, with evidence suggesting that DPO plays a critical role in achieving the final results.\\n- The paper is well-written and easy to understand.\",\n \"weaknesses\": \"- The diagrams could benefit from more detailed captions to enhance clarity. For example, Figure 2 requires additional context to quickly convey the relationship between [TOK] and the 3D blue rectangle, as this took some time to interpret.\\n- The fairness of the comparisons is questionable, as many previous works do not utilize DPO in their training. This difference may give the proposed method an advantage, making it challenging to assess its improvements solely based on the new pooling technique.\",\n \"questions\": \"- Since the proposed method builds on the image-domain LLaVA, would it be feasible to adapt this approach to existing video LLMs directly? It would be interesting to understand any potential challenges or modifications required for integration with current video-specific models.\"\n },\n {\n \"id\": \"Ipl6mLVhGq\",\n \"initial_rating\": 3,\n \"confidence\": 5,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"The paper proposes a novel method named PPLLAVA, which is based on Video LLM. my concerns are as below.\\n1. The authors claim that the method is for long video, however, I cannot see the comparison of performances when applying the method to long/short videos. Also, how to define \\\"long video\\\"? 1 hour long?\\n2. I think LLAVA is for images, instead of video. While if the authors want to apply LLAVA to videos, why not do like this: a. locate the related frames; b. VQA on frames. I cannot see the necessity of the three steps way.\\n3. The authors seems want to satisfy the user's needs/reply to user's questions. What if the questions are open-ended questions without an answer?\\n4. why we need \\\"Prompt-Guided Pooling\\\"? I cannot see the necessity of prompt here.\",\n \"strengths\": \"The paper is well-written, with clear pipeline, framework, and experimental results.\",\n \"weaknesses\": \"As can be found in the summary. I cannot see why the approach should be applied to videos instead of image-level applications.\",\n \"questions\": \"Will the method also be applied to image-level applications? is video necessary?\"\n },\n {\n \"id\": \"z97QpYzXlO\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper proposed PPLLAVA, a video-LLM based on a prompt-guide pooling strategy. The core idea is to conduct text query/prompt-dependent pooling for video features before putting them into LLM. The authors conduct extensive experiments to show the effectiveness of the proposed method. The proposed PPLLAVA outperforms other training-free/training-based video-LLM at a similar model scale.\",\n \"strengths\": \"(1) this paper conducts extensive experiments to show the effectiveness of the proposed methods.\\n\\n(2) pooling redundant tokens based on visual-text similarity is an efficient solution to capture query-related information in a video with large redundancy.\\n\\n(3) The design of extending the CLIP content window is smart enough to adapt CLIP to a longer context with minimal modification.\",\n \"weaknesses\": \"(1) one thing I'm a bit confused about is the video captioning setting when adapting this prompt-guided pooling strategy. As the caption prompts are not as diverse as that question answering, holistic captioning should be affected unless the user is querying a specific object-related caption. I would suggest some experiments on video caption benchmarks, e.g. activitynet caption or newer DREAM-1K, to further support the strong video understanding ability claim.\\n\\n(2) it seems the paper missed some related baseline methods, see LongVA [1], and Kangaroo [2]. It should be helpful to include a more comprehensive analysis and comparison with those methods, even if some of them achieve better performance on some datasets. \\n\\n(3) My other big concern is the novelty side. While I understand this paper did a good job of validating their idea/design with extensive experiments and ablations, comparing some zero-shot baseline like PLLAVA/LLaVA-NeXT-Video, the big boost of the performance might come from fine-tuning on 1.3M multimodal data and the prompt-guided pooling seems a bit incremental from my personal perspective. So I am a bit worried that if we conduct the same level of training with a stronger LLM backbone that has a long content window, the model can learn this query-related attention itself, so the proposed core idea, prompt-guided pooling, seems sub-optimal. \\n\\n(4) A potential solution might be to fine-tune zero methods that conduct their token merging idea with the same data and show the performance difference.\\n\\n[1] Long Context Transfer from Language to Vision\\n[2] Kangaroo: A powerful video-language model supporting long-context video input\",\n \"questions\": \"Please see the weaknesses.\"\n },\n {\n \"id\": \"DbXjUMw9uV\",\n \"initial_rating\": 3,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"The paper introduces a novel approach to video understanding by leveraging prompt guidance to enhance the performance of video language models (VLMs). The methodology focuses on reducing video redundancy and extracting key content to enhance the performance of VLMs. It uses CLIP-based visual-prompt alignment to extract relevant visual information and compresses visual sequences using convolution-style pooling. Direct Preference Optimization (DPO) was also used to improve its performance. In experiments, PPLLaVA demonstrated good results on both long and short video benchmarks, and achieves over an 80% compression rate.\",\n \"strengths\": \"1. The paper introduces methods for video understanding by leveraging prompt guidance through the use of CLIP-based visual-prompt alignment and convolution-style pooling.\\n2. PPLLaVA shows versatility by performing well on both long and short video benchmarks, demonstrating robust performance for varied video sequence understanding. This adaptability is crucial for handling diverse video lengths and complexities, making it a robust solution for varied video sequence understanding5.\\n3. PPLLaVA uses Direct Preference Optimization (DPO) to reduce hallucinations in video-based dialogue and also applies CLIP Context Extension to expand text encoding capacity.\",\n \"weaknesses\": \"1. PPLLaVA does not show leading results compared to some training-free compression methods like SLOWFAST-LLAVA[1], on benchmarks such as MSVD and MSRVTT.\\n2. The use of Direct Preference Optimization (DPO) and Proximal Policy Optimization (PPO) lacks innovation. Also, LLaVA-Next-Video also achieve great accuracy improvements using above methods, but this paper does not highlight any unique advantages of these methods within PPLLaVA. \\n\\n[1] SlowFast-LLaVA: A Strong Training-Free Baseline for Video Large Language Models\",\n \"questions\": \"1. The method seems similar to the involution kernel[1]. What are the differences between the two? \\n2. Have any ablation studies been conducted using regular 3D convolution for pooling instead of prompt-guided methods? \\n3. In Table 5, why is the context length for average pooling set to 576 instead of 1024?\\n4. Can PPLLaVA extend to multimodal **generative** models?\\n\\n[1] Involution: Inverting the Inherence of Convolution for Visual Recognition\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;3;5;6;6\",\n \"rating_avg\": 4.6,\n \"confidence\": \"4;5;4;5;4\",\n \"confidence_avg\": 4.4,\n \"soundness\": \"3;3;3;3;3\",\n \"soundness_avg\": 3,\n \"contribution\": \"2;3;2;4;3\",\n \"contribution_avg\": 2.8,\n \"presentation\": \"3;3;2;3;3\",\n \"presentation_avg\": 2.8\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"Submitted to ICLR 2025\",\n \"venueid\": \"ICLR.cc/2025/Conference/Rejected_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.713531\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"hhTjDBCYvW\",\n \"metareview\": \"The paper proposes PPLLaVA, a video LLM utilizing prompt-guided pooling to efficiently process short and long videos. The method demonstrates strong performance across multiple video benchmarks. However, reviewers raised several concerns, including incremental novelty, CLIP dependency, fairness of comparisons and writting issues. Some of these concerns are addressed and confirmed by reviewers, while some of them are not well addressed. \\n\\nWhile the contributions are promising, the paper would benefit from addressing these concerns, including a deeper exploration of motivation and novelty, and a more thorough comparison with related works and baselines. Given the average score of 4.80 and intense competition at ICLR, the AC recommends revising the paper and considering submission to a future conference.\",\n \"additional_comments\": \"Reviewers raised several concerns, including incremental novelty, CLIP dependency, fairness of comparisons and writting issues. Some of these concerns are addressed and confirmed by reviewers, while some of them are not well addressed.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Reject\"\n}"}}},{"rowIdx":3395,"cells":{"paper_id":{"kind":"string","value":"qVyjN01x4P"},"arxiv_id":{"kind":"string","value":"2410.09836v1"},"title":{"kind":"string","value":"Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract Time series forecasting, which aims to predict future values based on historical data, has garnered significant attention due to its broad range of applications.\\nHowever, real-world time series often exhibit complex non-uniform distribution with varying patterns across segments, such as season, operating condition, or semantic meaning, making accurate forecasting challenging.\\nExisting approaches, which typically train a single model to capture all these diverse patterns, often struggle with the pattern drifts between patches and may lead to poor generalization.\\nTo address these challenges, we propose TFPS , a novel architecture that leverages pattern-specific experts for more accurate and adaptable time series forecasting. TFPS employs a dual-domain encoder to capture both time-domain and frequency-domain features, enabling a more comprehensive understanding of temporal dynamics. It then uses subspace clustering to dynamically identify distinct patterns across data patches. Finally, pattern-specific experts model these unique patterns, delivering tailored predictions for each patch. By explicitly learning and adapting to evolving patterns, TFPS achieves significantly improved forecasting accuracy. Extensive experiments on real-world datasets demonstrate that TFPS outperforms state-of-the-art methods, particularly in long-term forecasting, through its dynamic and pattern-aware learning approach. The data and codes are available: https://github.com/syrGitHub/TFPS .\\n\\n## 1 Introduction\\n\\nTime series forecasting plays a critical role in various domains, such as finance (Huang et al., ), weather (Bi et al., ; Wu et al., ; Lam et al., ), traffic (Long et al., ; Kong et al., ), and others (Wang et al., ; Liu et al., ), by modeling the relationship between historical data and future outcomes. However, the inherent complexity of time series data, including temporal dependencies and non-stationarity, poses significant challenges in achieving reliable forecasting results.\\n\\nRecent works have shown the effectiveness of Transformer-based models for time series forecasting, due to their ability to capture long-range dependencies (Zhou et al., ; Wu et al., ; Liu et al., ). In particular, models like PatchTST (Nie et al., ) operate by splitting the continuous time series into discrete patches and processing them with Transformer blocks.\\nHowever, closely examining these patches shows that they often exhibit distribution shifts, which can be attributed to various factors such as concept drift (Lu et al., ). These shifts can manifest as sudden or gradual changes in the underlying patterns and distributions of the time series data. For example, patches corresponding to different regimes, seasons, or operating modes may have distinct statistical properties.\\nDespite the remarkable success of time series forecasting models (Nie et al., ; Zeng et al., ; Eldele et al., ), they adopt the Uniform Distribution Modeling (UDM) strategy, which fails to account for the drifts and discrepancies between patches. This problem may result in poor generalization, hindering the performance of time series forecasting.\\n\\nTo quantify these distributional shifts, we split the ETTh1 dataset into patches and examined sudden drift and gradual drift in the time and frequency domains as shown in Figure 1. Specifically, we compute the maximum mean discrepancy (MMD) between patches and display the results as a heatmap. Notably, sudden drift (Figure 1 (a)) leads to patches with distinctly different distributions, while gradual drift (Figure 1 (b)) results in more pronounced drift in the time domain, making forecasting more challenging. Furthermore, the information in the frequency domain offers a complementary perspective on concept shifts. These observations highlight that time series data often exhibits a complex structure that evolves over time, with different segments having varying densities and underlying patterns (Sanakoyeu et al., ).\\n\\nTo address the challenges posed by distribution shifts in time series data, we propose a novel Time-Frequency Pattern-Specific (TFPS) architecture to effectively model the complex temporal patterns.\\nIn particular, TFPS consist of the following three key components.\\nFirst, TFPS employs a Dual-Domain Encoder (DDE) to capture temporal dependencies in the data. DDE extracts features from both time and frequency domains to provide a comprehensive representation of the time series data, enabling the model to capture both short-term and long-term dependencies.\\nSecond, TFPS addresses the issue of concept drift by incorporating a Pattern Identifier (PI), that utilizes a subspace clustering approach to dynamically identify the distinct patterns present in different patches. Therefore, it can effectively handle nonlinear cluster boundaries and accurately assign patches to their corresponding clusters.\\nFinally, TFPS constructs a Mixture of Pattern Experts (MoPE), a set of specialized expert models, each tailored to a specific pattern identified by the PI. By dynamically assigning patches to the appropriate expert based on their identified patterns, MoPE enables the model to effectively handle patch sequences across varying patterns and densities. This pattern-specific modeling approach allows our TFPS model to capture the unique characteristics and dynamics of each pattern, leading to improved forecasting accuracy.\\n\\nIn summary, the key contributions of this work are:\\n\\n- •\\nWe introduce a novel pattern-specific modeling strategy that decomposes the complex, evolving time series into multiple segments. Each segment is modeled by specialized experts, in contrast to the conventional UDM approach.\\n- •\\nWe propose the TFPS framework, which explicitly addresses concept drift in time series forecasting by leveraging both time-domain and frequency-domain features. Our approach employs a clustering mechanism to dynamically assign patches to specific experts, allowing the model to better handle distributional shifts.\\n- •\\nWe evaluate our approach on eight real-world multivariate time series datasets, demonstrating its effectiveness. Our model achieves top-1 performance in 50 out of 64 settings, showcasing its competitive edge in improving forecasting accuracy.\\n\\nFigure: (a) Sudden drift: A new concept occurs within a short time.\\nRefer to caption: extracted/5922744/figure/fig-1-a.png\\n\\n## 2 Related Work\\n\\nTime Series Forecasting Models.\\nIn recent years, deep models with elaborately designed architectures have achieved great progress in time series forecasting (Liu & Wang, ; Qiu et al., ). Approaches like TimesNet (Wu et al., ) and ModernTCN (Luo & Wang, ) utilize convolutional neural networks with time-series-specific modifications, making them better suited for forecasting tasks.\\nAdditionally, simpler architectures such as Multi-Layer Perceptron (MLP)-based models (Zeng et al., ; Ekambaram et al., ) have demonstrated competitive performance.\\nHowever, Transformer-based models have gained particular prominence due to their ability to model long-term dependencies in time series (Zhou et al., ; Wu et al., ; Zhou et al., ; Liu et al., ).\\nNotably, PatchTST (Nie et al., ) has become a widely adopted Transformer variant, introducing a channel-independent patching mechanism to enhance temporal representations. This approach has been further extended by subsequent models (Liu et al., ; Eldele et al., ).\\n\\nWhile previous work has primarily focused on capturing nonlinear dependencies in time series through enhanced model structures, our approach addresses the distribution shifts caused by evolving patterns within the data, which is a key limitation of existing methods. We emphasize tackling these shifts to improve forecasting performance in complex real-world scenarios.\\n\\nThe Combination of Time and Frequency Domains.\\nTime-domain models excel at capturing sequential trends, while frequency-domain models are essential for identifying periodic and oscillatory patterns.\\nRecent research has increasingly emphasized integrating information from both domains to better interpret underlying patterns.\\nFor instance, ATFN (Yang et al., ) demonstrates the advantage of frequency domain methods for forecasting strongly periodic time series through a time–frequency adaptive network.\\nTFDNet (Luo et al., ) adopts a branching structure to capture long-term latent patterns and temporal periodicity from both domains.\\nSimilarly, JTFT (Chen et al., ) utilizes the frequency domain representation to extract multi-scale dependencies while enhancing local relationships modeling through time domain representation.\\nYan et al. () propose TFMRN, which expands data in both domains to capture finer details that may not be evident in the original data.\\nRecently, TSLANet (Eldele et al., ) leverages Fourier analysis to enhance feature representation and capture both long-term and short-term interactions.\\n\\nBuilding on these approaches, our proposed method, TFPS, introduces a novel Dual-Domain Encoder that effectively combines time and frequency domain information to capture both trend and periodic patterns. By integrating time-frequency features, TFPS significantly advances the field in addressing the complexities inherent in time series forecasting.\\n\\nNon-stationary Time Series Forecasting.\\nConcept drift describes unforeseeable changes in the underlying distribution of data over time, posing a significant challenge for time series forecasting (Lu et al., ). These non-stationarities complicate predictive modeling, necessitating effective solutions to handle shifting distributions.\\nTo address varying distributions, normalization techniques have emerged as a focal point in recent research, aiming to mitigate non-stationary elements and align data to a consistent distribution.\\n\\nFor instance, adaptive norm (Ogasawara et al., ) applies z-score normalization using global statistics and DAIN (Passalis et al., ) introduces a neural layer for adaptively normalizing each input instance.\\nKim et al. () propose a reversible instance normalization (RevIN) to alleviate series shift.\\nFurthermore, Non-stationary transformer (Liu et al., ) points that directly stationarizing time series will damage the model’s capability to capture specific temporal dependencies. This work addresses the problem by introducing an innovative de-stationary attention mechanism within self-attention frameworks.\\nRecent advancement include (Fan et al., ), which identifies both intra- and inter-space distribution shifts in time series data, and SAN (Liu et al., ), which applies normalization at the slice level, thus opening new avenues for handling non-stationary time series data.\\nLastly, SIN (Han et al., ) introduces a novel method to selecting the statistics and learning normalization transformations to capture local invariance in time series data.\\n\\nHowever, over-reliance on normalization can lead to over-stationarization, where important patterns or variations in the data are smoothed out (Liu et al., ).\\nAdditionally, different patterns follow distinct internal dynamics, making a unified modeling approach inefficient.\\nOur approach brings the intrinsic non-stationarity of the original series back to latent representation, enabling better handling of distribution shifts by tailoring the experts to the evolving patterns and densities within the data.\\n\\n## 3 Method\\n\\n### 3.1 Preliminaries\\n\\nTime series forecasting aims to uncover relationships between historical time series data and future data.\\nLet $\\\\mathcal{X}$ denote the time series, and $x_{t}$ represent the value at timestep $t$.\\nGiven the historical time series data $X=[x_{t-L+1},\\\\cdots,x_{t}]\\\\in\\\\mathbb{R}^{L\\\\times C}$, where $L$ is the length of the look-back window and $C>1$ is the number of features in each timestep, the objective is to predict the future series $Y=[x_{t+1},\\\\cdots,x_{t+H}]\\\\in\\\\mathbb{R}^{H\\\\times C}$, where $H$ is the forecast horizon.\\n\\nFigure: Figure 2: The structure of our proposed TFPS. The input time series is divided into patches, and positional embeddings are added. These embeddings are processed through two branches: time-domain branch and frequency-domain branch. Each branch consists of three key components: (1) an encoder to capture patch-wise features, (2) a clustering mechanism to identify patches with similar patterns, and (3) a mixture of pattern experts block to model the patterns of each cluster. Finally, the outputs from both branches are combined for the final prediction.\\nRefer to caption: extracted/5922744/figure/fig-2.png\\n\\n### 3.2 Overall Architecture\\n\\nOur model introduces three novel components: the Dual-Domain Encoder (DDE), the Pattern Identifier (PI), and the Mixture of Pattern Experts (MoPE), as illustrated in Figure 2.\\nThe DDE goes beyond traditional time-domain encoding by incorporating a frequency encoder that applies Fourier analysis, transforming time series data into the frequency domain. This enables the model to capture periodic patterns and frequency-specific features, providing a more comprehensive understanding of the data. The PI is a clustering-based module that distinguishes patches with distinct patterns, effectively addressing the variability in the data. MoPE then utilizes multiple MLP-based experts, each dedicated to modeling a specific pattern, thereby enhancing the model’s ability to adapt to the temporal dynamics of time series. Collectively, these components form a cohesive framework that effectively handles concept drift between patches, leading to more accurate time series forecasting.\\n\\n### 3.3 Embedding Layer\\n\\nFirstly, the input sequence $X\\\\in\\\\mathbb{R}^{L\\\\times C}$ is divided into patches of length $P$, resulting in $N=\\\\lfloor\\\\frac{(L-P)}{S}+2\\\\rfloor$ tokens, where $S$ denotes the stride, defining the non-overlapping region between consecutive patches. Each patch is denoted as $\\\\mathcal{P}_{i}\\\\in\\\\mathbb{R}^{C\\\\times P}$. These patches are then projected into a new dimension $D$, via a linear transformation, such that, $\\\\mathcal{P}_{i}\\\\rightarrow\\\\mathcal{P}^{\\\\prime}_{i}\\\\in\\\\mathbb{R}^{C\\\\times D}$.\\n\\nNext, positional embeddings are added to each patch to preserve the temporal ordering disrupted during the segmentation process. The position embedding for the $i$-th patch, denoted as $E_{i}$, is a vector of the same dimension as the projected patch. The enhanced patch is computed by summing the original patch and its positional embedding: $X_{PE_{i}}=\\\\mathcal{P}^{\\\\prime}_{i}+E_{i}$, and $X_{PE}=\\\\{X_{PE_{1}},X_{PE_{2}},\\\\cdots,X_{PE_{N}}\\\\}$. Notably, the positional embeddings are learnable parameters, which enables the model to capture the temporal dependencies in the time series more effectively.\\nAs a result, the final enriched patch representations are $X_{PE}\\\\in\\\\mathbb{R}^{C\\\\times N\\\\times D}$.\\n\\n### 3.4 Dual-Domain Encoder\\n\\nAs shown in Figure 1, both time and frequency domains reveal distinct concept drifts that can significantly affect the performance of forecasting models.\\nTo effectively address these drifts, we propose a Dual-Domain Encoder (DDE) architecture that captures both temporal and frequency dependencies inherent in time series data.\\n\\nWe utilize the patch-based Transformer (Nie et al., ) as an encoder to extract embeddings for each patch, capturing the global trend feature.\\nThe multi-head attention is employed to obtain the attention output $\\\\mathbf{O}_{t}\\\\in\\\\mathbf{R}^{N\\\\times D}$ as follows:\\n\\n$$ $\\\\begin{split}\\\\mathbf{O}_{t}=\\\\text{Attention}(Q,K,V)=\\\\text{Softmax}\\\\left(\\\\frac{ QK^{T}}{\\\\sqrt{d_{k}}}\\\\right)V,\\\\\\\\ Q=X_{PE}\\\\mathbf{W}_{Q},\\\\quad K=X_{PE}\\\\mathbf{W}_{K},\\\\quad V=X_{PE}\\\\mathbf{W}_{ V}.\\\\end{split}$ (1) $$\\n\\nThe encoder block also incorporates BatchNorm layers and a feed-forward network with residual connections, as shown in Figure 2 (b). This process generates the temporal features $z_{t}\\\\in\\\\mathbb{R}^{C\\\\times N\\\\times D}$.\\n\\nIn parallel with the time encoder, we incorporate a Frequency Encoder by replacing the self-attention sublayer of the Transformer with a Fourier sublayer (Lee-Thorp et al., ). This sublayer applies a 2D Fast Fourier Transform (the number of patches, hidden dimension) to the patch representation, expressed as:\\n\\n$$ $\\\\displaystyle\\\\mathbf{O}_{f}=\\\\mathcal{F}_{patch}(\\\\mathcal{F}_{h}(X_{PE})).$ (2) $$\\n\\nWe only keep the real part of the result, and hence, we do not modify the feed-forward layers in the Transformer. The structure of the Frequency Encoder is depicted in Figure 2 (c), yielding frequency features $z_{f}\\\\in\\\\mathbb{R}^{C\\\\times N\\\\times D}$.\\n\\nBy modeling data in both the time and frequency domains, the DDE provides a more comprehensive understanding of the underlying patterns in time series data. This dual-domain perspective enables the model to better address complexities like concept drift and evolving temporal dynamics, ultimately improving its robustness and predictive accuracy. Through this approach, we aim to create a versatile framework capable of adapting to the intricate nature of real-world time series data.\\n\\nFigure: Figure 3: Illustration of the proposed Pattern Identifier and Mixture of Pattern Experts. The embedded representation $\\\\mathbf{z}$ from DDE combines with subspace $\\\\mathbf{D}$ to construct the subspace affinity vector, which yields the normalized subspace affinity $S$. Subsequently, the refined subspace affinity $\\\\widetilde{S}$ is computed from $S$ to provide self-supervised information. Then, we assign the corresponding patch-wise experts to the embedded representation $\\\\mathbf{z}$ according to $S$ for modeling.\\nRefer to caption: extracted/5922744/figure/fig-3.png\\n\\n### 3.5 Pattern Identifier\\n\\nTo address the complex and evolving patterns in time series data, we introduce a novel Pattern Identifier (PI) module, an essential innovation within our framework. Unlike traditional approaches that treat the entire time series uniformly, our PI module dynamically classifies patches based on their distributional characteristics, enabling a more precise and adaptive modeling strategy.\\n\\nThe core of our approach lies in leveraging subspace clustering to detect concept shifts across multiple subspaces, as illustrated in Figure 3.\\nThis enables the PI module to distinguish patches by identifying their underlying patterns in both the time and frequency domains.\\n\\nThe PI module’s uniqueness lies in its ability to directly analyze the properties of each patch, clustering them into distinct groups. In the time domain, PI allows our framework, TFPS, to detect shifts related to temporal characteristics, such as seasonality and trends, which can influence forecasting accuracy. In the frequency domain, the PI captures shifts associated with frequency-specific features, like periodic behaviors and spectral changes, offering a comprehensive view of pattern evolution across the entire time series.\\n\\nThis dual-domain capability represents a significant advancement in our framework, making it highly sensitive to pattern shifts occurring across both temporal and frequency dimensions. By focusing on both domains, our model overcomes the limitations of existing methods that rely solely on one representation, ensuring robustness in diverse scenarios.\\n\\nTo provide clarity, Figure 3 showcases an application of the PI module exclusively within the time domain. However, the insights and methodology seamlessly extend to the frequency domain, presenting a unified solution to the challenge of concept shifts.\\n\\nThe PI module refines subspace bases iteratively, where the improved subspaces, in turn, enhance the representation learning in deep neural networks. This iterative refinement of subspaces is a key contribution of our work, leading to more accurate identification and modeling of evolving patterns.\\nThe PI module operates in three key steps explained next.\\n\\nConstruction of subspace bases.\\nWe define a new variable $\\\\mathbf{D}=[\\\\mathbf{D}^{(1)},\\\\mathbf{D}^{(2)},\\\\cdots,\\\\mathbf{D}^{(k)}]$ to represent the bases of $k$ subspaces, where $\\\\mathbf{D}$ consists of $k$ blocks, each $\\\\mathbf{D}^{(j)}\\\\in\\\\mathbf{R}^{q\\\\times d}$, $\\\\left\\\\|\\\\mathbf{D}_{u}^{(j)}\\\\right\\\\|=1,u=1,\\\\cdots d,j=1,\\\\cdots,k$.\\nTo control the size of the columns of $\\\\mathbf{D}$, we impose the following constraint:\\n\\n$$ $\\\\displaystyle R_{1}=\\\\frac{1}{2}\\\\left\\\\|\\\\mathbf{D}^{T}\\\\mathbf{D}\\\\odot\\\\mathbf{I}- \\\\mathbf{I}\\\\right\\\\|_{F}^{2},$ (3) $$\\n\\nwhere $\\\\odot$ denotes the Hadamard product, and $\\\\mathbf{I}$ is an identity matrix of size $kd\\\\times kd$.\\n\\nSubspaces differentiation.\\nTo ensure the dissimilarity between different subspaces, we introduce the second constraint:\\n\\n$$ $\\\\displaystyle\\\\begin{split}R_{2}&=\\\\frac{1}{2}\\\\left\\\\|\\\\mathbf{D}^{(j)T}\\\\mathbf{D} ^{(l)}\\\\right\\\\|_{F}^{2},\\\\quad j\\\\neq l,\\\\\\\\ &=\\\\frac{1}{2}\\\\left\\\\|\\\\mathbf{D}^{T}\\\\mathbf{D}\\\\odot\\\\mathbf{O}\\\\right\\\\|_{F}^{2}, \\\\end{split}$ (4) $$\\n\\nwhere $\\\\mathbf{O}$ is a matrix with all off-diagonal $d$-size blocks set to 1 and diagonal blocks set to 0. Combining $D_{1}$ and $D_{2}$ yields the regularization term for $\\\\mathbf{D}$:\\n\\n$$ $\\\\displaystyle R=\\\\alpha(R_{1}+R_{2}),$ (5) $$\\n\\nwhere $\\\\alpha$ is a tuning parameters, fixed at $10^{-3}$ in this work.\\n\\nSubspace affinity and refinement.\\nWe propose a novel subspace affinity measure $\\\\mathbf{S}$ to assess the relationship between the embedded representation $\\\\mathbf{z}$ from DDE and the subspace bases $\\\\mathbf{D}$. The affinity $s_{ij}$, representing the probability that the embedded $\\\\mathbf{z}_{i}$ belongs to the $j$-th subspace, is defined as:\\n\\n$$ $\\\\displaystyle s_{ij}=\\\\frac{\\\\left\\\\|\\\\mathbf{z}_{i}^{T}\\\\mathbf{D}^{(j)}\\\\right\\\\|_{ F}^{2}+\\\\eta d}{\\\\sum_{j}(\\\\left\\\\|\\\\mathbf{z}_{i}^{T}\\\\mathbf{D}^{(j)}\\\\right\\\\|_{F}^ {2}+\\\\eta d)},$ (6) $$\\n\\nwhere $\\\\eta$ is a parameter controlling the smoothness.\\nTo emphasize more confident assignments, we introduce a refined subspace affinity $\\\\widetilde{S}$:\\n\\n$$ $\\\\displaystyle\\\\widetilde{s}_{ij}=\\\\frac{s_{ij}^{2}/\\\\sum_{i}s_{ij}}{\\\\sum_{j}(s_{ ij}^{2}/\\\\sum_{i}s_{ij})}.$ (7) $$\\n\\nThis refinement sharpens the clustering by weighting high-confidence assignments more heavily. The subspace clustering objective objective based on the Kullback-Leibler divergence is then:\\n\\n$$ $\\\\displaystyle\\\\mathcal{L}_{sub}=KL(\\\\widetilde{S}\\\\parallel S)=\\\\sum_{i}\\\\sum_{j} \\\\widetilde{s}_{ij}log\\\\frac{\\\\widetilde{s}_{ij}}{s_{ij}}.$ (8) $$\\n\\nThe clustering loss is defined as:\\n\\n$$ $\\\\displaystyle\\\\mathcal{L}_{PI}=R+\\\\beta\\\\mathcal{L}_{sub},$ (9) $$\\n\\nwhere $\\\\beta$ is a hyperparameter balancing the regularization and subspace clustering terms.\\n\\n### 3.6 Mixture of Pattern Experts\\n\\nTraditional time series forecasting methods often rely on a uniform distribution modeling (UDM) approach, which struggles to adapt to the complexities of diverse and evolving patterns in real-world data. To address this limitation, we introduce the Mixture of Pattern Experts module (MoPE), which assigns specialized experts to patches based on their unique underlying patterns, enabling more precise and adaptive forecasting.\\n\\nGiven the cluster assignments $s$ obtained from the PI module, we apply the Patch-wise MoPE to the feature tensor $z\\\\in\\\\mathbb{R}^{C\\\\times N\\\\times D}$. The MoPE module consists of the following key components:\\n\\nGating Network:\\nThe gating network $G$ calculates the gating weights for each expert based on the cluster assignment $s$ and selects the top $k$ experts. The gating weights are computed as:\\n\\n$$ $\\\\displaystyle G(s)=\\\\text{Softmax}(\\\\text{TopK}(s)).$ (10) $$\\n\\nHere, the top $k$ logits are selected and normalized using the Softmax function to produce the gating weights.\\n\\nExpert Networks:\\nThe MoPE contains $K$ expert networks, denoted as ${E_{1},\\\\dots,E_{K}}$. Each expert network is modeled as an MLP consisting of two linear layers and a ReLU activation. Given a patch-wise feature $z$, each expert network $E_{k}$ processes the input to generate its respective output.\\n\\nOutput Aggregation:\\nThe final output $h$ of the MoPE module is a weighted sum of the outputs from all the selected experts, with the weights provided by the gating network:\\n\\n$$ $\\\\displaystyle h=\\\\sum_{k=1}^{K}G(s)E_{k}(z).$ (11) $$\\n\\nAfter the frequency branch is processed by the inverse Fast Fourier transform, the time-frequency outputs $h_{t}$ and $h_{f}$, are concatenated to form $h=\\\\text{concat}(h_{t},h_{f})\\\\in\\\\mathbb{R}^{C\\\\times N\\\\times 2D}$.\\n\\nFinally, a linear transformation is applied to the concatenated output $h$ to generate the prediction: $\\\\hat{Y}=\\\\text{Linear}(h)\\\\in\\\\mathbb{R}^{H\\\\times C}$.\\n\\nThis approach ensures that the MoPE dynamically assigns and aggregates contributions from various experts based on the evolving patterns, improving the model’s adaptability and accuracy.\\n\\n### 3.7 Loss Function\\n\\nFollowing the approach outlined in Nie et al. (), we use the Mean Squared Error (MSE) loss to quantify the discrepancy between predicted values $\\\\hat{Y}$ and ground truth values $Y$:\\n$\\\\mathcal{L}_{MSE}=(\\\\hat{Y}-Y)^{2}$.\\nIn addition to the MSE loss, we incorporate the clustering regularization loss from the PI module, yielding the final loss function:\\n\\n$$ $\\\\displaystyle\\\\mathcal{L}=\\\\mathcal{L}_{MSE}+\\\\mathcal{L}_{PI_{t}}+\\\\mathcal{L}_{ PI_{f}}.$ (12) $$\\n\\nThis combined loss ensures that the model not only minimizes forecasting errors but also accurately identifies and maintains the integrity of pattern clusters across time. The algorithm is provided in the Appendix G.\\n\\n## 4 Experiments\\n\\nIn this section, we present experimental results to demonstrate the effectiveness of our proposed TFPS framework, including its forecasting performance and model analysis.\\n\\n### 4.1 Experimental Setup\\n\\nDataset and Baselines.\\nWe conducted our experiments on eight publicly available real-world multivariate time series datasets, i.e., ETT (ETTh1, ETTh2, ETTm1, ETTm2), Exchange, Weather, Electricity, and ILI. These datasets are provided in (Wu et al., ) for time series forecasting.\\nWe followed the standard protocol for data preprocessing. Specifically, we split the datasets into training, validation, and testing by a ratio of 6:2:2 for the ETT dataset and 7:1:2 for the other dataset (Zeng et al., ). Table 1 shows the statistics of these datasets.\\n\\nIn our experiments, we employed a diverse set of state-of-the-art forecasting models as baselines, categorized based on the type of information they utilize as follows.\\n(1) Time-domain methods: PatchTST (Nie et al., ), DLinear (Zeng et al., ), TimesNet (Wu et al., ) and iTransformer (Liu et al., );\\n(2) Frequency-domain methods: FEDformer (Zhou et al., ) and FITS (Xu et al., );\\n(3) Time-frequency methods: TFDNet-IK (Luo et al., ) and TSLANet (Eldele et al., ).\\nWe rerun all the experiments with codes provided by their official implementation.\\n\\nNote that some recent foundation models such as Time-LLM (Jin et al., ) and MOIRAI (Woo et al., ) have demonstrated remarkable performance in time series forecasting by leveraging knowledge from diverse datasets through pretraining. However, our TFPS model and the baselines above focus on specific dataset for training and testing. Therefore, we did not include these pretrained foundation models in comparison.\\n\\n**Table 1: The statistics of the datasets.**\\n| Datasets | ETTh1 & ETTh2 | ETTm1 & ETTm2 | Exchange-Rate | Weather | Electricity | ILI |\\n| --- | --- | --- | --- | --- | --- | --- |\\n| Variates | 7 | 7 | 8 | 21 | 321 | 7 |\\n| Timesteps | 17,420 | 69,680 | 7,588 | 52,696 | 26,304 | 966 |\\n| Granularity | 1 hour | 15 min | 1 day | 10 min | 1 hour | 1 week |\\n\\nExperiments details.\\nFollowing previous works (Nie et al., ), we used ADAM (Kingma & Ba, ) as the default optimizer across all the experiments. We employed the MSE and mean absolute error (MAE) as the evaluation metrics, and a lower MSE/MAE value indicates a better performance. TFPS was implemented by PyTorch (Paszke et al., ) and trained on a single NVIDIA RTX 3090 24GB GPU.\\nWe conducted grid search to optimize the following three parameters, i.e., $\\\\text{learning rate}=\\\\{0.0001,0.0005,0.001,0.005,0.01,0.05\\\\}$, $K_{t}=\\\\{1,2,4,8\\\\}$, and $K_{f}=\\\\{1,2,4,8\\\\}$.\\nThe lookback length $L$ was set to 104 for ILI and 96 for other datasets.\\n\\n### 4.2 Overall Performance Comparison\\n\\nTable 2 highlights the consistent superiority of TFPS across multiple datasets and prediction horizons, securing the top performance in 50 out of 64 experimental configurations.\\nIn particular, TFPS demonstrates significant improvements over time-domain methods, with an overall improvement of 8.7% in MSE and 5.9% in MAE. Compared to frequency-domain methods, TFPS shows even more pronounced enhancements, with MSE improved by 15.8% and MAE by 11.6%.\\n\\nWhile the time-frequency methods like TSLANet and TFDNet perform competitively on several datasets, TFPS still outperforms them, showing improvement of 4.5% in MSE and 1.9% in MAE. These substantial improvements can be attributed to the integration of both time- and frequency-domain information, combined with our innovative approach to modeling distinct patterns with specialized experts. By addressing the underlying concept shifts and capturing complex, evolving patterns in time series data, TFPS achieves more accurate predictions than other baseline models.\\n\\n**Table 2: Multivariate long-term forecasting results with prediction lengths $H\\\\in\\\\{24,36,48,60\\\\}$ for ILI and $H\\\\in\\\\{96,192,336,720\\\\}$ for others. The input lengths are $L=104$ for ILI and $L=96$ for others. The best results are highlighted in bold and the second best are \\\\ulunderlined.**\\n| Model | IMP. | TFPS | TSLANet | FITS | iTransformer | TFDNet-IK | PatchTST | TimesNet | DLinear | FEDformer | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| (Our) | () | () | () | () | () | () | () | () | | | | | | | | | | | | |\\n| Metric | MSE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |\\n| ETTh1 | 96 | -1.1% | 0.398 | 0.413 | 0.387 | 0.405 | 0.395 | 0.403 | \\\\ul0.387 | \\\\ul0.405 | 0.396 | 0.409 | 0.413 | 0.419 | 0.389 | 0.412 | 0.398 | 0.410 | 0.385 | 0.425 |\\n| 192 | 4.8% | 0.423 | 0.423 | 0.448 | 0.436 | 0.445 | 0.432 | 0.441 | 0.436 | 0.451 | 0.441 | 0.460 | 0.445 | 0.441 | 0.442 | \\\\ul0.434 | \\\\ul0.427 | 0.441 | 0.461 | |\\n| 336 | 1.8% | 0.484 | 0.461 | 0.491 | 0.487 | \\\\ul0.489 | 0.463 | 0.491 | 0.463 | 0.495 | \\\\ul0.462 | 0.497 | 0.463 | 0.491 | 0.467 | 0.499 | 0.477 | 0.491 | 0.473 | |\\n| 720 | 3.0% | 0.488 | 0.476 | 0.505 | 0.486 | 0.496 | 0.485 | 0.509 | 0.494 | \\\\ul0.492 | \\\\ul0.482 | 0.501 | 0.486 | 0.512 | 0.491 | 0.508 | 0.503 | 0.501 | 0.499 | |\\n| ETTh2 | 96 | -2.0% | 0.313 | 0.355 | \\\\ul0.290 | 0.345 | 0.295 | \\\\ul0.344 | 0.301 | 0.350 | 0.289 | 0.337 | 0.299 | 0.348 | 0.324 | 0.368 | 0.315 | 0.374 | 0.342 | 0.383 |\\n| 192 | -2.9% | 0.405 | 0.410 | 0.362 | 0.391 | 0.382 | 0.396 | 0.380 | 0.399 | \\\\ul0.379 | \\\\ul0.395 | 0.383 | 0.398 | 0.393 | 0.410 | 0.432 | 0.447 | 0.434 | 0.440 | |\\n| 336 | 10.5% | 0.392 | 0.415 | \\\\ul0.401 | \\\\ul0.419 | 0.416 | 0.425 | 0.424 | 0.432 | 0.416 | 0.422 | 0.424 | 0.431 | 0.429 | 0.437 | 0.486 | 0.481 | 0.512 | 0.497 | |\\n| 720 | 12.6% | 0.410 | 0.433 | 0.419 | 0.439 | \\\\ul0.418 | \\\\ul0.437 | 0.430 | 0.447 | 0.424 | 0.441 | 0.429 | 0.445 | 0.433 | 0.448 | 0.732 | 0.614 | 0.467 | 0.476 | |\\n| ETTm1 | 96 | 4.1% | 0.327 | 0.367 | \\\\ul0.329 | \\\\ul0.368 | 0.354 | 0.375 | 0.342 | 0.377 | 0.331 | 0.369 | 0.331 | 0.370 | 0.337 | 0.377 | 0.346 | 0.374 | 0.360 | 0.406 |\\n| 192 | 2.6% | 0.374 | 0.395 | 0.376 | \\\\ul0.383 | 0.392 | 0.393 | 0.383 | 0.396 | 0.376 | 0.381 | \\\\ul0.374 | 0.395 | 0.395 | 0.406 | 0.382 | 0.392 | 0.395 | 0.427 | |\\n| 336 | 4.2% | 0.401 | 0.408 | 0.403 | 0.414 | 0.425 | 0.415 | 0.418 | 0.418 | 0.405 | \\\\ul0.410 | \\\\ul0.402 | 0.412 | 0.433 | 0.432 | 0.414 | 0.414 | 0.448 | 0.458 | |\\n| 720 | -0.7% | 0.479 | 0.456 | 0.445 | \\\\ul0.438 | 0.486 | 0.449 | 0.487 | 0.457 | 0.471 | 0.437 | \\\\ul0.466 | 0.446 | 0.484 | 0.458 | 0.478 | 0.455 | 0.491 | 0.479 | |\\n| ETTm2 | 96 | 6.9% | 0.170 | 0.255 | 0.179 | 0.261 | 0.183 | 0.266 | 0.186 | 0.272 | \\\\ul0.176 | 0.267 | 0.177 | \\\\ul0.260 | 0.182 | 0.262 | 0.184 | 0.276 | 0.193 | 0.285 |\\n| 192 | 7.1% | 0.235 | 0.296 | \\\\ul0.243 | 0.303 | 0.247 | 0.305 | 0.254 | 0.314 | 0.245 | \\\\ul0.302 | 0.248 | 0.306 | 0.252 | 0.307 | 0.282 | 0.357 | 0.256 | 0.324 | |\\n| 336 | 4.6% | 0.297 | 0.335 | 0.308 | 0.345 | 0.307 | 0.342 | 0.316 | 0.351 | \\\\ul0.303 | \\\\ul0.340 | 0.303 | 0.341 | 0.312 | 0.346 | 0.324 | 0.364 | 0.321 | 0.364 | |\\n| 720 | 3.6% | 0.401 | 0.397 | \\\\ul0.403 | 0.400 | 0.407 | 0.401 | 0.414 | 0.407 | 0.405 | \\\\ul0.399 | 0.405 | 0.403 | 0.417 | 0.404 | 0.441 | 0.454 | 0.434 | 0.426 | |\\n| Exchange | 96 | 12.7% | 0.083 | 0.205 | 0.085 | 0.206 | 0.088 | 0.210 | 0.086 | 0.206 | \\\\ul0.084 | \\\\ul0.205 | 0.089 | 0.206 | 0.105 | 0.233 | 0.089 | 0.219 | 0.136 | 0.265 |\\n| 192 | 11.2% | 0.174 | 0.297 | 0.178 | 0.300 | 0.181 | 0.304 | 0.181 | 0.304 | \\\\ul0.176 | \\\\ul0.299 | 0.178 | 0.302 | 0.219 | 0.342 | 0.180 | 0.319 | 0.279 | 0.384 | |\\n| 336 | 10.4% | 0.310 | 0.398 | 0.329 | 0.415 | 0.324 | 0.413 | 0.338 | 0.422 | 0.321 | \\\\ul0.409 | 0.326 | 0.411 | 0.353 | 0.433 | \\\\ul0.313 | 0.423 | 0.465 | 0.504 | |\\n| 720 | -13.3% | 1.011 | 0.756 | 0.850 | 0.693 | 0.846 | 0.696 | 0.853 | 0.696 | 0.835 | 0.689 | 0.840 | 0.690 | 0.912 | 0.724 | \\\\ul0.837 | \\\\ul0.690 | 1.169 | 0.826 | |\\n| Weather | 96 | 15.6% | 0.154 | 0.202 | 0.176 | 0.216 | 0.167 | 0.214 | 0.176 | 0.216 | \\\\ul0.165 | \\\\ul0.209 | 0.177 | 0.219 | 0.168 | 0.218 | 0.197 | 0.257 | 0.236 | 0.325 |\\n| 192 | 10.6% | 0.205 | 0.249 | 0.226 | 0.258 | 0.215 | 0.257 | 0.225 | 0.257 | \\\\ul0.214 | \\\\ul0.252 | 0.225 | 0.259 | 0.226 | 0.267 | 0.237 | 0.294 | 0.268 | 0.337 | |\\n| 336 | 9.1% | 0.262 | 0.289 | 0.279 | 0.299 | 0.270 | 0.299 | 0.281 | 0.299 | \\\\ul0.267 | \\\\ul0.298 | 0.278 | 0.298 | 0.283 | 0.305 | 0.283 | 0.332 | 0.366 | 0.402 | |\\n| 720 | 4.1% | 0.344 | 0.342 | 0.355 | 0.355 | 0.347 | \\\\ul0.345 | 0.358 | 0.350 | \\\\ul0.347 | 0.346 | 0.351 | 0.346 | 0.355 | 0.353 | 0.347 | 0.382 | 0.407 | 0.422 | |\\n| Electricity | 96 | 14.6% | 0.149 | 0.236 | 0.155 | 0.249 | 0.200 | 0.278 | \\\\ul0.151 | \\\\ul0.241 | 0.171 | 0.254 | 0.166 | 0.252 | 0.168 | 0.272 | 0.195 | 0.277 | 0.189 | 0.304 |\\n| 192 | 12.0% | 0.162 | 0.253 | 0.170 | 0.264 | 0.200 | 0.281 | \\\\ul0.167 | \\\\ul0.258 | 0.189 | 0.269 | 0.174 | 0.261 | 0.186 | 0.289 | 0.194 | 0.281 | 0.198 | 0.312 | |\\n| 336 | 0.2% | 0.200 | 0.310 | 0.197 | 0.282 | 0.214 | 0.295 | 0.179 | 0.271 | 0.205 | 0.284 | \\\\ul0.190 | \\\\ul0.277 | 0.197 | 0.298 | 0.207 | 0.296 | 0.212 | 0.326 | |\\n| 720 | 7.2% | 0.220 | 0.320 | \\\\ul0.224 | \\\\ul0.318 | 0.256 | 0.328 | 0.229 | 0.319 | 0.247 | 0.318 | 0.230 | 0.312 | 0.225 | 0.322 | 0.243 | 0.330 | 0.242 | 0.351 | |\\n| ILI | 24 | 40.9% | 1.349 | 0.760 | 1.749 | 0.898 | 3.489 | 1.373 | 2.443 | 1.078 | 1.824 | \\\\ul0.824 | \\\\ul1.614 | 0.835 | 1.699 | 0.871 | 2.239 | 1.041 | 3.217 | 1.246 |\\n| 36 | 43.6% | 1.239 | 0.752 | 1.754 | 0.912 | 3.530 | 1.370 | 2.455 | 1.086 | 1.699 | \\\\ul0.813 | \\\\ul1.475 | 0.859 | 1.733 | 0.913 | 2.238 | 1.049 | 2.688 | 1.074 | |\\n| 48 | 40.4% | 1.461 | 0.801 | 2.050 | 0.984 | 3.671 | 1.391 | 3.437 | 1.331 | 1.762 | \\\\ul0.831 | \\\\ul1.642 | 0.880 | 2.272 | 0.999 | 2.252 | 1.064 | 2.540 | 1.057 | |\\n| 60 | 39.8% | 1.458 | 0.836 | 2.240 | 1.039 | 4.030 | 1.462 | 2.734 | 1.155 | 1.758 | \\\\ul0.863 | \\\\ul1.608 | 0.885 | 1.998 | 0.974 | 2.236 | 1.057 | 2.782 | 1.136 | |\\n| $1^{\\\\text{st}}$ Count | 50 | 3 | 1 | 2 | 6 | 1 | 0 | 0 | 1 | | | | | | | | | | | |\\n\\n### 4.3 Ablation Study\\n\\nTable 3 presents the MSE results of TFPS and its variants with different combinations of encoders, PI, and MoPE.\\n1) Best Result.\\nThe full TFPS model, i.e., both the time and frequency branches, along with their respective encoders, PI, and MoPE are included, performs the best across all the forecast horizons for both datasets.\\n2) Linear vs. PI.\\nWe replace PI with a linear layer and find that it generally results in higher MSE in most cases, indicating that accurately capturing specific patterns is crucial.\\n3) Impact of Pattern-aware Modeling.\\nAdditionally, when comparing the results with the encoder-only configuration, two variants with MoPE in each branch achieved improved MSE, further supporting the necessity of patter-aware modeling.\\n4) Importance of DDE.\\nFurthermore, we find that both the time encoder and frequency encoder alone yield worse performance, with the time encoder playing a more significant role.\\nIn summary, incorporating both branches with PI and MoPE provides the best performance, while simpler configurations result in higher MSE.\\n\\n**Table 3: Ablation study of TFPS components. The model variants in our ablation study include the following configurations across both time and frequency branches: (a) inclusion of the encoder, PI and MoPE; (b) PI replaced with Linear; (c) only the encoder. The best results are in bold.**\\n| Time Branch | Frequency Branch | ETTh1 | ETTh2 | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| Encoder | PI | MoPE | Encoder | PI | MoPE | 96 | 192 | 336 | 720 | 96 | 192 | 336 | 720 |\\n| ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 0.398 | 0.423 | 0.484 | 0.488 | 0.313 | 0.405 | 0.392 | 0.410 |\\n| ✓ | ✓ | ✓ | | | | \\\\ul0.401 | 0.459 | \\\\ul0.486 | \\\\ul0.492 | \\\\ul0.318 | 0.409 | \\\\ul0.400 | \\\\ul0.428 |\\n| ✓ | Linear | ✓ | | | | 0.401 | \\\\ul0.451 | 0.494 | 0.509 | 0.325 | 0.411 | 0.400 | 0.434 |\\n| ✓ | | | | | | 0.414 | 0.460 | 0.501 | 0.500 | 0.339 | 0.411 | 0.426 | 0.431 |\\n| | | | ✓ | ✓ | ✓ | 0.455 | 0.507 | 0.539 | 0.576 | 0.324 | \\\\ul0.407 | 0.417 | 0.436 |\\n| | | | ✓ | Linear | ✓ | 0.503 | 0.535 | 0.558 | 0.583 | 0.398 | 0.446 | 0.457 | 0.444 |\\n| | | | ✓ | | | 0.552 | 0.583 | 0.591 | 0.594 | 0.371 | 0.426 | 0.418 | 0.463 |\\n\\n### 4.4 Comparsion With Normalization Methods\\n\\n**Table 4: Comparison between TFPS and normalization approaches.**\\n| Model | TFPS | FEDformer | | |\\n| --- | --- | --- | --- | --- |\\n| + SIN | + Dish-TS | + NST | | |\\n| ETTh1 | 0.448 | 0.458 | 0.461 | 0.456 |\\n| ETTh2 | 0.427 | 0.457 | 0.565 | 0.453 |\\n| ETTm1 | 0.422 | 0.465 | 0.689 | 0.462 |\\n| ETTm2 | 0.400 | 0.480 | 0.825 | 0.481 |\\n| Weather | 0.380 | 0.501 | 1.005 | 0.481 |\\n\\nNormalization methods such as SIN (Han et al., ), Dish-TS (Fan et al., ), and Non-Stationary Transformers (Liu et al., ) can reduce fluctuations to enhance performance and are widely used for non-stationary time series forecasting.\\nWe compare our TFPS with these state-of-the-art normalization methods and Table 4 presents the average MSE evaluation across all forecasting lengths for each dataset.\\nWhile normalization methods contribute to data stabilization, TFPS provides a more nuanced approach by leveraging distribution-specific modeling, leading to significant improvements with an average MSE decrease of 37.5%. Detailed results for all cases can be found in Appendix E.2.\\n\\n### 4.5 Visualization\\n\\nWe visualize the prediction curves for ETTh1 with $H=192$. Given that DLinear exhibits competitive performance, we compare its results with those of TFPS in Figure 4 under two scenarios: (a) sudden drift caused by external factors or random events, and (b) gradual drift where the trend is dominant.\\nIt is evident that DLinear struggles to achieve accurate predictions in both scenarios. In contrast, our TFPS consistently produces accurate forecasts despite these challenges, demonstrating its robustness in dealing with various concept dynamics.\\n\\nFigure: (a) Sudden Drift\\nRefer to caption: extracted/5922744/figure/fig-4-a.png\\n\\nFigure: (a) Expert 0\\nRefer to caption: extracted/5922744/figure/fig-5-a.png\\n\\n### 4.6 Analysis of experts\\n\\nQualitative Visualizations of Pattern Identifier.\\nThrough training, pattern experts in MoPE spontaneously specialize, and we present two examples in Figure 6. We visualize the expert with the highest score as the routed expert for each instance pair. In the provided examples, we observe that expert-0 specialize in downward-related concepts, while expert-4 focuses on parabolic trend. These examples also demonstrate the interpretability of MoPE.\\n\\nNumber of Experts.\\nIn Figure 6, we set the learning rate to 0.0001 and conducted four sets of experiments on the ETTh1 and ETTh2 datasets, T1F1, T1F2, T1F4, T1F8, to explore the effect of the number of frequency experts on the results.\\nFor example, T1F4 means that the TFPS contains 1 time experts and 4 frequency experts.\\nWe observed that T1F2 outperformed T1F4 in both cases, suggesting that increasing the number of experts does not always lead to better performance.\\n\\nIn addition, we conducted three experiments based on the optimal number of frequency experts to verify the impact of varying the number of time experts on the results.\\nAs shown in Figure 6, the best results for ETTh1 were obtained with T4F2, while for ETTh2, the optimal results were achieved with T2F2.\\nCombined with the average MMD in Table 5 (Appendix A), we attribute this to the fact that, in cases where concept drift is more severe, such as ETTh1 in the time domain, more experts are needed, whereas fewer experts are sufficient when the drift is less severe.\\n\\n## 5 Conclusion\\n\\nIn this paper, we propose a novel pattern-aware time series forecasting framework, TFPS, which incorporates a dual-domain mixture of pattern experts approach.\\nOur TFPS framework aims to address the distribution shift across time series patches and effectively assigns pattern-specific experts to model them.\\nExperimental results across eight diverse datasets demonstrate that TFPS surpasses state-of-the-art methods in both quantitative metrics and visualizations.\\nFuture work will focus on investigating evolving distribution shifts, particularly those introduced by the emergence of new patterns, such as unforeseen epidemics or outbreaks.\\n\\n## Appendix A Dataset\\n\\nWe evaluate the performance of TFPS on eight widely used datasets, including four ETT datasets (ETTh1, ETTh2, ETTm1 and ETTm2), Exchange, Weather, Electricity, and ILI. This subsection provides a summary of the datasets:\\n\\n- •\\nETT (^1^11[https://github.com/zhouhaoyi/ETDataset](https://github.com/zhouhaoyi/ETDataset)) (Zhou et al., ) (Electricity Transformer Temperature) dataset contains two electric transformers, ETT1 and ETT2, collected from two separate counties. Each of them has two versions of sampling resolutions (15min & 1h). Thus, there are four ETT datasets: ETTm1, ETTm2, ETTh1, and ETTh2.\\n- •\\nExchange-Rate (^2^22[https://github.com/laiguokun/multivariate-time-series-data](https://github.com/laiguokun/multivariate-time-series-data)) (Lai et al., ) the exchange-rate dataset contains the daily exchange rates of eight foreign countries including Australia, British, Canada, Switzerland, China, Japan, New Zealand, and Singapore ranging from 1990 to 2016.\\n- •\\nWeather (^3^33[https://www.bgc-jena.mpg.de/wetter/](https://www.bgc-jena.mpg.de/wetter/)) (Wu et al., ) dataset contains 21 meteorological indicators in Germany, such as humidity and air temperature.\\n- •\\nElectricity (^4^44[https://archive.ics.uci.edu/ml/datasets/ElectricityLoadDiagrams20112014](https://archive.ics.uci.edu/ml/datasets/ElectricityLoadDiagrams20112014)) (Wu et al., ) is a dataset that describes 321 customers’ hourly electricity consumption.\\n- •\\nILI (^5^55[https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html](https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html)) (Wu et al., ) dataset collects the number of patients and influenza-like illness ratio in a weekly frequency.\\n\\nFor the data split, we follow Zeng et al. () and split the data into training, validation, and testing by a ratio of 6:2:2 for the ETT datasets and 7:1:2 for the others. Details are shown in Table 5. The best parameters are selected based on the lowest validation loss and then applied to the test set for performance evaluation.\\n\\n**Table 5: The statistics of the datasets.**\\n| Datasets | Variates | Prediction Length | Timesteps | Granularity | Average MMD^*<br>(Time Domain) | Average MMD^*<br>(Frequency Domain) |\\n| --- | --- | --- | --- | --- | --- | --- |\\n| ETTh1 | 7 | {96, 192, 336, 720} | 17,420 | 1 hour | 0.938 | 0.340 |\\n| ETTh2 | 7 | {96, 192, 336, 720} | 17,420 | 1 hour | 0.582 | 0.635 |\\n| ETTm1 | 7 | {96, 192, 336, 720} | 69,680 | 15 min | 1.371 | 0.328 |\\n| ETTm2 | 7 | {96, 192, 336, 720} | 69,680 | 15 min | 1.213 | 0.815 |\\n| Exchange-Rate | 8 | {96, 192, 336, 720} | 7,588 | 1 day | 0.805 | 0.485 |\\n| Weather | 21 | {96, 192, 336, 720} | 52,696 | 10 min | 0.129 | 0.236 |\\n| Electricity | 321 | {96, 192, 336, 720} | 26,304 | 1 hour | 0.026 | 0.005 |\\n| ILI | 7 | {24, 36, 48, 60} | 966 | 1 week | 0.125 | 0.234 |\\n| ^* A large MMD indicates a more severe drift. | | | | | | |\\n\\n## Appendix B Maximum Mean Discrepancy\\n\\nMaximum mean discrepancy (MMD) is a kernel-based statistical test used to determine whether given two distribution are the same.\\nGiven an $X$, the feature map $\\\\phi$ transforms $X$ to an another space $\\\\mathcal{H}$ such that $\\\\phi(X)\\\\in\\\\mathcal{H}$. $\\\\mathcal{H}$ is Reproducing Kernel Hilbert Space (RKHS) and we can leverage the kernel trick to compute inner products in $\\\\mathcal{H}$:\\n\\n$$ $\\\\displaystyle X,Y\\\\text{\\\\quad such that\\\\quad}k(X,Y)=\\\\langle\\\\phi(X),\\\\phi(Y) \\\\rangle_{\\\\mathcal{H}}.$ (13) $$\\n\\nFeature means.\\nThe mean embeddings of a probability distribution $P$ is a feature map that transforms $\\\\phi(X)$ into the mean of each coordinate of $\\\\phi(X)$:\\n\\n$$ $\\\\displaystyle\\\\mu_{P}(\\\\phi(X))=[\\\\mathbb{E}[\\\\phi(X_{1})],\\\\cdots,\\\\mathbb{E}[\\\\phi( X_{m})]]^{T}.$ (14) $$\\n\\nThe inner product of the mean embeddings of $X\\\\sim P$ and $Y\\\\sim Q$ can be written in terms of kernel function:\\n\\n$$ $\\\\displaystyle\\\\langle\\\\mu_{P}(\\\\phi(X)),\\\\mu_{Q}(\\\\phi(Y))\\\\rangle_{\\\\mathcal{H}}= \\\\mathbb{E}_{P,Q}[\\\\langle\\\\phi(X),\\\\phi(Y)\\\\rangle_{\\\\mathcal{H}}]=\\\\mathbb{E}_{P,Q} [k(X,Y)].$ (15) $$\\n\\nMaximum mean discrepancy.\\nThe MMD measures the distance between the mean embeddings of two samples, $X$ and $Y$, in the RKHS:\\n\\n$$ $\\\\displaystyle\\\\operatorname{MMD}^{2}(P,Q)=\\\\left\\\\|\\\\mu_{P}-\\\\mu_{Q}\\\\right\\\\|_{ \\\\mathcal{H}}^{2},$ (16) $$\\n\\nFor convenience we omit the $\\\\phi(\\\\cdot)$ terms. If we use the norm induced by the inner product such that $\\\\|x\\\\|=\\\\sqrt{\\\\langle x,x\\\\rangle}$, the Eq. 16 becomes:\\n\\n$$ $\\\\displaystyle\\\\operatorname{MMD}^{2}(P,Q)=\\\\langle\\\\mu_{p}-\\\\mu_{Q},\\\\mu_{p}-\\\\mu_{Q }\\\\rangle=\\\\langle\\\\mu_{p},\\\\mu_{p}\\\\rangle-2\\\\langle\\\\mu_{p},\\\\mu_{Q}\\\\rangle+\\\\langle \\\\mu_{Q},\\\\mu_{Q}\\\\rangle.$ (17) $$\\n\\nUsing the Eq. 15, finally above expression becomes:\\n\\n$$ $\\\\displaystyle\\\\operatorname{MMD}^{2}(P,Q)=\\\\mathbb{E}_{P}[k(X,X)]-2\\\\mathbb{E}_{P ,Q}[k(X,Y)]+\\\\mathbb{E}_{Q}[k(Y,Y)].$ (18) $$\\n\\nEmpirical estimation of MMD.\\nIn real-world applications, the underlying distribution are usually unknown. Thus, an empirical estimate of Eq. 18 can be used:\\n\\n$$ $\\\\displaystyle\\\\operatorname{MMD}^{2}(X,Y)=\\\\frac{1}{m(m-1)}\\\\sum_{i\\\\neq j}k\\\\left( x_{i},x_{j}\\\\right)-\\\\frac{2}{mn}\\\\sum_{i,j}k\\\\left(x_{i},x_{j}\\\\right)+\\\\frac{1}{n( n-1)}\\\\sum_{i\\\\neq j}k\\\\left(y_{i},y_{j}\\\\right),$ (19) $$\\n\\nwhere $x_{i}$ and $x_{j}$ are samples from $P$, $y_{i}$ and $y_{j}$ are samples from $Q$, and $k(x,y)$ is the kernel function, often the Gaussian (RBF) kernel.\\n\\n## Appendix C Distribution shifts in both time and frequency domains\\n\\nThe time series $\\\\mathcal{X}$ is segmented into $N$ patches, where each patch $\\\\mathcal{P}_{n}=\\\\{x_{n1},x_{n2},\\\\dots,x_{nP}\\\\}$ consists of $P$ consecutive timesteps for $n=1,2,\\\\cdots,N$.\\nFor the frequency domain, we apply a Fourier transform $\\\\mathcal{F}$ to each patch $\\\\mathcal{P}_{n}$, obtaining its frequency-domain representation as $\\\\hat{\\\\mathcal{P}}_{n}=\\\\mathcal{F}(\\\\mathcal{P}_{n})$.\\n\\nEach patch’s probability distribution in the time domain is denoted as $p_{t}(\\\\mathcal{P}_{n})$, representing the statistical properties of $\\\\mathcal{P}_{n}$, while its frequency domain distribution, denoted as $p_{f}(\\\\hat{\\\\mathcal{P}}_{n})$, captures its spectral characteristics.\\n\\nThe distribution shifts between two patches $\\\\mathcal{P}_{i}$ and $\\\\mathcal{P}_{j}$ are characterized by the comparing their probability distributions in both time and frequency domains. These shifts are defined as:\\n\\n$$ $\\\\displaystyle\\\\mathcal{D}_{t}(\\\\mathcal{P}_{i},\\\\mathcal{P}_{j})$ $\\\\displaystyle=|d(p_{t}(\\\\mathcal{P}_{i}),p_{t}(\\\\mathcal{P}_{j}))|>\\\\theta,$ (20) $\\\\displaystyle\\\\mathcal{D}_{f}(\\\\hat{\\\\mathcal{P}}_{i},\\\\hat{\\\\mathcal{P}}_{j})$ $\\\\displaystyle=|d(p_{f}(\\\\hat{\\\\mathcal{P}}_{i}),p_{f}(\\\\hat{\\\\mathcal{P}}_{j}))|>\\\\theta,$ (21) $$\\n\\nwhere $d$ is a distance metric, such as MMD values or Kullback-Leibler divergence, and $\\\\theta$ is a threshold indicating a significant distribution shift. If $\\\\mathcal{D}_{t}(\\\\mathcal{P}_{i},\\\\mathcal{P}_{j})$ or $\\\\mathcal{D}_{f}(\\\\hat{\\\\mathcal{P}}_{i},\\\\hat{\\\\mathcal{P}}_{j})$ exceeds $\\\\theta$, this implies a significant distribution shift between the two patches in either domain.\\n\\n## Appendix D Related Work\\n\\nMixture-of-Experts.\\nMixture-of-Experts (MoE) models have gained attention for their ability to scale efficiently by activating only a subset of experts for each input, as first introduced by Shazeer et al. (). Despite their success, challenges such as training instability, expert redundancy, and limited expert specialization have been identified (Puigcerver et al., ; Dai et al., ). These issues hinder the full potential of MoE models in real-world tasks.\\n\\nRecent advances have integrated MoE with Transformers to improve scalability and efficiency. For example, GLaM (Du et al., ) and Switch Transformer (Fedus et al., ) interleave MoE layers with Transformer blocks, reducing computational costs.\\nOther models like state space models (SSMs) (Pióro et al., ; Anthony et al., ) combines MoE with alternative architectures for enhanced scalability and inference speed.\\n\\nIn contrast, our approach introduces MoE into time series forecasting by assigning experts to specific time-frequency patterns, enabling more effective, patch-level adaptation. This approach represents a significant innovation in time series forecasting, offering a more targeted and effective way to handle varying patterns across both time and frequency domains.\\n\\n## Appendix E More Model Analysis\\n\\n### E.1 Analysis of experts\\n\\nDetailed Results on the Number of Experts.\\n\\nWe provide the full results on the number of experts for the ETTh1 and ETTh2 dataset in Figure 7.\\n\\nIn Figure 7, we set the learning rate to 0.0001 and conducted four sets of experiments on the ETTh1 and ETTh2 datasets, T1F1, T1F2, T1F4, T1F8, to explore the effect of the number of frequency experts on the results.\\nFor example, T1F4 means that the TFPS contains 1 time experts and 4 frequency experts.\\nWe observed that T1F2 outperformed T1F4 in four cases, suggesting that increasing the number of experts does not always lead to better performance.\\n\\nIn addition, we conducted three experiments based on the optimal number of frequency experts to verify the impact of varying the number of time experts on the results.\\nAs shown in Figure 7, the best results for ETTh1 were obtained with T4F2, T8F4, T4F4, T4F4, while for ETTh2, the optimal results were achieved with T2F2, T2F4, T4F2 and T4F2.\\nCombined with the average MMD in Table 5, we attribute this to the fact that, in cases where concept drift is more severe, such as ETTh1 in the time domain, more experts are needed, whereas fewer experts are sufficient when the drift is less severe.\\n\\nFigure: Figure 7: Results of expert number experiments for ETTh1 and ETTh2.\\nRefer to caption: extracted/5922744/figure/fig-7.png\\n\\nComparing Inter- and Intra-Cluster Differences via MMD.\\n\\nWe present the heatmaps of inter-cluster and intra-cluster MMD values obtained using linear layers and PI in Figure 8.\\nThe diagonal elements represent the average MMD values of patches within the same clusters. If these values are small, it indicates that the difference of patches within the same cluster is relatively similar.\\nThe off-diagonal elements represent the average MMD values between patches from different clusters, where larger values mean significant differences between the clusters.\\nWe observe that when using PI, the intra-cluster drift is smaller, while the inter-cluster shift is more pronounced compared to the linear layer. This indicates that our identifier effectively classifies and distinguishes between different patterns.\\n\\nFigure: (a) Linear layer\\nRefer to caption: extracted/5922744/figure/fig-8-a.png\\n\\n### E.2 Results of the Comparison between TFPS and Normalization Methods\\n\\nIn this section, we provide the detailed experimental results of the comparison between TFPS and five state-of-the-art normalization methods for non-stationary time series forecasting: SIN (Han et al., ), SAN (Liu et al., ), Dish-TS (Fan et al., ), Non-Stationary Transformers (NST) (Liu et al., ), and RevIN (Kim et al., ).\\nThe results of SIN are from Han et al. (), other results are from Liu et al. ().\\nWe report the evaluation of FEDformer over all the forecasting lengths for each dataset and the relative improvements in Table 6.\\nIt can be concluded that TFPS achieves the best performance among existing methods in most cases. The improvement is significant with an average MSE decrease of 18.9%.\\nWe attribute this improvement to the accurate identification of pattern groups and the provision of specialized experts for each group, thereby avoiding the over-stationarization problem often associated with normalization methods.\\n\\n**Table 6: Detailed results of the comparison between TFPS and normalization methods. The best results are highlighted in bold and the second best are \\\\ulunderlined.**\\n| | | | FEDformer | | | | | | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | | TFPS | + SIN | + SAN | + Dish-TS | + NST | + RevIN | | | | | | | |\\n| Model | IMP. | (Our) | () | () | () | () | () | | | | | | | |\\n| Metric | MSE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |\\n| | 96 | -1.0% | 0.398 | 0.413 | 0.413 | 0.372 | 0.383 | \\\\ul0.409 | \\\\ul0.390 | 0.424 | 0.394 | 0.414 | 0.392 | 0.413 |\\n| | 192 | 3.8% | 0.423 | \\\\ul0.423 | 0.443 | 0.417 | \\\\ul0.431 | 0.438 | 0.441 | 0.458 | 0.441 | 0.442 | 0.443 | 0.444 |\\n| | 336 | -0.3% | 0.484 | 0.461 | 0.465 | 0.448 | \\\\ul0.471 | \\\\ul0.456 | 0.495 | 0.486 | 0.485 | 0.466 | 0.495 | 0.467 |\\n| ETTh1 | 720 | 4.5% | 0.488 | 0.476 | 0.509 | 0.490 | \\\\ul0.504 | \\\\ul0.488 | 0.519 | 0.509 | 0.505 | 0.496 | 0.520 | 0.498 |\\n| | 96 | 31.3% | \\\\ul0.313 | 0.355 | 0.412 | 0.357 | 0.300 | \\\\ul0.355 | 0.806 | 0.589 | 0.381 | 0.403 | 0.380 | 0.402 |\\n| | 192 | 26.0% | \\\\ul0.405 | 0.410 | 0.472 | 0.453 | 0.392 | \\\\ul0.413 | 0.936 | 0.659 | 0.478 | 0.453 | 0.457 | 0.443 |\\n| | 336 | 36.7% | 0.392 | 0.415 | 0.527 | 0.527 | \\\\ul0.459 | \\\\ul0.462 | 1.039 | 0.702 | 0.561 | 0.499 | 0.515 | 0.479 |\\n| ETTh2 | 720 | 37.9% | 0.410 | 0.433 | 0.593 | 0.639 | \\\\ul0.462 | \\\\ul0.472 | 1.237 | 0.759 | 0.502 | 0.481 | 0.507 | 0.487 |\\n| | 96 | 4.1% | \\\\ul0.327 | 0.367 | 0.373 | 0.320 | 0.311 | \\\\ul0.355 | 0.348 | 0.397 | 0.336 | 0.382 | 0.340 | 0.385 |\\n| | 192 | 2.9% | \\\\ul0.374 | 0.395 | 0.394 | 0.366 | 0.351 | \\\\ul0.383 | 0.406 | 0.428 | 0.386 | 0.409 | 0.390 | 0.411 |\\n| | 336 | 5.3% | \\\\ul0.401 | 0.408 | 0.418 | 0.405 | 0.390 | \\\\ul0.407 | 0.438 | 0.450 | 0.438 | 0.441 | 0.432 | 0.436 |\\n| ETTm1 | 720 | -0.5% | 0.479 | \\\\ul0.456 | 0.451 | 0.475 | \\\\ul0.456 | 0.444 | 0.497 | 0.481 | 0.483 | 0.460 | 0.497 | 0.466 |\\n| | 96 | 33.5% | 0.170 | \\\\ul0.255 | 0.326 | 0.211 | \\\\ul0.175 | 0.266 | 0.394 | 0.395 | 0.191 | 0.272 | 0.192 | 0.272 |\\n| | 192 | 32.3% | 0.235 | 0.296 | 0.402 | 0.316 | \\\\ul0.246 | \\\\ul0.315 | 0.552 | 0.472 | 0.270 | 0.321 | 0.270 | 0.320 |\\n| | 336 | 35.0% | 0.297 | 0.335 | 0.465 | 0.399 | \\\\ul0.315 | \\\\ul0.362 | 0.808 | 0.601 | 0.353 | 0.371 | 0.348 | 0.367 |\\n| ETTm2 | 720 | 35.9% | 0.401 | 0.397 | 0.555 | 0.547 | \\\\ul0.412 | 0.422 | 1.282 | 0.771 | 0.445 | 0.422 | 0.430 | \\\\ul0.415 |\\n| | 96 | 28.4% | 0.154 | 0.202 | 0.280 | \\\\ul0.215 | \\\\ul0.179 | 0.239 | 0.244 | 0.317 | 0.187 | 0.234 | 0.187 | 0.234 |\\n| | 192 | 23.3% | 0.205 | 0.249 | 0.314 | \\\\ul0.264 | \\\\ul0.234 | 0.296 | 0.320 | 0.380 | 0.235 | 0.272 | 0.235 | 0.272 |\\n| | 336 | 19.8% | 0.262 | 0.289 | 0.329 | \\\\ul0.293 | 0.304 | 0.348 | 0.424 | 0.452 | 0.289 | 0.308 | \\\\ul0.287 | 0.307 |\\n| Weather | 720 | 18.4% | 0.344 | 0.342 | 0.382 | \\\\ul0.370 | 0.400 | 0.404 | 0.604 | 0.553 | \\\\ul0.359 | 0.352 | 0.361 | 0.353 |\\n| $1^{\\\\text{st}}$ ($2^{\\\\text{nd}}$) Count | 24 (8) | 9 (4) | 7 (24) | 0 (1) | 0 (1) | 0 (2) | | | | | | | | |\\n\\n## Appendix F Metric Illustration\\n\\nWe use mean square error (MSE) and mean absolute error (MAE) as our metrics for evaluation of all forecasting models. Then calculation of MSE and MAE can be described as:\\n\\n$$ $\\\\displaystyle\\\\text{MSE}=\\\\frac{1}{H}\\\\sum_{i=L+1}^{L+H}(\\\\hat{Y}_{i}-Y_{i})^{2},$ (22) $$\\n\\n$$ $\\\\displaystyle\\\\text{MAE}=\\\\frac{1}{H}\\\\sum_{i=L+1}^{L+H}\\\\left|\\\\hat{Y}_{i}-Y_{i} \\\\right|,$ (23) $$\\n\\nwhere $\\\\hat{Y}$ is predicted vector with $H$ future values, while $Y$ is the ground truth.\\n\\n## Appendix G Algorithm of TFPS\\n\\nWe provide the pseudo-code of TFPS in Algorithm 1.\\n\\nFigure: Algorithm 1 Time-Frequency Pattern-Specific architecture - Overall Architecture.\\n\\n## Appendix H Broader Impact\\n\\nReal-world applications. TFPS addresses the crucial challenge of time series forecasting, which is a valuable and urgent demand in extensive applications. Our method achieves consistent state-of-the-art performance in four real-world applications: electricity, weather, exchange rate, illness. Researchers in these fields stand to benefit significantly from the enhanced forecasting capabilities of TFPS. We believe that improved time series forecasting holds the potential to empower decision-making and proactively manage risks in a wide array of societal domains.\\n\\nAcademic research. TFPS draws inspiration from classical time series analysis and stochastic process theory, contributing to the field by introducing a novel framework with the assistance pattern recognition. This innovative architecture and its associated methodologies represent significant advancements in the field of time series forecasting, enhancing the model’s ability to address distribution shifts and complex patterns effectively.\\n\\nModel Robustness. Extensive experimentation with TFPS reveals robust performance without exceptional failure cases. Notably, TFPS exhibits impressive results and maintains robustness in datasets with distribution shifts. The pattern identifier structure within TFPS groups the time series into distinct patterns and adopts a mixture of pattern experts for further prediction, thereby alleviating prediction difficulties. However, it is essential to note that, like any model, TFPS may face challenges when dealing with unpredictable patterns, where predictability is inherently limited. Understanding these nuances is crucial for appropriately applying and interpreting TFPS’s outcomes.\\n\\nOur work only focuses on the scientific problem, so there is no potential ethical risk.\\n\\n## Appendix I Limitations\\n\\nThough TFPS demonstrates promising performance on the benchmark dataset, there are still some limitations of this method.\\nFirst, the patch length is primarily chosen heuristically, and the current design struggles with handling indivisible lengths or multi-period characteristics in time series. While this approach works well in experiments, it lacks generalizability for real-world applications.\\nSecond, the real-world time series data undergo expansion, implying that the new patterns continually emerge over time, such as an epidemic or outbreak that had not occurred before.\\nTherefore, future work will focus on developing a more flexible and automatic patch length selection mechanism, as well as an extensible solution to address these evolving distribution shifts.\",\n \"metadata\": {\n \"authors\": [\n \"Yanru Sun, Zongxia Xie\",\n \", Emadeldeen Eldele\",\n \", Dongyue Chen, Qinghua Hu, Min Wu\",\n \"College of Intelligence and Computing, Tianjin University, China\",\n \",\"\n ],\n \"title\": \"Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift\",\n \"total_chars\": 59551,\n \"total_lines\": 543,\n \"updated_at\": \"2026-01-25T15:02:51.294512\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"GMo5faOa1t","initial_rating":6,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"The paper innovatively addresses the diversity of time series patterns by introducing a Mixture of Experts (MoE) approach for decoupled modeling. It leverages a unique PI module as the gating function to route different patterns to the appropriate experts. The experimental results convincingly demonstrate the superiority of this method, complemented by comprehensive ablation studies validating the effectiveness of each component. The writing is clear, with the authors articulating the problem and solution effectively. However, the design of the expert models appears somewhat simplistic, and the decoupling of time and frequency domains is already a well-established approach in time series analysis, making it less of an innovative contribution. Overall, the method shows sufficient technical depth and originality, despite some areas that could benefit from further enhancement.","strengths":"The authors conducted a detailed experimental analysis and identified that different time series exhibit unique patterns. Traditional models typically employ a unified modeling approach for these varying patterns, which can limit their effectiveness. To address this issue, the authors propose a Mixture of Experts (MoE) approach that enables tailored modeling for different patterns. Additionally, they decompose the time series data into two dimensions: time and frequency, using a dual encoder to model both types of information separately. To ensure that the MoE effectively learns distinct patterns, the authors introduce a novel gating mechanism. This mechanism leverages subspace affinity to allocate sequences with different patterns to the appropriate experts.","weaknesses":"The decoupling of time-domain and frequency-domain information, as discussed in the paper, is already a common approach in the field of time series analysis and cannot be considered a novel contribution. Additionally, regarding the MoE (Mixture of Experts) section, the use of multiple MLPs seems more akin to employing multiple output predictors with weighted combinations rather than a true MoE structure. Lastly, with respect to the normalization technique, would the authors consider adding experimental results comparing their approach to REVIN [1]? REVIN has shown strong performance across various time series forecasting tasks and could provide a valuable benchmark.\n\n\n[1] Kim T, Kim J, Tae Y, et al. Reversible instance normalization for accurate time-series forecasting against distribution shift[C]//International Conference on Learning Representations. 2021.","questions":"1. In the PI module, the number of experts K is currently adjusted manually through parameter tuning. Is it possible to directly relate the value of K to the number of patterns inherent in the time series data itself?\n2. On line 317, there appear to be two identical objectives listed, which seems to be a typographical error."},{"id":"ICzcRPYHvX","initial_rating":5,"confidence":4,"soundness":3,"contribution":3,"presentation":2,"summary":"The paper addresses the challenge of distributional shift in time series data by proposing a novel framework called the Time Frequency Pattern-Specific (TFPS) architecture. This method is designed to effectively model complex patterns in time series, enhancing the model's ability to manage distributional shifts more robustly.","strengths":"1. The paper is well written and easy to follow.\n2. The paper is well motivated.\n3. The method shows promising results compared to the baselines.","weaknesses":"1. The number of subspace variables $k$, does not appear to be clearly specified in the paper. Given that these variables are essential for modeling the patterns of patches, it is crucial to understand how to set an appropriate value for $k$. The authors should provide further discussion on this aspect. Additionally, an ablation study examining the impact of different values of $k$ would be beneficial.\n\n2. The paper doesn't specify how the subspace variables are initialized. I think the initialization of subspace variables is crucial to achieve optimal performance.\n\n3. Since the subspace variables is utilized for clustering. It is better to provide the relevant visualization (e.g., tsne) to show the effectiveness.\n\n4. Some important information, such as the number of MoPE, the value of hyper-parameters $\\alpha$, $\\beta$ used for the results in the Table 2 are not clearly specified.\n\n5. What do the notations $K_t$ and $K_f$ mean? The paper doesn't provide the clear definition.","questions":"see weakness"},{"id":"OTVhiImh3T","initial_rating":5,"confidence":2,"soundness":3,"contribution":2,"presentation":3,"summary":"The paper proposes a pattern-based mixture of experts model for time series prediction. In this approach time series patches are first extracted and embedded into a sequence of \"tokens\". This sequence is then encoded with time and frequency encoders and mined for representative patterns that can aid prediction via a mixture of experts approach.","strengths":"The paper is well written and relatively easy to follow. The proposed approach is interesting and explores time and frequency aspect of time series prediction. Authors conduct extensive experiments on real world datasets showing that the purposed approach outperforms a number of baselines.","weaknesses":"I have several concerns about this method. First, it is quite complex, the loss in Eq 12 has three terms and both L_{PI_t} and L_{PI_f} have three tunable hyper parameters \\alpha, \\beta and \\nu (Eq 5, 6 and 9). So there are at least six hyper parameters to tune in addition to balancing the three loss terms that likely requires more hyper parameters. There is nothing in the experimental section on these hyper parameters and no ablation study is conducted. I've worked with these datasets myself, they are quite small and easy to overfit to which raises a major concern when one has to tune 6+ hyper parameters just in the loss function. Second, the proposed mixture of experts in Eq 10 and 11 looks nearly identical to self attention with the exception of the top-k selection. So I suspect that this method will, despite significant added complexity, have a similar representation power to simply stacking attention layers over patches, as all operations including subspace bases affinity are nearly identical to appropriately parametrized self attention.","questions":"Do you have ablation study on the hyper parameters in the loss function? Which ranges did you try and how sensitive are the results to the particular choice? Also, did you have to balance the contribution of the three terms in the loss?"},{"id":"fBRZmcdewX","initial_rating":3,"confidence":4,"soundness":2,"contribution":2,"presentation":2,"summary":"Real-world time series often exhibit varying degrees of distribution shift, posing challenges for time series forecasting. This paper employs subspace clustering from both time-domain and frequency-domain perspectives to identify different patterns within data segments. It utilizes multiple experts to specifically model temporal patterns. Extensive experiments conducted on eight real-world time series datasets demonstrate that the proposed method outperforms other state-of-the-art approaches in terms of predictive performance.","strengths":"1. Distribution shifts often lead to changes in frequency-domain information, making it a reasonable and effective approach to model time series from both time-domain and frequency-domain perspectives.\n2. The main contribution of this paper is to utilize subspace clustering to detect concept drift between multiple subspaces and model them separately, thereby achieving more accurate and adaptive modeling. \n3. Extensive experiments demonstrate that the proposed method outperforms other state-of-the-art approaches across various time series datasets.","weaknesses":"1. The frequency-domain encoder part of the dual-domain encoder implements a simple feedforward layer by discarding the imaginary part. This leads to a loss of information in the frequency domain. Does this contradict the original intention of using the dual-domain encoder to provide a comprehensive representation of the time series? Considering that the time-domain encoder directly utilizes the PatchTST encoder, the frequency-domain part could also use an existing frequency-domain encoder.\n2. The Pattern Identifter module employs multiple hyperparameters $\\alpha、\\beta$ to mix different components of the loss function. Given the importance of the loss function for experimental results, it is necessary to include ablation experiments for these hyperparameters.\n3. In the final loss function, is it reasonable to simply add $\\mathcal{L}_{MSE}、\\mathcal{L}_{PI_t}、\\mathcal{L}_{PI_f}$? Given that the severity of distribution shifts varies across different datasets, and that the importance of frequency-domain information is relatively low in such datasets, the model should be allowed to learn the appropriate weights for both components on its own.\n4. It is noted that in the experiments, the sequence length (seq_len) was uniformly set to 96, which undermines the performance of other baselines, as FITS[1], PatchTST[2], and DLinear[3] have indicated that their methods perform better with longer input sequences. It is suggested to provide experimental results comparing seq_len as a hyperparameter rather than fixing it at 96.\n5. It is noted that multiple experts are used in both the time domain and frequency domain, which will increase the runtime of the model. It is suggested to compare the runtime with other methods.\n\n[1]Xu Z, Zeng A, Xu Q. FITS: Modeling Time Series with 10 k Parameters[C]. In ICLR.\n\n[2]Nie Y, Nguyen N H, Sinthong P, et al. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers[C]. In ICLR.\n\n[3]Zeng A, Chen M, Zhang L, et al. Are transformers effective for time series forecasting? In AAAI.","questions":"Please refer to weeknesses."},{"id":"GEapmSbf6Z","initial_rating":5,"confidence":4,"soundness":2,"contribution":2,"presentation":3,"summary":"This paper proposes a new architecture, Time-Frequency Pattern-Specific (TFPS), designed for time series forecasting, particularly under challenging conditions involving concept drift within the data. The key idea revolves around addressing the limitations of conventional uniform distribution modeling (UDM) by recognizing that different segments or \"patches\" within a time series exhibit distinct patterns and distributional shifts. These shifts may stem from factors such as sudden events, gradual trend changes, or different operating modes, making accurate forecasting difficult for models trained on a single global pattern. TFPS tackles this problem through a multi-faceted approach. First, it employs a Dual-Domain Encoder (DDE) that analyzes both time and frequency domain features, enabling a richer understanding of temporal dynamics and their potential shifts. Second, a Pattern Identifier (PI) utilizes subspace clustering to dynamically group patches exhibiting similar patterns. Finally, a Mixture of Pattern Experts (MoPE) leverages multiple specialized expert models, each trained on a specific pattern identified by the PI. This allows TFPS to adapt its predictions based on the identified pattern of a given patch, leading to improved accuracy.","strengths":"(1) Utilizing both time and frequency domain information provides a comprehensive perspective on data, capturing both trend and periodic patterns, which is essential for handling complex time series.\n(2) The use of PI and MoPE allows TFPS to handle distribution shifts by learning and adapting to specific patterns within different data segments.\n(3) Extensive experiments on real-world datasets demonstrate the effectiveness and competitiveness of TFPS compared to existing methods.","weaknesses":"(1) The authors acknowledge that the patch length is currently determined heuristically, which might limit generalizability and performance in cases with indivisible lengths or multi-period characteristics.\n(2) The model's ability to adapt to entirely new patterns, such as those arising from unforeseen events, is not explicitly addressed and remains an open question.\n(3) While not explicitly mentioned, the use of multiple expert models and the dual-domain encoding approach could increase computational complexity compared to simpler models. This aspect would require further analysis and optimization for practical implementation in real-time applications.","questions":"(1) In Figure 1, the authors posit that a combined time and frequency domain perspective provides a more comprehensive view of data shifts. However, the provided heatmaps do not clearly support this claim. For instance, in Figure 1(a), the time-domain heatmap highlights significant MMD values for patch #10, while the actual drift begins at patch #9. Similarly, the frequency-domain heatmap includes patches #7 and #8 in the drift region, which is inaccurate. A similar discrepancy is observed in Figure 1(b), where the differences between patches 5, 6, 7, 8, and subsequent patches are not readily apparent. Consequently, this figure does not provide compelling evidence for the superiority of the combined domain approach in detecting shifts.\n\n(2) Based on Figure 1, it appears that the sudden drift is detected due to the data's relatively consistent cyclical patterns across patches. How would the method perform if the data lacks such clear cyclical properties? Would the entire sequence of patches be incorrectly identified as a drift, even if the underlying data distribution changes gradually?\n\n(3) Although this research draws comparisons to traditional time-domain and frequency-domain techniques, a more rigorous evaluation would involve comparisons with MoE-based methods. A list of relevant works is provided below.\n\n* Dish-ts: a general paradigm for alleviating distribution shift in time series forecasting. (AAAI-23) .\n* Reversible Instance Normalization for Accurate Time-Series Forecasting against Distribution Shift. (ICLR 2022).\n* OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling. (NeurIPS 2023).\n* Calibration of Time-Series Forecasting: Detecting and Adapting Context-Driven Distribution Shift. (KDD '24).\n* Addressing Distribution Shift in Time Series Forecasting with Instance Normalization Flows. arXiv preprint arXiv:2401.16777.\n* MixMamba: Time series modeling with adaptive expertise. (Inf. Fusion 2024).\n* Mixture-of-Linear-Experts for Long-term Time Series Forecasting. (AISTATS 2024).\n\n(4) Please elucidate the specific contributions of the PI the gate network to TFPS. Why both components are essential for the system’s performance would be beneficial. Furthermore, conducting an ablation study, which involves comparing the model’s performance with and without the separate PI module, would provide empirical validation of its significance.\n\n(5) A rigorous computational complexity analysis would provide valuable insights into the trade-offs between model complexity and performance gains.\n\n(6) I suggest that authors: Provide clear definitions for q and d in D. Explain the rationale behind controlling column size using Equation (3). Clarify the purpose of the second constraint in Equation (4). Include a theoretical justification for how these constraints improve representation learning. Conduct an ablation study comparing model performance with and without these constraints.\n\n(7) As noted in Shazer et al.’s work on Mixture-of-Experts, gating networks often exhibit a tendency to select the same k experts for routing patches. To mitigate this issue and encourage diversity among the expert modules, regularization and load balancing techniques are typically employed. However, it remains unclear how the proposed model addresses this specific challenge and promotes diversity among its expert modules.\n\n(8) The datasets employed in this study are relatively low-dimensional. It is recommended to conduct experiments on high-dimensional time series datasets, such as the Traffic dataset. Additionally, a discussion on potential scalability challenges and necessary modifications to the TFPS architecture for efficient handling of high-dimensional data would be valuable.\n\n(9) Given that the Patch-TST module used as encoder in this work already incorporates an ReVIN layer to mitigate distribution shifts in time series data. I am wondering if authors consider this point and how it affect the process of PI?"}],"string":"[\n {\n \"id\": \"GMo5faOa1t\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"The paper innovatively addresses the diversity of time series patterns by introducing a Mixture of Experts (MoE) approach for decoupled modeling. It leverages a unique PI module as the gating function to route different patterns to the appropriate experts. The experimental results convincingly demonstrate the superiority of this method, complemented by comprehensive ablation studies validating the effectiveness of each component. The writing is clear, with the authors articulating the problem and solution effectively. However, the design of the expert models appears somewhat simplistic, and the decoupling of time and frequency domains is already a well-established approach in time series analysis, making it less of an innovative contribution. Overall, the method shows sufficient technical depth and originality, despite some areas that could benefit from further enhancement.\",\n \"strengths\": \"The authors conducted a detailed experimental analysis and identified that different time series exhibit unique patterns. Traditional models typically employ a unified modeling approach for these varying patterns, which can limit their effectiveness. To address this issue, the authors propose a Mixture of Experts (MoE) approach that enables tailored modeling for different patterns. Additionally, they decompose the time series data into two dimensions: time and frequency, using a dual encoder to model both types of information separately. To ensure that the MoE effectively learns distinct patterns, the authors introduce a novel gating mechanism. This mechanism leverages subspace affinity to allocate sequences with different patterns to the appropriate experts.\",\n \"weaknesses\": \"The decoupling of time-domain and frequency-domain information, as discussed in the paper, is already a common approach in the field of time series analysis and cannot be considered a novel contribution. Additionally, regarding the MoE (Mixture of Experts) section, the use of multiple MLPs seems more akin to employing multiple output predictors with weighted combinations rather than a true MoE structure. Lastly, with respect to the normalization technique, would the authors consider adding experimental results comparing their approach to REVIN [1]? REVIN has shown strong performance across various time series forecasting tasks and could provide a valuable benchmark.\\n\\n\\n[1] Kim T, Kim J, Tae Y, et al. Reversible instance normalization for accurate time-series forecasting against distribution shift[C]//International Conference on Learning Representations. 2021.\",\n \"questions\": \"1. In the PI module, the number of experts K is currently adjusted manually through parameter tuning. Is it possible to directly relate the value of K to the number of patterns inherent in the time series data itself?\\n2. On line 317, there appear to be two identical objectives listed, which seems to be a typographical error.\"\n },\n {\n \"id\": \"ICzcRPYHvX\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"The paper addresses the challenge of distributional shift in time series data by proposing a novel framework called the Time Frequency Pattern-Specific (TFPS) architecture. This method is designed to effectively model complex patterns in time series, enhancing the model's ability to manage distributional shifts more robustly.\",\n \"strengths\": \"1. The paper is well written and easy to follow.\\n2. The paper is well motivated.\\n3. The method shows promising results compared to the baselines.\",\n \"weaknesses\": \"1. The number of subspace variables $k$, does not appear to be clearly specified in the paper. Given that these variables are essential for modeling the patterns of patches, it is crucial to understand how to set an appropriate value for $k$. The authors should provide further discussion on this aspect. Additionally, an ablation study examining the impact of different values of $k$ would be beneficial.\\n\\n2. The paper doesn't specify how the subspace variables are initialized. I think the initialization of subspace variables is crucial to achieve optimal performance.\\n\\n3. Since the subspace variables is utilized for clustering. It is better to provide the relevant visualization (e.g., tsne) to show the effectiveness.\\n\\n4. Some important information, such as the number of MoPE, the value of hyper-parameters $\\\\alpha$, $\\\\beta$ used for the results in the Table 2 are not clearly specified.\\n\\n5. What do the notations $K_t$ and $K_f$ mean? The paper doesn't provide the clear definition.\",\n \"questions\": \"see weakness\"\n },\n {\n \"id\": \"OTVhiImh3T\",\n \"initial_rating\": 5,\n \"confidence\": 2,\n \"soundness\": 3,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"The paper proposes a pattern-based mixture of experts model for time series prediction. In this approach time series patches are first extracted and embedded into a sequence of \\\"tokens\\\". This sequence is then encoded with time and frequency encoders and mined for representative patterns that can aid prediction via a mixture of experts approach.\",\n \"strengths\": \"The paper is well written and relatively easy to follow. The proposed approach is interesting and explores time and frequency aspect of time series prediction. Authors conduct extensive experiments on real world datasets showing that the purposed approach outperforms a number of baselines.\",\n \"weaknesses\": \"I have several concerns about this method. First, it is quite complex, the loss in Eq 12 has three terms and both L_{PI_t} and L_{PI_f} have three tunable hyper parameters \\\\alpha, \\\\beta and \\\\nu (Eq 5, 6 and 9). So there are at least six hyper parameters to tune in addition to balancing the three loss terms that likely requires more hyper parameters. There is nothing in the experimental section on these hyper parameters and no ablation study is conducted. I've worked with these datasets myself, they are quite small and easy to overfit to which raises a major concern when one has to tune 6+ hyper parameters just in the loss function. Second, the proposed mixture of experts in Eq 10 and 11 looks nearly identical to self attention with the exception of the top-k selection. So I suspect that this method will, despite significant added complexity, have a similar representation power to simply stacking attention layers over patches, as all operations including subspace bases affinity are nearly identical to appropriately parametrized self attention.\",\n \"questions\": \"Do you have ablation study on the hyper parameters in the loss function? Which ranges did you try and how sensitive are the results to the particular choice? Also, did you have to balance the contribution of the three terms in the loss?\"\n },\n {\n \"id\": \"fBRZmcdewX\",\n \"initial_rating\": 3,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"Real-world time series often exhibit varying degrees of distribution shift, posing challenges for time series forecasting. This paper employs subspace clustering from both time-domain and frequency-domain perspectives to identify different patterns within data segments. It utilizes multiple experts to specifically model temporal patterns. Extensive experiments conducted on eight real-world time series datasets demonstrate that the proposed method outperforms other state-of-the-art approaches in terms of predictive performance.\",\n \"strengths\": \"1. Distribution shifts often lead to changes in frequency-domain information, making it a reasonable and effective approach to model time series from both time-domain and frequency-domain perspectives.\\n2. The main contribution of this paper is to utilize subspace clustering to detect concept drift between multiple subspaces and model them separately, thereby achieving more accurate and adaptive modeling. \\n3. Extensive experiments demonstrate that the proposed method outperforms other state-of-the-art approaches across various time series datasets.\",\n \"weaknesses\": \"1. The frequency-domain encoder part of the dual-domain encoder implements a simple feedforward layer by discarding the imaginary part. This leads to a loss of information in the frequency domain. Does this contradict the original intention of using the dual-domain encoder to provide a comprehensive representation of the time series? Considering that the time-domain encoder directly utilizes the PatchTST encoder, the frequency-domain part could also use an existing frequency-domain encoder.\\n2. The Pattern Identifter module employs multiple hyperparameters $\\\\alpha、\\\\beta$ to mix different components of the loss function. Given the importance of the loss function for experimental results, it is necessary to include ablation experiments for these hyperparameters.\\n3. In the final loss function, is it reasonable to simply add $\\\\mathcal{L}_{MSE}、\\\\mathcal{L}_{PI_t}、\\\\mathcal{L}_{PI_f}$? Given that the severity of distribution shifts varies across different datasets, and that the importance of frequency-domain information is relatively low in such datasets, the model should be allowed to learn the appropriate weights for both components on its own.\\n4. It is noted that in the experiments, the sequence length (seq_len) was uniformly set to 96, which undermines the performance of other baselines, as FITS[1], PatchTST[2], and DLinear[3] have indicated that their methods perform better with longer input sequences. It is suggested to provide experimental results comparing seq_len as a hyperparameter rather than fixing it at 96.\\n5. It is noted that multiple experts are used in both the time domain and frequency domain, which will increase the runtime of the model. It is suggested to compare the runtime with other methods.\\n\\n[1]Xu Z, Zeng A, Xu Q. FITS: Modeling Time Series with 10 k Parameters[C]. In ICLR.\\n\\n[2]Nie Y, Nguyen N H, Sinthong P, et al. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers[C]. In ICLR.\\n\\n[3]Zeng A, Chen M, Zhang L, et al. Are transformers effective for time series forecasting? In AAAI.\",\n \"questions\": \"Please refer to weeknesses.\"\n },\n {\n \"id\": \"GEapmSbf6Z\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 3,\n \"summary\": \"This paper proposes a new architecture, Time-Frequency Pattern-Specific (TFPS), designed for time series forecasting, particularly under challenging conditions involving concept drift within the data. The key idea revolves around addressing the limitations of conventional uniform distribution modeling (UDM) by recognizing that different segments or \\\"patches\\\" within a time series exhibit distinct patterns and distributional shifts. These shifts may stem from factors such as sudden events, gradual trend changes, or different operating modes, making accurate forecasting difficult for models trained on a single global pattern. TFPS tackles this problem through a multi-faceted approach. First, it employs a Dual-Domain Encoder (DDE) that analyzes both time and frequency domain features, enabling a richer understanding of temporal dynamics and their potential shifts. Second, a Pattern Identifier (PI) utilizes subspace clustering to dynamically group patches exhibiting similar patterns. Finally, a Mixture of Pattern Experts (MoPE) leverages multiple specialized expert models, each trained on a specific pattern identified by the PI. This allows TFPS to adapt its predictions based on the identified pattern of a given patch, leading to improved accuracy.\",\n \"strengths\": \"(1) Utilizing both time and frequency domain information provides a comprehensive perspective on data, capturing both trend and periodic patterns, which is essential for handling complex time series.\\n(2) The use of PI and MoPE allows TFPS to handle distribution shifts by learning and adapting to specific patterns within different data segments.\\n(3) Extensive experiments on real-world datasets demonstrate the effectiveness and competitiveness of TFPS compared to existing methods.\",\n \"weaknesses\": \"(1) The authors acknowledge that the patch length is currently determined heuristically, which might limit generalizability and performance in cases with indivisible lengths or multi-period characteristics.\\n(2) The model's ability to adapt to entirely new patterns, such as those arising from unforeseen events, is not explicitly addressed and remains an open question.\\n(3) While not explicitly mentioned, the use of multiple expert models and the dual-domain encoding approach could increase computational complexity compared to simpler models. This aspect would require further analysis and optimization for practical implementation in real-time applications.\",\n \"questions\": \"(1) In Figure 1, the authors posit that a combined time and frequency domain perspective provides a more comprehensive view of data shifts. However, the provided heatmaps do not clearly support this claim. For instance, in Figure 1(a), the time-domain heatmap highlights significant MMD values for patch #10, while the actual drift begins at patch #9. Similarly, the frequency-domain heatmap includes patches #7 and #8 in the drift region, which is inaccurate. A similar discrepancy is observed in Figure 1(b), where the differences between patches 5, 6, 7, 8, and subsequent patches are not readily apparent. Consequently, this figure does not provide compelling evidence for the superiority of the combined domain approach in detecting shifts.\\n\\n(2) Based on Figure 1, it appears that the sudden drift is detected due to the data's relatively consistent cyclical patterns across patches. How would the method perform if the data lacks such clear cyclical properties? Would the entire sequence of patches be incorrectly identified as a drift, even if the underlying data distribution changes gradually?\\n\\n(3) Although this research draws comparisons to traditional time-domain and frequency-domain techniques, a more rigorous evaluation would involve comparisons with MoE-based methods. A list of relevant works is provided below.\\n\\n* Dish-ts: a general paradigm for alleviating distribution shift in time series forecasting. (AAAI-23) .\\n* Reversible Instance Normalization for Accurate Time-Series Forecasting against Distribution Shift. (ICLR 2022).\\n* OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling. (NeurIPS 2023).\\n* Calibration of Time-Series Forecasting: Detecting and Adapting Context-Driven Distribution Shift. (KDD '24).\\n* Addressing Distribution Shift in Time Series Forecasting with Instance Normalization Flows. arXiv preprint arXiv:2401.16777.\\n* MixMamba: Time series modeling with adaptive expertise. (Inf. Fusion 2024).\\n* Mixture-of-Linear-Experts for Long-term Time Series Forecasting. (AISTATS 2024).\\n\\n(4) Please elucidate the specific contributions of the PI the gate network to TFPS. Why both components are essential for the system’s performance would be beneficial. Furthermore, conducting an ablation study, which involves comparing the model’s performance with and without the separate PI module, would provide empirical validation of its significance.\\n\\n(5) A rigorous computational complexity analysis would provide valuable insights into the trade-offs between model complexity and performance gains.\\n\\n(6) I suggest that authors: Provide clear definitions for q and d in D. Explain the rationale behind controlling column size using Equation (3). Clarify the purpose of the second constraint in Equation (4). Include a theoretical justification for how these constraints improve representation learning. Conduct an ablation study comparing model performance with and without these constraints.\\n\\n(7) As noted in Shazer et al.’s work on Mixture-of-Experts, gating networks often exhibit a tendency to select the same k experts for routing patches. To mitigate this issue and encourage diversity among the expert modules, regularization and load balancing techniques are typically employed. However, it remains unclear how the proposed model addresses this specific challenge and promotes diversity among its expert modules.\\n\\n(8) The datasets employed in this study are relatively low-dimensional. It is recommended to conduct experiments on high-dimensional time series datasets, such as the Traffic dataset. Additionally, a discussion on potential scalability challenges and necessary modifications to the TFPS architecture for efficient handling of high-dimensional data would be valuable.\\n\\n(9) Given that the Patch-TST module used as encoder in this work already incorporates an ReVIN layer to mitigate distribution shifts in time series data. I am wondering if authors consider this point and how it affect the process of PI?\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;5;5;5;6\",\n \"rating_avg\": 4.8,\n \"confidence\": \"4;4;2;4;4\",\n \"confidence_avg\": 3.6,\n \"soundness\": \"2;2;3;3;3\",\n \"soundness_avg\": 2.6,\n \"contribution\": \"2;2;2;3;3\",\n \"contribution_avg\": 2.4,\n \"presentation\": \"2;3;3;2;3\",\n \"presentation_avg\": 2.6\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"Submitted to ICLR 2025\",\n \"venueid\": \"ICLR.cc/2025/Conference/Rejected_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.714271\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"NucDEaNtDh\",\n \"metareview\": \"This paper presents a pattern-based mixture of experts model for time series prediction. Reviewers agreed that this paper is well written and easy to follow, and the paper aims to address a critical problem, i.e., patch-level distributional shift in time series forecasting. Meanwhile, reviewers raised many concerns about novelty, technical details, comparisons with baselines, missing related work, etc. During the post-rebuttal discussions, reviewers still believed that some major issues still remain. For instance, the paper fails to exhibit a significant efficiency advantage over SOTA baselines. Overall, this work in its current version is not ready for publication at ICLR.\",\n \"additional_comments\": \"Reviewers had many concerns about novelty, technical details, comparisons with baselines, missing related work, etc. The authors provided detailed responses, but they cannot fully address the reviewers' concerns, such as the comparisons with SOTA methods and the efficiency of the proposed method.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Reject\"\n}"}}},{"rowIdx":3396,"cells":{"paper_id":{"kind":"string","value":"qYniSDqk8a"},"arxiv_id":{"kind":"string","value":"2409.17671v2"},"title":{"kind":"string","value":"Leveraging Anthropometric Measurements to Improve Human Mesh Estimation and Ensure Consistent Body Shapes"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract The basic body shape of a person does not change within a single video. However, most SOTA human mesh estimation (HME) models output a slightly different body shape for each video frame, which results in inconsistent body shapes for the same person. In contrast, we leverage anthropometric measurements like tailors are already obtaining from humans for centuries. We create a model called A2B that converts such anthropometric measurements to body shape parameters of human mesh models. Moreover, we find that finetuned SOTA 3D human pose estimation (HPE) models outperform HME models regarding the precision of the estimated keypoints. We show that applying inverse kinematics (IK) to the results of such a 3D HPE model and combining the resulting body pose with the A2B body shape leads to superior and consistent human meshes for challenging datasets like ASPset or fit3D, where we can lower the MPJPE by over 30 mm compared to SOTA HME models. Further, replacing HME models estimates of the body shape parameters with A2B model results not only increases the performance of these HME models, but also leads to consistent body shapes.\\n\\n## 1 Introduction\\n\\nCreating an accurate 3D mesh from monocular images or videos creates new opportunities in fields like 3D animation, gaming, fashion, sports, etc. In many of these application fields, videos are of main interest. While applying HME to videos, one would expect to get a mesh sequence per person with those meshes just changing their poses, but not their body shape.\\nHowever, analyses of results of SOTA HME models in challenging scenarios show that the body shape of the meshes of the same person differs from frame to frame. This is because most HME models work per image and are unable to process a whole video. Worse, an analysis of currently used 3D mesh and pose datasets reveals the same inconsistencies in the provided ground truth (GT) data. For a precise body posture analysis, as it is necessary in many sports disciplines, an exact model of the athlete’s body shape is required. Therefore, many professional athletes are measured anthropometrically during performance assessments. Moreover, the body shape of an actor performing motions for 3D animations needs to be consistent as the basic body shapes does not change during performances. Changes are only due to different poses and are modeled separately besides the core shape. Thus, the changing body shapes of HME models for the same person are highly unwanted and simply wrong.\\n\\nOur work aims to create a single perfectly fitting basic body shape for each human and reuse it for all videos with this person. Measuring the human body has already been done for centuries to fit suits or dresses perfectly to a specific body shape. Athletes are also measured for decades for precise performance assessments. In many applications, measuring the person in action would add only a marginal overhead, but ease the postprocessing steps. This is the reason why we propose to use these measurements. However, body shape parameters of common human mesh models like SMPL-X (Pavlakos et al., ) are not human interpretable. Therefore, it is not possible to obtain the perfect body shape parameters by anthropometric measurements. Hence, we train a machine learning model (called *A2B*, anthropometric measurements to body shape) to translate those measurements into body shape parameters for HME. With this approach, measuring a person once creates the body shape that can be used for all frames in all evaluation videos.\\n\\nHME models are currently performing well on everyday data. However, in more challenging scenarios like sports, their performance is still inferior to finetuned SOTA 3D HPE models. 3D HPE models only predict 3D keypoints resulting in a stickfigure pose, whereas HME models output a posed mesh including the human’s surface. Due to the lack of GT meshes, HME models cannot be trained on datasets with solely 3D keypoint annotations which are easier to create than mesh annotations. The usage of synthetic data is emerging in the field, but is not applicable to challenging or specific scenarios like sports. In this paper, we propose a solution to that problem. With our A2B model and anthropometric measurements, we can now create the body shape parameters of humans needed for HME. We further apply inverse kinematics (IK) to produce the rotations that are missing in the 3D stick-figure model that is created by 3D HPE models. Together with our A2B body shape, we are able to generate human meshes that have a consistent body shape and a precise pose. Evaluations show that the performance of this composed approach is superior compared to HME models. We show qualitative examples of our model and a SOTA HME model, SMPLer-X (Cai et al., ), in Figure [1](#S0.F1).\\nOur approach is generally applicable to any HME problem. We choose sports datasets to validate our proposed approach, since the poses in sports change rapidly, which exacerbates the problem of inconsistent body shapes.\\nOur contributions can be summarized as follows:\\n\\n- •\\nWe reveal inconsistencies in the GT data of ASPset (Nibali et al., ) and fit3D (Fieraru et al., ). The body shape of a single person varies mistakenly in the GT.\\n- •\\nWe create and evaluate different models for converting between anthropometric measurements and SMPL-X body shape parameters.\\nWe call these models *A2B*. We are the first to intoduce a possibility to convert from anthropometric measurements to body shape parameters.\\n- •\\nWe analyze and compare the performance of existing HME models on ASPset and fit3D. Replacing the estimated body shape parameters (and keeping the pose) of each HME model with A2B body shape parameters increases the performance of all models.\\n- •\\nWith finetuned SOTA 2D and 3D HPE models (Xu et al., ; Einfalt et al., ), inverse kinematics (IK), anthropometric measurements, and our A2B model, we estimate accurate human meshes with a consistent body shape. We show that this approach achieves superior results to SOTA HME models, although still evaluated on the inconsistent GT.\\n- •\\nOur models and code for our approach are publicly available: [https://anonymous.4open.science/r/A2B_human_mesh-FA54/](https://anonymous.4open.science/r/A2B_human_mesh-FA54/)\\n\\n## 2 Related Work\\n\\nHuman Mesh Estimation (HME) is an active area of research. Body models like SMPL (Loper et al., ) and its successor SMPL-X (Pavlakos et al., ) are broadly used. Their advantage is that they decouple human pose and shape. The pose parameters $\\\\theta$ give the rotations of the joints relative to the parent joint. The shape parameters $\\\\beta$ model the basic body shape. At first, a mesh is created with a linear mapping from $\\\\beta$ parameters to a T-shaped pose. Next, some pose-specific shape deformations are applied and then the mesh is rotated at the joints according to the $\\\\theta$ parameters.\\n\\nThe first HME model that estimates SMPL-X meshes from images was introduced along SMPL-X (Pavlakos et al., ). This model, called SMPLify-X, detects 2D image features and then fits an SMPL-X model to these. To achieve that, they incorporate a pose prior trained on a large motion capture dataset and an interpenetration test. A more recent model for HME is Multi-HMR (Baradel et al., ). It predicts 2D heatmaps for person centers and based on that the human mesh with a human prediction head. OSX (Lin et al., ) is another HME model. It uses a component aware transformer that is composed of a global body encoder and local decoders for face and hands. SMPLer-X (Cai et al., ) is introduced as a generalist foundation model for HME, which is trained on a large amount of datasets. It mainly uses vision transformers. There is a multitude of other recent HME models, some focussing more on whole-body HME (Choutas et al., ; Feng et al., ; Moon et al., ), others on multi-person HME - either with a two stage approach using a person detector and a single person human mesh estimator (Choi et al., ; Goel et al., ; Qiu et al., ), or a single stage approach estimating the meshes of all persons at once (Qiu et al., ; Sun et al., ; Zhang et al., ).\\n\\nChoutas et al. () observed that existing HME models focus more on the body pose than the shape, although the shape is equally important for many applications. They propose SHAPY, a model that uses anthropometric and linguistic attributes to create accurate body shapes. Moreover, Sarkar et al. () introduce SoY, which contains specific loss functions to enhance the body shape accuracy. They further propose a refinement step during test time that enhances the shape quality even more.\\nKBody (Zioulis & O’Brien, ) follows a predict and optimize approach for HME. It leverages virtual joints in order to achieve that and focuses on pixel alignment to accurately capture the shape of the human.\\nAnthroNet (Picetti et al., ) propose a new body model that is learned with an end-to-end trainable pipeline. It takes anthropometric measurements as an input to learn a mesh model that accurately captures shapes of humans, but this model is different from the commonly used SMPL-X model. We use the common SMPL-X body model and decouple the estimation of the shape from the estimation of the pose. This way, we ensure the consistency of the body shape over time.\\n\\nInverse kinematics (IK) are common in the field of robotics. In the last years, 3D HME approaches leveraged IK to enhance their output. HybrIK (Li et al., ) transforms 3D joint coordinates to relative body-part rotations for 3D HME by using a twist-and-swing decomposition. HybrIK-X (Li et al., ) further enhances HybrIK with expressive face and hands.\\nCha et al. (Cha et al., ) leverage IK to tackle the challenge of person-to-person occlusions in images with interacting persons. PLIKS (Shetty et al., ) (Pseudo-Linear Inverse Kinematic Solver) approaches HME as a model-in-the-loop optimization problem by analytically reconstructing the human model via 2D pixel-aligned vertices in an IK-like manner. NIKI (Li et al., ) tries to unite robustness to occlusions and pixel-aligned accuracy in non-occlusion cases by modeling bi-directional errors. NIKI can learn from both the forward and inverse processes, whereby it emulates the analytical inverse kinematics algorithms with the twist-and-swing decomposition for better interpretability.\\n\\nAlthough HME is an active area of research, it is yet not common in computer vision for sports. Due to high velocities and a great variation of poses, sports is a challenging scenario for all kinds of human pose and shape estimation. The fit3D dataset (Fieraru et al., ) is a dataset which consists of videos from gym sports exercises with repetitions and is annotated with human meshes. AIFit (Fieraru et al., ) is a tool trained on fit3D which can reconstruct 3D human poses, reliably segment exercise repetitions, and identify the deviations between standards learned from trainers, and the execution of a trainee to give feedback to trainees. Other sports datasets only consist of 3D joint annotations, like ASPset (Nibali et al., ) or SportsPose (Ingwersen et al., ). SportsCap (Chen et al., ) is an approach for simultaneously capturing 3D human motions and understanding fine-grained actions from monocular challenging sports videos. Baumgartner & Klatt () make use of partial sports field registration to enhance 3D HPE results for athletes running on a track.\\n\\n## 3 Errors in 3D Human Shape Ground Truth\\n\\nEach person has a specific body shape that does not change over a short time period. Therefore, the SMPL-X body model decouples the human pose encoded by $\\\\theta$ parameters from the body shape encoded by $\\\\beta$ parameters. Deformations to the mesh that are caused by the pose are modeled separately. Therefore, it makes sense to assign a single set of shape parameters $\\\\beta$ to a person to describe his/her shape for a given short time period such as a recorded action. Further, there are lengths that can be calculated from 3D joints that should never change, since individual bones of humans are rigid and should not be deformed by different poses. Our approach enforces a single set of shape parameters per person and immutable bone lengths.\\n\\nAs a first step, we analyze if the GT data of our used datasets fulfills these properties.\\n\\n**Table 1: GT data analysis for ASPset (left) and fit3D (right): Standard deviation $\\\\sigma$, relative standard deviation $\\\\frac{\\\\sigma}{\\\\textit{avg}}$ and relative range $\\\\frac{\\\\max-\\\\min}{\\\\textit{avg}}$ of anthropometric measurements. Standard deviations are given in cm, but for the $\\\\beta$ parameters. The values are averaged between left and right body parts and between all persons in the test set of each dataset. The $\\\\beta$ parameter standard deviation is averaged over all $\\\\beta$ parameters.**\\n| ASPset | fit3D | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- |\\n| Measurement | $\\\\sigma$ | r. $\\\\sigma$ | r. range | Measurement | $\\\\sigma$ | r. $\\\\sigma$ | r. range |\\n| head | 0.91 | 5.98% | 57.91% | head | 0.69 | 2.60% | 14.70% |\\n| hip width | 1.71 | 9.48% | 85.46% | hip circ. | 0.80 | 0.76% | 5.44 % |\\n| forearm | 1.99 | 8.37% | 92.04% | forearm | 0.33 | 1.40% | 7.64% |\\n| upper arm | 1.72 | 6.29% | 66.35% | arm | 0.76 | 1.53% | 8.32% |\\n| lower leg | 1.44 | 3.60% | 41.36% | lower leg | 0.43 | 1.14% | 11.14% |\\n| thigh | 1.65 | 4.23 % | 35.46% | thigh | 0.37 | 1.03% | 9.21% |\\n| | | | | height | 1.65 | 0.98% | 6.45% |\\n| | | | | $\\\\beta$ param. | 0.65 | | |\\n\\nIn this paper, we use ASPset (Nibali et al., ) and fit3D (Fieraru et al., ), since both datasets consist of videos with fast changing poses and 3D GT. Results for the Human3.6m (Ionescu et al., ) and MPI-INF-3DHP (Mehta et al., ) datasets are presented in the supplementary. For ASPset, we analyze bone lengths, since it has only GT annotations for 3D joints. For fit3D, GT SMPL-X $\\\\beta$ parameters are available, hence we can analyze the $\\\\beta$ parameters directly and further the derived anthropometric measurements. These values are the output of our deterministic B2A function: It generates a standard T-pose with the given $\\\\beta$ parameters and computes 36 anthropometric measurements from the resulting mesh. Results of our GT analysis for a subset of the anthropometric values are shown in Table [1](#S3.T1). We can see that the GT itself is not consistent. The deviations are larger for ASPset, but although we have GT SMPL-X meshes for fit3D, the $\\\\beta$ parameters of a single person have a standard deviation of 0.65 on average.(^1^11Averaged standard deviation means (in the whole paper) that the standard deviation is calculated per person, and the mean of the resulting standard deviations is calculated afterwards.) This is a relevant flaw in the GT shape annotation, since based on the model, the GT shape should be static for each human. Nevertheless, we use the given inconsistent GT for our evaluations for comparability with related work and as we have no good means to correct them. The reader should keep this in mind. Nevertheless, we want to encourage future research in the field of 3D human pose and mesh data collection to try to eliminate these flaws in the provided GT.\\n\\n## 4 From Anthropometric Measurements to the Body Shape\\n\\nHumans have been measured for centuries (Doyon et al., ). Tailors know exactly which measurements to take for perfectly fitting a suit or dress to the body shape of a customer. In sports, professional athletes are measured for precise performance assessments, too. Measuring a human is easy and well understood. In contrast, the parameters of the body shape for human mesh models like SMPL-X (Pavlakos et al., ) are not humanly interpretable. The $\\\\beta$ parameters describe the principal components of the human body shape with typically around 10 to 16 values and are the result of a PCA executed on the human meshes of a training dataset while learning the SMPL-X model. Fixing all $\\\\beta$ parameters despite one and looking at the results lets human observers get a notion of what this parameter might mean, but in total, the $\\\\beta$ parameters and their interactions are not well interpretable. Therefore, we want to leverage the well established technique of measuring humans to create precise body shape parameters for the commonly used SMPL-X human mesh model. We call our approach to convert from 36 Anthropometric measurements to Body shape parameters *A2B*. Since there is no known relation between anthropometric measurements and $\\\\beta$ parameters, our aim is to learn this mapping. We are the first to present a method to convert from anthropometric measurements to body shape parameters. The reverse direction, *B2A*, is a deterministic function of the human mesh, as the anthropometric measurements can be measured from the mesh.\\n\\n### 4.1 Data Generation\\n\\nWe select the 36 anthropometric measurements for our models based on the selections of AnthroNet (Picetti et al., ) and an anthropometry study of the U.S. army (Gordon et al., ). They can be categorized into 23 lengths and 13 circumferences. Apart from the bone lenghts like arm length, thigh length, etc., this includes also detailed measurements like shoulder width, front torso height, lateral neck length, waist circumference, calf circumference, etc. A visualization and precise description of the selected measurements can be found in the supplementary.\\n\\nMany existing datasets provide a wide range of different poses, but most incorporate the same humans. In order to learn a conversion model from anthropometric measurements to $\\\\beta$ parameters, we need a lot of samples for different humans, no matter the pose. With given shape parameters, we can use the B2A function to compute the anthropometric measurements. Recall, B2A is a deterministic function measuring the anthropometric values from the meshes.\\n\\nBecause of the need for many different body shapes for the learning process, we use the AGORA (Patel et al., ) dataset. It consists of 1447 male and 1588 female subjects, which is comparably large. We are not able to use the larger dataset from AnthroNet (Picetti et al., ), since it uses its own mesh model and the authors did not publish their conversion to the SMPL-X model, which we want to use as it is most commonly used in research. Although comparably large, 1447/1588 subjects is still a very little amount of data to learn a model. Hence, we analyze the $\\\\beta$ parameters in the AGORA dataset with the aim to randomly sample more data with realistic body shapes. Histograms (see Figure [2](#S4.F2)) of the occurring $\\\\beta$ parameters show that their distribution roughly follows a normal distribution. Therefore, we train our models with randomly sampled data according to the distributions, either assuming a normal distribution fitted to the histograms or a uniform distribution with the same minimum and maximum values as in the data analysis. This means that we sample each $\\\\beta$ parameter according to the selected distribution, create the mesh according to the sampled values and derive the anthropometric measurements with B2A. With this strategy, we can create a dataset with as many subjects as we need.\\nWe expect the analyzed data to not cover the full range of human body shapes as AGORA is a synthetic dataset. Therefore, we also train with extended distributions, meaning that we increase the standard deviation $\\\\sigma$ to $\\\\alpha_{n}\\\\sigma$ in the case of a normal distribution or stretch the interval by a factor $\\\\alpha_{u}$ in case of a uniform distribution.\\n\\nFigure: Figure 2: Histograms and fitted normal distribution (orange) for the first two $\\\\beta$ parameters for all male (left) and female (right) subjects of the AGORA (Patel et al., ) dataset.\\nRefer to caption: /html/2409.17671/assets/img/histograms.png\\n\\n### 4.2 Models\\n\\nWe use the same number of $\\\\beta$ parameters for each gender as used in the AGORA dataset, meaning $11$ for male, $10$ for female, and $16$ for neutral subjects. With $36$ anthropometric measurements as input values and $10-16$ output values for our A2B models, the dimensionality of the data is low. Therefore, we experiment with Support Vector Regression (SVR) and with small neural networks (NN). We split the AGORA dataset in a 80% train, 15% test and 5% validation subset. For SVR, we additionally randomly sample $10,000$ subjects for training. We use a hyperparameter search based on the validation split to determine the optimal settings, which leads us to a radial basis function kernel, an error margin of $\\\\epsilon=0.012$ and a regularization constant of $C=3791$. For the NNs, we randomly sample new data in each iteration. The hyperparameter search for the NNs results in a model with $4$ layers, $330$ neurons per layer, tanh as activation function, and Xavier Gloriot as initialization. We use mean squared error on the model output (the $\\\\beta$ parameters) to train the models.\\n\\n### 4.3 Results\\n\\n**Table 2: Results of our A2B models on the test split of the AGORA dataset. The first block ($\\\\beta$) shows the error if we take the GT $\\\\beta$ parameters, derive 36 anthropometric measurements (B2A), input them into the A2B models and evaluate the MSE of the predicted $\\\\beta$ parameters in the scale $10^{-3}$. The second block ($A$) calculates B2A from the predicted $\\\\beta$ parameters and evaluates the mean difference between the GT and predicted anthropometric measurements (all 36) in mm. Results are given for m(ale), f(emale), and n(eutral) models. A visualization is provided in the supplementary.**\\n| | | $\\\\beta$ | $A$ | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- |\\n| Model | train data | m | f | n | m | f | n |\\n| NN | AGORA | 9.11 | 13.9 | 24.0 | 0.814 | 0.934 | 1.459 |\\n| NN | normal | 2.62 | 4.34 | 18.0 | 0.356 | 0.392 | 1.711 |\\n| NN | normal ext. | 1.87 | 3.69 | 14.8 | 0.248 | 0.285 | 1.384 |\\n| NN | uniform | 5.08 | 1.25 | 18.3 | 0.243 | 0.268 | 2.381 |\\n| NN | uniform ext. | 1.61 | 3.20 | 16.3 | 0.274 | 0.419 | 1.774 |\\n| SVR | AGORA | 2.56 | 16.1 | 3.82 | 1.659 | 5.195 | 2.557 |\\n| SVR | normal | 4.08 | 17.8 | 59.0 | 2.975 | 4.303 | 14.63 |\\n| SVR | normal ext. | 0.210 | 4.60 | 6.27 | 0.280 | 1.090 | 2.211 |\\n| SVR | uniform | 0.0396 | 0.0350 | 0.162 | 0.124 | 0.284 | 0.214 |\\n| SVR | uniform ext. | 0.0252 | 0.0193 | 0.306 | 0.082 | 0.136 | 0.164 |\\n\\nWe train each model (NN and SVR) for each gender and with different dataset variants: We train solely on the AGORA train split, as well as on uniformly and normally distributed randomly sampled data according to the data analysis, and we further extend the range of the data as described in Section [4.1](#S4.SS1) with $\\\\alpha_{n}=\\\\alpha_{u}=1.5$.\\nThe results are displayed in Table [2](#S4.T2). We evaluate the performance of our models in two ways. At first, we calculate the error of the predicted and GT $\\\\beta$ parameters. Second, we calculate the mean deviation of the anthropometric measurements of the meshes from the predicted and GT $\\\\beta$ parameters ($A$). Therefore, this evaluation can further be seen as a kind of cycle consistency evaluation of A2B (our learned model) and B2A (the deterministic measuring function). We provide a visualization of the evaluation process in the supplementary.\\nThe anthropometric error is our main metric as these values reflect the desired body shape given as an input by the user and are further interpretable. The $\\\\beta$ parameters are somehow arbitrary in their scale. For all genders and SVR, using an extended uniformly sampled dataset works best. For the NNs, a uniformly sampled dataset works best for male (m) and female (f) genders and an extended normally sampled dataset for the neutral (n) meshes. The results for the neutral model are worse in general, especially in the case of the NNs, which might be due to the fact that the neutral model needs to express a more diverse range of body shapes. Furthermore, the SVR achieves better results for all genders.\\nThus, we use these models now for all datasets, without any finetuning or adaptation to specific datasets.\\n\\n## 5 Leveraging A2B Model Results for HME\\n\\nNow that we have trained the A2B models, we can use them to generate precise body shape parameters upfront and reuse them for every evaluation of a specific person. In the next section, we describe how the A2B results can be used to improve existing HME models (see Section [5.1](#S5.SS1)). Further, we introduce a new approach to HME (see Section [5.2](#S5.SS2)). We leverage the good performance of a sequence-based 2D-to-3D uplifting HPE model and convert the 3D (stick-figure) poses to human meshes with the help of the A2B models. With this new approach, we achieve superior results compared to existing HME models.\\n\\nWe evaluate all models on ASPset (Nibali et al., ), which is a 3D human pose dataset. It consists of various different sports motion clips performed by different subjects, recorded from three camera perspectives. We evaluate on the test set, which contains two subjects and 30 videos for each subject. In the test set, only one camera perspective is public, so we evaluate on this perspective. Evaluating SMPL-X meshes for ASPset is non-trivial. Regressing standard SMPL-X joints from SMPL-X meshes is built-in, but for all other keypoint definitions it is necessary to define a custom regressor. Since there is no regressor available for ASPset, we create a custom SMPL-X regressor for the keypoints head, head top, neck, l./r. hip, and torso. For left ankle and elbow, we mirror the corresponding right regressor, as it is not the exact mirrored version in the standard regressor. We use the code from (Russo, ) and update it to our needs.\\n\\nWe further evaluate on fit3D (Fieraru et al., ), since this is the only sports dataset with public SMPL-X annotations. We evaluate on the SMPL-X joints here since they are available. We select a subset of 37 SMPL-X joints. Since our focus is mainly on the body and not on the hands and face, we remove a lot of these joints. A list of the selected joints can be found in the supplementary. For both datasets, we do not have access to the athletes to measure their anthropometric values. Therefore, we use the ground truth to obtain the anthropometric measurements that are needed as an input for the A2B models, details can be found in the supplementary. Since there is no GT available for the official test set evaluation on the evaluation server of fit3d, we split the official training dataset into a training, validation, and test set for our evaluations. We choose the last subject (s11) with all 188 videos as the test set.\\n\\nSports datasets differ from most commonly used everyday activity datasets in the aspect that the poses are more diverse and the motions are faster, which makes sports datasets more difficult. In some cases, the poses are so difficult that some models do not detect a human at all. This makes a fair evaluation hard, since the standard MPJPE metric takes the mean of the joint position errors. Assuming a default pose for all frames where no person is detected would result in a very high error that shifts the mean enormously. Hence, we report the MPJPE only on the frames where persons are detected. Since mostly difficult frames are omitted, this will result in a slightly easier setting for methods that find less persons, but we include the number of missing frames in our results for comparison.\\n\\n### 5.1 Improving HME Model Results\\n\\nAs already described, a major problem for HME based analyses is a varying body shape within a single video. Using $\\\\beta$ parameters generated with A2B models solves this problem.\\nThe necessary 36 anthropometric measurements are either measured from the human directly or - as in our case - averaged from the provided GT (fit3D) or averaged from IK applied to the GT poses (ASPset). We call these measurements pseudo GT in the following. More details can be found in the supplementary.\\nWe combine existing HME models with the body shape estimated by our A2B models by replacing the estimated $\\\\beta$ parameters with the ones predicted by the A2B models.\\nWe select three recent well performing models on the AGORA dataset (SMPLer-X (Cai et al., ), OSX (Lin et al., ), Multi-HMR (Baradel et al., )), and the first HME method developed by the SMPL-X authors, SMPLify (Pavlakos et al., ). Since SMPLer-X is trained on the official training data of fit3D, an evaluation with this model is not meaningful and we omit it. Moreover, SMPLify-X is not SOTA any more and achieved the worst results for ASPset, therefore we omit it, too.\\n\\nThe first evaluation contains the original result from the respective model, and evaluations where the pose from the model is kept, but the $\\\\beta$ parameters are replaced with the A2B body shape parameters with pseudo GT input. In order to emphasize the variation of the body shape in the HME model results, we evaluate the standard deviation of the body height per person.\\nResults are displayed in Table [3](#S5.T3). We can see that for all models, replacing the estimated $\\\\beta$ parameters by $\\\\beta$ parameters from our A2B models with pseudo GT input leads to an improvement. For some models, the male meshes outperform the neutral ones and vice versa. The test sets of both datasets contain only male subjects, therefore we cannot evaluate female meshes here. Interestingly, the NN outperforms the SVR for all neutral experiments, although the SVRs achieved better results on the AGORA dataset evaluation. The reason could be that AGORA is a synthetic dataset and does not reflect reality. SMPLer-X achieves the best results for ASPset and Multi-HMR for fit3D, both with a significant margin. OSX performs worse on fit3D than on ASPset, but Multi-HMR performs better by a large margin and surpasses OSX. All methods benefit from our A2B $\\\\beta$ parameters based on pseudo GT with improvements from 11 mm to 2 mm.\\n\\nWe further evaluate the capabilities of a fixed body shape without available GT anthropometric measurements to ensure consistent body shapes also in the case that no measurements are available.\\n\\n**Table 3: MPJPE results in mm for existing models on the test splits of ASPset (top) and fit3D (bottom). The second column (*orig.*) contains the original results, the other columns results with replaced $\\\\beta$ parameters from our A2B models with pseudo GT anthropometric measurements as input and either male (m) or neutral (n) meshes, and the percentage of frames with no result (no r.). The $\\\\sigma$ column displays the mean standard deviation of the body height per subject in cm for the original results. With A2B body shapes, $\\\\sigma=0$.**\\n| | Model | orig. | $\\\\sigma$ | NN m | SVR m | NN n | SVR n | no r. ($\\\\downarrow$) |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| ASPset | SMPLer-X (Cai et al., ) | 86.02 | 1.8 | 78.88 | 78.50 | 78.38 | 78.47 | 0.11% |\\n| OSX (Lin et al., ) | 92.34 | 0.2 | 89.58 | 89.28 | 89.44 | 89.56 | 0.10% | |\\n| Multi-HMR (Baradel et al., ) | 102.54 | 3.6 | 100.04 | 100.25 | 99.28 | 99.53 | 0.44% | |\\n| SMPLify-X (Pavlakos et al., ) | 138.18 | 13.0 | 127.73 | 127.36 | 126.78 | 126.89 | 0.02% | |\\n| fit3D | OSX (Lin et al., ) | 99.20 | 4.8 | 93.22 | 92.58 | 91.72 | 92.21 | 3.45% |\\n| Multi-HMR (Baradel et al., ) | 72.87 | 3.0 | 70.72 | 71.65 | 70.70 | 71.74 | 1.54% | |\\n\\n**Table 4: MPJPE results in mm for existing models on the test split of the ASPset (top) and fit3D (bottom) datasets. The second column contains the original results, the other columns results with replaced $\\\\beta$ parameters. Either the median $\\\\beta$ parameters are used or the results from our A2B models with median anthropometric measurements from the respective model as input. For *no r.* see Table [3](#S5.T3).**\\n| | Model | orig. | median | NN m | SVR m | NN n | SVR n |\\n| --- | --- | --- | --- | --- | --- | --- | --- |\\n| ASPset | SMPLer-X (Cai et al., ) | 86.02 | 86.04 | 85.89 | 85.69 | 86.03 | 85.99 |\\n| OSX (Lin et al., ) | 92.34 | 92.37 | 92.44 | 92.17 | 92.33 | 92.38 | |\\n| Multi-HMR (Baradel et al., ) | 102.54 | 102.05 | 102.59 | 102.96 | 102.07 | 102.16 | |\\n| SMPLify-X (Pavlakos et al., ) | 138.18 | 133.59 | 133.81 | 133.46 | 133.56 | 133.48 | |\\n| fit3D | OSX (Lin et al., ) | 99.20 | 96.70 | 98.20 | 96.07 | 96.60 | 96.72 |\\n| Multi-HMR (Baradel et al., ) | 72.87 | 72.08 | 72.62 | 72.37 | 72.06 | 71.92 | |\\n\\nHence, we use the meshes originally created by the HME models, compute the anthropometric measurements of each mesh with B2A, calculate their median values and convert them to $\\\\beta$ parameters via the A2B models.\\nResults are displayed in Table [4](#S5.T4).\\nFor SMPLer-X and OSX, using the median $\\\\beta$ parameters lead to worse results on ASPset. Regarding ASPset, for all models except Multi-HMR, using our A2B models increases the performance slightly. Switching from the neutral output that these models all have to a gendered model works best in these cases, but the neutral A2B models also lead to a marginal improvement. Regarding fit3D, using the median $\\\\beta$ parameters already enhances the results. Using $\\\\beta$ parameters from an A2B model leads to further improvement, OSX achieves the best results with SVR and the male model, Multi-HMR with SVR and the neutral model.\\n\\nThey can further be used to easily convert between neutral and gendered (male or female) models. In contrast, $\\\\beta$ parameters are not transferable between models of different genders. Therefore, until now, the conversion could only be achieved by minimizing the vertex error between meshes of different genders in an iterative process. With our approach, we can now use the B2A fuction to obtain anthropometric measurements for a mesh of one gender and apply the A2B model of the other gender to these anthropometric measurements in order to get the corresponding $\\\\beta$ parameters for this gender.\\n\\n### 5.2 Human Mesh Estmation with Sequence Based 3D HPE and A2B Results\\n\\nAll evaluated HME models are working image-wise. In contrast, SOTA 3D HPE models take a long sequence of 2D poses as an input, which helps to capture movements precisely. The models are called uplifting models, since they lift 2D pose sequences to 3D pose sequences. We use the efficent SOTA 3D HPE model *uplift and upsample* (UU) (Einfalt et al., ) to estimate the 3D poses on videos. To estimate the required 2D poses from the video frames, we use ViTPose (Xu et al., ), a SOTA 2D pose estimation model. It is important to note that UU operates on pose sequences instead of single frames like the HME models in Section [5.1](#S5.SS1) and can leverage the information of neighboring frames to estimate a more sophisticated pose. Since we have GT 3D joints available, we can finetune the models (ViTpose for 2D HPE and UU for 3D HPE) on our data. This is also necessary to adapt the model to the dataset specific joint definitions since many 3D HPE models like UU are pretrained on datasets like Human3.6m (Ionescu et al., ), but those joint definitions do not match ASPset nor fit3D. We finetune both 2D and 3D HPE models on the training subsets. On the test subsets, UU achieves an MPJPE of 63.85 mm on ASPset and an MPJPE of 29.60 mm on fit3D, which is better than the best existing HME model for both datasets (see Section [5.1](#S5.SS1)). However, UU only outputs 3D joints, no meshes. Moreover, a stick-figure 3D pose is not sufficient to model the pose parameters $\\\\theta$ of the SMPL-X mesh, since some rotations are missing. Hence, it is impossible to calculate the necessary rotation parameters directly from the UU result.\\n\\n#### 5.2.1 Inverse Kinematics for Full Pose Estimation\\n\\nTherefore, we use the well established approach of inverse kinematics (IK) to obtain the missing rotations by fitting an SMPL-X mesh to the 3D joint locations estimated by UU. We use the inverse kinematics approach with the VPoser extension (Pavlakos et al., ). VPoser is a learned prior for human poses, since the raw SMPL-X model definition allows impossible poses for humans. VPoser learned plausible poses from the large AMASS (Mahmood et al., ) dataset and helps IK to generate only plausible poses. IK learns the best SMPL-X parameters ($\\\\beta$ and $\\\\theta$) that fit the mesh to the given 3D joint locations by minimizing the error between the given joint locations and the regressed joint locations from the mesh.\\nIK is an iterative algorithm and adjusts the pose and the shape parameters with a gradient descent minimization approach in each step. Besides the already described joint error, IK further penalizes abnormal poses with a VPoser error and extreme body shapes with a $\\\\beta$ parameter error. We execute IK per frame, which results in a slight jitter in between the frames, but leads to more accurate joint positions. Since IK needs multiple iterations to adjust the standard T-pose parameters to achieve a pose that is roughly close to the desired UU pose, we speed up the process by initializing the pose and shape parameters with the result from the previous frame if available. This also enhances the final result slightly.\\n\\n#### 5.2.2 Experiments and Results\\n\\nFigure: Figure 3: Overview of our approach. The pose and shape parameters are obtained either from IK applied to UU results (Sec. [5.2.2](#S5.SS2.SSS2)) or from an HME model (Sec. [5.1](#S5.SS1)). In real applications, the anthropometric measurements will be taken directly from the humans . For our evaluations, we use the GT shape parameters and further experiment with the shape parameters of the respective model (IK or HME).\\nRefer to caption: /html/2409.17671/assets/x2.png\\n\\nWe evaluate different experiments in Table [5](#S5.T5). For comparison, we mention the UU 3D HPE performance (first rows for each dataset in Tab. [5](#S5.T5)). These results correspond to stick-figure poses and not the required human meshes. Therefore, they are not directly comparable to the other results.\\n\\nOur main approach is displayed in the second rows in Table [5](#S5.T5), respectively. We evaluate the results of IK applied to the UU joint locations with original, median and pseudo GT based A2B $\\\\beta$ parameters. The final real-world scenario corresponds to the following approach. GT anthropometric values can be measured from the athlete directly and the 3D pose can be estimated with UU and IK. The $\\\\beta$ parameters are estimated with the A2B models. A visualization of this pipeline can be found in Figure [3](#S5.F3).\\nWe include the best result from existing HME models in the respective last rows for comparison and provide qualitative results in Figure [1](#S0.F1). Our approach outperforms the best existing HME model for both datasets by a large margin.\\n\\nWe analyze the results of the building blocks of our model in detail. Applying IK to the UU results deteriorates the UU results by nearly 4 mm for ASPset and 8 mm for fit3D (see Tab. [5](#S5.T5), first and second rows, column *orig.*), but the UU result is only a stick-figure pose and not a human mesh, hence it is not sufficient for our purpose. Moreover, these results are still better than the best existing HME model.\\n\\nNext, we replace the inconsistent $\\\\beta$ parameters with the results from our A2B models.\\nFor ASPSet, using pseudo GT anthropometric measurements results in a large improvement of over 12 mm. Remarkably, this result surpasses even the original UU result by 8 mm. It seems that incorporating a clearly defined mesh helps to fix some typical errors of UU and enhance its result in case of ASPset.\\nIn general, the error on fit3D is much lower for UU based approaches. The reason might be that it consists of much more data, such that we can finetune UU for a longer time. Further, the videos are recorded in a lab in comparison to the in-the-wild videos of ASPset. Therefore, the results of ASPset are more relevant for future applications of our approach, where we assume only a few available 3D annotations and in-the-wild recordings. For fit3D, applying the A2B body shapes from pseudo GT anthropometric measurements leads to a slight decrease in performance of 0.6mm. Inconsistent shapes in the GT (see Section [3](#S3)) are likely to cause this behavior. Still, our approach using a 3D HPE model and IK outperforms all existing HME models, no matter if the original inconsistent or the consistent body shapes from A2B are used.\\n\\n**Table 5: MPJPE results in mm on the test splits of ASPset (top) and fit3D (bottom) of our approach compared to the respective best HME model. The *pose* column indicates the origin of the pose. The *orig* column contains the result as it is estimated from the method indicated in the *pose* column (with inconsistent body shapes). The right block contains the results with the originally estimated $\\\\beta$ parameters replaced by consistent ones. The *measurements* column indicates which anthropometric measurements are used for the A2B computation (which $beta$ parameters are used for the median computation) whose results are the replacement $\\\\beta$ parameters in the last five columns. We highlight the best results for *estimated* meshes with *consistent shapes*.**\\n| | *inconsistent shape* | *consistent shape (ours)* | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| DS | pose | orig. | measurements | NN m | SVR m | NN n | SVR n | median |\\n| ASPset | UU | 63.85 | no mesh | | | | | |\\n| IK-UU | 67.54 | GT | 56.44 | 56.56 | 55.14 | 55.19 | - | |\\n| IK-UU | 67.54 | IK-UU | 66.92 | 66.60 | 67.25 | 67.12 | 67.16 | |\\n| SMPLer-X | 86.02 | GT | 85.89 | 85.69 | 86.03 | 85.99 | 86.04 | |\\n| fit3D | UU | 29.60 | no mesh | | | | | |\\n| IK-UU | 36.89 | GT | 39.36 | 38.69 | 37.46 | 37.89 | - | |\\n| IK-UU | 36.89 | IK-UU | 40.33 | 38.82 | 38.14 | 38.10 | 38.29 | |\\n| Multi-HMR | 72.87 | GT | 72.62 | 72.37 | 72.06 | 71.92 | 72.08 | |\\n\\nAs already described in Section [5.1](#S5.SS1), we further evaluate the capabilities of a consistent shape without available GT anthropometric measurements. The naive approach is to use the median of the estimated inconcistent $\\\\beta$ parameters (see Tab. [5](#S5.T5), column *median*). Another approach is to use the meshes created by IK applied to the UU results, compute the anthropometric measurements with B2A, calculate the median anthropometric values and convert them to $\\\\beta$ parameters via the A2B models. Results are displayed in Table [5](#S5.T5), row three. For ASPset, using fixed body shape parameters from A2B models based on the measurements from UU results achieves a slightly better score than the results with inconsistent body shapes. For fit3d, the MPJPE increases by another 0.6 mm, but the A2B model results are a slighly better alternative for consistent body shapes compared to the median $\\\\beta$ parameters.\\n\\nFurther, our approach with IK can be used to generate pseudo GT meshes for datasets with only 3D keypoint annotations. We can use these pseudo GT meshes to finetune HME models and increase their performance regarding the estimated keypoints for the specific dataset. However, these results are still worse than the results of our approach. We present the results in the supplementary.\\n\\n## 6 Conclusion\\n\\nIn this paper, we address the problem of inconsistent estimated body shapes of humans in videos. We analyze the GT data of 3D pose and mesh datasets and find inconsistencies already in their annotations. Then, we propose a family of learned *A2B* models to convert 36 anthropometric measurements to SMPL-X $\\\\beta$ parameters. This can be used to measure a human once and use the resulting shape of the A2B model for all evaluations. With this strategy, the body shape is accurate and consistent per person. Evaluations show that using IK on the results of a SOTA 3D HPE model to estimate the mesh pose combined with our A2B model’s shape parameters leads to superior and consistent results compared to existing HME models. Moreover, HME models also benefit from our approach. Replacing their estimated shape parameters with the A2B shape parameters created from (pseudo) GT anthropometric measurements leads to an improvement of their score and consistent body shapes.\\n\\n## Appendix A Anthropometric Measurements\\n\\nThe selection of the anthropometric measurements is mainly adopted from AnthroNet (Picetti et al., ). In total, 36 measurements are selected, which can be divided into 23 lengths and 13 circumferences. All measurements are taken based on the standard SMPL-X T-pose. The reference landmarks are chosen by matching the vertices on the default mesh with the landmarks defined by the anthropometric survey of the U.S. army personnel (Gordon et al., ). A visualization of the landmarks can be found in Figure [4](#A1.F4) and [5(a)](#A1.F5.sf1). The lengths are calculated by computing the Euclidean distance between two landmarks or the difference along the coordinate axis pointing upwards for certain heights.\\nThe lenghts are visualized in Figure [5(b)](#A1.F5.sf2) and [6](#A1.F6). Table [6](#A1.T6) lists the enclosing landmarks for each length. To measure the circumferences, we adopt the code from (Bojanic, ). For each measurement, a plane is created, the intersection between the mesh and the plane are extracted and the convex hull of the result is calculated.\\nDuring this process, the mesh is restricted to the body part to be measured. A visualization of the circumferences can be found in Figure [7](#A1.F7) and a list of the landmarks and the normal vectors spanning the plane in Table [7](#A1.T7).\\n\\nFigure: Figure 4: Visualization of the used landmarks with a standard T-pose SMPL-X mesh in front view.\\nRefer to caption: /html/2409.17671/assets/img/points_front.png\\n\\n**Table 6: Definitions of lengths by their two enclosing landmarks.**\\n| Idx | Length Name | From | To |\\n| --- | --- | --- | --- |\\n| 1 | Shoulder width | Left shoulder tip (left acromion) | Right shoulder tip |\\n| 2 | Back torso height | Cervicale | Back belly button |\\n| 3 | Front torso height | Suprasternale (top of the breast bone) | Belly button |\\n| 4 | Head | Head top | Cervicale |\\n| 5 | Midline neck | Chin | Suprasternale |\\n| 6 | Lateral neck | Center between the ears | Cervicale |\\n| 7 | Height | Head top | Center between heels |\\n| 8/9 | Hand right/left | Center between middle and ring finger | Stylion rotated downwards |\\n| 10/11 | Arm right/left | Acromion | Wrist |\\n| 12/13 | Forearm right/left | Elbow | Stylion rotated downwards |\\n| 14/15 | Thigh right/left | Outer point at the femur (Trochanterion) | Knee cap |\\n| 16/17 | Calf right/left | Knee cap | Ankle |\\n| 18/19 | Foot width right/left | Small toe | Big toe |\\n| 20/21 | Heel to ball right/left | Heel | Ball |\\n| 22/23 | Heel to toe right/left | Heel | Big toe |\\n\\nFigure: (a) Visualization of a subset of the used landmarks.\\nRefer to caption: /html/2409.17671/assets/img/points_back.png\\n\\n**Table 7: Definitions of circumferences by landmarks and the normal vector spanning the plane.**\\n| Idx | Circumference | Normal Vector | Position |\\n| --- | --- | --- | --- |\\n| 1 | Waist | Up | Belly button |\\n| 2 | Chest | Up | Nipple |\\n| 3 | Hip | Up | Pubic bone |\\n| 4 | Head | Up | Head temple |\\n| 5 | Neck | Spine to head | Adam’s apple |\\n| 6/7 | Upper Arm | Shoulder to elbow | Center of the bicep |\\n| 8/9 | Forearm | Elbow to wrist | Widest point of the forearm |\\n| 10/11 | Thigh | Up | Center of the thigh |\\n| 12/13 | Calf | Up | Widest point of the calf |\\n\\nFigure: Figure 6: Visualization of used lengths with a standard T-pose SMPL-X mesh in front view.\\nRefer to caption: /html/2409.17671/assets/img/lengths-frontview.png\\n\\nFigure: Figure 7: Visualization of used circumferences with a standard T-pose SMPL-X mesh in front view.\\nRefer to caption: /html/2409.17671/assets/img/circumferences.png\\n\\n## Appendix B 3D Human Shape Ground Truth Analysis\\n\\nWe further analyze the GT shape consistency for the common datasets Human3.6m (Ionescu et al., ) and MPI-INF-3DHP (Mehta et al., ). We find that for Human3.6m, the bone lengths derived from the 3D annotations are fixed, but not for MPI-INF-3DHP. Therefore, we do not report the deviations of 3D joint annotations for Human3.6m, since there are none. We further evaluate the SMPL-X annotations for both datasets provided by NeuralAnnot (Moon et al., ) which are used by HME models as GT for training. See Tables [8](#A2.T8), [9](#A2.T9) for details.\\n\\n**Table 8: GT data analysis for MPI-INF-3DHP (Mehta et al., ). Bone length analysis based on the 3D joint locations (left) and on SMPL-X annotations by NeuralAnnot (right). Standard deviation $\\\\sigma$, relative standard deviation $\\\\frac{\\\\sigma}{\\\\textit{avg}}$ and relative range $\\\\frac{\\\\max-\\\\min}{\\\\textit{avg}}$ of anthropometric measurements are reported. Standard deviations are given in cm, except for the $\\\\beta$ parameters. The values are averaged between left and right body parts and between all persons in each dataset. The $\\\\beta$ parameter standard deviation is averaged over all $\\\\beta$ parameters.**\\n| 3D joint annotations | SMPL-X annotations | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- |\\n| Measure | $\\\\sigma$ | r. $\\\\sigma$ | r. range | Measure | $\\\\sigma$ | r. $\\\\sigma$ | r. range |\\n| head | 0.19 | 1.03% | 2.08% | head | 0.21 | 0.75% | 4.87% |\\n| hip width | 0.22 | 0.89% | 1.80% | hip circ. | 1.16 | 1.16% | 9.13 % |\\n| forearm | 0.21 | 0.87% | 1.77% | forearm | 0.45 | 1.80% | 9.75% |\\n| upper arm | 0.29 | 0.90% | 1.82% | arm | 0.83 | 1.59% | 8.19% |\\n| lower leg | 0.60 | 1.49% | 3.06% | lower leg | 1.05 | 2.56% | 11.54% |\\n| thigh | 3.83 | 7.91 % | 41.90% | thigh | 0.77 | 2.02% | 9.47% |\\n| | | | | height | 2.76 | 1.56% | 8.24% |\\n| | | | | $\\\\beta$ param. | 0.18 | | |\\n\\n**Table 9: GT data analysis for Human3.6m (Mehta et al., ): Analysis of SMPL-X annotations by NeuralAnnot. Standard deviation $\\\\sigma$, relative standard deviation $\\\\frac{\\\\sigma}{\\\\textit{avg}}$ and relative range $\\\\frac{\\\\max-\\\\min}{\\\\textit{avg}}$ of anthropometric measurements are reported. Standard deviations are given in cm, except for the $\\\\beta$ parameters. The values are averaged between left and right body parts and between all persons in each dataset. The $\\\\beta$ parameter standard deviation is averaged over all $\\\\beta$ parameters.**\\n| SMPL-X annotations | | | |\\n| --- | --- | --- | --- |\\n| Measure | $\\\\sigma$ | r. $\\\\sigma$ | r. range |\\n| head | 0.41 | 1.51% | 10.28% |\\n| hip circ. | 1.24 | 1.19% | 8.90% |\\n| forearm | 0.83 | 3.30% | 27.93% |\\n| arm | 0.77 | 2.58% | 22.88% |\\n| lower leg | 0.43 | 1.18% | 12.20% |\\n| thigh | 0.66 | 1.27% | 9.43% |\\n| height | 3.40 | 2.06% | 15.66% |\\n| $\\\\beta$ param. | 0.20 | | |\\n\\nFigure: Figure 8: Visualization of the A2B evaluation and training procedures. The part involved in training the A2B models is highlighted with thicker arrows. B2A is a deterministic function and not learned.\\nRefer to caption: /html/2409.17671/assets/x3.png\\n\\n## Appendix C Evaluating A2B Models\\n\\nWe measure two types of errors to evaluate the performance of our A2B models. The first type ($\\\\beta$ error) shows the error if we take the GT $\\\\beta$ parameters, derive anthropometric measurements (B2A), input them into the A2B models and evaluate the MSE of the predicted $\\\\beta$ parameters. The second type ($A$ error) calculates B2A from the predicted $\\\\beta$ parameters and evaluates the mean difference between the GT and predicted anthropometric measurements (all 36) in mm. These evaluations are a kind of cycle consistency evaluation for A2B and B2A. Figure [8](#A2.F8) provides a visualization of the evaluation scheme. The part that is also included in the training is highlighted.\\n\\n## Appendix D Keypoint Selection for fit3D\\n\\nWe use the fit3D (Fieraru et al., ) dataset for our evaluations, since this is the only sports dataset with public SMPL-X annotations. We evaluate on the SMPL-X joints, since these are trivial to obtain from SMPL-X meshes and there is no regressor available for the fit3D annotated 3D joints. SMPL-X has 144 defined joints. Since our focus is mainly on the body and not on the hands and face, we remove most of these joints. In the end, we select a subset of 37 SMPL-X joints: pelvis, left hip, right hip, spine1, left knee, right knee, spine2, left ankle, right ankle, spine3, left foot, right foot, neck, left collar, right collar, head, left shoulder, right shoulder, left elbow, right elbow, left wrist, right wrist, left index, left thumb, right index, right thumb, left big toe, left small toe, left heel, right big toe, right small toe, right heel, right eye, left eye, right ear, left ear, nose.\\n\\n## Appendix E Generation of Pseudo GT Anthropometric Measurements\\n\\nAs we do not have access to the athletes of ASPset and fit3d to obtain real anthropometric measurements, we need an alternative to kind-of simulate this process. For ASPset, as a first step, we run IK on the GT 3D joint locations. We obtain the necessary anthropometric parameters from the generated meshes with B2A. Then, we use the median values of these measurements as the GT anthropometric values. We call these parameters *pseudo GT* throughout this paper, since this is not directly the GT, but obtained from IK executed on the GT 3D joint locations and the B2A computation from the created meshes. These parameters are used in this paper to generate the pseudo GT $\\\\beta$ parameters by A2B prediction.\\n\\nWe do not have access to the athletes of the fit3D dataset either. Therefore, we need some kind of GT data to mimic measurements. Obviously, there is no GT available for the official test set evaluation on the evaluation server. We therefore split the official training dataset into a training, validation, and test set for our evaluations. Details can be found in the main paper.\\nWith this selection, we have GT shape parameters available. We do not use these directly, but apply B2A and use the median measurements over time in order to mimic the measuring process and obtain a single set of anthropometric measurements per person (which is not the case for the provided GT parameters, see Section 3 in the main paper). In real applications, this step is omitted because the anthropometric parameters can be measured directly from the athletes before starting the recording.\\n\\n## Appendix F Finetuning HME Models with Pseudo GT Meshes\\n\\nFinetuning existing HME models on pure 3D joints datasets is not possible, since they need mesh annotations for training. However, with IK, we can generate pseudo GT meshes. We exemplary test a finetuning of SMPLer-X on ASPset with this approach. Experiments show that using their finetuning script with 1.6M iterations leads to worse results than the results without finetuning. Therefore, we reduce the number of iterations with early stopping and achieve better results with finetuning only for 32K iterations.\\n\\nThe results shown in Table [10](#A6.T10) prove that finetuning on IK generated meshes can lead to a significant improvement of the scores. Replacing the $\\\\beta$ parameters of the finetuned results with the A2B $\\\\beta$ parameters boosts the performance even more. These are the best results achieved with any existing HME model throughout this study.\\n\\nMoreover, we experiment with using the SMPLer-X body shape parameters combined with the poses estimated by IK applied to the UU results (see last two rows of Table [10](#A6.T10)). Using the $\\\\beta$ parameters from SMPLer-X leads to a slightly better result than the original 3D joint based result (without IK). This evaluation shows that 3D HPE models are better in precisely locating the joints of humans than HME models, but HME models are better in estimating the shape of humans. We also try to use the $\\\\beta$ parameters of the finetuned variant together with the UU IK poses like before. However, this resulted in a performance drop compared to the body shape parameters from the original SMPLer-X without finetuning. These experiments show that finetuning HME models on pseudo ground truth leads to a better performance regarding the keypoints, but the estimated $\\\\beta$ parameters have worse quality. This can further be proven by replacing the $\\\\beta$ parameters from the finetuned SMPLer-X variant with the $\\\\beta$ parameters from the not finetuned model, which results in a performance gain of over 5 mm compared to the original results from the finetuned version (rows 2 and 4 in Tab. [10](#A6.T10)). However, our method using the UU IK poses and the A2B body shape parameters with GT anthropometric measurments achieves the overall best results.\\n\\n**Table 10: MPJPE results in mm for the test split of ASPset. Results are given for different methods and replaced $beta$ parameters with A2B results (columns NN/SVR) or the median of the original $\\\\beta$ parameters from the model noted in the *measurements* column. SMPLer-X FT stands for the best finetuned variant of SMPLer-X (finetuned with the meshes obtained from IK executed on the GT 3D joints). The *orig* column contains the results without replaced $\\\\beta$ parameters. We highlight the best result for each model and the best option for the combination of UU IK pose and SMPLer-X $\\\\beta$ parameters, since this combination outperforms the original UU IK result, too.**\\n| model | orig. | measurements | NN m | SVR m | NN n | SVR n | median |\\n| --- | --- | --- | --- | --- | --- | --- | --- |\\n| SMPLer-X | 86.02 | SMPLer-X | 85.89 | 85.69 | 86.03 | 85.99 | 86.04 |\\n| SMPLer-X FT | 79.09 | SMPLer-X FT | 78.92 | 78.88 | 79.44 | 79.37 | 79.44 |\\n| SMPLer-X FT | - | GT | 65.63 | 65.84 | 64.71 | 64.76 | - |\\n| SMPLer-X FT | - | SMPLer-X | 73.41 | 73.29 | 73.65 | 73.63 | 73.66 |\\n| UU IK | 67.54 | UU | 66.92 | 66.60 | 67.25 | 67.12 | 67.16 |\\n| UU IK | - | SMPLer-X | 63.80 | 63.64 | 63.81 | 63.78 | 63.82 |\\n| UU IK | - | SMPLer-X FT | 69.46 | 69.27 | 69.70 | 69.63 | 69.69 |\\n| UU IK | - | GT | 56.44 | 56.56 | 55.14 | 55.19 | - |\\n\\nWe provide a comprehensive summary and visualization of all results on the ASPset dataset in Section [G](#A7). This includes results of existing HME models, results of our approach, and the finetuning results.\\n\\n## Appendix G Summary of the Results\\n\\nWe execute a multitude of experiments with different combinations of pose and shape parameters. Figure [10](#A7.F10) summarizes the results with their pose and shape origins for ASPset. In general, the poses estimated by IK based on the UU results (red branch in Fig. [10](#A7.F10)) are more precise than the poses estimated by SMPLer-X (light blue branch in Fig. [10](#A7.F10)). Further, the body shape parameters from our A2B models with GT anthropometric measurements (green boxes in Fig. [10](#A7.F10)) achieve the best results for all poses.\\nWe provide more qualitative examples comparing SMPler-X with this approach in Figure [9](#A7.F9). Without access to the GT, all models benefit slightly from A2B model results with the median anthropometric measurements from B2A of the estimated meshes by the respective model (boxes with same color for all three branches in Fig. [10](#A7.F10)).\\nMoreover, SMPLer-X A2B body shape parameters perform best when analyzing body shapes without GT access (light blue boxes in Fig. [10](#A7.F10)). Finetuning SMPLer-X with IK created meshes (dark blue branch in Fig. [10](#A7.F10)) improves the performance of SMPLer-X, although the quality of the body shape deteriorates.\\n\\nFigure: Figure 9: Qualitative results of SMPLer-X and our approach for example frames from ASPSet. GT joints and estimated joints are color-coded. Corresponding joints are connected.\\nRefer to caption: /html/2409.17671/assets/x4.png\\n\\nFigure: Figure 10: Overview of the main results for the ASPset dataset. All results are MPJPE results in mm. Results below *mesh* boxes show the result with the original $\\\\beta$ parameters. All results after arrows to the right are results with replaced $\\\\beta$ parameters. The type of the $\\\\beta$ parameters is noted on the arrow and is color-coded: pseudo GT (green), SMPLer-X (light blue), SMPler-X finetuned (dark blue), UU IK (red).\\nRefer to caption: /html/2409.17671/assets/x5.png\\n\\nThis can be seen as by comparing the shapes from SMPLer-X and finetuned SMPLer-X (dark blue and light blue boxes in Fig. [10](#A7.F10)) with finetuned and IK poses.\\n\\nSince fit3D is a larger dataset, finetuning UU works better, which further leads to better IK meshes with an MPJPE of 37.02 mm. Enforcing consistent meshes with GT or IK A2B shape parameters decreases the performance slightly in this case. However, A2B shape parameters achieve slightly better scores than median values. This also holds for OSX and Multi-HMR. Overall, the approach with UU, IK, and A2B body shape parameters achieves an over 33 mm lower MPJPE than any HME model.\",\n \"metadata\": {\n \"authors\": [\n \"Katja Ludwig, Julian Lorenz, Daniel Kienzle, Tuan Bui & Rainer Lienhart\",\n \"Chair for Machine Learning & Computer Vision\",\n \"University of Augsburg, Germany\"\n ],\n \"title\": \"Leveraging Anthropometric Measurements to Improve Human Mesh Estimation and Ensure Consistent Body Shapes\",\n \"total_chars\": 60554,\n \"total_lines\": 334,\n \"updated_at\": \"2026-01-25T15:02:53.882580\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"cJ0IhFOM3t","initial_rating":6,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper proposes an intuitive way to improve the estimation of human body shape: learn a mapping model from easily observed spatial measurements, here using anthropometric measurements, to the PCA parameter betas of the SMPL model.\n\nThis paper conducts a thorough analysis of the ASPset and fit3D dataset. It proves the inconsistency in temporal distribution, which should be blamed on the SMPL model's imperfect decoupling of theta and betas parameters.","strengths":"The perspective of the paper is clear and useful. The method is quite simple and intuitive, by learning a mapping from anthropometric measurements to the betas parameter. The anthropometric measurements include 23 lengths and 13 circumferences. The author trained their method on the Agora dataset, which has the existing largest individual human shapes.\n\nThe A2B method could also help Other SOTA HME methods. The experiments could prove this.\n\nThe complete pipeline that combines HPE, A2B, and IK models aligns well with the core idea that we solve body shape from explicit spatial clues and use the pre-trained A2B model which possesses the body shape prior knowledge to solve the body shape.","weaknesses":"Not enough quality results are shown to prove the idea.\n\nThe paper focuses too much on expressing the operation details but has not shown enough vivid digrams.\n\nI am confused about how to get the anthropometric measurements on some random videos. The HPE model could only help to get the bone length, but how to get the extra 13 circumferences? This part is not clear.","questions":"Please help me solve the question of how to get the extra 13 circumferences. If you could do this on any given videos, why do you only compare on such few datasets? The experiments on popular video test benchmarks are not included, like emdb, human3.6m, 3dpw, etc."},{"id":"BEQmrtAMGy","initial_rating":5,"confidence":3,"soundness":2,"contribution":3,"presentation":4,"summary":"This paper propose a framework to retrieve shape-consistent human mesh estimation results using anthropometric measurements. The authors fit a small model (A2B model) that converts anthropometric measurements to SMPL-X shape parameters. The authors replace the shape estimation outputs from existing methods with the shape derived from the anthropometric measurements (from GT or IK) with their proposed A2B model, and observe improved MPJPE results on the test set. The authors point out that the datasets for evaluation themselves have inconsistent anthropometric measurements or shape parameters.","strengths":"A substantive assessment of the strengths of the paper, touching on each of the following dimensions: originality, quality, clarity, and significance. We encourage reviewers to be broad in their definitions of originality and significance. For example, originality may arise from a new definition or problem formulation, creative combinations of existing ideas, application to a new domain, or removing limitations from prior results. You can incorporate Markdown and Latex into your review. See https://openreview.net/faq.\n1. This paper is clearly written and easy to understand.\n2. This paper propose a framework to improve shape consistent for HMR using anthropometric measurements.\n3. The authors propose a model (A2B model) to convert anthropometric measurements to SMPL-X shape parameters, as well as training data generation methods for the model. The proposed model has values in fast registering new human subjects to the SMPL-X body model.\n4. The authors provide the code and model along with their paper.","weaknesses":"1. This paper does not provide sufficient explanation for how inconsistencies between anthropometric measurements and SMPL-X shape parameters lead to inconsistencies in human shapes. For example, there is no information on whether real subject anthropometric measurements will remain unchanged under different poses or in motion (though obtaining measurements in the latter situation is challenging).\n2. In evaluation, the authors use anthropometric measurements derived from GT subject shapes (``pseudo GT'' in the text). Considering the A2B model has low error, this could be equivalent to feeding actual GT shapes during evaluation. However, there is no direct comparison between results using converted shapes from pseudo GT and those using actual GT shapes.\n3. The only metric used in evaluation is MPJPE. The authors could evaluate their predicted results using the same criteria applied when they analyze the shape inconsistencies within existing datasets.","questions":"See the weakness above. If the authors can fully address the weaknesses above, I am willing to re-consider my scores."},{"id":"9nQ2n9OABp","initial_rating":5,"confidence":4,"soundness":3,"contribution":3,"presentation":4,"summary":"To address the issue of inconsistent shape parameters estimation, the authors used anthropometric measurements.\n\nBy replacing the originally estimated shape parameters with those obtained through the A2B model, they achieved performance improvements.","strengths":"1. The approach of mapping complex shape parameters to more understandable anthropometric measurements is innovative.\n\n2. The analysis of existing data to identify flaws in the original data is clearly explained and easy to understand.\n\n3. The authors tried to demonstrate the superiority of the proposed method through various experiments.\n\n4. The paper is well-written and easy to read.","weaknesses":"1. Using anthropometric measurements obtained from GT in experiments does not appear fair (Table 3).\n\n2. The experiment using the median of measurements as A2B input seems unjustified (Table 4).\n\n3. Both experiments appear inadequate in addressing the issue of noise in the shape parameter estimates of the existing model.\n\n4. Although the authors mention that there is no good means to correct the inaccurate GT at present, relying on noisy GT shape parameters to measure the performance may not sufficiently demonstrate the effectiveness of the proposed method.","questions":"Are there datasets available that include anthropometric measurements GT? It would be helpful to see qualitative comparisons, such as comparing the output mesh from the existing method and that from the proposed method using the real anthropometric measurements of the authors or other person."},{"id":"zwyH3EXcWy","initial_rating":3,"confidence":4,"soundness":2,"contribution":2,"presentation":2,"summary":"This paper presents a 3D human mesh estimation system that utilizes human anthropometric information for more accurate 3D body shape. To this end, the authors first introduce the A2B model, a model that converts human anthropometric information to the SMPL-X shape parameter. Based on the A2B model, the authors report two cases where the A2B model could be useful. First, while keeping estimated 3D pose from prior 3D human mesh estimation methods and changing the shape parameter to theirs, 3D errors become less. Second, from 2D and 3D human keypoint estimators, the authors perform the inverse kinematics using the shape parameter from the A2B model.","strengths":"As the authors mentioned, most works are focusing only on estimating correct 3D poses without careful consideration of the 3D body shape. The pursuing research direction of this paper is interesting.","weaknesses":"1. Given anthropometric information, regressing 3D body shape parameters is quite straightforward as we could get a large amount of synthetic datasets to train the regressor like the authors did. The problem is that given a single image/video, getting the accurate anthropometric information is not trivial. The authors said that they can use real anthropometric information if they are available in real-world applications (Fig. 3). In the real world, getting such anthropometric information is not trivial as we hardly bring measurements in our daily life. Instead, the authors used GT or median of predicted shape parameters from off-the-shelf estimators if the video of a single person is available. First, using GT does not make sense at all. Assuming GT information during the test is cheating. Also, using median value and converting it with B2A and A2B models (L372) do not make sense at all. This is kind of averaging shape parameters from previous works, not predicting actual 3D body shape based on the image evidence. Hence, I do not think the effectiveness and benefit of the proposed A2B model is justified.\n\n2. The two use cases that the authors introduced are not impressive. First, changing the shape parameter to the A2B’s output uses GT (L347). This is cheating and makes the comparison unfair. Also, changing the shape parameter could make the results worse as it changes the bone length as well. With the same 3D pose and changed bone length, the 3D positions of keypoints could change, which could make 3D errors higher. Second, performing the inverse kinematics based on the off-the-shelf estimators’ output is quite widely used and is not novel at all. Actually, many people try to avoid this when designing 3D pose estimators as it makes the running time greatly slow due to the iterative optimization. Although the authors tried to make it fast (L460), I’m guessing the running time is slower than 5 fps.\n\n3. There are no qualitative results that show the body shape becomes better. There are few qualitative results, but most of them are trying to show corrected 3D pose after the inverse kinematics. As mentioned in the above, the inverse kinematics is quite straightforward and getting better at the cost of the running time is expected. Instead, there should be side-by-side comparison that show the proposed one is able to recover accurate body shapes for diverse humans, for example,fat/thin persons.","questions":"N/A"}],"string":"[\n {\n \"id\": \"cJ0IhFOM3t\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper proposes an intuitive way to improve the estimation of human body shape: learn a mapping model from easily observed spatial measurements, here using anthropometric measurements, to the PCA parameter betas of the SMPL model.\\n\\nThis paper conducts a thorough analysis of the ASPset and fit3D dataset. It proves the inconsistency in temporal distribution, which should be blamed on the SMPL model's imperfect decoupling of theta and betas parameters.\",\n \"strengths\": \"The perspective of the paper is clear and useful. The method is quite simple and intuitive, by learning a mapping from anthropometric measurements to the betas parameter. The anthropometric measurements include 23 lengths and 13 circumferences. The author trained their method on the Agora dataset, which has the existing largest individual human shapes.\\n\\nThe A2B method could also help Other SOTA HME methods. The experiments could prove this.\\n\\nThe complete pipeline that combines HPE, A2B, and IK models aligns well with the core idea that we solve body shape from explicit spatial clues and use the pre-trained A2B model which possesses the body shape prior knowledge to solve the body shape.\",\n \"weaknesses\": \"Not enough quality results are shown to prove the idea.\\n\\nThe paper focuses too much on expressing the operation details but has not shown enough vivid digrams.\\n\\nI am confused about how to get the anthropometric measurements on some random videos. The HPE model could only help to get the bone length, but how to get the extra 13 circumferences? This part is not clear.\",\n \"questions\": \"Please help me solve the question of how to get the extra 13 circumferences. If you could do this on any given videos, why do you only compare on such few datasets? The experiments on popular video test benchmarks are not included, like emdb, human3.6m, 3dpw, etc.\"\n },\n {\n \"id\": \"BEQmrtAMGy\",\n \"initial_rating\": 5,\n \"confidence\": 3,\n \"soundness\": 2,\n \"contribution\": 3,\n \"presentation\": 4,\n \"summary\": \"This paper propose a framework to retrieve shape-consistent human mesh estimation results using anthropometric measurements. The authors fit a small model (A2B model) that converts anthropometric measurements to SMPL-X shape parameters. The authors replace the shape estimation outputs from existing methods with the shape derived from the anthropometric measurements (from GT or IK) with their proposed A2B model, and observe improved MPJPE results on the test set. The authors point out that the datasets for evaluation themselves have inconsistent anthropometric measurements or shape parameters.\",\n \"strengths\": \"A substantive assessment of the strengths of the paper, touching on each of the following dimensions: originality, quality, clarity, and significance. We encourage reviewers to be broad in their definitions of originality and significance. For example, originality may arise from a new definition or problem formulation, creative combinations of existing ideas, application to a new domain, or removing limitations from prior results. You can incorporate Markdown and Latex into your review. See https://openreview.net/faq.\\n1. This paper is clearly written and easy to understand.\\n2. This paper propose a framework to improve shape consistent for HMR using anthropometric measurements.\\n3. The authors propose a model (A2B model) to convert anthropometric measurements to SMPL-X shape parameters, as well as training data generation methods for the model. The proposed model has values in fast registering new human subjects to the SMPL-X body model.\\n4. The authors provide the code and model along with their paper.\",\n \"weaknesses\": \"1. This paper does not provide sufficient explanation for how inconsistencies between anthropometric measurements and SMPL-X shape parameters lead to inconsistencies in human shapes. For example, there is no information on whether real subject anthropometric measurements will remain unchanged under different poses or in motion (though obtaining measurements in the latter situation is challenging).\\n2. In evaluation, the authors use anthropometric measurements derived from GT subject shapes (``pseudo GT'' in the text). Considering the A2B model has low error, this could be equivalent to feeding actual GT shapes during evaluation. However, there is no direct comparison between results using converted shapes from pseudo GT and those using actual GT shapes.\\n3. The only metric used in evaluation is MPJPE. The authors could evaluate their predicted results using the same criteria applied when they analyze the shape inconsistencies within existing datasets.\",\n \"questions\": \"See the weakness above. If the authors can fully address the weaknesses above, I am willing to re-consider my scores.\"\n },\n {\n \"id\": \"9nQ2n9OABp\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 4,\n \"summary\": \"To address the issue of inconsistent shape parameters estimation, the authors used anthropometric measurements.\\n\\nBy replacing the originally estimated shape parameters with those obtained through the A2B model, they achieved performance improvements.\",\n \"strengths\": \"1. The approach of mapping complex shape parameters to more understandable anthropometric measurements is innovative.\\n\\n2. The analysis of existing data to identify flaws in the original data is clearly explained and easy to understand.\\n\\n3. The authors tried to demonstrate the superiority of the proposed method through various experiments.\\n\\n4. The paper is well-written and easy to read.\",\n \"weaknesses\": \"1. Using anthropometric measurements obtained from GT in experiments does not appear fair (Table 3).\\n\\n2. The experiment using the median of measurements as A2B input seems unjustified (Table 4).\\n\\n3. Both experiments appear inadequate in addressing the issue of noise in the shape parameter estimates of the existing model.\\n\\n4. Although the authors mention that there is no good means to correct the inaccurate GT at present, relying on noisy GT shape parameters to measure the performance may not sufficiently demonstrate the effectiveness of the proposed method.\",\n \"questions\": \"Are there datasets available that include anthropometric measurements GT? It would be helpful to see qualitative comparisons, such as comparing the output mesh from the existing method and that from the proposed method using the real anthropometric measurements of the authors or other person.\"\n },\n {\n \"id\": \"zwyH3EXcWy\",\n \"initial_rating\": 3,\n \"confidence\": 4,\n \"soundness\": 2,\n \"contribution\": 2,\n \"presentation\": 2,\n \"summary\": \"This paper presents a 3D human mesh estimation system that utilizes human anthropometric information for more accurate 3D body shape. To this end, the authors first introduce the A2B model, a model that converts human anthropometric information to the SMPL-X shape parameter. Based on the A2B model, the authors report two cases where the A2B model could be useful. First, while keeping estimated 3D pose from prior 3D human mesh estimation methods and changing the shape parameter to theirs, 3D errors become less. Second, from 2D and 3D human keypoint estimators, the authors perform the inverse kinematics using the shape parameter from the A2B model.\",\n \"strengths\": \"As the authors mentioned, most works are focusing only on estimating correct 3D poses without careful consideration of the 3D body shape. The pursuing research direction of this paper is interesting.\",\n \"weaknesses\": \"1. Given anthropometric information, regressing 3D body shape parameters is quite straightforward as we could get a large amount of synthetic datasets to train the regressor like the authors did. The problem is that given a single image/video, getting the accurate anthropometric information is not trivial. The authors said that they can use real anthropometric information if they are available in real-world applications (Fig. 3). In the real world, getting such anthropometric information is not trivial as we hardly bring measurements in our daily life. Instead, the authors used GT or median of predicted shape parameters from off-the-shelf estimators if the video of a single person is available. First, using GT does not make sense at all. Assuming GT information during the test is cheating. Also, using median value and converting it with B2A and A2B models (L372) do not make sense at all. This is kind of averaging shape parameters from previous works, not predicting actual 3D body shape based on the image evidence. Hence, I do not think the effectiveness and benefit of the proposed A2B model is justified.\\n\\n2. The two use cases that the authors introduced are not impressive. First, changing the shape parameter to the A2B’s output uses GT (L347). This is cheating and makes the comparison unfair. Also, changing the shape parameter could make the results worse as it changes the bone length as well. With the same 3D pose and changed bone length, the 3D positions of keypoints could change, which could make 3D errors higher. Second, performing the inverse kinematics based on the off-the-shelf estimators’ output is quite widely used and is not novel at all. Actually, many people try to avoid this when designing 3D pose estimators as it makes the running time greatly slow due to the iterative optimization. Although the authors tried to make it fast (L460), I’m guessing the running time is slower than 5 fps.\\n\\n3. There are no qualitative results that show the body shape becomes better. There are few qualitative results, but most of them are trying to show corrected 3D pose after the inverse kinematics. As mentioned in the above, the inverse kinematics is quite straightforward and getting better at the cost of the running time is expected. Instead, there should be side-by-side comparison that show the proposed one is able to recover accurate body shapes for diverse humans, for example,fat/thin persons.\",\n \"questions\": \"N/A\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"3;5;5;6\",\n \"rating_avg\": 4.75,\n \"confidence\": \"4;4;3;4\",\n \"confidence_avg\": 3.75,\n \"soundness\": \"2;3;2;3\",\n \"soundness_avg\": 2.5,\n \"contribution\": \"2;3;3;3\",\n \"contribution_avg\": 2.75,\n \"presentation\": \"2;4;4;3\",\n \"presentation_avg\": 3.25\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"ICLR 2025 Conference Withdrawn Submission\",\n \"venueid\": \"ICLR.cc/2025/Conference/Withdrawn_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.715754\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"\",\n \"metareview\": \"\",\n \"additional_comments\": \"\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"\"\n}"}}},{"rowIdx":3397,"cells":{"paper_id":{"kind":"string","value":"qZwtPEw2qN"},"arxiv_id":{"kind":"string","value":"2411.02780v1"},"title":{"kind":"string","value":"How Much is a Noisy Image Worth? Data Scaling Laws for Ambient Diffusion."},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 80 80 80 models on data with different corruption levels across three datasets ranging from 30 , 000 30 000 30,000 30 , 000 to ≈ 1.3 absent 1.3 \\\\approx 1.3 ≈ 1.3 M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g. 10 % percent 10 10\\\\% 10 % of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.\\n\\n## 1 Introduction\\n\\nA key factor behind the remarkable success of modern generative models, from image Diffusion Models (DMs) to Large Language Models (LLMs), is the curation of large scale datasets (Gadre et al., ; Li et al., ). However, in certain applications, access to high-quality data is scarce, expensive, or impossible. For example, in Magnetic Resonance Imaging (MRI) the quality of the data is proportional to the time spent in the scanner (Jalal et al., ) and, in black-hole imaging, it is never possible to get full measurements from the object of interest (Lin et al., ). Constructing a (copyright-free) large-scale dataset of high-quality general domain images is also an expensive and complex process. Enterprise text-to-image image DMs rely on proprietary datasets, often acquired from third-party vendors at significant cost (Betker et al., ; Imagen-Team-Google et al., ). State-of-the-art open-source DMs are typically trained by crawling a large pool of images from the Web and filtering them for quality with a pipeline that deems each sample as suitable or non-suitable for training (Gadre et al., ). However, this binary treatment of samples is problematic because often low-quality images still contain useful information. For example, a blurry image might get dismissed from the filtering pipeline to avoid blurry generations at inference time, yet the image might still contain important information about the world, such as the type of objects present at the scene.\\n\\nRecently, there has been a growing interest in developing frameworks for training generative models using corrupted data, e.g. from blurry or noisy images (Bora et al., ; Daras et al., ; Kawar et al., ; Aali et al., ; Daras et al., ; Bai et al., ; Rozet et al., ; Wang et al., ; Kelkar et al., ). Most frameworks that are applicable to diffusion models introduce training or sampling approximations, which significantly hurt performance. A recent work, Consistent Diffusion Meets Tweedie (Daras et al., ), proposes a method that guarantees exact sampling, at least asymptotically as the number of noisy samples tends to infinity. For realistic sample sizes, however, models trained on noisy data using this method (or any other proposed method) are significantly inferior to models trained on clean data. How do we overcome this challenge?\\n\\nFigure: Figure 1: ImageNet FID performance (lower is better) for models trained with different amounts of clean and noisy data. Performance of models trained with only clean data (red curve) reduces as we decrease the amount of data used. Training with purely noisy data (right-most points) also gives poor performance – even if $100\\\\%$ of the dataset is available. Training with a mix of noisy and clean data strikes an interesting balance: a model trained with $90\\\\%$ noisy and $10\\\\%$ clean data is almost as good as a model trained with $100\\\\%$ clean data.\\nRefer to caption: x1.png\\n\\nA fundamental limitation facing existing approaches for leveraging corrupted data is that, so far, they have been studied under the assumption that no access to clean samples is available. As we show in this work, it is theoretically and experimentally impossible to compensate for the lack of clean data without a significant hit (that is exponential in the number of classes in our theoretical analysis) in the number of noisy datapoints. On the other hand, we show that a combination of a small set of clean images (e.g. 10% of the total dataset) and a large set of noisy images (e.g. 90% of the total dataset) suffices to maintain state-of-the-art performance. Models trained on this data mixture significantly outperform two natural baselines: i) training only on the small set of clean images; and ii) training only on the large set of noisy images (see also Figure 1 and Table 1). We validate our finding by training more than 80 models across various noise scales and corruption ratios on ImageNet, CelebA-HQ, and CIFAR-10.\\n\\n**Table 1: FID scores for models trained on datasets with different percentages of noisy and clean data. Training with a mix of 90% noisy and 10% clean data achieves much better performance than training the same number of purely noisy samples, or just the clean samples. The standard deviation of the additive Gaussian noise for this experiment is $\\\\sigma=0.2$, which corresponds to SNR $\\\\approx 14.15\\\\mathrm{dB}$.**\\n| Available Data | CIFAR-10 | CelebA | ImageNet |\\n| --- | --- | --- | --- |\\n| 100% clean | $1.99\\\\scriptstyle{\\\\pm 0.02}$ | $2.40\\\\scriptstyle{\\\\pm 0.07}$ | $1.41\\\\scriptstyle{\\\\pm 0.03}$ |\\n| 100% noisy | $11.93\\\\scriptstyle{\\\\pm 0.09}$ | $12.97\\\\scriptstyle{\\\\pm 0.11}$ | $5.32\\\\scriptstyle{\\\\pm 0.08}$ |\\n| 10% clean (smaller dataset) | $17.30\\\\scriptstyle{\\\\pm 0.14}$ | $11.92\\\\scriptstyle{\\\\pm 0.05}$ | $10.57\\\\scriptstyle{\\\\pm 0.06}$ |\\n| 90% noisy + 10% clean | $2.81\\\\scriptstyle{\\\\pm 0.02}$ | $2.75\\\\scriptstyle{\\\\pm 0.02}$ | $1.68\\\\scriptstyle{\\\\pm 0.02}$ |\\n\\nTheoretically, we consider a novel variant of the classical problem of learning Gaussian Mixture Models (GMMs) with heterogeneous noise levels. In contrast to the classical setting, each sample is generated with a (potentially) different noise level reflective of how clean or noisy the data point is. We derive minimax optimal estimation rates, which showcase the differing utility of clean and noisy data. Concretely, having lots of noisy data enables identification of the right low-dimensional structure for learning the mixture components, while a more moderate number of clean data allows fine-grained differentiation of the components in low dimensions. In particular, effective learning is possible even when the number of clean samples is substantially smaller than the dimension. At the same time, relying solely on noisy data requires exponentially (in the number of components) noisy samples than clean ones. This theoretical result could justify why training on a mixture of clean and noisy data significantly outperforms training solely on either one of the clean or the noisy sets. In summary, our contributions are as follows:\\n\\n- •\\nWe train more than 80 models at different datasets, noise levels and corruption ratios.\\n- •\\nWe show that as long as a few clean images are available, models trained with corrupted data perform on par with models trained on clean data. We further show that training on a combination of a small set of clean images and a large set of noisy images significantly outperforms training solely on either one of these sets.\\n- •\\nWe provide a theoretical explanation for this phenomenon by developing novel sample complexity bounds for the case of GMMs with heterogeneous variances. Our minimax rates show that the availability of noisy data removes the polynomial dependence on dimension in the number of clean samples while simultaneously showing exponentially more noisy samples are required to compensate for the lack of clean data.\\n- •\\nThrough our theoretical analysis and our experimental validation, we pinpoint the price of noisy images for different datasets and noise levels. These insights can potentially guide budget allocation for dataset curation.\\n- •\\nWe open-source our code and pre-trained models to facilitate further research in this area: [https://github.com/giannisdaras/ambient-laws](https://github.com/giannisdaras/ambient-laws).\\n\\n## 2 Background and Related Work\\n\\n### 2.1 Diffusion modeling\\n\\nThe dominant paradigm for learning distributions is diffusion models. A diffusion model is trained to denoise images at different levels of additive Gaussian noise (Ho et al., ; Song & Ermon, ; Song et al., ). To establish some notation, we will use $t\\\\in[0,T]$ for the diffusion time and $\\\\sigma_{t}$ for the associated standard deviation of the added noise. Let ${\\\\bm{X}}_{0}\\\\sim p_{0}$ be a sample from the distribution of interest and let ${\\\\bm{X}}_{t}\\\\sim p_{t}$ a sample of the noisy distribution at time $t$, where it holds that ${\\\\bm{X}}_{t}={\\\\bm{X}}_{0}+\\\\sigma_{t}{\\\\bm{Z}},{\\\\bm{Z}}\\\\sim\\\\mathcal{N}(\\\\bm{0},I)$. At training time, the goal is to learn $\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ for all levels $t$. Diffusion models are trained to approximate this quantity using the following objective(^1^11In practice, a non-uniform distribution for $t$ and a loss weighting $w(t)$ are often used (Karras et al., ).) (Vincent, ):\\n\\n$$ $\\\\displaystyle J_{\\\\mathrm{DSM}}(\\\\theta)=\\\\mathbb{E}_{{\\\\bm{x}}_{0}\\\\sim p_{0}} \\\\mathbb{E}_{t\\\\sim U[0,T]}\\\\mathbb{E}_{{\\\\bm{x}}_{t}\\\\sim p_{t}({\\\\bm{x}}_{t}|{\\\\bm{ X}}_{0}={\\\\bm{x}}_{0})}\\\\left\\\\|{\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t},t)-{\\\\bm{x}}_{0} \\\\right\\\\|^{2}.$ (1) $$\\n\\nOnce trained, the model is used for sampling following a discretized version of the update rule (Song et al., ; ):\\n\\n$$ $\\\\displaystyle\\\\mathrm{d}{\\\\bm{x}}_{t}=-\\\\mathrm{d}\\\\sigma_{t}\\\\frac{{\\\\bm{h}}_{ \\\\theta}({\\\\bm{x}}_{t},t)-{\\\\bm{x}}_{t}}{\\\\sigma_{t}},$ (2) $$\\n\\nthat is guaranteed to sample from $p_{0}$ given that it is initialized from $p_{T}$ and ${\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t},t)=\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}\\n}_{t}]$. In practice, there are errors due to initialization, discretization, and improper learning of the score (Chen et al., ; ).\\n\\n### 2.2 Learning Diffusion Models from Noisy Data\\n\\nThe training objective of Equation 1 requires access to data from the distribution $p_{0}$. We will refer to this data as clean for the rest of this paper. As explained in the Introduction, in many applications access to clean data is scarce and hence methods for training diffusion models from corrupted data have been developed.\\n\\nAmbient Diffusion (Daras et al., ) proposes a framework to train diffusion models from linear measurements. An alternative framework to Ambient Diffusion leverages Stein’s Unbiased Risk Estimate (SURE) (Kawar et al., ; Aali et al., ). These works extend classical results for training restoration models from corrupted data (Moran et al., ; Stein, ; Xu et al., ; Pang et al., ; Krull et al., ; Batson & Royer, ) to the setting of learning generative models under corruption. Unfortunately, these methods induce sampling approximations that significantly hurt the performance.\\nA different thread of papers on this topic relies on the Expectation-Maximization (EM) algorithm (Bai et al., ; Rozet et al., ; Wang et al., ). The convergence of these models to the true distribution depends on the convergence of the EM algorithm, which might get stuck in a local minimum.\\n\\nConsistent Diffusion Meets Tweedie (Daras et al., ; ) generalized Ambient Diffusion to handle additive Gaussian noise and became the first framework with provably exact sampling given infinite (noisy) data. In what follows, we give a brief description of the method, since we are going to use this in the rest of this paper.\\n\\n#### Problem Setting.\\n\\nAssume that we are given samples at a specific noise level $t_{n}$ (nature noise level). The question becomes how we can leverage these samples to learn the optimal denoiser $\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ for all noise levels $t$.\\n\\n#### Learning the optimal denoiser for high noise levels.\\n\\nThe first task is to learn the optimal denoiser for $t>t_{n}$. To perform this goal, one can leverage the following Lemma:\\n\\n###### Lemma 2.1 ( (Daras et al., 2024 ) ) .\\n\\nLet ${\\\\bm{X}}_{t_{n}}={\\\\bm{X}}_{0}+\\\\sigma_{t_{n}}{\\\\bm{Z}}_{1}$ and ${\\\\bm{X}}_{t}={\\\\bm{X}}_{0}+\\\\sigma_{t}{\\\\bm{Z}}_{2},\\\\quad{\\\\bm{Z}}_{1},{\\\\bm{Z}}_{2\\n}\\\\sim\\\\mathcal{N}(\\\\bm{0},I)$ i.i.d. Then, for any $\\\\sigma_{t}>\\\\sigma_{t_{n}}$, we have that:\\n\\n$$ $\\\\displaystyle\\\\underbrace{\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]}_{ \\\\textrm{removes all the noise}}=\\\\frac{\\\\sigma_{t}^{2}}{\\\\sigma_{t}^{2}-\\\\sigma_{t _{n}}^{2}}\\\\underbrace{\\\\mathbb{E}[{\\\\bm{X}}_{t_{n}}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]}_ {\\\\textrm{removes additional noise}}-\\\\frac{\\\\sigma_{t_{n}}^{2}}{\\\\sigma_{t}^{2}- \\\\sigma_{t_{n}}^{2}}{\\\\bm{x}}_{t}.$ (3) $$\\n\\nThis Lemma states that to remove all the noise there is, it suffices to remove the noise that we added on top of the dataset noisy samples from the R.V. ${\\\\bm{X}}_{t_{n}}$. One can train the denoiser $\\\\mathbb{E}[{\\\\bm{X}}_{t_{n}}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ with supervised learning, as in Equation 1.\\nThe following loss will train the network to estimate $\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ directly:\\n\\n$$ $\\\\displaystyle J_{\\\\mathrm{Ambient\\\\ DSM}}(\\\\theta)=\\\\mathbb{E}_{{\\\\bm{x}}_{t_{n}} \\\\sim p_{t_{n}}}\\\\mathbb{E}_{t\\\\sim U(t_{n},T]}\\\\mathbb{E}_{{\\\\bm{x}}_{t}\\\\sim p_{t} ({\\\\bm{x}}_{t}|{\\\\bm{X}}_{t_{n}}={\\\\bm{x}}_{t_{n}})}\\\\left\\\\|\\\\frac{\\\\sigma_{t}^{2}- \\\\sigma_{t_{n}}^{2}}{\\\\sigma_{t}^{2}}{\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t},t)+\\\\frac{ \\\\sigma_{t_{n}}^{2}}{\\\\sigma_{t}^{2}}{\\\\bm{x}}_{t}-{\\\\bm{x}}_{t_{n}}\\\\right\\\\|^{2}.$ (4) $$\\n\\nThis idea is closely related to Noisier2Noise (Moran et al., ). We underline that there are also alternative ways to learn the optimal denoiser in this regime, such as SURE (Stein, ). However, SURE-based methods usually bring a computational overhead, as one needs to compute (or approximate) a Jacobian Vector Product.\\n\\n###### Lemma 2.1 ( (Daras et al., 2024 ) ) .\\n\\n#### Learning the optimal denoiser for low noise levels.\\n\\nLearning the optimal denoiser for $t<t_{n}$ is a significantly harder problem since there is no available data in this regime. Most of the prior works did not even attempt to solve this problem. At training time, a denoiser ${\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t},t)$ is trained for all $t\\\\geqslant t_{n}$. At sampling time, one can: i) also use ${\\\\bm{h}}_{\\\\theta}$ for times $t<t_{n}$, even though the model was not trained in this regime, hoping that the neural network will extrapolate in a meaningful way, or ii) truncate the sampling at time $t_{n}$, by predicting $\\\\hat{\\\\bm{x}}_{0}={\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t_{n}},t_{n})$. In Algorithm 2 of the Appendix, we provide a reference implementation of the truncated sampling idea. A more principled attempt was introduced by Daras et al. () where the authors attempt to learn the optimal denoiser for low noise levels by enforcing a consistency loss. Specifically, for $t<t_{n}$, the network is trained with the following objective:\\n\\n$$ $\\\\displaystyle J_{\\\\mathrm{C}}(\\\\theta)=\\\\mathbb{E}_{t,t^{\\\\prime},t^{\\\\prime\\\\prime} \\\\sim\\\\mathcal{U}(t_{n},T],\\\\mathcal{U}(\\\\epsilon,t),\\\\mathcal{U}(t^{\\\\prime}- \\\\epsilon,t^{\\\\prime})}\\\\mathbb{E}_{{\\\\bm{x}}_{t}}\\\\mathbb{E}_{{\\\\bm{x}}_{t^{\\\\prime} }|{\\\\bm{x}}_{t}}[\\\\left|\\\\left|{\\\\bm{h}}_{\\\\theta}({\\\\bm{x}}_{t^{\\\\prime}},t^{\\\\prime} )-\\\\mathbb{E}_{{\\\\bm{x}}_{t^{\\\\prime\\\\prime}}\\\\sim p_{\\\\theta}({\\\\bm{x}}_{t^{\\\\prime \\\\prime}},t^{\\\\prime\\\\prime}|{\\\\bm{x}}_{t^{\\\\prime}},t^{\\\\prime})}\\\\left[{\\\\bm{h}}_{ \\\\theta}({\\\\bm{x}}_{t^{\\\\prime\\\\prime}},t^{\\\\prime\\\\prime})\\\\right]\\\\right|\\\\right|^{2} \\\\bigg{]},$ (5) $$\\n\\nwhere $p_{\\\\theta}$ is the distribution induced by the SDE version of Equation 2 (we refer the interested reader to the works of Song et al. (), Daras et al. ()). Assuming that the network has been perfectly trained to predict $\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ for all times $t\\\\geqslant t_{n}$, the minimizer of this loss will be $\\\\mathbb{E}[{\\\\bm{X}}_{0}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ also for times $t\\\\leqslant t_{n}$. There are a few important drawbacks though. First, the consistency loss adds a significant training overhead since at each training step: i) expectations need to be computed and ii) sampling steps need to be performed. Second, the theoretical guarantees only hold given perfect learning of the conditional expectation for $t\\\\geqslant t_{n}$ and it is unclear how errors propagate. Finally, even for slight corruption, the method leads to a significant performance deterioration (Daras et al., ).\\n\\n## 3 Method\\n\\n#### Problem Setting.\\n\\nThe need for consistency or sampling approximations arises from the fact that we do not have samples to train the network in the regime $t\\\\in(t_{n},0]$. We relax this assumption by considering the setting where a small set of clean and a large set of noisy images are available.\\nTo establish the notation, let’s use $S_{\\\\mathrm{clean}}$ to denote the clean set and $S_{\\\\mathrm{noisy}}$ to denote the noisy set.\\nThe clean samples are realizations of the R.V. ${\\\\bm{X}}_{0}\\\\sim p_{0}$ and the noisy samples realizations of the R.V. ${\\\\bm{X}}_{t_{n}}={\\\\bm{X}}_{0}+\\\\sigma_{t_{n}}{\\\\bm{Z}}$ for some fixed noise level $t_{n}$. We underline that our method can be naturally extended to handle arbitrary per-sample noise levels, but for the ease of the presentation, we focus on the setting of two noise levels: clean data (no noise) and noisy data (at noise level $t_{n}$).\\n\\n#### Training algorithm.\\n\\nOur training algorithm leverages samples from both sets. For times $t\\\\in[t_{n},0]$, we will rely solely on clean samples. On the other hand, for $t\\\\in[T,t_{n})$, we will leverage both the clean and the noisy samples. The clean samples will be used as usual, following the Denoising Score Matching objective, defined in Equation 1. The noisy samples in this regime will utilize Equation 4 to learn a denoiser by relating it to the quantity $\\\\mathbb{E}[{\\\\bm{X}}_{t_{n}}|{\\\\bm{X}}_{t}={\\\\bm{x}}_{t}]$ through the use of Lemma 2.1 (see Algorithm 1).\\n\\nFigure: Algorithm 1 Algorithm for training using both clean and noisy samples.\\n\\n#### Method Discussion.\\n\\nIn prior work (Daras et al., ), the optimal denoiser for times $t<t_{n}$ was learned through the (expensive) consistency loss. In our setting, we assume access to a small set of clean images that we are using to learn the optimal denoiser for these times. The question then becomes: “does a small set of clean images suffice to learn the optimal denoiser for low-noise levels?” As we show in this paper, the answer to this question is affirmative, i.e. we only need a handful of uncorrupted images to learn the optimal denoiser for low corruption.\\n\\nThe intuition is as follows. To learn the distribution, we need to be able to generate accurately both structural information (low-frequencies) and texture (high-frequencies). Clean samples have both low-frequency and high-frequency content. The addition of noise corrupts the high-frequency content faster (for a discussion, see Dieleman ()). Hence, noisy images are mostly useful to learn the low-frequency content of the distribution, i.e. they are useful to learn to generate structure. Humans, and metrics that are trying to model human preferences (such as FID), are more perceptible to errors in structural information than errors in the high-entropy image texture. So even though it might be impossible to perfectly generate high-frequency content using only a few clean images, metrics, such as FID, are going to penalize these errors less, given that the model can accurately generate the low-frequency content.\\n\\nThe method we developed in Algorithm 1 can be trivially extended to more than two sets of points. In fact, each point ${\\\\bm{x}}_{i}$ in the training set can have its own noise level $t_{i}$. In that case, our algorithm would use each point ${\\\\bm{x}}_{i}$ to learn the optimal denoiser for $t\\\\geqslant t_{i}$. For the ease of presentation, we stick to two noise levels for the rest of this paper.\\n\\n## 4 Theoretical Results\\n\\n### 4.1 Setting\\n\\nBefore presenting our experiments, we establish theoretical results that will support our experimental findings. We note that most theoretical works on distribution learning operate under the assumption of i.i.d samples from a fixed distribution. In contrast, the goal of our paper is to understand the effects that heterogeneity in sample quality has on estimation error. This setting is quite niche and creates space for interesting theory to be developed.\\n\\nWe develop our results for the Gaussian Mixture Model that is commonly used in diffusion theory (Shah et al., ; Gatmiry et al., ; Gu et al., ; Chidambaram et al., ; Li & Chen, ; Cui et al., ; Chen et al., ). We examine the following adaptation of the classical estimation problem to the heterogeneous setting:\\n\\n###### Definition 4.1 .\\n\\nWe are given $X_{1},\\\\dots,X_{n}$ independently drawn from the following distribution:\\n\\n$$ $\\\\vspace{-1em}X_{i}\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}_{i}I),\\\\text { where }\\\\mathcal{D}=\\\\sum_{i=1}^{k}w_{i}\\\\delta_{\\\\mu_{i}}$ $$\\n\\nwhere $\\\\delta_{\\\\mu}$ denotes the Dirac distribution at $\\\\mu$ and $\\\\ast$ the convolution operator. The goal is to output $\\\\widehat{\\\\mathcal{D}}$ minimizing:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\coloneqq\\\\min_{C( \\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})}\\\\mathbb{E}_{(X,X^{\\\\prime})\\\\thicksim C}[ \\\\lVert X-X^{\\\\prime}\\\\rVert]$ $$\\n\\nwhere $C(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})$ is a coupling of $\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}}$ with marginals equal to $\\\\mathcal{D}$ and $\\\\widehat{\\\\mathcal{D}}$.\\n\\nNote now that variance in sample quality can now be naturally expressed in terms of the noise level, $\\\\sigma_{i}$, of the individual observations with the larger $\\\\sigma_{i}$ denoting lower-quality samples and vice-versa.\\n\\n###### Definition 4.1 .\\n\\n### 4.2 Main theoretical results and discussion\\n\\n###### Theorem 4.2 (Upper bound) .\\n\\nLet $\\\\mathchoice{\\\\leavevmode\\\\hbox to19.21pt{\\\\vbox to4.31pt{\\\\pgfpicture\\\\makeatletter\\n\\\\hbox{\\\\hskip 9.60376pt\\\\lower 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}{{}{}{{\\n{}{}}}{\\n{}{}}\\n{{}{{}}}{{}{}}{}{{}{}}\\n{\\n}{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1\\n.0}{-6.18332pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{rgb\\n}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\n\\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptstyle\\n\\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{LimeGreen!1\\n7}$\\\\displaystyle\\\\mathstrut k$}}{\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\textstyle\\n\\\\mathstrut k$}}{\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\scriptstyle\\\\mathstrut k$}}{\\n\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\scriptscriptstyle\\\\mathstrut k$}}$}}\\n}}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{\\n{}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\n\\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to\\n8.83pt{\\\\vbox to3.47pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 4.41664pt\\\\lower 0.0\\npt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor\\n}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\n\\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt}\\n\\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{\\n\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\n\\\\pgfsys@invoke{ }{}{\\n{{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{\\n{}{}}}{\\n{}{}}\\n{{}{{}}}{{}{}}{}{{}{}}\\n{\\n}{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1\\n.0}{-4.41664pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{rgb\\n}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\n\\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptscriptstyle\\n\\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{LimeGreen!1\\n7}$\\\\displaystyle\\\\mathstrut k$}}{\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\textstyle\\n\\\\mathstrut k$}}{\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\scriptstyle\\\\mathstrut k$}}{\\n\\\\hbox{\\\\pagecolor{LimeGreen!17}$\\\\scriptscriptstyle\\\\mathstrut k$}}$}}\\n}}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{\\n{}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\n\\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}\\\\in\\\\mathbb{N}$, $R>0$,\\n# samples and $\\\\delta\\\\in(0,1/2)$. Suppose $\\\\mathcal{D}=\\\\sum_{i=1}^{k}w_{i}\\\\delta_{\\\\mu_{i}}$ is a $k$-atomic distribution over $\\\\mathbb{R}^{d}$ with $\\\\lVert\\\\mu_{i}\\\\rVert\\\\leqslant R$.\\ndimension\\n# classesThen, there is a procedure which when given $n$ independent samples $X_{1},\\\\dots,X_{n}$ such that $X_{i}\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$ with $\\\\sigma_{i}\\\\geqslant 1$ satisfying:\\n\\n$$ $\\\\displaystyle\\\\max_{i}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\leqslant\\\\frac{c_{1}}{(d+\\\\log(1/ \\\\delta))}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}},\\\\quad\\\\max_{i}\\\\frac{1}{\\\\sigma_{ i}^{4k-2}}\\\\leqslant\\\\frac{c_{2}}{\\\\log(1/\\\\delta)+k\\\\log(k)}\\\\mathchoice{ \\\\leavevmode\\\\hbox to86.42pt{\\\\vbox to20.49pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{ \\\\hskip 43.20871pt\\\\lower-10.00012pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor}{rgb}{0,0,0} \\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@color@rgb@fill{0}{0} {0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt}\\\\pgfsys@invoke{ }\\\\nullfont \\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-43.20871pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\displaystyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Salmon!17}$ \\\\displaystyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{ \\\\pagecolor{Salmon!17}$\\\\textstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4 k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac {1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptscriptstyle \\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 86.42pt{\\\\vbox to20.49pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 43.20871pt\\\\lower- 10.00012pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-43.20871pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\textstyle\\\\definecolor {currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Salmon!17}$ \\\\displaystyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{ \\\\pagecolor{Salmon!17}$\\\\textstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4 k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac {1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptscriptstyle \\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 60.49pt{\\\\vbox to14.35pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 30.24606pt\\\\lower- 7.00009pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-30.24606pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Salmon!17}$ \\\\displaystyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{ \\\\pagecolor{Salmon!17}$\\\\textstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4 k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac {1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptscriptstyle \\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 43.21pt{\\\\vbox to10.25pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 21.60432pt\\\\lower- 5.00006pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-21.60432pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptscriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Salmon!17}$ \\\\displaystyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{ \\\\pagecolor{Salmon!17}$\\\\textstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4 k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptstyle\\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac {1}{\\\\sigma_{i}^{4k-2}}$}}{\\\\hbox{\\\\pagecolor{Salmon!17}$\\\\scriptscriptstyle \\\\mathstrut\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}$ $$\\n\\nand $\\\\delta>0$, returns an estimate $\\\\widehat{\\\\mathcal{D}}$ with:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\leqslant C\\\\left( \\\\mathchoice{\\\\leavevmode\\\\hbox to200.91pt{\\\\vbox to27.5pt{\\\\pgfpicture \\\\makeatletter\\\\hbox{\\\\hskip 100.45442pt\\\\lower-8.75006pt\\\\hbox to0.0pt{ \\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor}{rgb}{0,0,0} \\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@color@rgb@fill{0}{0} {0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt}\\\\pgfsys@invoke{ }\\\\nullfont \\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-100.45442pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\displaystyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Plum!17}$ \\\\displaystyle\\\\mathstrut k\\\\left(\\\\frac{d+\\\\log(1/\\\\delta)}{\\\\sum_{i=1}^{n}1/\\\\sigma_ {i}^{4}}\\\\right)^{1/4}$}}{\\\\hbox{\\\\pagecolor{Plum!17}$\\\\textstyle\\\\mathstrut k\\\\left (\\\\frac{d+\\\\log(1/\\\\delta)}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4}$}}{\\\\hbox {\\\\pagecolor{Plum!17}$\\\\scriptstyle\\\\mathstrut k\\\\left(\\\\frac{d+\\\\log(1/\\\\delta)}{ \\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4}$}}{\\\\hbox{\\\\pagecolor{Plum!17}$ \\\\scriptscriptstyle\\\\mathstrut k\\\\left(\\\\frac{d+\\\\log(1/\\\\delta)}{\\\\sum_{i=1}^{n}1/ \\\\sigma_{i}^{4}}\\\\right)^{1/4}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 200.91pt{\\\\vbox to27.5pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 100.45442pt\\\\lower -8.75006pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-100.45442pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\textstyle\\\\definecolor 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\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}\\\\right),$ $$\\n\\nwith probability at least $1-\\\\delta$. Furthermore, the runtime of the algorithm is $\\\\widetilde{O}_{k}(nd)$.\\n\\n###### Theorem 4.2 (Upper bound) .\\n\\n#### Discussion.\\n\\nThe full proof of this result is given in Appendix C. We follow a two-stage process where in the first stage we reduce the dimensionality of the estimation problem, from the dimension $d$, to the number of components, $k$. Next, we run a low-dimensional estimation procedure using the $k$-dimensional projected data. The two terms in the error bound reflect the contributions of each of these steps. The first corresponds to the error in estimating the low-dimensional sub-space and the second to the low-dimensional estimation procedures. The two conditions (on $\\\\max 1/\\\\sigma_{i}^{4}$ and $\\\\max 1/\\\\sigma_{i}^{4k-2}$) lower bound the effective number of samples for the dimensionality-reduction and low-dimensional estimation steps respectively. The first requires that at least $d$ (effective) samples are available for dimensionality reduction while at least $k$ are available for low-dimensional estimation.\\n\\nObserving the two terms of the bound, we see that, compared to the high-quality points, the low-quality points have relatively more utility in the dimensionality-reduction step versus the lower-dimensional estimation step. This observation is made clearer in the following corollary in the simplified setting with $2$ noise levels.\\n\\n###### Corollary 4.3 .\\n\\nAssume the setting of Theorem 4.2. 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}\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{\\n\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\n\\\\pgfsys@invoke{ }{}{\\n{{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{\\n{}{}}}{\\n{}{}}\\n{{}{{}}}{{}{}}{}{{}{}}\\n{\\n}{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1\\n.0}{-5.63501pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{rgb\\n}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\n\\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptstyle\\n\\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Tan!17}$\\n\\\\displaystyle\\\\mathstrut p$}}{\\\\hbox{\\\\pagecolor{Tan!17}$\\\\textstyle\\\\mathstrut p$}\\n}{\\\\hbox{\\\\pagecolor{Tan!17}$\\\\scriptstyle\\\\mathstrut p$}}{\\\\hbox{\\\\pagecolor{Tan!17\\n}$\\\\scriptscriptstyle\\\\mathstrut 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}{}{\\n{{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{\\n{}{}}}{\\n{}{}}\\n{{}{{}}}{{}{}}{}{{}{}}\\n{\\n}{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1\\n.0}{-4.025pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{rgb}{\\n0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@color@rgb@fill\\n{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptscriptstyle\\\\definecolor{currentcolor}\\n{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{Tan!17}$\\\\displaystyle\\\\mathstrut p$}}{\\n\\\\hbox{\\\\pagecolor{Tan!17}$\\\\textstyle\\\\mathstrut p$}}{\\\\hbox{\\\\pagecolor{Tan!17}$\\n\\\\scriptstyle\\\\mathstrut p$}}{\\\\hbox{\\\\pagecolor{Tan!17}$\\\\scriptscriptstyle\\n\\\\mathstrut p$}}$}}\\n}}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}}\\n}\\n\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{\\n{}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\n\\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}\\\\in[0,1]$, we additionally have that $\\\\sigma_{1},\\\\dots,\\\\sigma_{pn}=1$ and $\\\\sigma_{pn+1},\\\\dots,\\\\sigma_{n}=\\\\sigma\\\\geqslant 1$. Then, the guarantees of Theorem 4.2 reduce to:\\nPercentage of “clean” points\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\leqslant C\\\\left(k\\\\left (\\\\frac{d+\\\\log(1/\\\\delta)}{n(p+\\\\mathchoice{\\\\leavevmode\\\\hbox to147.1pt{\\\\vbox to10 pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 73.54778pt\\\\lower-2.5pt\\\\hbox to0.0pt{ \\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor}{rgb}{0,0,0} \\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@color@rgb@fill{0}{0} {0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt}\\\\pgfsys@invoke{ }\\\\nullfont \\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-73.54778pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\displaystyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{ForestGreen !17}$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!1 7}$\\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 147.1pt{\\\\vbox to10pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 73.54778pt\\\\lower-2.5 pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor }{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-73.54778pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\textstyle\\\\definecolor {currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 113.63pt{\\\\vbox to7pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 56.8166pt\\\\lower-1.75 pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor }{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-56.8166pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{rgb }{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{ForestGreen !17}$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!1 7}$\\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 91.32pt{\\\\vbox to5pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 45.66249pt\\\\lower-1.25 pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor }{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-45.66249pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptscriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{ForestGreen !17}$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!1 7}$\\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}{\\\\hbox{\\\\pagecolor{ForestGreen!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}})}\\\\right)^{1/4}+k^{3} \\\\left(\\\\frac{k\\\\log k+\\\\log(1/\\\\delta)}{n\\\\left(p+\\\\mathchoice{\\\\leavevmode\\\\hbox to 173.7pt{\\\\vbox to10pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 86.84775pt\\\\lower-2.5 pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor }{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-86.84775pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\displaystyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{BrickRed!17 }$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 173.7pt{\\\\vbox to10pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 86.84775pt\\\\lower-2.5 pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{pgfstrokecolor }{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-86.84775pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\textstyle\\\\definecolor {currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 132.25pt{\\\\vbox to7pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 66.12659pt\\\\lower-1.7 5pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-66.12659pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{BrickRed!17 }$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}{\\\\leavevmode\\\\hbox to 104.62pt{\\\\vbox to5pt{\\\\pgfpicture\\\\makeatletter\\\\hbox{\\\\hskip 52.31245pt\\\\lower-1.2 5pt\\\\hbox to0.0pt{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\definecolor{ pgfstrokecolor}{rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\pgfsys@setlinewidth{0.4pt} \\\\pgfsys@invoke{ }\\\\nullfont\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@invoke{ \\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{\\\\pgfsys@beginscope \\\\pgfsys@invoke{ }{}{ {{}}\\\\hbox{\\\\hbox{{\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }{{}{}{{ {}{}}}{ {}{}} {{}{{}}}{{}{}}{}{{}{}} { }{{{{}}\\\\pgfsys@beginscope\\\\pgfsys@invoke{ }\\\\pgfsys@transformcm{1.0}{0.0}{0.0}{1 .0}{-52.31245pt}{0.0pt}\\\\pgfsys@invoke{ }\\\\hbox{{\\\\definecolor{pgfstrokecolor}{ rgb}{0,0,0}\\\\pgfsys@color@rgb@stroke{0}{0}{0}\\\\pgfsys@invoke{ } \\\\pgfsys@color@rgb@fill{0}{0}{0}\\\\pgfsys@invoke{ }\\\\hbox{{$\\\\scriptscriptstyle \\\\definecolor{currentcolor}{rgb}{0,0,0}\\\\mathchoice{\\\\hbox{\\\\pagecolor{BrickRed!17 }$\\\\displaystyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\textstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}{\\\\hbox{\\\\pagecolor{BrickRed!17}$ \\\\scriptscriptstyle\\\\mathstrut(1-p)/\\\\sigma^{4k-2}$}}$}} }}\\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope}}} } \\\\pgfsys@invoke{\\\\lxSVG@closescope }\\\\pgfsys@endscope\\\\hbox to0.0pt{}{{ {}{}{}}}{}{}\\\\hss}\\\\pgfsys@discardpath\\\\pgfsys@invoke{\\\\lxSVG@closescope } \\\\pgfsys@endscope\\\\hss}}\\\\lxSVG@closescope\\\\endpgfpicture}}}\\\\right)}\\\\right)^{1/(4k -2)}\\\\right).$ $$\\n\\nWe see that the noisy samples are downweighted only by $1/\\\\sigma^{4}$ for the dimensionality-reduction step whereas for the fine-grained estimation procedure, its discounting is much more substantial at $1/\\\\sigma^{4k-2}$. Next, we present a matching lower bound establishing that the rate achieved by Theorem 4.2 is optimal for learning with heterogenous samples.\\n\\n###### Theorem 4.4 (Lower bound) .\\n\\nLet $k\\\\in\\\\mathbb{N}$. Let $n,k,d\\\\in\\\\mathbb{N}$, $\\\\delta\\\\in(0,1/4]$, and $\\\\{\\\\sigma_{i}\\\\}_{i=1}^{n}\\\\geqslant 1$ be such that $d\\\\geqslant 3$ and:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\geqslant\\\\left(Ck\\\\right)^{2k-1}\\\\log(1 /\\\\delta)\\\\text{ and }\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\geqslant C(d+\\\\log(1 /\\\\delta))$ $$\\n\\nFor any estimator $\\\\widehat{T}$, there exists a $k$-atomic distribution $\\\\mathcal{D}$ supported on $\\\\mathbb{B}_{1}$ such that for $\\\\bm{X}\\\\thicksim\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$:\\n\\n$$ $\\\\mathbb{P}_{\\\\bm{X}}\\\\left\\\\{\\\\operatorname{W_{1}}(\\\\widehat{T}(\\\\bm{X},\\\\mathcal{D}) )\\\\geqslant c\\\\max\\\\left\\\\{\\\\left(\\\\frac{d+\\\\log(1/\\\\delta)}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i }^{4}}\\\\right)^{1/4},\\\\frac{1}{k}\\\\left(\\\\frac{1}{\\\\log(1/\\\\delta)}\\\\cdot\\\\sum_{i=1}^{ n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\right)^{-1/(4k-2)}\\\\right\\\\}\\\\right\\\\}\\\\geqslant\\\\delta.$ $$\\n\\nIn the remainder of the section, we present a proof of the upper bound (Theorem 4.2) in the simplified setting of $d=1$.\\n\\n###### Corollary 4.3 .\\n\\n###### Theorem 4.4 (Lower bound) .\\n\\n### 4.3 Proof: One-dimensional Setting\\n\\nWe draw upon the approach of Wu & Yang () for the homogeneous setting. We start by recalling some notation from Wu & Yang (). For $l\\\\in\\\\mathbb{N}$ and distribution, $\\\\mathcal{D}$, over $\\\\mathbb{R}$:\\n\\n$$ $m_{l}(\\\\mathcal{D})\\\\coloneqq\\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{D}}[X^{l}]\\\\quad\\\\text {and}\\\\quad\\\\mathbf{m}_{l}(\\\\mathcal{D})\\\\coloneqq[m_{0}(\\\\mathcal{D}),m_{1}( \\\\mathcal{D}),\\\\dots,m_{l}(\\\\mathcal{D})].$ $$\\n\\nThe estimator of Wu & Yang () utilizes the Hermite polynomials defined as:\\n$H_{r}(x)=r!\\\\sum_{j=0}^{\\\\lfloor r/2\\\\rfloor}\\\\frac{(-1/2)^{j}}{j!(r-2j)!}x^{r-2j}$.\\nThese polynomials satisfy the following crucial denoising property: $\\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{N}(\\\\mu,1)}[H_{r}(X)]=\\\\mu^{r}$.\\nLinearity of expectation now allows for denoising general convolutions with Gaussians:\\n\\n$$ $\\\\gamma_{r,\\\\sigma}(x)\\\\coloneqq\\\\sigma^{r}H_{r}(x/\\\\sigma)=r!\\\\sum_{j=0}^{\\\\lfloor r /2\\\\rfloor}\\\\frac{(-1/2)^{j}}{j!(r-2j)!}\\\\sigma^{2j}x^{r-2j}\\\\text{ satisfies } \\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(\\\\mu,\\\\sigma^{2})}[\\\\gamma_{r, \\\\sigma}(X)]=E_{X\\\\thicksim\\\\mathcal{D}}[X^{r}].$ $$\\n\\nHence, they allow approximate recovery of the moments of the $k$-atomic distribution that was convolved with a Gaussian to produce the final mixture. The main issue with this approach is that the moments are only recovered approximately. The following technical result, implicit in Wu & Yang () and proved in Appendix B, shows that error in estimating the moments can be directly translated to an error in Wasserstein distance in an estimation procedure.\\n\\n###### Lemma 4.1 .\\n\\n(Wu & Yang ()).\\nLet $k\\\\in\\\\mathbb{N}$, $\\\\delta\\\\in[0,1]$. Let $\\\\mathcal{D}$ be a $k$-atomic distribution supported on $[-1,1]$ and $\\\\widetilde{m}_{1},\\\\dots,\\\\widetilde{m}_{2k-1}$ be estimates satisfying $\\\\lvert\\\\widetilde{m}_{i}-m_{i}(\\\\mathcal{D})\\\\rvert\\\\leqslant\\\\delta$ for all $i\\\\in[2k-1]$. Then there is a procedure running in time $O_{k}(1)$, which on input $\\\\left\\\\{\\\\widetilde{m}_{i}\\\\right\\\\}_{i=1}^{2k-1}$, returns distribution $\\\\widehat{\\\\mathcal{D}}$ satisfying:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\leqslant O(k\\\\delta^{ \\\\frac{1}{2k-1}}).$ $$\\n\\nFinally, the error in the moment estimates can be bounded by the variance of the Hermite polynomials.\\n\\n###### Lemma 4.5 ( Wu & Yang ( 2020 ) ) .\\n\\nLet $M>0$ and $X\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2})$ with $\\\\mathcal{D}$ supported on $[-M,M]$. Then,\\n\\n$$ $\\\\forall r\\\\in\\\\mathbb{N}:\\\\mathrm{Var}(\\\\gamma_{r,\\\\sigma}(X))\\\\leqslant(O(M+\\\\sigma \\\\sqrt{r}))^{2r}.$ $$\\n\\nLemmas 4.5 and 4.1 now reduce the problem of estimating the parameters of the mixture to that of estimating its first $2k-1$ moments. Our algorithm is presented in Algorithm 3. The key step in the algorithm is the addition of the weights, $\\\\alpha_{i}$, which down-weight samples with large variance. These weights are chosen to minimize the variance of obtained moment estimates. Intuitively, samples with large variance are less reliable and their contributions discounted. Interestingly, the degree of down weighting also scales with the complexity of the distribution, measured by $k$. Next, we formally establish the correctness of Algorithm 3 through the following simplified theorem.\\n\\n###### Theorem 4.6 .\\n\\nLet $M>1$ be a constant and $k,n\\\\in\\\\mathbb{N}$. Suppose $\\\\mathcal{D}$ is a $k$-atomic distribution supported on $[-M,M]$ and that $\\\\bm{X}=\\\\{X_{i}\\\\}_{i=1}^{n}$ are generated as $X_{i}\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})$ with $\\\\sigma_{i}\\\\geqslant 1$. Then, Algorithm 3 given as input $\\\\bm{X}$ and $\\\\{\\\\sigma_{i}\\\\}_{i\\\\in[n]}$ returns with probability at least $3/4$ a $k$-atomic distribution $\\\\widehat{\\\\mathcal{D}}$ satisfying:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\leqslant Ck^{2}\\\\cdot \\\\left(\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\right)^{-1/(4k-2)}$ $$\\n\\n###### Proof.\\n\\nWe start by rescaling the distribution so that $M=1$. Next, we get from Lemma 4.5 that for all $r\\\\in[2k-1]$:\\n\\n$$ $\\\\mathrm{Var}(\\\\widetilde{m}_{r})=\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}\\\\mathrm{Var}\\\\left( \\\\gamma_{r,\\\\sigma_{i}}(X_{i})\\\\right)\\\\leqslant\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}(C \\\\sqrt{k}\\\\sigma_{i})^{4k-2}=(C\\\\sqrt{k})^{4k-2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{1} {\\\\sigma_{i}^{4k-2}}\\\\right)^{-1}\\\\eqqcolon\\\\sigma_{m}^{2}.$ $$\\n\\nTherefore, we get by a consequence of Chebyshev’s inequality for any $r\\\\in[2k-1]$:\\n\\n$$ $\\\\lvert\\\\widetilde{m}_{r}-m_{r}\\\\rvert\\\\leqslant 4\\\\sqrt{k}\\\\sigma_{m}$ $$\\n\\nwith probability at least $1-1/16k$. Hence, we get by the union bound:\\n\\n$$ $\\\\forall r\\\\in[2k-1]:\\\\lvert\\\\widetilde{m}_{r}-m_{r}\\\\rvert\\\\leqslant 4\\\\sqrt{k} \\\\sigma_{m}$ $$\\n\\nwith probability at least $3/4$. Conditioned on this event, 4.1 concludes the proof of the theorem.\\n∎\\n\\nThe proof of the high-dimensional setting is presented in Appendix C. Algorithmically, the high-dimensional setting uses two different weighting schemes; one for computing the appropriate low-dimensional subspace that is independent of $k$ and another for an exhaustive search algorithm similar to Doss et al. (). Furthermore, our algorithm and analysis diverge from and refine the results of Doss et al. (). Consequently, the dependence on the failure probability improved from $\\\\sqrt{\\\\log(1/\\\\delta)}$ to the optimal\\n$(\\\\log(1/\\\\delta))^{1/(4k-2)}$ dependence. Our key technical improvement is due to a robustness analysis on the approximation of the high-dimensional Wasserstein distance by one-dimensional projections (see Subsection C.2). This allows bypassing the chaining-based arguments of Doss et al. () and instead employing a median-of-means based approach with a simple covering number argument.\\n\\n###### Lemma 4.1 .\\n\\n###### Lemma 4.5 ( Wu & Yang ( 2020 ) ) .\\n\\n###### Theorem 4.6 .\\n\\n###### Proof.\\n\\n## 5 Experiments\\n\\n### 5.1 Training only with corrupted data\\n\\nWe start our experimental section by presenting results in the setting of prior work (Daras et al., ; ), i.e. using only noisy data.\\nWe train models at three different levels of corruption: i) $\\\\sigma=0.05$, ii) $\\\\sigma=0.1$, iii) $\\\\sigma=0.2$, across three different datasets of different sizes: CIFAR-10 (60K samples), CelebA-HQ (30K samples) and ImageNet ($\\\\approx 1.3$M images). We underline that prior work (Daras et al., ) only finetuned with noisy data. Instead, we opt for training from scratch which allows us to measure different quantities of interest in a more controlled setting.\\n\\nFor reference, we visualize the corruption levels in Figure 3. We train models with and without consistency. For our experiments, training with consistency was $2-3$x slower and used $2$x GPUs. The full experimental results are provided in Appendix F. For the models without consistency, we report results for both truncated (see Algorithm 2) and full sampling. For the models trained with consistency, we report results for the full sampling algorithm, as consistency is supposed to help mostly with times $t<t_{n}$. The results of this experiment are summarized in Table 2.\\n\\nThe findings are the following: i) the results are very poor for a model trained without consistency when the full-sampling algorithm is used, i.e. the model cannot extrapolate to times $t<t_{n}$, if it was only trained for times $t\\\\geqslant t_{n}$, ii) Truncated Sampling helps, but still, even for low corruptions, (e.g. for $\\\\sigma=0.05$) the performance is relatively weak, and, iii) training with consistency is beneficial, particularly for $\\\\sigma=0.05$ and $\\\\sigma=0.1$, but as the corruption increases the benefits of it are shrinking. Another interesting observation is that the performance deteriorates less (for the same corruption level) compared to the clean performance as the dataset size grows. This is expected: in the limit of infinite data, models trained with solely noisy data can still, in theory, perfectly recover the distribution (Daras et al., ). That said, even for ImageNet level datasets, at high corruption the best performance, obtained by training with the expensive consistency loss, is significantly inferior to the performance obtained by training with clean data.\\n\\n**Table 2: FID comparisons between models trained on solely noisy data across different datasets and noise levels. In the first two columns, we report results for models trained without consistency loss, with and without sampling truncation. Training with consistency (third col.) significantly improves the results, but still, the performance is poor compared to the clean data performance, especially for high corruption ($\\\\sigma=0.2$).**\\n| Dataset | Noise Level | Full Sampling | Truncated Sampling | Consistency + Full Sampling |\\n| --- | --- | --- | --- | --- |\\n| CIFAR-10 | 0.00 | $1.99\\\\pm\\\\scriptstyle{0.02}$ | NA | NA |\\n| 0.05 | $8.78\\\\pm\\\\scriptstyle{0.02}$ | $4.53\\\\pm\\\\scriptstyle{0.08}$ | $2.82\\\\pm\\\\scriptstyle{0.02}$ | |\\n| 0.10 | $25.55\\\\pm\\\\scriptstyle{0.10}$ | $7.55\\\\pm\\\\scriptstyle{0.07}$ | $3.63\\\\pm\\\\scriptstyle{0.03}$ | |\\n| 0.20 | $60.73\\\\pm\\\\scriptstyle{0.21}$ | $12.12\\\\pm\\\\scriptstyle{0.03}$ | $11.93\\\\pm\\\\scriptstyle{0.09}$ | |\\n| CelebA-HQ | 0.00 | $2.40\\\\pm\\\\scriptstyle{0.07}$ | NA | NA |\\n| 0.05 | $12.77\\\\pm\\\\scriptstyle{0.02}$ | $6.73\\\\pm\\\\scriptstyle{0.02}$ | $5.50\\\\pm\\\\scriptstyle{0.03}$ | |\\n| 0.10 | $45.90\\\\pm\\\\scriptstyle{0.08}$ | $10.27\\\\pm\\\\scriptstyle{0.01}$ | $9.38\\\\pm\\\\scriptstyle{0.02}$ | |\\n| 0.20 | $61.14\\\\pm\\\\scriptstyle{0.14}$ | $13.90\\\\pm\\\\scriptstyle{0.01}$ | $12.97\\\\pm\\\\scriptstyle{0.11}$ | |\\n| ImageNet | 0.00 | $1.41\\\\pm\\\\scriptstyle{0.03}$ | NA | NA |\\n| 0.05 | $2.39\\\\pm\\\\scriptstyle{0.01}$ | $2.53\\\\pm\\\\scriptstyle{0.01}$ | $2.26\\\\pm\\\\scriptstyle{0.01}$ | |\\n| 0.10 | $6.23\\\\pm\\\\scriptstyle{0.01}$ | $3.67\\\\pm\\\\scriptstyle{0.01}$ | $2.99\\\\pm\\\\scriptstyle{0.05}$ | |\\n| 0.20 | $18.08\\\\pm\\\\scriptstyle{0.05}$ | $6.03\\\\pm\\\\scriptstyle{0.02}$ | $5.32\\\\pm\\\\scriptstyle{0.08}$ | |\\n\\n### 5.2 Training with a mixture of clean and noisy data\\n\\nThe previous experiments showed that training with solely highly noisy data leads to a significant performance deterioration, at least for datasets with sizes up to ImageNet, and this also comes at a significant computational cost because of the consistency loss. But what if a small set of clean images is available? Arguably, this setting is fairly realistic since in the dataset design process one can spend some initial effort (measured in money, computation, or otherwise) to collect some high-quality data points and then rely on cheaper noisy points for the rest of the dataset. To the best of our knowledge, this setting has not been explored by prior work. To study this, we fix the dataset size and we change the percentage $p\\\\%$ of clean data. For every value of $p\\\\in\\\\{0.0,0.1,0.3,0.5,0.7,0.9,1.0\\\\}$, we train models with: i) $p\\\\%$ clean data, and, ii) with $p\\\\%$ clean data and $(1-p)\\\\%$ of noisy data at different levels of noise. To train with both clean and noisy data we used the method described in Section 3 and in Algorithm 1. We underline that for these experiments we do not use consistency loss and hence the training cost stays the same as training with clean data.\\n\\nWe report our results in Table 3 and we highlight a subset of the results in Table 1. The results show that even when we have $90\\\\%$ noisy data and high-corruption, i.e. $\\\\sigma=0.2$, the performance stays near the state-of-the-art as long as a small set ($10\\\\%$) of clean data is available. In fact, the obtained performance is far superior to the performance obtained by training only with clean data and the performance obtained by training with only noisy data, indicating that the benefit comes from the mixture of the two. The difference is quite dramatic: i) $10\\\\%$ clean ImageNet samples $\\\\Rightarrow 10.57$ FID, ii) $100\\\\%$ noisy samples (at $\\\\sigma=0.2$) $\\\\Rightarrow 5.32$ FID, iii) $90\\\\%$ noisy samples and $10\\\\%$ clean samples $\\\\Rightarrow\\\\bm{1.68}$ FID. This phenomenon is further illustrated in Figure 1.\\n\\n**Table 3: FID comparisons as we change the mix of clean and noisy data. Data availability is reported as percentage of the total dataset size: 60K for CIFAR, 30K for CelebA-HQ and $\\\\approx 1.3$M for ImageNet. Training with a mix of clean and noisy data is significantly better than training purely on a few clean data points or purely on the full noisy dataset.**\\n| Dataset | Available Data | Noise<br>Level | p% of clean data | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| | | | 100% | 90% | 70% | 50% | 30% | 10% | 0% |\\n| CIFAR-10 | p% clean | N/A | $1.99\\\\scriptstyle{\\\\pm 0.02}$ | $2.07\\\\scriptstyle{\\\\pm 0.01}$ | $2.20\\\\scriptstyle{\\\\pm 0.03}$ | $2.40\\\\scriptstyle{\\\\pm 0.02}$ | $3.99\\\\scriptstyle{\\\\pm 0.01}$ | $17.30\\\\scriptstyle{\\\\pm 0.14}$ | N/A |\\n| p% clean, (1-p)% noisy | 0.05 | $2.04\\\\scriptstyle{\\\\pm 0.02}$ | $2.04\\\\scriptstyle{\\\\pm 0.03}$ | $2.06\\\\scriptstyle{\\\\pm 0.00}$ | $2.11\\\\scriptstyle{\\\\pm 0.02}$ | $2.17\\\\scriptstyle{\\\\pm 0.04}$ | $8.78\\\\scriptstyle{\\\\pm 0.02}$ | | |\\n| 0.10 | $2.06\\\\scriptstyle{\\\\pm 0.03}$ | $2.14\\\\scriptstyle{\\\\pm 0.03}$ | $2.15\\\\scriptstyle{\\\\pm 0.01}$ | $2.24\\\\scriptstyle{\\\\pm 0.02}$ | $2.34\\\\scriptstyle{\\\\pm 0.03}$ | $25.55\\\\scriptstyle{\\\\pm 0.10}$ | | | |\\n| 0.20 | $2.06\\\\scriptstyle{\\\\pm 0.03}$ | $2.14\\\\scriptstyle{\\\\pm 0.02}$ | $2.24\\\\scriptstyle{\\\\pm 0.01}$ | $2.42\\\\scriptstyle{\\\\pm 0.03}$ | $2.81\\\\scriptstyle{\\\\pm 0.02}$ | $60.73\\\\scriptstyle{\\\\pm 0.21}$ | | | |\\n| CelebA-HQ | p% clean | N/A | $2.40\\\\scriptstyle{\\\\pm 0.07}$ | $2.50\\\\scriptstyle{\\\\pm 0.01}$ | $2.68\\\\scriptstyle{\\\\pm 0.00}$ | $2.83\\\\scriptstyle{\\\\pm 0.01}$ | $3.72\\\\scriptstyle{\\\\pm 0.01}$ | $11.92\\\\scriptstyle{\\\\pm 0.05}$ | N/A |\\n| p% clean, (1-p)% noisy | 0.05 | $2.40\\\\scriptstyle{\\\\pm 0.01}$ | $2.45\\\\scriptstyle{\\\\pm 0.01}$ | $2.45\\\\scriptstyle{\\\\pm 0.02}$ | $2.50\\\\scriptstyle{\\\\pm 0.01}$ | $2.50\\\\scriptstyle{\\\\pm 0.02}$ | $12.77\\\\scriptstyle{\\\\pm 0.02}$ | | |\\n| 0.10 | $2.40\\\\scriptstyle{\\\\pm 0.01}$ | $2.48\\\\scriptstyle{\\\\pm 0.02}$ | $2.51\\\\scriptstyle{\\\\pm 0.04}$ | $2.51\\\\scriptstyle{\\\\pm 0.01}$ | $2.67\\\\scriptstyle{\\\\pm 0.01}$ | $45.90\\\\scriptstyle{\\\\pm 0.10}$ | | | |\\n| 0.20 | $2.50\\\\scriptstyle{\\\\pm 0.00}$ | $2.51\\\\scriptstyle{\\\\pm 0.11}$ | $2.52\\\\scriptstyle{\\\\pm 0.01}$ | $2.67\\\\scriptstyle{\\\\pm 0.02}$ | $2.75\\\\scriptstyle{\\\\pm 0.02}$ | $61.14\\\\scriptstyle{\\\\pm 0.14}$ | | | |\\n| ImageNet | p% clean | N/A | $1.41\\\\scriptstyle{\\\\pm 0.03}$ | $1.50\\\\scriptstyle{\\\\pm 0.02}$ | $1.65\\\\scriptstyle{\\\\pm 0.01}$ | $2.15\\\\scriptstyle{\\\\pm 0.01}$ | $4.34\\\\scriptstyle{\\\\pm 0.06}$ | $10.57\\\\scriptstyle{\\\\pm 0.06}$ | N/A |\\n| p% clean, (1-p)% noisy | 0.05 | $1.46\\\\scriptstyle{\\\\pm 0.02}$ | $1.46\\\\scriptstyle{\\\\pm 0.02}$ | $1.46\\\\scriptstyle{\\\\pm 0.02}$ | $1.47\\\\scriptstyle{\\\\pm 0.02}$ | $1.51\\\\scriptstyle{\\\\pm 0.02}$ | $2.40\\\\scriptstyle{\\\\pm 0.02}$ | | |\\n| 0.10 | $1.48\\\\scriptstyle{\\\\pm 0.01}$ | $1.48\\\\scriptstyle{\\\\pm 0.02}$ | $1.49\\\\scriptstyle{\\\\pm 0.01}$ | $1.49\\\\scriptstyle{\\\\pm 0.01}$ | $1.57\\\\scriptstyle{\\\\pm 0.02}$ | $6.23\\\\scriptstyle{\\\\pm 0.01}$ | | | |\\n| 0.20 | $1.50\\\\scriptstyle{\\\\pm 0.02}$ | $1.51\\\\scriptstyle{\\\\pm 0.02}$ | $1.51\\\\scriptstyle{\\\\pm 0.02}$ | $1.59\\\\scriptstyle{\\\\pm 0.03}$ | $1.68\\\\scriptstyle{\\\\pm 0.02}$ | $18.08\\\\scriptstyle{\\\\pm 0.05}$ | | | |\\n\\nWe test the limits of our method by evaluating it in extreme corruption, either in terms of number of clean samples or in terms of the amount of noise. For computational reasons, we only present these results for CIFAR-10.\\n\\nHigher corruption. We use $90\\\\%$ noisy and $10\\\\%$ clean data and we increase the corruption to $\\\\sigma=0.4$. The FID becomes $\\\\bm{3.56\\\\pm 0.03}$, which is still much better than the performance ($17.30$) obtained by using $10\\\\%$ of clean data.\\n\\nLess clean data. We fix $\\\\sigma=0.2$ and we severely decrease the number of clean data. Specifically, we evaluate performance when $1\\\\%$ of clean data and $99\\\\%$ of noisy data are available. The performance of this model is $\\\\bm{3.53\\\\pm 0.03}$. For reference, the performance of the model trained with $100\\\\%$ noisy data at this noise level is $60.73$ without Truncated Sampling and $11.93$ with consistency training. Hence, $1\\\\%$ of clean data has a tremendous effect in performance.\\n\\n### 5.3 Pushing performance to its limit\\n\\nIn all our previous experiments, we used the EDM (Karras et al., ) hyperparameters that were tuned for clean data training. Here, we ablate different parameters that can further increase the performance of training with data mixtures. The first observation is that data corruption increases the time for convergence. In Figure 4 we plot the FID as a function of training time for a model trained with data mixtures. As shown, the FID keeps dropping as we train, indicating that the default parameters might lead to undertrained models when there is training data corruption. Hence, we take the ImageNet training run\\nwith $90\\\\%$ noisy data and $10\\\\%$ clean data, which has reported performance $1.68$ in Table 3 and we train the model for $500$K more steps. This alone decreases the FID from $1.68$ to $1.63$.\\n\\nWe then argue that for times $t\\\\leqslant t_{n}$ we should expect sub-optimal estimates since only a few (clean) samples were used. We attempt to balance the higher learning error with reduced discretization error by increasing the number of sampling steps spent on these noise levels during sampling. This further improves the performance from $1.63$ to $1.60$.\\n\\nNext, we use consistency loss to improve the learning for $t<t_{n}$, that was previously trained only with the clean points. We note that we only use consistency loss for this final part of the $500$k training steps. Consistency fine-tuning improves the FID to $1.58$. Finally, we use weight decay as a regularization technique to mitigate instabilities caused by the increased training variance. This further reduces the FID to $1.55$. It is possible that more optimizations could further decrease the FID but at this point we are already close to the optimal $1.41$ obtained using 100% clean samples.\\n\\nFigure: Figure 2: Evaluation of training and sampling improvements for models trained with noisy data.\\n\\n### 5.4 How much is a noisy image worth?\\n\\nHow much exactly is a noisy image worth? In what follows, we address the question of data pricing. Given finite resources for data curation, how should we allocate them to obtain the best performance? On the flip side, what is a fair pricing scheme that reflects data utility? We approach this through the notion of effective sample size suggested by our theoretical model. Let:\\n\\n$$ $n_{d}={\\\\frac{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}{\\\\max_{i}1/\\\\sigma_{i}^{4}}}\\\\quad n _{l}=\\\\frac{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4k-2}}{\\\\max_{i}1/\\\\sigma_{i}^{4k-2}},$ $$\\n\\nbe the two terms that appear in the bound of Theorem 4.2.\\nAssume that we operate in the asymptotic setting with large $n$ and with the fraction of clean and noisy data bounded away from 0 0 by a constant independent of $n$. In this regime, the dominant term in Theorem 4.2 is the second due to its slower rate of convergence. Therefore, the effective sample size for low-dimensional estimation, $n_{l}$, is the main determinant of the error.\\n\\nThis implies that we can use a fixed pricing scheme, largely independent of the sample size $n$. To validate this theoretical prediction, let’s price clean samples at $1\\\\$$ per unit and noisy samples at $c_{\\\\sigma}\\\\$$ per unit, for a parameter $c_{\\\\sigma}$ that we will bound using data from our experiments. Specifically, to bound $c_{\\\\sigma}$ we can derive inequalities by comparing performances from Table 3. For example, the CIFAR-10 performance using $90\\\\%$ clean data is $2.07$ which is better than the $2.42$ FID performance obtained using $30\\\\%$ clean and $70\\\\%$ noisy samples at $\\\\sigma=0.2$, which implies that:\\n\\n$$ $0.9n\\\\geqslant 0.3n+c_{0.2}0.7n\\\\implies c_{0.2}\\\\leqslant\\\\frac{6}{7}.$ $$\\n\\nWe repeat this computation for all pairs of the table and derive more inequalities. We restrict comparisons to settings with at least $10\\\\%$ clean samples to ensure we remain in the asymptotic regime. The best upper and lower bounds are:\\n\\n$$ $\\\\displaystyle\\\\text{CIFAR-10, CelebA:}\\\\ \\\\boxed{1.17\\\\leqslant\\\\frac{1}{c_{0.05}} \\\\leqslant 1.25},\\\\quad\\\\text{ImageNet:}\\\\ \\\\boxed{1.125\\\\leqslant\\\\frac{1}{c_{0.05}} \\\\leqslant 1.17}$ $\\\\displaystyle\\\\text{CIFAR-10, CelebA:}\\\\ \\\\boxed{1.25\\\\leqslant\\\\frac{1}{c_{0.1}} \\\\leqslant 1.5},\\\\quad\\\\text{ImageNet:}\\\\ \\\\boxed{1.125\\\\leqslant\\\\frac{1}{c_{0.1}} \\\\leqslant 1.17}$ $\\\\displaystyle\\\\text{CIFAR-10, CelebA, ImageNet:}\\\\ \\\\boxed{1.5\\\\leqslant\\\\frac{1}{c _{0.2}}\\\\leqslant 1.75}$ $$\\n\\nThe quantity $1/c_{\\\\sigma}$ measures the number of noisy samples required to compensate for a clean one. In line with intuition, for larger values of $\\\\sigma$ (i.e. the noisier the sample), more noisy samples required to replace a clean one. In addition, this ratio is the lowest for the largest dataset, ImageNet. The narrow ranges of the upper and lower bounds, lend credibility to this data pricing approach. Finer-grid evaluation at Table 3 would allow for even narrower estimates.\\n\\n## 6 Limitations and Future Work\\n\\nIn this paper, we only studied the case of additive Gaussian Noise corruption. In practice, the corruption might be more complex or even unknown. We further focused on the scale of having two noise levels, i.e. clean data and noisy data. The approach can be naturally extended to arbitrary many noise levels. Further, all the results in this work were developed for pixel-space diffusion models. A promising avenue for future research is to extend these findings to latent diffusion models. Finally, due to the high computational training requirements, we were only able to scale up to ImageNet and $64\\\\times 64$ resolution. It is worth exploring how these behaviors change as we further increase the dimension and the dataset size. On the theory side, our Gaussian Mixtures Model might not capture all the intricacies of real distributions and while being a useful tool, we should always interpret these results with caution.\\n\\n## 7 Acknowledgments\\n\\nThis research has been supported by NSF Grants AF 1901292, CNS 2148141, Tripods CCF 1934932, IFML CCF 2019844 and research gifts by Western Digital, Amazon, WNCG IAP, UT Austin Machine Learning Lab (MLL), Cisco and the Stanly P. Finch Centennial Professorship in Engineering. Constantinos Daskalakis has been supported by NSF Awards CCF-1901292, DMS-2022448 and DMS-2134108, a Simons Investigator Award, and the Simons Collaboration on the Theory of Algorithmic Fairness. Giannis Daras has been supported by the Onassis Fellowship (Scholarship ID: F ZS 012-1/2022-2023), the Bodossaki Fellowship and the Leventis Fellowship.\\n\\n## Appendix A Appendix\\n\\nFigure: Algorithm 2 Truncated Sampling Sampling Algorithm.\\n\\nFigure: Algorithm 3 Denoised Method of Moments with Heterogenous Variances\\n\\n## Appendix B Proof of 4.1\\n\\nIn this section, we establish 4.1 used to prove the weakened bound for the one-dimensional setting in Theorem 4.6. This result is implicit in Wu & Yang () and we include the proof here for completeness. Before we proceed, we reproduce the following result from Wu & Yang () which shows that for two distributions with finite support and close moments, their Wasserstein distance is also close.\\n\\n###### Proposition B.1 .\\n\\nLet $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ be $k$-atomic distributions supported on $[-1,1]$. If $\\\\lvert m_{i}(\\\\mathcal{D})-m_{i}(\\\\mathcal{D}^{\\\\prime})\\\\rvert\\\\leqslant\\\\delta$ for $i=1,\\\\dots,2k-1$, then:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\mathcal{D}^{\\\\prime})\\\\leqslant O(k\\\\delta^{ \\\\frac{1}{2k-1}}).$ $$\\n\\nWe reproduce the statement of 4.1 and include its proof below.\\nSee 4.1\\n\\n###### Proof.\\n\\nWe recall some preliminaries from Wu & Yang (). First, the moment space defined for a set $K\\\\subset\\\\mathbb{R}$:\\n\\n$$ $\\\\mathcal{M}_{r}(K)=\\\\{\\\\mathbf{m}_{r}(\\\\pi):\\\\pi\\\\text{ is supported on }K\\\\}.$ $$\\n\\nSpecifically when $K=[a,b]$, $\\\\mathcal{M}_{r}$ is fully characterized by the following convex constraints:\\n\\n$$ $\\\\displaystyle{\\\\mathbf{M}}_{0,r}\\\\succcurlyeq 0,\\\\quad(a+b){\\\\mathbf{M}}_{1,r-1} \\\\succcurlyeq ab{\\\\mathbf{M}}_{0,r-2}+{\\\\mathbf{M}}_{2,r}\\\\text{ for even }r$ $\\\\displaystyle b{\\\\mathbf{M}}_{0,r-1}\\\\succcurlyeq{\\\\mathbf{M}}_{1,r}\\\\succcurlyeq{ \\\\mathbf{M}}_{0,r-1}\\\\quad\\\\text{ for odd }r,$ (MOM-CHAR) $$\\n\\nwhere the matrices ${\\\\mathbf{M}}_{i,j}$ are defined as follows for $m\\\\in\\\\mathcal{M}_{r}$:\\n\\n$$ ${\\\\mathbf{M}}_{i,j}=\\\\begin{bmatrix}m_{i}&m_{i+1}&\\\\cdots&m_{\\\\frac{i+j}{2}}\\\\\\\\ m_{i+1}&m_{i+2}&\\\\cdots&m_{\\\\frac{i+j}{2}+1}\\\\\\\\ \\\\vdots&\\\\vdots&\\\\ddots&\\\\vdots\\\\\\\\ m_{\\\\frac{i+j}{2}}&m_{\\\\frac{i+j}{2}+1}&\\\\cdots&m_{j}\\\\end{bmatrix}.$ $$\\n\\nAs noted in Wu & Yang (), these constraints are easy to see as necessary. Surprisingly, they also turn out be sufficient for characterizing the space $\\\\mathcal{M}_{r}$ Shohat & Tamarkin ().\\n\\nThe algorithm now establishing 4.1 is presented in Algorithm 4. By our assumptions on the input, we have:\\n\\n$$ $\\\\forall i\\\\in[2k-1]:\\\\lvert\\\\widehat{m}_{i}-\\\\widetilde{m}_{i}\\\\rvert\\\\leqslant \\\\delta\\\\implies\\\\lvert\\\\widehat{m}_{i}-m_{i}(\\\\mathcal{D})\\\\rvert\\\\leqslant\\\\delta$ $$\\n\\nwhere the first inequality follows from the fact that $\\\\widehat{m}$ is the minimizer of the convex program and $\\\\mathcal{D}$ certifies that a solution with small error exists and the second follows from the triangle inequality. Next, since $\\\\widehat{\\\\mathbf{m}}$ corresponds to the moments of a valid distribution from the sufficiency criterion for one-dimensional distributions, Algorithm 5 returns a $k$ atomic distribution matching the moments $\\\\widehat{\\\\mathbf{m}}$. An application of Proposition B.1 establishes the lemma.\\n∎\\n\\nFigure: Algorithm 4 Estimate Distribution from Moments\\n\\nFigure: Algorithm 5 Gauss Quadrature\\n\\n###### Proposition B.1 .\\n\\n###### Proof.\\n\\n## Appendix C High-dimensional Upper Bound: Proof of Theorem 4.2\\n\\nIn this section, we prove Theorem 4.2. Here, we adopt the techniques from Doss et al. () which reduces the high dimensional setting to the one-dimensional setting through a series of reductions. The first reduces the $d$-dimensional setting to the $k$-dimensional setting by a projection onto the principal components of the data. This is a standard procedure that is frequently employed to reduce high-dimensional estimation to their more tractable low-dimensional counterparts. The second step follows by establishing a result which shows that any candidate mixture whose one-dimensional marginals are approximately consistent with the original mixture is close to the original mixture in Wasserstein distance. In the remainder of the section, Subsection C.1 analyzes the low-dimensional projection step, Subsection C.2 presents the low-dimensional estimation algorithm and finally, Subsection C.3 establishes Theorem 4.2.\\n\\n### C.1 Reduction to Low-dimensions\\n\\nHere, we establish concentration bounds on the matrix, $\\\\widehat{\\\\Sigma}$, used to compute the low-dimensional projection in Algorithm 8. We recall the following result that we will repeatedly use in our proofs:\\n\\n###### Lemma C.1 (Exercise 4.4.3 Vershynin ( 2018 ) ) .\\n\\nLet $d\\\\in\\\\mathbb{N}$ and $\\\\mathcal{G}$ be an ${\\\\varepsilon}$-net of the unit sphere. Then, we have for any symmetric $M\\\\in\\\\mathbb{R}^{d\\\\times d}$:\\n\\n$$ $\\\\lVert M\\\\rVert\\\\leqslant\\\\frac{1}{1-{\\\\varepsilon}}\\\\max_{v\\\\in\\\\mathcal{G}}\\\\lvert v ^{\\\\top}Mv\\\\rvert.$ $$\\n\\nWe first bound the noise terms that arise when computing the high-dimensional covariance.\\n\\n###### Lemma C.2 .\\n\\nLet $g_{1},\\\\dots,g_{n}\\\\overset{i.i.d}{\\\\thicksim}\\\\mathcal{N}(0,I)$ and $\\\\alpha_{i}\\\\geqslant 0$ for $i\\\\in[n]$ with $\\\\sum_{i=1}^{n}\\\\alpha_{i}=1$. Then, we have:\\n\\n$$ $\\\\left\\\\lVert\\\\sum_{i=1}^{n}\\\\alpha_{i}g_{i}g_{i}^{\\\\top}-I\\\\right\\\\rVert\\\\leqslant \\\\max\\\\left(\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}},(d+\\\\log(1/ \\\\delta))\\\\max_{i}\\\\alpha_{i}\\\\right)$ $$\\n\\nwith probability at least $1-\\\\delta$.\\n\\n###### Proof.\\n\\nAs is standard, we note the following characterization of the spectral norm for any symmetric $M\\\\in\\\\mathbb{R}^{d\\\\times d}$:\\n\\n$$ $\\\\lVert M\\\\rVert=\\\\max_{\\\\lVert v\\\\rVert=1}\\\\lvert v^{\\\\top}Mv\\\\rvert$ $$\\n\\nand start with a fixed $v$. The extension to the remainder of values is obtained through a discretization argument, a net over the unit sphere and a union bound. Now, for fixed $\\\\lVert v\\\\rVert=1$, consider the random variable:\\n\\n$$ $W_{v}\\\\coloneqq v^{\\\\top}\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}g_{i}g_{i}^{\\\\top}-I\\\\right )v=\\\\sum_{i=1}^{n}\\\\alpha_{i}(\\\\langle g_{i},v\\\\rangle^{2}-1).$ $$\\n\\nWe now prove that $W$ is sub-exponential:\\n\\n###### Claim C.3 .\\n\\nWe have for any $\\\\lvert\\\\lambda\\\\rvert<1/4$ and $g\\\\thicksim\\\\mathcal{N}(0,1)$:\\n\\n$$ $\\\\mathbb{E}[\\\\exp\\\\lambda(g^{2}-1)]\\\\leqslant\\\\exp(4\\\\lambda^{2}).$ $$\\n\\n###### Proof.\\n\\nWe have for any $\\\\lvert\\\\lambda\\\\rvert<1/4$ and $g\\\\thicksim\\\\mathcal{N}(0,1)$:\\n\\n$$ $\\\\displaystyle\\\\mathbb{E}[\\\\exp(\\\\lambda(g^{2}-1))]$ $\\\\displaystyle=e^{-\\\\lambda}\\\\int_{-\\\\infty}^{\\\\infty}\\\\frac{1}{\\\\sqrt{2\\\\pi}}\\\\exp \\\\left\\\\{(\\\\lambda g^{2})-\\\\frac{g^{2}}{2}\\\\right\\\\}dg$ $\\\\displaystyle=e^{-\\\\lambda}\\\\int_{\\\\-\\\\infty}^{\\\\infty}\\\\frac{1}{\\\\sqrt{2\\\\pi}}\\\\exp \\\\left\\\\{-\\\\frac{(1-2\\\\lambda)}{2}\\\\cdot g^{2}\\\\right\\\\}dg$ $\\\\displaystyle=e^{-\\\\lambda}\\\\cdot\\\\frac{1}{\\\\sqrt{1-2\\\\lambda}}=e^{-\\\\lambda}\\\\cdot \\\\frac{\\\\sqrt{1+2\\\\lambda}}{\\\\sqrt{1-4\\\\lambda^{2}}}$ $\\\\displaystyle\\\\leqslant e^{-\\\\lambda}\\\\cdot\\\\frac{e^{\\\\lambda}}{\\\\sqrt{1-4\\\\lambda^{2 }}}\\\\leqslant\\\\frac{1}{\\\\sqrt{e^{-8\\\\lambda^{2}}}}=\\\\exp(4\\\\lambda^{2})$ $$\\n\\nconcluding the proof of the claim.\\n∎\\n\\nHence, we have that each of the $(\\\\langle g_{i},v\\\\rangle^{2}-1)$ are $C$-sub-exponential random variables for some constant $C>0$. Hence, we have by Bernstein’s inequality (Vershynin, , Theorem 2.8.2):\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{W_{v}\\\\geqslant t\\\\right\\\\}\\\\leqslant 2\\\\exp\\\\left(-c\\\\min\\\\left( \\\\frac{t^{2}}{\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}},\\\\frac{t}{\\\\max_{i}\\\\alpha_{i}}\\\\right) \\\\right).$ $$\\n\\nNow, let $\\\\mathcal{Q}$ be a $1/4$-cover of the set $\\\\{x:\\\\lVert x\\\\rVert=1\\\\}$ with $\\\\lvert Q\\\\rvert\\\\leqslant 9^{d}$. Then, we have by the union bound:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\exists v\\\\in Q:W_{v}\\\\geqslant t\\\\right\\\\}\\\\leqslant 2\\\\cdot 9^{d} \\\\exp\\\\left(-c\\\\min\\\\left(\\\\frac{t^{2}}{\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}},\\\\frac{t}{\\\\max _{i}\\\\alpha_{i}}\\\\right)\\\\right).$ $$\\n\\nChoosing $t^{*}$ as:\\n\\n$$ $t^{*}=\\\\max\\\\left(\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}},(d+\\\\log( 1/\\\\delta))\\\\max_{i}\\\\alpha_{i}\\\\right)$ $$\\n\\nyields:\\n\\n$$ $\\\\max_{v\\\\in Q}W_{v}\\\\leqslant t^{*}$ $$\\n\\nwith probability at least $1-\\\\delta$. Observing that:\\n\\n$$ $\\\\lVert M\\\\rVert=\\\\max_{\\\\lVert v\\\\rVert=1}\\\\lvert v^{\\\\top}Mv\\\\rvert\\\\leqslant 2\\\\max_{ v\\\\in\\\\mathcal{Q}}\\\\lvert v^{\\\\top}Mv\\\\rvert$ $$\\n\\nfor any symmetric matrix $M$ (Lemma C.1), concludes the proof.\\n∎\\n\\nNow, we formally establish concentration of the second moment matrix $\\\\widehat{\\\\Sigma}$, in spectral norm.\\n\\n###### Lemma C.4 .\\n\\nLet $\\\\mathcal{D}$ be a $k$-atomic distribution supported such that each element, $x$, in its support satisfies $\\\\lVert x\\\\rVert\\\\leqslant R$. Furthermore, suppose $X_{1},\\\\dots,X_{n}$ are independent samples with $X_{i}\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$ with $\\\\sigma_{i}^{2}>0$ for all $i\\\\in[n]$. Then, we have:\\n\\n$$ $\\\\left\\\\lVert\\\\sum_{i=1}^{n}\\\\alpha_{i}X_{i}X_{i}^{\\\\top}-\\\\bar{\\\\sigma}^{2}I-\\\\mathbb {E}_{X\\\\thicksim\\\\mathcal{D}}[XX^{\\\\top}]\\\\right\\\\rVert\\\\leqslant\\\\\\\\ \\\\max\\\\left(\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}\\\\sigma_{i}^{2} \\\\max(\\\\sigma_{i}^{2},R^{2})},(d+\\\\log(1/\\\\delta))\\\\max_{i}\\\\alpha_{i}\\\\sigma_{i}^{2} ,R^{2}k\\\\sqrt{\\\\log(k/\\\\delta)\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}}\\\\right)$ $$\\n\\nwhere $\\\\alpha_{i}=\\\\frac{1/\\\\sigma_{i}^{4}}{\\\\sum_{j=1}^{n}1/\\\\sigma_{j}^{4}}\\\\text{ and }\\n\\\\bar{\\\\sigma}^{2}=\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}^{2}$ with probability at least $1-\\\\delta$.\\n\\n###### Proof.\\n\\nNote that we may write $X_{i}=Y_{i}+\\\\sigma_{i}g_{i}$ where $Y_{i}\\\\thicksim\\\\mathcal{D}$ and $g_{i}\\\\thicksim\\\\mathcal{N}(0,I)$ independently. Now, we write the error term as follows:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\alpha_{i}X_{i}X_{i}^{\\\\top}-\\\\bar{\\\\sigma}^{2}I-\\\\mathbb{E}_{X \\\\thicksim\\\\mathcal{D}}[XX^{\\\\top}]\\\\\\\\ =\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}Y_{i}Y_{i}^{\\\\top}-\\\\mathbb{E}_{X\\\\thicksim \\\\mathcal{D}}[XX^{\\\\top}]\\\\right)+\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}^{2}g_{ i}g_{I}^{\\\\top}-\\\\bar{\\\\sigma}^{2}I\\\\right)+\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}(Y_{ i}g_{i}^{\\\\top}+g_{i}Y_{i}^{\\\\top}).$ $$\\n\\nThe proof proceeds by bounding the errors of each of the three terms separately. We start with the middle term which we bound with Lemma C.2 to obtain the following:\\n\\n$$ $\\\\left\\\\lVert\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}^{2}g_{i}g_{I}^{\\\\top}-\\\\bar{\\\\sigma }^{2}I\\\\right\\\\rVert\\\\leqslant\\\\max\\\\left(\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{i=1}^{n} \\\\alpha_{i}^{2}\\\\sigma_{i}^{4}},(d+\\\\log(1/\\\\delta))\\\\max_{i}\\\\alpha_{i}\\\\sigma_{i}^{ 2}\\\\right).$ $$\\n\\nFor the first term, note that the error matrix may be written as follows:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\alpha_{i}Y_{i}Y_{i}^{\\\\top}-\\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{D}}[ XX^{\\\\top}]=\\\\sum_{i=1}^{k}(\\\\widehat{w}_{i}-w_{i})\\\\mu_{i}\\\\mu_{i}^{\\\\top}$ $$\\n\\nwhere $\\\\widehat{w}_{i}\\\\coloneqq\\\\sum_{j=1}^{n}\\\\alpha_{j}\\\\bm{1}\\\\left\\\\{Y_{j}=\\\\mu_{i}\\\\right\\\\}$ corresponds to the empirical counterpart of the mixture weights. Now, we have for any $\\\\lVert v\\\\rVert=1$:\\n\\n$$ $\\\\left\\\\lvert v^{\\\\top}\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}Y_{i}Y_{i}^{\\\\top}-\\\\mathbb{E} _{X\\\\thicksim\\\\mathcal{D}}[XX^{\\\\top}]\\\\right)v\\\\right\\\\rvert\\\\leqslant R^{2}\\\\sum_{i= 1}^{k}\\\\lvert\\\\widehat{w}_{i}-w_{i}\\\\rvert.$ $$\\n\\nAn application of Hoeffding’s inequality and the union bound obtains:\\n\\n$$ $\\\\forall i\\\\in[k]:\\\\lvert\\\\widehat{w}_{i}-w_{i}\\\\rvert\\\\leqslant C\\\\sqrt{\\\\log(k/ \\\\delta)\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}}$ $$\\n\\nwith probability at least $1-\\\\delta/4$. Conditioned on this event, we have:\\n\\n$$ $\\\\left\\\\lVert\\\\sum_{i=1}^{n}\\\\alpha_{i}Y_{i}Y_{i}^{\\\\top}-\\\\mathbb{E}_{X\\\\thicksim \\\\mathcal{D}}[XX^{\\\\top}]\\\\right\\\\rVert\\\\leqslant CR^{2}k\\\\sqrt{\\\\log(k/\\\\delta)\\\\sum_{ i=1}^{n}\\\\alpha_{i}^{2}}.$ $$\\n\\nWe now proceed to the final term. Consider a $1/4$-net of the unit sphere, $\\\\mathcal{G}$. We have for any fixed $v\\\\in\\\\mathcal{G}$:\\n\\n$$ $v^{\\\\top}\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}(Y_{i}g_{i}^{\\\\top}+g_{i}Y_{i}^ {\\\\top})\\\\right)v=\\\\sum_{i=1}^{n}2\\\\alpha_{i}\\\\sigma_{i}\\\\langle v,Y_{i}\\\\rangle \\\\langle v,g_{i}\\\\rangle.$ $$\\n\\nNoting that $\\\\langle v,g_{i}\\\\rangle$ is a standard Gaussian random variable and that $\\\\lVert Y_{i}\\\\rVert\\\\leqslant R$, we get that each term in the sum is sub-Gaussian and as a consequence, we get by Hoeffding’s inequality:\\n\\n$$ $\\\\left\\\\lvert v^{\\\\top}\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i}\\\\sigma_{i}(Y_{i}g_{i}^{\\\\top} +g_{i}Y_{i}^{\\\\top})\\\\right)v\\\\right\\\\rvert\\\\leqslant C\\\\sqrt{\\\\log(1/\\\\delta^{\\\\prime} )\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}\\\\sigma_{i}^{2}R^{2}}$ $$\\n\\nwith probability at least $1-\\\\delta^{\\\\prime}$.\\nHence, we get by the union bound over all $v\\\\in\\\\mathcal{G}$ and the size of $\\\\mathcal{G}$:\\n\\n$$ $\\\\forall v\\\\in\\\\mathcal{G}:\\\\left\\\\lvert v^{\\\\top}\\\\left(\\\\sum_{i=1}^{n}\\\\alpha_{i} \\\\sigma_{i}(Y_{i}g_{i}^{\\\\top}+g_{i}Y_{i}^{\\\\top})\\\\right)v\\\\right\\\\rvert\\\\leqslant C \\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{i=1}^{n}\\\\alpha_{i}^{2}\\\\sigma_{i}^{2}R^{2}}.$ $$\\n\\nFinally, this yields the same bound on spectral norm from Lemma C.1. The three bounds previously proved now conclude the proof of the lemma by the triangle inequality.\\n∎\\n\\n###### Lemma C.1 (Exercise 4.4.3 Vershynin ( 2018 ) ) .\\n\\n###### Lemma C.2 .\\n\\n###### Proof.\\n\\n###### Claim C.3 .\\n\\n###### Proof.\\n\\n###### Lemma C.4 .\\n\\n###### Proof.\\n\\n### C.2 Estimation in Low-dimensions\\n\\nThe following lemma is a generalization of a key technical lemma in Doss et al. (). This lemma establishes that the Wasserstein distance between two $k$-atomic distributions over $\\\\mathbb{R}^{d}$ can be approximated through various one-dimensional projections. While the version in Doss et al. () required the supremum in the conclusion to be taken over all vectors on the unit sphere, our result only requires a supremum over a grid of the unit sphere. Crucially, the size of the grid is independent of $n$ and hence, the final error. Our algorithmic approach benefits from this since to establish concentration over these one-dimensional projections, we may use more robust median-of-means based approaches to obtain these individual estimates as opposed to the more intricate chaining-based techniques of Doss et al. () which necessarily incurs the sub-optimal $\\\\sqrt{\\\\log(1/\\\\delta)}$ dependence features in their final bound. The chaining-based techniques in Doss et al. () are required since the grid size resulting from the previous approach is dependent on $n$ and hence, the simple techniques we employ incur additional factors depending on $n$. Technically, our improvement arises from a robustness analysis of the randomized one-dimensional projection argument employed in the proof.\\n\\n###### Lemma C.5 .\\n\\nLet $d,k\\\\in\\\\mathbb{N}$ and $\\\\mathcal{G}$ be a $1/(32k^{2}\\\\sqrt{d})$-net of $\\\\mathbb{S}^{d-1}$. Then, for two $k$-atomic distributions, $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$:\\n\\n$$ $\\\\sup_{v\\\\in\\\\mathcal{G}}\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v},\\\\mathcal{D}^{\\\\prime }_{v})\\\\leqslant\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\mathcal{D}^{\\\\prime})\\\\leqslant 1 6k^{2}\\\\sqrt{d}\\\\sup_{v\\\\in\\\\mathcal{G}}\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v}, \\\\mathcal{D}^{\\\\prime}_{v}).$ $$\\n\\n###### Proof.\\n\\nThe lower bound follows from (Doss et al., , Lemma 3.1). For the upper bound, we proceed as in (Doss et al., , Lemma 3.1) starting with a simple probabilistic argument. However, we additionally analyze the robustness properties of their construction to account for the discretization in our bound. First, define the set of vectors:\\n\\n$$ $Q\\\\coloneqq\\\\left\\\\{\\\\frac{x-y}{\\\\lVert x-y\\\\rVert}:x,y\\\\in\\\\{\\\\mu_{i}\\\\}_{i=1}^{k}\\\\cup \\\\{\\\\mu^{\\\\prime}_{i}\\\\}_{i=1}^{k}\\\\text{ and }x\\\\neq y\\\\right\\\\}.$ $$\\n\\nNote that $Q$ is of size at most $k^{2}$. We follow now the probabilistic argument also utilized in Doss et al. () to establish the existence of a vector $v\\\\in\\\\mathbb{S}^{d-1}$ which satisfies:\\n\\n$$ $\\\\forall u\\\\in Q:\\\\lVert u\\\\rVert\\\\leqslant Ck^{2}\\\\sqrt{d}\\\\lvert\\\\langle v,u\\\\rangle\\\\rvert.$ $$\\n\\nNow, draw $v$ from the uniform distribution on $\\\\mathbb{S}^{d-1}$. For any $u\\\\in Q$, we have by standard results for $t\\\\leqslant 1/2$:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\lvert\\\\langle v,u\\\\rangle\\\\rvert\\\\leqslant t\\\\right\\\\}=\\\\frac{ \\\\Gamma(d/2)}{\\\\sqrt{\\\\pi}\\\\Gamma((d-1)/2)}\\\\int_{-t}^{t}(1-x^{2})^{(d-3)/2}dx \\\\leqslant 4t\\\\sqrt{d}.$ $$\\n\\nThen, we get via a union bound:\\n\\n$$ $\\\\forall u\\\\in Q:8k^{2}\\\\sqrt{d}\\\\langle v,u\\\\rangle\\\\geqslant 1$ $$\\n\\nwith probability at least $1/2$. Hence, we have for such a $v$:\\n\\n$$ $\\\\forall x,y\\\\in\\\\{\\\\mu_{i}\\\\}_{i=1}^{k}\\\\cup\\\\{\\\\mu^{\\\\prime}_{i}\\\\}_{i=1}^{k}:\\\\lVert x -y\\\\rVert\\\\leqslant 8k^{2}\\\\sqrt{d}\\\\lvert\\\\langle v,x-y\\\\rangle\\\\rvert.$ $$\\n\\nNow, let $\\\\widetilde{v}$ be the closest neighbor of $v$ in $\\\\mathcal{G}$. We now have for any $u\\\\in Q$:\\n\\n$$ $\\\\lvert\\\\langle\\\\widetilde{v},u\\\\rangle\\\\rvert\\\\geqslant\\\\lvert\\\\langle v,u\\\\rangle \\\\rvert-\\\\lVert\\\\widetilde{v}-v\\\\rVert\\\\geqslant\\\\frac{1}{16k^{2}\\\\sqrt{d}}.$ $$\\n\\nFor this $\\\\widetilde{v}$, observe that each of the elements in $\\\\{\\\\mu_{i}\\\\}_{i=1}^{k}\\\\cup\\\\{\\\\mu^{\\\\prime}_{i}\\\\}_{i=1}^{k}$ is mapped to a distinct real number. Hence, every coupling of $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ correspond to a coupling on the projections of the distributions $\\\\mathcal{D}_{\\\\widetilde{v}}$ and $\\\\mathcal{D}^{\\\\prime}_{\\\\widetilde{v}}$ and vice-versa. Then, consider any coupling of $\\\\mathcal{D}_{\\\\widetilde{v}}$ and $\\\\mathcal{D}^{\\\\prime}_{\\\\widetilde{v}}$, $C(Y,Y^{\\\\prime})$ and its corresponding high-dimensional analogue, $C_{d}(X,X^{\\\\prime})$. Then, we have:\\n\\n$$ $16k^{2}\\\\sqrt{d}\\\\mathbb{E}_{(Y,Y^{\\\\prime})\\\\thicksim C}[\\\\lvert Y-Y^{\\\\prime} \\\\rvert]\\\\geqslant\\\\mathbb{E}_{(X,X^{\\\\prime})\\\\thicksim C}[\\\\lVert X-X^{\\\\prime} \\\\rVert]\\\\geqslant W_{1}(\\\\mathcal{D},\\\\mathcal{D}^{\\\\prime}).$ $$\\n\\nBy maximizing over all such couplings, we derive the conclusion of the lemma.\\n∎\\n\\nThe key benefit of Lemma C.5 is that it only requires us to obtain an candidate distribution whose marginals are close in Wasserstein distance to the marginals along a subset of directions independent of $n$. In the remainder of the proof, we will assume that $d=k$ as we may project the data down to $k$ dimensions by computing the PCA of the centered covariance matrix. Before we adapt the analysis of Doss et al. (), we will prove a moment concentration result which will enable a tightening of the dependence on the failure probability. While Doss et al. () obtain an upper bound with a $\\\\sqrt{\\\\log(1/\\\\delta)}$ dependence, our bound will instead grow was $(\\\\log(1/\\\\delta))^{1/(4k-2)}$.\\n\\n###### Lemma C.6 .\\n\\nLet $k,m,n\\\\in\\\\mathbb{N}$, $\\\\delta\\\\in(0,1/2)$, and $R>0$ be a constant. Suppose $\\\\mathcal{D}$ be a $k$-atomic distribution over $\\\\mathbb{R}^{k}$ with each $x$ in its support satisfying $\\\\lVert x\\\\rVert\\\\leqslant R$. Then, there is a procedure which when given independent samples $X_{1},\\\\dots,X_{n}$ distributed according to $X_{i}\\\\thicksim\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$ with $\\\\sigma_{i}\\\\geqslant 1$ and $\\\\max_{i}1/\\\\sigma_{i}^{4k-2}\\\\leqslant c\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4k-2}/(\\\\log(\\n1/\\\\delta)+k\\\\log(k))$, returns one-dimensional estimates, $\\\\left\\\\{\\\\mathcal{D}_{v}\\\\right\\\\}_{v\\\\in\\\\mathcal{G}}$, satisfying:\\n\\n$$ $\\\\forall v\\\\in\\\\mathcal{G}:\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v},\\\\widehat{\\\\mathcal {D}}_{v})\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\frac{1}{(k\\\\log(k)+\\\\log(1/\\\\delta))}\\\\cdot \\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\right)^{-1/(4k-2)}$ $$\\n\\nwhere $\\\\mathcal{G}$ is a $(1/\\\\operatorname*{poly}(k))$-net of $\\\\mathbb{S}^{k-1}$ with probability at least $1-\\\\delta$.\\n\\n###### Proof.\\n\\nWe start by defining a partition $\\\\pi:[n]\\\\to[m]$ where $m=C(\\\\log(1/\\\\delta)+k\\\\log(k))$ satisfying the following:\\n\\n$$ $\\\\forall j\\\\in[m]:\\\\sum_{i,\\\\pi(i)=j}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\geqslant\\\\frac{1}{ 2m}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}.$ $$\\n\\nSuch a partition may be found in linear time by Lemma C.7. For all $v\\\\in\\\\mathcal{G},\\\\ell\\\\in[m]$, let $\\\\widehat{\\\\mathcal{D}}_{v,\\\\ell}$ be the one-dimensional $k$-atomic mixture obtained by running Algorithm 3 on the points $\\\\{\\\\langle X_{i},v\\\\rangle\\\\}_{i,\\\\pi(i)=\\\\ell}$. From Theorem 4.6, we get that:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v},\\\\widehat{\\\\mathcal{D}}_{v ,\\\\ell})\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma_{i}^{4k-2}} \\\\right)^{-1/(4k-2)}\\\\right\\\\}\\\\geqslant\\\\frac{3}{4}.$ $$\\n\\nDefining the random variables $Q_{v,\\\\ell}$ as follows:\\n\\n$$ $Q_{v,\\\\ell}=\\\\bm{1}\\\\left\\\\{\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v},\\\\widehat{\\\\mathcal {D}}_{v,\\\\ell})\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma_{i}^{4k -2}}\\\\right)^{-1/(4k-2)}\\\\right\\\\},$ $$\\n\\nwe get that $\\\\mathbb{E}[Q_{v,\\\\ell}]\\\\geqslant 3/4$. Therefore, we get by an application of Hoeffding’s inequality for a fixed $v\\\\in\\\\mathcal{G}$:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\sum_{i=1}^{m}Q_{v,\\\\ell}\\\\leqslant 0.6m\\\\right\\\\}\\\\leqslant\\\\exp(- cm).$ $$\\n\\nBy a union bound, we get from our setting of $m$:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\exists v\\\\in\\\\mathcal{G}:\\\\sum_{i=1}^{m}Q_{v,\\\\ell}\\\\leqslant 0.6 m\\\\right\\\\}\\\\leqslant\\\\lvert\\\\mathcal{G}\\\\rvert\\\\exp(-cm)\\\\leqslant\\\\delta.$ $$\\n\\nWe now condition on the above event. At this point, we have $m$ estimates $\\\\widehat{D}_{v,\\\\ell}$ for each direction $v\\\\in\\\\mathcal{G}$. To obtain a single estimate for each direction, $v$, observe the following by the triangle inequality for any $j,j^{\\\\prime}\\\\in[m]$ such that $Q_{v,j},Q_{v,j^{\\\\prime}}=1$:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}}_{v,j},\\\\widehat{\\\\mathcal{D}}_{v,j^{ \\\\prime}})\\\\leqslant\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}}_{v,j},\\\\mathcal{D} _{v})+\\\\operatorname{W_{1}}(\\\\mathcal{D}_{v},\\\\widehat{\\\\mathcal{D}}_{v,j^{\\\\prime} })\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma_{i}^{4k-2}}\\\\right)^ {-1/(4k-2)}.$ $$\\n\\nNow, as a consequence, the following set exists:\\n\\n$$ $\\\\mathcal{J}\\\\coloneqq\\\\left\\\\{j\\\\in[m]:\\\\left\\\\lvert\\\\left\\\\{\\\\ell\\\\in[m]:\\\\operatorname{ W_{1}}(\\\\widehat{\\\\mathcal{D}}_{v,j},\\\\widehat{\\\\mathcal{D}}_{v,\\\\ell})\\\\leqslant Ck ^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma_{i}^{4k-2}}\\\\right)^{-1/(4k-2)} \\\\right\\\\}\\\\right\\\\rvert\\\\geqslant 0.6m\\\\right\\\\}.$ $$\\n\\n$\\\\mathcal{J}$ is computable from the estimates $\\\\widehat{\\\\mathcal{D}}_{v,j}$ and we now show that any arbitrary element of $\\\\mathcal{J}$ suffices. Let $j^{*}_{v}\\\\in\\\\mathcal{J}$ and notice by the pigeonhole principle and the definition of $\\\\mathcal{J}$, that there exists $\\\\ell\\\\in[m]$ such that $Q_{v,\\\\ell}=1$ and furthermore,\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}}_{v,j^{*}_{v}},\\\\widehat{\\\\mathcal{D}} _{v,\\\\ell})\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma_{i}^{4k-2}} \\\\right)^{-1/(4k-2)}\\\\implies\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}}_{v,j^{*} _{v}},\\\\mathcal{D}_{v})\\\\leqslant Ck^{2}\\\\cdot\\\\left(\\\\sum_{i=1}^{n}\\\\frac{m}{\\\\sigma _{i}^{4k-2}}\\\\right)^{-1/(4k-2)}$ $$\\n\\nby the triangle inequality and the definition of $Q_{v,\\\\ell}$. The lemma follows from the estimates $\\\\{\\\\widehat{\\\\mathcal{D}}_{v,j^{*}}\\\\}$ for $v\\\\in\\\\mathcal{G}$.\\n∎\\n\\nOur algorithm uses a median-of-means based approach to recover the moments of the one-dimensional projections. Since the variances are non-uniform, we use a deterministic partitioning algorithm to partition points to ensure buckets of roughly equal size. The following lemma establishes guarantees on the sample partitioning algorithm.\\n\\n###### Lemma C.7 .\\n\\nGiven $k\\\\in\\\\mathbb{N}$ and $n$ numbers, $\\\\alpha_{1},\\\\dots,\\\\alpha_{n}\\\\geqslant 0$ such that $\\\\max_{i}\\\\alpha_{i}\\\\leqslant\\\\nicefrac{{\\\\sum_{i=1}^{n}\\\\alpha_{i}}}{{4k}}$, it is possible to find a partition $\\\\pi:[n]\\\\to[k]$ such that:\\n\\n$$ $\\\\min_{i}\\\\sum_{j:\\\\pi(j)=i}\\\\alpha_{j}\\\\geqslant\\\\frac{\\\\sum_{i=1}^{n}\\\\alpha_{i}}{2k}.$ $$\\n\\nFurthermore, the runtime of this procedure is $O(n\\\\log(k))$.\\n\\n###### Proof.\\n\\nWe will analyze the simple greedy procedure in Algorithm 6 where ties are broken arbitrarily. Define:\\n\\n$$ $M^{i}_{j}\\\\coloneqq\\\\sum_{\\\\ell\\\\leqslant i,\\\\pi(\\\\ell)=j}\\\\alpha_{\\\\ell}.$ $$\\n\\nWe will prove by induction on $i$ that:\\n\\n$$ $\\\\forall j,\\\\ell\\\\in[k]:\\\\lvert M^{i}_{j}-M^{i}_{\\\\ell}\\\\rvert\\\\leqslant\\\\alpha_{ \\\\mathrm{max}}.$ $$\\n\\nThe case for $i=1$ is trivially true. Suppose the condition is true for $i=m$. To extend to $m+1$, let $j_{M}\\\\coloneqq\\\\operatorname*{arg\\\\,max}_{i}M^{m}_{i}$ and $j_{m}\\\\coloneqq\\\\operatorname*{arg\\\\,min}_{i}M^{m}_{i}$. Then, we must $\\\\operatorname*{arg\\\\,max}_{j}M^{m+1}_{j}\\\\in\\\\{j_{M},j_{m}\\\\}$. Note now that for all $\\\\ell\\\\neq j_{M},j_{m}$:\\n\\n$$ $\\\\lvert M^{m+1}_{j_{M}}-M^{m+1}_{\\\\ell}\\\\rvert\\\\leqslant\\\\alpha_{\\\\mathrm{max}}, \\\\qquad\\\\lvert M^{m+1}_{j_{m}}-M^{m+1}_{\\\\ell}\\\\rvert=\\\\lvert(M^{m}_{\\\\ell}-M^{m}_{j _{m}})-\\\\alpha_{i+1}\\\\rvert\\\\leqslant\\\\alpha_{i+1}\\\\leqslant\\\\alpha_{\\\\mathrm{max}}.$ $$\\n\\nFinally, we have:\\n\\n$$ $\\\\lvert M^{m+1}_{j_{m}}-M^{m+1}_{j_{M}}\\\\rvert=\\\\lvert(M^{m}_{j_{M}}-M^{m}_{j_{m} })-\\\\alpha_{i}\\\\rvert\\\\leqslant\\\\alpha_{i}\\\\leqslant\\\\alpha_{\\\\mathrm{max}}$ $$\\n\\nconcluding the proof of the inductive claim and consequently, establishes the correctness of the algorithm. The runtime follows from the fact that the scores may be stored in a self-balancing binary tree.\\n\\nFigure: Algorithm 6 Partition Mass\\n\\n∎\\n\\nIn the next, we use the techniques of Doss et al. () to improve the computational properties of the estimation algorithm. This part of the proof is essentially identical to Doss et al. (). However, we include minor changes which allow tightening the bounds. The next lemma shows that the set $\\\\mathcal{C}$ defined in Algorithm 7, which defines the low-dimensional estimation algorithm, has a good solution.\\n\\nFigure: Algorithm 7 Low-dimensional Algorithm\\n\\n###### Lemma C.8 .\\n\\nLet $d,k\\\\in\\\\mathbb{N}$ and let $\\\\mathcal{D}=\\\\sum_{i=1}^{k}w_{i}\\\\delta_{\\\\mu_{i}}$ be a $k$-atomic mixture over $\\\\mathbb{R}^{d}$ with $\\\\lVert\\\\mu_{i}\\\\rVert\\\\leqslant R$ for all $i\\\\in[k]$. Furthermore, for each $i\\\\in[d]$, let $\\\\widehat{\\\\mathcal{D}}_{e_{i}}=\\\\sum_{j=1}^{k}\\\\widehat{w}^{i}_{j}\\\\delta_{\\\\mu^{i}\\n_{j}}$ be $k$-atomic distributions over $\\\\mathbb{R}$, each satisfying:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D}_{e_{i}},\\\\widehat{\\\\mathcal{D}}_{e_{i}}) \\\\leqslant\\\\nu.$ $$\\n\\nThen, for any $(\\\\nu/R)$-net over the probability simplex, $\\\\mathcal{W}$, there exists a solution $\\\\widehat{\\\\mathcal{D}}=\\\\sum_{i=1}^{k}\\\\widehat{w}_{i}\\\\delta_{\\\\widehat{\\\\mu}_{i}}$ such that:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}},\\\\mathcal{D})\\\\leqslant 2d\\\\nu\\\\text{ where }\\\\widehat{w}\\\\in\\\\mathcal{W}\\\\text{ and }\\\\widehat{\\\\mu}_{i}\\\\in\\\\{\\\\widehat{\\\\mu }^{1}_{j}\\\\}_{j=1}^{k}\\\\times\\\\{\\\\widehat{\\\\mu}^{2}_{j}\\\\}_{j=1}^{k}\\\\times\\\\dots \\\\times\\\\{\\\\widehat{\\\\mu}^{k}_{j}\\\\}_{j=1}^{k}.$ $$\\n\\n###### Proof.\\n\\nWe have as a consequence of the assumption of the lemma:\\n\\n$$ $\\\\forall j\\\\in[d]:\\\\sum_{i=1}w_{i}\\\\min_{\\\\ell\\\\in[k]}\\\\lvert\\\\langle\\\\mu_{i},e_{j} \\\\rangle-\\\\widehat{\\\\mu}^{j}_{\\\\ell}\\\\rvert\\\\leqslant\\\\nu.$ $$\\n\\nDefining now:\\n\\n$$ $\\\\forall i\\\\in[k]:\\\\widehat{\\\\mu}_{i}=(\\\\widetilde{\\\\mu}^{1}_{i},\\\\dots,\\\\widetilde{ \\\\mu}^{d}_{i})\\\\text{ where }\\\\widehat{\\\\mu}^{j}_{\\\\ell}\\\\coloneqq\\\\operatorname*{arg \\\\,min}_{\\\\widetilde{\\\\mu}\\\\in\\\\{\\\\widehat{\\\\mu}^{j}_{m}\\\\}_{m=1}^{k}}\\\\lvert\\\\langle\\\\mu _{\\\\ell},e_{j}\\\\rangle-\\\\widetilde{\\\\mu}\\\\rvert\\\\text{ for all }\\\\ell\\\\in[k],j\\\\in[d].$ $$\\n\\nWe have for the mixture $\\\\widetilde{\\\\mathcal{D}}=\\\\sum_{i=1}^{k}w_{i}\\\\delta_{\\\\widehat{\\\\mu}_{i}}$:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widetilde{\\\\mathcal{D}})\\\\leqslant\\\\sum_{i=1}^{ k}w_{i}\\\\lVert\\\\mu_{i}-\\\\widehat{\\\\mu}_{i}\\\\rVert\\\\leqslant\\\\sum_{i=1}^{k}w_{i}\\\\lVert \\\\mu_{i}-\\\\widehat{\\\\mu}_{i}\\\\rVert_{1}=\\\\sum_{i=1}^{k}w_{i}\\\\sum_{j=1}^{d}\\\\lvert \\\\langle\\\\mu_{i},e_{j}\\\\rangle-\\\\widetilde{\\\\mu}^{j}_{i}\\\\rvert=\\\\sum_{j=1}^{d}\\\\sum_{ i=1}^{k}w_{i}\\\\lvert\\\\langle\\\\mu_{i},e_{j}\\\\rangle-\\\\widetilde{\\\\mu}^{j}_{i}\\\\rvert \\\\leqslant d\\\\nu.$ $$\\n\\nFinally, let $\\\\widehat{w}\\\\in\\\\mathcal{W}$ be such that $\\\\lVert\\\\widehat{w}-w\\\\rVert_{1}\\\\leqslant\\\\nu/R$. We have for the mixture $\\\\widehat{\\\\mathcal{D}}=\\\\sum_{i=1}^{k}\\\\widehat{w}_{i}\\\\delta_{\\\\widehat{\\\\mu}_{i}}$:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\mathcal{D}})\\\\leqslant\\\\operatorname{ W_{1}}(\\\\mathcal{D},\\\\widetilde{\\\\mathcal{D}})+\\\\operatorname{W_{1}}(\\\\widetilde{ \\\\mathcal{D}},\\\\widehat{\\\\mathcal{D}})\\\\leqslant d\\\\nu+\\\\sum_{i=1}^{k}\\\\lvert\\\\widehat {w}_{i}-w_{i}\\\\rvert\\\\max_{j,\\\\ell\\\\in[k]}\\\\lVert\\\\widehat{\\\\mu}_{j}-\\\\widehat{\\\\mu}_{ \\\\ell}\\\\rVert\\\\leqslant d\\\\nu+2\\\\sqrt{d}R\\\\sum_{i=1}^{k}\\\\lvert\\\\widehat{w}_{i}-w_{i} \\\\rvert\\\\leqslant 2d\\\\nu$ $$\\n\\nconcluding the proof of the lemma.\\n∎\\n\\n###### Lemma C.5 .\\n\\n###### Proof.\\n\\n###### Lemma C.6 .\\n\\n###### Proof.\\n\\n###### Lemma C.7 .\\n\\n###### Proof.\\n\\n###### Lemma C.8 .\\n\\n###### Proof.\\n\\n### C.3 Proof of Theorem 4.2\\n\\nThe complete high-dimensional estimation algorithm is presented in Algorithm 8. The algorithm splits the points into two sets, and utilizes the first to compute a low-dimensional sub-space that (approximately) contains the means of the components of the mixture and then, runs the low-dimensional estimation algorithm Algorithm 7 on the second set. Before proceeding with the proof, we recall another lemma from Doss et al. () which relates the loss in accuracy caused by the low-dimensional projection to the error in estimating the low-dimensional projection in Lemma C.4.\\n\\n###### Lemma C.9 .\\n\\nLet $\\\\mathcal{D}=\\\\sum_{j=1}^{k}w_{j}\\\\delta_{\\\\mu_{j}}$ be a $k$-atomic distribution. Let $\\\\Sigma=\\\\mathbb{E}_{X\\\\sim\\\\mathcal{D}}[UU^{\\\\top}]=\\\\sum_{j=1}^{k}w_{j}\\\\mu_{j}\\\\mu_\\n{j}^{\\\\top}$ with eigenvalues $\\\\lambda_{1}\\\\geqslant\\\\cdots\\\\geqslant\\\\lambda_{d}$. Let $\\\\Sigma^{\\\\prime}$ be a symmetric matrix and $\\\\Pi^{\\\\prime}_{r}$ be the projection matrix onto the subspace spanned by the top $r$ eigenvectors of $\\\\Sigma^{\\\\prime}$. Then,\\n\\n$$ $\\\\operatorname{W_{1}}^{2}(\\\\Gamma,\\\\Gamma_{\\\\Pi^{\\\\prime}_{r}})\\\\leqslant k\\\\left( \\\\lambda_{r+1}+2\\\\|\\\\Sigma-\\\\Sigma^{\\\\prime}\\\\|_{2}\\\\right).$ $$\\n\\nFigure: Algorithm 8 High-dimensional Gaussian Mixtures\\n\\n###### Proof of Theorem 4.2 .\\n\\nThe algorithm that achieves the guarantees of the theorem is defined in Algorithm 8. We first show that the partitioning step induces balanced partitions for the subspace computation and low-dimensional estimation steps.\\n\\n###### Claim C.10 .\\n\\nWe have the following:\\n\\n$$ $\\\\displaystyle\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\geqslant\\\\frac{1 }{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}$ $\\\\displaystyle\\\\frac{c_{2}}{4(\\\\log(1/\\\\delta)+k\\\\log(k)}\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}} \\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\geqslant\\\\frac{1}{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{ i}^{4k-2}}$ $$\\n\\nwith probability at least $1-\\\\delta/4$.\\n\\n###### Proof.\\n\\nFor the first, observe that:\\n\\n$$ $\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}\\\\frac{1}{\\\\sigma_{i}^{4}}=\\\\sum_{i=1}^{n}W_{i}\\\\text{ where }W_{i}\\\\coloneqq\\\\frac{\\\\bm{1}\\\\left\\\\{X_{i}\\\\in\\\\bm{X}_{1}\\\\right\\\\}}{\\\\sigma_{i} ^{4}}.$ $$\\n\\nNow, we have by Hoeffding’s inequality:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\sum_{i=1}^{n}W_{i}-\\\\mathbb{E}\\\\left[\\\\sum_{i=1}^{n}W_{i}\\\\right ]\\\\leqslant-t\\\\right\\\\}\\\\leqslant\\\\exp\\\\left\\\\{-\\\\frac{2t^{2}}{\\\\sum_{i=1}^{n}1/\\\\sigma_ {i}^{8}}\\\\right\\\\}\\\\leqslant\\\\exp\\\\left\\\\{-2\\\\cdot\\\\frac{t}{\\\\max_{i}(1/\\\\sigma_{i}^{4}) }\\\\cdot\\\\frac{t}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right\\\\}$ $$\\n\\nNow, setting:\\n\\n$$ $t=\\\\frac{1}{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\implies\\\\frac{t}{\\\\max_{i}(1 /\\\\sigma_{i})^{4}}\\\\cdot\\\\frac{t}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}=\\\\frac{1}{16} \\\\cdot\\\\frac{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}{\\\\max_{i}(1/\\\\sigma_{i}^{4})} \\\\geqslant 4\\\\log(1/\\\\delta).$ $$\\n\\nObserving that:\\n\\n$$ $\\\\mathbb{E}\\\\left[\\\\sum_{i=1}^{n}W_{i}\\\\right]=\\\\frac{1}{2}\\\\sum_{i=1}^{n}\\\\frac{1}{ \\\\sigma_{i}^{4}}$ $$\\n\\nyields the first claim with probability at least $1-\\\\delta/8$. For the second, similarly define:\\n\\n$$ $\\\\sum_{X_{i}\\\\in\\\\bm{X}_{2}}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}=\\\\sum_{i=1}^{n}Q_{i}\\\\text{ where }Q_{i}\\\\coloneqq\\\\frac{\\\\bm{1}\\\\left\\\\{X_{i}\\\\in\\\\bm{X}_{2}\\\\right\\\\}}{\\\\sigma_{i }^{4k-2}}.$ $$\\n\\nAs before, we have by Hoeffding’s inequality:\\n\\n$$ $\\\\mathbb{P}\\\\left\\\\{\\\\sum_{i=1}^{n}Q_{i}-\\\\mathbb{E}\\\\left[\\\\sum_{i=1}^{n}Q_{i}\\\\right ]\\\\leqslant-t\\\\right\\\\}\\\\leqslant\\\\exp\\\\left\\\\{-\\\\frac{2t^{2}}{\\\\sum_{i=1}^{n}1/\\\\sigma_ {i}^{8k-4}}\\\\right\\\\}\\\\leqslant\\\\exp\\\\left\\\\{-2\\\\cdot\\\\frac{t}{\\\\max_{i}(1/\\\\sigma_{i}^{ 4k-2})}\\\\cdot\\\\frac{t}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4k-2}}\\\\right\\\\}$ $$\\n\\nNow, setting:\\n\\n$$ $t=\\\\frac{1}{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\implies\\\\frac{t}{\\\\max_{i }(1/\\\\sigma_{i})^{4k-2}}\\\\cdot\\\\frac{t}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4k-2}}=\\\\frac{ 1}{16}\\\\cdot\\\\frac{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4k-2}}{\\\\max_{i}(1/\\\\sigma_{i}^{4k- 2})}\\\\geqslant 4\\\\log(1/\\\\delta).$ $$\\n\\nObserving,\\n\\n$$ $\\\\mathbb{E}\\\\left[\\\\sum_{i=1}^{n}Q_{i}\\\\right]=\\\\frac{1}{2}\\\\sum_{i=1}^{n}\\\\frac{1}{ \\\\sigma_{i}^{4k-2}}$ $$\\n\\nyields the second claim with probability at least $1-\\\\delta/8$. A union bound establishes the claim.\\n∎\\n\\nWe will now assume the event in the conclusion of Claim C.10 in the remainder of the proof. We have as a consequence of Claims C.10 and C.4:\\n\\n$$ $\\\\left\\\\lVert\\\\widehat{\\\\Sigma}-\\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{D}}[XX^{\\\\top}] \\\\right\\\\rVert\\\\leqslant\\\\max\\\\left(\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1 }}\\\\alpha_{i}^{2}\\\\sigma_{i}^{4}},(d+\\\\log(1/\\\\delta))\\\\max_{i}\\\\alpha_{i}\\\\sigma_{i} ^{2},k\\\\sqrt{\\\\log(k/\\\\delta)\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}\\\\alpha_{i}^{2}}\\\\right).$ $$\\n\\nFor the second term, we have for any $X_{i}\\\\in\\\\bm{X}_{1}$:\\n\\n$$ $\\\\displaystyle(d+\\\\log(1/\\\\delta))\\\\alpha_{i}\\\\sigma_{i}^{2}\\\\leqslant\\\\sqrt{(d+\\\\log( 1/\\\\delta))}\\\\sqrt{(d+\\\\log(1/\\\\delta))\\\\alpha_{i}^{2}\\\\sigma_{i}^{4}}\\\\leqslant c \\\\sqrt{\\\\frac{d+\\\\log(1/\\\\delta)}{\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}1/\\\\sigma_{i}^{4}}}.$ $$\\n\\nHence, we get that the second is dominated by the first as:\\n\\n$$ $\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}\\\\alpha_{i}^{2}\\\\sigma_{i}^{4}=\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1} }\\\\frac{(1/\\\\sigma_{i})^{4}}{(\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}1/\\\\sigma_{i}^{4})^{2}}= \\\\frac{1}{\\\\sum_{X_{i}\\\\in\\\\bm{X}_{1}}1/\\\\sigma_{i}^{4}}.$ $$\\n\\nFinally, the third term is dominated by the second as $\\\\sigma_{i}\\\\geqslant 1$. To conclude, we get by Claim C.10 and the previous discussion that:\\n\\n$$ $\\\\left\\\\lVert\\\\widehat{\\\\Sigma}-\\\\mathbb{E}_{X\\\\thicksim\\\\mathcal{D}}[XX^{\\\\top}] \\\\right\\\\rVert\\\\leqslant\\\\sqrt{\\\\frac{(d+\\\\log(1/\\\\delta))}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i }^{4}}}.$ $$\\n\\nTherefore, we have for the subspace $U$ in Algorithm 8 by Lemma C.9:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\mathcal{D}_{U})\\\\leqslant Ck\\\\sqrt[4]{\\\\frac{(d +\\\\log(1/\\\\delta))}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}}.$ $$\\n\\nwith probability at least $1-\\\\delta/4$. Next, since $\\\\bm{X}_{2}$ are independent of $\\\\bm{X}_{1}$ (and hence, the subspace $U$), we get by Claim C.10 and Lemmas C.6 and C.8 that the solution $\\\\widehat{\\\\mathcal{D}}=(\\\\widehat{w}_{i},\\\\widehat{\\\\mu}_{i})_{i\\\\in[k]}$ satisfies:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}},\\\\mathcal{D}_{U})\\\\leqslant Ck^{3} \\\\left(\\\\sum_{i=1}^{k}\\\\frac{(k\\\\log(k)+\\\\log(1/\\\\delta))}{\\\\sigma_{i}^{4k-2}}\\\\right) ^{-1/(4k-2)}$ $$\\n\\nwith probability at least $1-\\\\delta/4$. By a union bound and the triangle inequality, we get:\\n\\n$$ $\\\\displaystyle\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}},\\\\mathcal{D})$ $\\\\displaystyle\\\\leqslant\\\\operatorname{W_{1}}(\\\\widehat{\\\\mathcal{D}},\\\\mathcal{D}_{ U})+\\\\operatorname{W_{1}}(\\\\mathcal{D}_{U},\\\\mathcal{D})$ $\\\\displaystyle\\\\leqslant C\\\\left(k\\\\left(\\\\frac{(d+\\\\log(1/\\\\delta))}{\\\\sum_{i=1}^{n}1 /\\\\sigma_{i}^{4}}\\\\right)^{1/4}+k^{3}\\\\left(\\\\sum_{i=1}^{k}\\\\frac{(k\\\\log(k)+\\\\log(1/ \\\\delta))}{\\\\sigma_{i}^{4k-2}}\\\\right)^{-1/(4k-2)}\\\\right)$ $$\\n\\nwith probability at least $1-\\\\delta$ establishing the correctness of Algorithm 8.\\n\\nFinally, to bound the runtime, the computation of the top-$k$ right singular subspace can be computed in time $\\\\widetilde{O}_{k}(nd)$ and projecting the points in $\\\\bm{X}_{2}$ onto the low dimensional subspace is also computable in time $\\\\widetilde{O}_{k}(nd)$. For the running of Algorithm 7, observe that the procedure in Lemma C.6 runs in time $\\\\widetilde{O}_{k}(\\\\lvert\\\\mathcal{G}\\\\rvert n)=\\\\widetilde{O}_{k}(n)$. Finally, for the remainder of Algorithm 7, note that the number of candidate vectors in $\\\\mathcal{C}$ is at most $k^{k}$ and the number of candidate weight vectors in $\\\\mathcal{W}$ is at most $n$. Therefore, the total number of candidates is at most $\\\\widetilde{O}_{k}(n)$. The time taken to check candidate solution is at most $\\\\widetilde{O}_{k}(1)$ for each $v\\\\in\\\\mathcal{G}$ and since there are at most $\\\\widetilde{O}_{k}(1)$ of these, the time to check a single candidate is $\\\\widetilde{O}_{k}(1)$. Thus the total runtime for the Algorithm 7 is at most $\\\\widetilde{O}_{k}(n)$ and as a consequence, the runtime of Algorithm 8 is bounded by $\\\\widetilde{O}_{k}(nd)$.\\n∎\\n\\n###### Lemma C.9 .\\n\\n###### Proof of Theorem 4.2 .\\n\\n###### Claim C.10 .\\n\\n###### Proof.\\n\\n## Appendix D Lower Bound: Proof of Theorem 4.4\\n\\nIn this section, we prove the lower bound Theorem 4.4. We prove the lower bound in three cases which will imply the final bound. Firstly, we prove the $k$-dependent term from the lower bound in Subsection D.1 and show that it holds in the one-dimensional setting. Then, we establish a pair of bounds for high-dimensional setting, one for the dimension-dependent term in and another for the failure probability $\\\\delta$, in Subsection D.2. We then combine these three results to obtain the final bound from Theorem 4.4. We will frequently make use of the following inequality which will be crucial in obtaining the high-probability lower bounds in the respective statements:\\n\\n###### Lemma D.1 ( Bretagnolle & Huber ( 1979 ); Tsybakov ( 2009 ); Canonne ( 2023 ) ) .\\n\\nWe have for any two distributions, $P$ and $Q$:\\n\\n$$ $\\\\operatorname{TV}(P,Q)\\\\leqslant 1-\\\\frac{1}{2}\\\\exp(D_{\\\\mathrm{KL}}(P\\\\|Q)).$ $$\\n\\n###### Lemma D.1 ( Bretagnolle & Huber ( 1979 ); Tsybakov ( 2009 ); Canonne ( 2023 ) ) .\\n\\n### D.1 One-dimensional Lower Bound\\n\\nHere, we establish a lower bound in one dimension for the estimation problem with $k$ components. We show that the $k$-dependent term in the lower bound is unavoidable even in the simpler one-dimensional setting. Our proof largely follows that in Wu & Yang () but is specialized to the setting of heterogeneous variances. We start by recalling some technical results from Wu & Yang ().\\n\\n###### Lemma D.2 .\\n\\nLet ${\\\\varepsilon}\\\\in[0,1]$ and $l\\\\in\\\\mathbb{N}$. Suppose now that $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ are centered distributions supported on $[-{\\\\varepsilon},{\\\\varepsilon}]$ satisfying $\\\\mathbf{m}_{l}(\\\\mathcal{D})=\\\\mathbf{m}_{l}(\\\\mathcal{D}^{\\\\prime})$. Then, we have the following:\\n\\n$$ $\\\\chi^{2}(\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,1)||\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}( 0,1))\\\\leqslant O\\\\left(\\\\left(\\\\frac{e{\\\\varepsilon}^{2}}{l+1}\\\\right)^{l+1}\\\\right).$ $$\\n\\nWe also note the following simple corollary by the invariance of $f$-Divergences to re-scaling of the distributions.\\n\\n###### Corollary D.3 .\\n\\nLet ${\\\\varepsilon}\\\\in[0,1]$ and $l\\\\in\\\\mathbb{N}$. Suppose now that $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ are centered distributions supported on $[-{\\\\varepsilon},{\\\\varepsilon}]$ satisfying $\\\\mathbf{m}_{l}(\\\\mathcal{D})=\\\\mathbf{m}_{l}(\\\\mathcal{D}^{\\\\prime})$. Then, we have the following for any $\\\\sigma^{2}\\\\geqslant 1$:\\n\\n$$ $\\\\chi^{2}(\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2})||\\\\mathcal{D}^{\\\\prime}\\\\ast \\\\mathcal{N}(0,\\\\sigma^{2}))\\\\leqslant O\\\\left(\\\\left(\\\\frac{e{\\\\varepsilon}^{2}}{(l+ 1)\\\\sigma^{2}}\\\\right)^{l+1}\\\\right).$ $$\\n\\nLemma D.2 implies that two Dirac distributions supported on a small range and matching a large number of moments are challenging to distinguish from each other. The following result from Wu & Yang () shows that when allowed a support size of $k$, there exist two distributions $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ supported on $[-{\\\\varepsilon},{\\\\varepsilon}]$ and more than ${\\\\varepsilon}/k$ apart but nevertheless matching their first $4k-2$ moments.\\n\\n###### Lemma D.4 .\\n\\nFor any ${\\\\varepsilon}\\\\geqslant 0$ and $k\\\\in\\\\mathbb{N}$, there exists two distributions $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ supported on $[-{\\\\varepsilon},{\\\\varepsilon}]$ satisfying:\\n\\n$$ $\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\mathcal{D}^{\\\\prime})\\\\geqslant\\\\Omega\\\\left( \\\\frac{{\\\\varepsilon}}{k}\\\\right)\\\\quad\\\\text{and}\\\\quad\\\\mathbf{m}_{2k-2}(\\\\mathcal{D })=\\\\mathbf{m}_{2k-2}(\\\\mathcal{D}^{\\\\prime}).$ $$\\n\\nFurthermore, $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ are supported on at most $k$ elements.\\n\\nNext, we prove the main one-dimensional lower bound.\\n\\n###### Theorem D.5 .\\n\\nThere exists an absolute constants $C,c>0$ such that the following holds. Let $n,k\\\\in\\\\mathbb{N}$, $\\\\delta\\\\in(0,1/4]$, and $\\\\sigma_{i}\\\\geqslant 1$ for $i\\\\in[n]$ be such that:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4k-2}}\\\\geqslant(C\\\\sqrt{k})^{4k-2}\\\\log(1/ \\\\delta).$ $$\\n\\nThen, there exist two distributions, $\\\\mathcal{D}_{1}$ and $\\\\mathcal{D}_{2}$, each supported on at most $k$-points in $[-1,1]$, such that the following holds for any estimator $\\\\widehat{\\\\theta}$:\\n\\n$$ $\\\\max_{\\\\mathcal{D}\\\\in\\\\{\\\\mathcal{D}_{1},\\\\mathcal{D}_{2}\\\\}}\\\\mathbb{P}_{\\\\bm{X}} \\\\left\\\\{\\\\operatorname{W_{1}}(\\\\mathcal{D},\\\\widehat{\\\\theta}(\\\\bm{X}))\\\\geqslant \\\\frac{c}{k}\\\\left(\\\\frac{1}{\\\\log(1/\\\\delta)}\\\\sum_{i=1}^{n}\\\\left(\\\\frac{1}{\\\\sigma_{ i}^{4k-2}}\\\\right)\\\\right)^{-1/(4k-2)}\\\\right\\\\}\\\\geqslant\\\\delta\\\\text{ where }\\\\bm{X }\\\\thicksim\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}).$ $$\\n\\n###### Proof.\\n\\nLet ${\\\\varepsilon}\\\\in[0,1]$ be a parameter to be chosen later and $\\\\mathcal{D}$ and $\\\\mathcal{D}^{\\\\prime}$ be two distributions whose existence is guaranteed by Lemma D.4. Then, observe that we have the following for all $i\\\\in[n]$:\\n\\n$$ $\\\\chi^{2}(\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})||\\\\mathcal{D}^{\\\\prime} \\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}))\\\\leqslant O\\\\left(\\\\left(\\\\frac{e{\\\\varepsilon}^ {2}}{(2k-1)\\\\sigma_{i}^{2}}\\\\right)^{2k-1}\\\\right).$ $$\\n\\nRecall the tensorization properties of the $\\\\chi_{2}$ divergence:\\n\\n$$ $\\\\chi_{2}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})|| \\\\prod_{i=1}^{n}\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})\\\\right)+1= \\\\prod_{i=1}^{n}\\\\left(\\\\chi_{2}\\\\left(\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2} )||\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})\\\\right)+1\\\\right).$ $$\\n\\nAs a consequence, we get that:\\n\\n$$ $\\\\chi_{2}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})|| \\\\prod_{i=1}^{n}\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})\\\\right) \\\\leqslant C\\\\sum_{i=1}^{n}\\\\left(\\\\frac{e{\\\\varepsilon}^{2}}{(2k-1)\\\\sigma_{i}^{2}} \\\\right)^{2k-1}\\\\text{ when }\\\\sum_{i=1}^{n}\\\\left(\\\\frac{e{\\\\varepsilon}^{2}}{(2k-1 )\\\\sigma_{i}^{2}}\\\\right)^{2k-1}\\\\leqslant c$ $$\\n\\nfor some absolute constants $C,c>0$. Finally, picking ${\\\\varepsilon}$ as:\\n\\n$$ ${\\\\varepsilon}=c\\\\left(\\\\frac{1}{\\\\log(1/\\\\delta)}\\\\sum_{i=1}^{n}\\\\left(\\\\frac{e}{(2k- 1)\\\\sigma_{i}^{2}}\\\\right)^{2k-1}\\\\right)^{-1/(4k-2)}$ $$\\n\\nfor $c>0$ yields:\\n\\n$$ $\\\\chi_{2}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})|| \\\\prod_{i=1}^{n}\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2})\\\\right) \\\\leqslant\\\\frac{\\\\log(1/\\\\delta)}{8}.$ $$\\n\\nAs a consequence, we get:\\n\\n$$ $\\\\gamma\\\\coloneqq D_{\\\\mathrm{KL}}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N} (0,\\\\sigma_{i}^{2})||\\\\prod_{i=1}^{n}\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0, \\\\sigma_{i}^{2})\\\\right)\\\\leqslant\\\\frac{\\\\log(1/\\\\delta)}{8}.$ $$\\n\\nBy the BH-inequality (Lemma D.1), we now get:\\n\\n$$ $\\\\operatorname{TV}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^ {2})||\\\\prod_{i=1}^{n}\\\\mathcal{D}^{\\\\prime}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}) \\\\right)\\\\leqslant 1-\\\\frac{1}{2}\\\\exp\\\\left(-\\\\gamma\\\\right)\\\\leqslant 1-\\\\delta.$ $$\\n\\nAn application of Le Cam’s (Wainwright, , Section 15.2) method now yields the result.\\n∎\\n\\n###### Lemma D.2 .\\n\\n###### Corollary D.3 .\\n\\n###### Lemma D.4 .\\n\\n###### Theorem D.5 .\\n\\n###### Proof.\\n\\n### D.2 High-dimensional Lower Bounds\\n\\nHere, we adapt the techniques of Wu & Zhou () to establish lower bounds in the setting of heterogenous variances. The dimension-dependent lower bound is established for the simple setting with two equally weighted components with means distributed symmetrically across the origin. Hence, the set of candidates mixtures $\\\\mathcal{M}_{\\\\mathrm{Dirac}}$ parameterized by $\\\\theta\\\\in\\\\mathbb{R}^{d}$ and defined below:\\n\\n$$ $\\\\mathcal{M}_{\\\\mathrm{Dirac}}=\\\\frac{1}{2}\\\\delta_{\\\\theta}+\\\\frac{1}{2}\\\\delta_{- \\\\theta}.$ $$\\n\\nIn the rest of this section, we will use $\\\\mathcal{D}_{\\\\theta}$ to refer to a member of this family. We now reproduce a technical result from Wu & Zhou () which bounds the KL-Divergence between two different Gaussian mixtures from this family in terms of the distance between their respective location parameters.\\n\\n###### Lemma D.6 .\\n\\nThen there exists a universal constant $C$ such that the following holds. For any $s\\\\in[0,1]$ and $u,v$ such that $\\\\lVert u\\\\rVert=\\\\lVert v\\\\rVert=1$, we have:\\n\\n$$ $D_{\\\\mathrm{KL}}(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,I)\\\\|\\\\mathcal{D}_{sv}\\\\ast \\\\mathcal{N}(0,I))\\\\leqslant C\\\\lVert u-v\\\\rVert^{2}s^{4}.$ $$\\n\\nFurthermore, we have by the scale-invariance of the KL-divergence, the following corollary.\\n\\n###### Corollary D.7 .\\n\\nAssume the setting of Lemma D.6. Then, for any $\\\\sigma\\\\geqslant 1$, we have:\\n\\n$$ $D_{\\\\mathrm{KL}}(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I)\\\\|\\\\mathcal{D}_{ sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I))\\\\leqslant C\\\\lVert u-v\\\\rVert^{2}\\\\left(\\\\frac{s }{\\\\sigma}\\\\right)^{4}.$ $$\\n\\nWe now present the main lower bound of the section:\\n\\n###### Theorem D.8 .\\n\\nThere exist absolute constants $C,c>0$ such that the following holds. Let $d\\\\geqslant 3$, $n\\\\in\\\\mathbb{N}$, and $\\\\left\\\\{\\\\sigma_{i}\\\\right\\\\}_{i=1}^{n}$ be such that $\\\\sigma_{i}\\\\geqslant 1$ for all $i\\\\in[n]$ and:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\geqslant Cd.$ $$\\n\\nThen, we have for any estimator $\\\\widehat{T}$:\\n\\n$$ $\\\\max_{\\\\theta\\\\in\\\\mathbb{R}^{d}}\\\\mathbb{P}_{\\\\bm{X}}\\\\left\\\\{\\\\operatorname{W_{1}}( \\\\widehat{T}(\\\\bm{X}),\\\\mathcal{D}_{\\\\theta})\\\\geqslant c\\\\left(\\\\frac{d}{\\\\sum_{i=1}^ {n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4}\\\\right\\\\}\\\\geqslant\\\\frac{1}{2}$ $$\\n\\nwhere $\\\\bm{X}=\\\\{X_{i}\\\\}_{i=1}^{n}$ are independent random vectors with $X_{i}\\\\thicksim\\\\mathcal{D}_{\\\\theta}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$.\\n\\n###### Proof.\\n\\nThe proof will use the standard testing to estimation framework for proving minimax lower bounds. First, let $\\\\mathcal{G}$ denote a $1/4$-packing of the unit sphere such that $\\\\lvert\\\\mathcal{G}\\\\rvert\\\\geqslant 4^{d-1}$. Now, we have from Corollary D.7, for any $u,v\\\\in\\\\mathcal{G}$ and $\\\\sigma\\\\geqslant 1$ and $s\\\\in[0,1]$:\\n\\n$$ $D_{\\\\mathrm{KL}}(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I)\\\\|\\\\mathcal{D}_{ sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I))\\\\leqslant C\\\\lVert u-v\\\\rVert^{2}\\\\left(\\\\frac{s }{\\\\sigma}\\\\right)^{4}\\\\leqslant 4C\\\\left(\\\\frac{s}{\\\\sigma}\\\\right)^{4}.$ $$\\n\\nHence, we get by the tensorization of the KL-divergence:\\n\\n$$ $D_{\\\\mathrm{KL}}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\prod_{i=1}^{n}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{ 2}I)\\\\right)\\\\\\\\ =\\\\sum_{i=1}^{n}D_{\\\\mathrm{KL}}\\\\left(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)\\\\right) \\\\leqslant Cs^{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}.$ $$\\n\\nNow, picking\\n\\n$$ $s=c\\\\left(\\\\frac{d}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4},$ $$\\n\\nwe get that:\\n\\n$$ $D_{\\\\mathrm{KL}}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\prod_{i=1}^{n}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{ 2}I)\\\\right)\\\\leqslant\\\\frac{d}{16}.$ $$\\n\\nAn application of Fano’s inequality (Wainwright, , Proposition 15.12) for the set of candidates $\\\\{su\\\\}_{u\\\\in\\\\mathcal{G}}$ and noting that $\\\\lvert\\\\mathcal{G}\\\\rvert\\\\geqslant 4^{d-1}$ yields the result from the observation that for any $u,v\\\\in\\\\mathcal{G}$, $\\\\operatorname{W_{1}}(\\\\mathcal{D}_{su},\\\\mathcal{D}_{sv})\\\\geqslant s/4$.\\n∎\\n\\nWe now establish a separate high-probability version of the bound.\\n\\n###### Theorem D.9 .\\n\\nThere exist absolute constants $C,c>0$ such that the following holds. Let $d\\\\geqslant 2$, $n\\\\in\\\\mathbb{N}$, $\\\\delta\\\\in(0,1/4]$, and $\\\\left\\\\{\\\\sigma_{i}\\\\right\\\\}_{i=1}^{n}$ be such that $\\\\sigma_{i}\\\\geqslant 1$ for all $i\\\\in[n]$ and:\\n\\n$$ $\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}\\\\geqslant C\\\\log(1/\\\\delta).$ $$\\n\\nThen, we have for any estimator $\\\\widehat{T}$:\\n\\n$$ $\\\\max_{\\\\theta\\\\in\\\\mathbb{R}^{d}}\\\\mathbb{P}_{\\\\bm{X}}\\\\left\\\\{\\\\operatorname{W_{1}}( \\\\widehat{T}(\\\\bm{X}),\\\\mathcal{D}_{\\\\theta})\\\\geqslant c\\\\left(\\\\frac{\\\\log(1/\\\\delta) }{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4}\\\\right\\\\}\\\\geqslant\\\\frac{1}{2}$ $$\\n\\nwhere $\\\\bm{X}=\\\\{X_{i}\\\\}_{i=1}^{n}$ are independent random vectors with $X_{i}\\\\thicksim\\\\mathcal{D}_{\\\\theta}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)$.\\n\\n###### Proof.\\n\\nLet $u=e_{1}$ and $v=e_{2}$. Then, we have by Corollary D.7 for any $\\\\sigma\\\\geqslant 1$ and $s\\\\in[0,1]$:\\n\\n$$ $D_{\\\\mathrm{KL}}(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I)\\\\|\\\\mathcal{D}_{ sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma^{2}I))\\\\leqslant 2C\\\\left(\\\\frac{s}{\\\\sigma}\\\\right)^{4}.$ $$\\n\\nWe now have by the tensorization of the KL-divergence:\\n\\n$$ $D_{\\\\mathrm{KL}}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\prod_{i=1}^{n}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{ 2}I)\\\\right)\\\\\\\\ =\\\\sum_{i=1}^{n}D_{\\\\mathrm{KL}}\\\\left(\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I)\\\\right) \\\\leqslant Cs^{4}\\\\sum_{i=1}^{n}\\\\frac{1}{\\\\sigma_{i}^{4}}.$ $$\\n\\nNow, setting:\\n\\n$$ $s=c\\\\left(\\\\frac{\\\\log(1/\\\\delta)}{\\\\sum_{i=1}^{n}1/\\\\sigma_{i}^{4}}\\\\right)^{1/4},$ $$\\n\\nwe get:\\n\\n$$ $D_{\\\\mathrm{KL}}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{ i}^{2}I)\\\\bigg{\\\\|}\\\\prod_{i=1}^{n}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{ 2}I)\\\\right)\\\\leqslant\\\\frac{\\\\log(1/\\\\delta)}{8}.$ $$\\n\\nAgain, we get by the BH-inequality (Lemma D.1):\\n\\n$$ $\\\\operatorname{TV}\\\\left(\\\\prod_{i=1}^{n}\\\\mathcal{D}_{su}\\\\ast\\\\mathcal{N}(0,\\\\sigma _{i}^{2}I),\\\\prod_{i=1}^{n}\\\\mathcal{D}_{sv}\\\\ast\\\\mathcal{N}(0,\\\\sigma_{i}^{2}I) \\\\right)\\\\leqslant 1-\\\\delta.$ $$\\n\\nAn application of Le Cam’s method (Wainwright, , Lemma 15.9) concludes the proof of the result.\\n∎\\n\\nFinally, we combine the three bounds to prove the complete lower bound from Theorem 4.4.\\n\\n###### Proof of Theorem 4.4 .\\n\\nThe proof follows from Theorems D.5, D.8 and D.9 by choosing the largest out of the three lower bounds in the conclusions of the results.\\n∎\\n\\n###### Lemma D.6 .\\n\\n###### Corollary D.7 .\\n\\n###### Theorem D.8 .\\n\\n###### Proof.\\n\\n###### Theorem D.9 .\\n\\n###### Proof.\\n\\n###### Proof of Theorem 4.4 .\\n\\n## Appendix E Additional Results\\n\\nIn what follows, we present some additional results that did not fit in the main paper.\\n\\nFigure: Figure 3: Dataset images with varying noise levels ($\\\\sigma$).\\nRefer to caption: x2.png\\n\\nFigure: Figure 4: FID as a function of training steps for a model trained with a mix of clean and noisy data. FID continues to go down as we train more and more, indicating that the model at 200K iterations is still undertrained.\\nRefer to caption: x11.png\\n\\n## Appendix F Experimental Details\\n\\n### F.1 Training\\n\\nWe train our CIFAR-10 models for 200,000 steps, our CelebA models for 100,000 steps and our ImageNet models for $2,500,000$ steps. All of our images are normalized in $[-1,1]$ prior to adding additive Gaussian Noise. We use the training hyperparameters from the EDM codebase (Karras et al., ). For our experiments with consistency, we use $8$ steps for the reverse sampling and $32$ samples to estimate the expectations. We use a fixed coefficient to weight the consistency loss that is chosen as a hyperparameter from the set of $\\\\{0.1,1.0,10.0\\\\}$ to maximize performance. Upon acceptance of this work, we will provide all the code and checkpoints to accelerate research in this area. Consistency leads to a $2\\\\times$ increase in hardware requirements (memory footprint) and $2\\\\times$ (ImageNet) to $3\\\\times$ (CIFAR, CelebA) slowdown.\\n\\nAll our code and models are available in the following URL: [https://github.com/giannisdaras/ambient-laws](https://github.com/giannisdaras/ambient-laws).\\n\\n### F.2 Evaluation\\n\\nWe generate 50,000 images to compute FID. Each FID number reported in this paper is the average of three independent FID computations that correspond to the seeds: 0-49,999, 50,000-99,999, 100,000-149999.\",\n \"metadata\": {\n \"authors\": [\n \"Giannis Daras\",\n \"CSAIL\",\n \"MIT, IFML\",\n \"Yeshwanth Cherapanamjeri\",\n \"MIT\",\n \"Costantinos Daskalakis\"\n ],\n \"title\": \"How much is a noisy image worth? Data Scaling Laws for Ambient Diffusion.\",\n \"total_chars\": 155995,\n \"total_lines\": 1468,\n \"updated_at\": \"2026-01-25T15:02:53.088652\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"4FsSTwDBcu","initial_rating":6,"confidence":3,"soundness":3,"contribution":3,"presentation":3,"summary":"The paper investigates the impact of noisy data on (ambient) diffusion models. The paper shows that noisy data can be leveraged to improve the performance of diffusion models. In addition they provide the data regime where the noisy data are useful.","strengths":"- the paper is well written\n- the tackled problem is very interesting\n- experiments are exhaustive and convincing (Figure 1 shows the regime of interest for using noisy data)","weaknesses":"- I am not familiar with proof techniques for the mixture of Gaussian sample complexity, but I am not sure I understood the goal/take-away of Theorems 4.2-4.4. IMO much more discussion is needed here.\n- Lack of motivation: the tackled problem is overall very interesting, but I am not sure that the authors provided a concrete application where such new noisy data are available, and known as such.","questions":"- ¨For example, a blurry image might get dismissed from the filtering pipeline¨ Can authors provide a real example of such a filtering, i.e., a real filter used and a real discarded image?\n- \"For realistic sample sizes\" Do you have an order of magnitude of \"realistic sample size\" in your context?\n- Figure 1: in addition to training on noisy data, are other data augmentation techniques used? if not, do you know how new noisy data would compare against already existing standard data augmentation?\n\n\n- The heteroscedastic model: I do not understand how the proposed model in Definition 4.1 is a heteroscedastic mixture of Gaussian. As currently written in the paper, it feels that all the points of the distribution are convolved with the Gaussian noise (which is coherent with the proposed setting). Following Shah (2023), shouldn't a heteroscedastic mixture of Gaussian write $X_i \\sim \\\\mathcal{N}(\\mu_i, \\sigma_i)$.\nIn other words, IMO maths matches the setting, but I am not sure of the ¨heteroscedastic mixture of Gaussian¨ terminology.\n\n- Regarding the cost of the augmentation, are all models trained with the augmentation, do you confirm that all models are trained with the same budget? (i.e., with the same number of images seen, since the datasets are different) I guess yes since EDM code takes ¨million number of images¨ as input\n\n\nTheorem 4.2:\n- what are $c_1$ and $c_2$? Absolute constants as defined in Vershynin (2018)?\n- \"Discussion\" I did not understand the discussion after Theorem 4.2, could you elaborate on the \"error in estimating the low-dimensional sub-space\" and the \"low-dimensional estimation procedures\"\n- \"Then, there is a procedure which when given n independent ....\" could you give a word on the procedure?\n\n- Algorithm 1: is the noise level of each sample require in Algorithm 1?"},{"id":"N2ABe9tw9u","initial_rating":5,"confidence":2,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper studies data scaling laws for ambient diffusion. The authors find that training on a small set of clean data and a large set of noisy data significantly outperforms training solely on either one of these sets. The paper provides both theoretical analysis and empirical results to verify their findings.","strengths":"1. The studied problem is interesting and important.\n2. The authors provide theoretical results to support their findings.","weaknesses":"1. I'm a bit confused about the relationship between thm 4.2 and alg 1. The thm 4.2 states that there exists a procedure which can return a good estimate of D. Is Algorithm 1 the procedure referenced in this theorem?\n2. Alg 1 need to know whether each data is clean or noisy. Is it possible to generalize the proposed algorithm to handle cases where clean and noisy data are mixed?\n3. In the experiments, The paper only presents the empirical results of the proposed method and does not compare it with previous work. (Daras et al., 2024; 2023b).","questions":"see weakness"},{"id":"l7W7fHy7UY","initial_rating":8,"confidence":3,"soundness":4,"contribution":3,"presentation":3,"summary":"Quick summary: This paper studies the performance of the diffusion model in the ambient diffusion scenario. Previous work shows that the diffusion model trained by noisy data is inferior to the model trained on clean data, and the consistent diffusion model requires the noisy samples to be infinity from the asymptotic view. This paper proposes to use the mixture of clean data (high-frequency feature) and corrupted data (low-frequency feature) to assist the ambient diffusion model to obtain a very close performance to the state-of-the-art and provide the theoretic analysis to support the experiment and evaluate the corresponding value of noise image using the inspiring sampling bounds from the theoretical results.\nQuality: The paper is well-written and well-motivated, and the proposed method is good with a theoretical foundation albeit a bit simple.\nOriginality: The theoretical analysis of the two sampling bounds is inspiring with practical meaning. \nSignificance: This is an important research direction because noise data is common in the real world.\nPros: * Important problem * theoretical foundation * nice results and sufficient experiments\nCons: * The solution is a bit simple and kind of engineering consideration. \nSummary: This is a nice paper that gives a simple solution to the ambient diffusion models with theoretic analysis and while not groundbreaking, certainly merits a publication.","strengths":"The theoretical analysis of the two sampling bounds is inspiring with practical meaning.","weaknesses":"The solution is a bit simple and kind of engineering consideration.","questions":"What's the exact number of samples or dimensions in your settings in line 93, page 2?"},{"id":"IB58uNafYK","initial_rating":8,"confidence":3,"soundness":3,"contribution":4,"presentation":3,"summary":"First, the paper empirically shows that training on entire noisy data will lead to bad performance, but as long as a few clean data (~10%) are available, models trained by the proposed algorithm are comparable to models trained on clean data. Second, the paper derives minimax optimal estimation bounds to explain the phenomenon. Third, the paper pinpoints the price of noisy images for different datasets and noise levels, which has practical implications.","strengths":"1. The paper is written clearly.\n2. In practice, we have small sets of clean data and large sets of noisy data, so the paper considers an important setting.\n3. The experiments on different realistic image datasets are sufficient to support the claim in the paper.\n4. The established estimation bounds are minimax optimal and discussed clearly. \n5. The price of noisy images is interesting.","weaknesses":"1. The obtained $\\hat{D}$ is the ERM result for the Wasserstein distance loss, which is mismatched with the loss of diffusion models. Thus, there exists a gap between theory and practice.\n2. The proposed algorithm and proof technique are mainly based on existing works, which may decrease the novelty of this paper.","questions":"1. How can we know the value $\\sigma_{t_n}$ in the inputs of Algorithm 1?"},{"id":"l7rTrHkltw","initial_rating":6,"confidence":3,"soundness":3,"contribution":3,"presentation":4,"summary":"This paper tackles a critical issue in training diffusion models with corrupted data when clean data is scarce or costly. The authors explore the effectiveness of a combination of a small clean dataset and a large noisy dataset, demonstrating that this approach can yield performance close to models trained solely on clean data. Theoretical analysis based on Gaussian Mixture Models (GMMs) with heterogeneous variances and experimental validation across multiple datasets support these claims. Additionally, the paper proposes a budget allocation mechanism for more efficient dataset curation by balancing the use of noisy and clean data.","strengths":"* The paper is well-written and logically structured, making the content easy to follow.\n* The theoretical analysis is rigorous and provides good intuition behind the proposed methods. The experiments are thorough, involving the training of more than 80 models across various datasets and noise levels.\n* The paper’s conclusions offer significant practical value for dataset curation and budget allocation strategies in real-world applications, where collecting clean data can be expensive.","weaknesses":"* The analysis is limited to Gaussian noise corruption and discrete distributions with finite support. Expanding this framework to continuous distributions and non-Gaussian noise would increase its impact.\n* The proposed method assumes that the noise level is known in advance, which may not be the case in real-world scenarios. Incorporating techniques and analysis to handle unknown noise levels would make the approach more practical.","questions":"It remains unclear why an exponentially larger amount of corrupted data is necessary to compensate for the lack of clean data. Can the authors provide more clarification for this point?"}],"string":"[\n {\n \"id\": \"4FsSTwDBcu\",\n \"initial_rating\": 6,\n \"confidence\": 3,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"The paper investigates the impact of noisy data on (ambient) diffusion models. The paper shows that noisy data can be leveraged to improve the performance of diffusion models. In addition they provide the data regime where the noisy data are useful.\",\n \"strengths\": \"- the paper is well written\\n- the tackled problem is very interesting\\n- experiments are exhaustive and convincing (Figure 1 shows the regime of interest for using noisy data)\",\n \"weaknesses\": \"- I am not familiar with proof techniques for the mixture of Gaussian sample complexity, but I am not sure I understood the goal/take-away of Theorems 4.2-4.4. IMO much more discussion is needed here.\\n- Lack of motivation: the tackled problem is overall very interesting, but I am not sure that the authors provided a concrete application where such new noisy data are available, and known as such.\",\n \"questions\": \"- ¨For example, a blurry image might get dismissed from the filtering pipeline¨ Can authors provide a real example of such a filtering, i.e., a real filter used and a real discarded image?\\n- \\\"For realistic sample sizes\\\" Do you have an order of magnitude of \\\"realistic sample size\\\" in your context?\\n- Figure 1: in addition to training on noisy data, are other data augmentation techniques used? if not, do you know how new noisy data would compare against already existing standard data augmentation?\\n\\n\\n- The heteroscedastic model: I do not understand how the proposed model in Definition 4.1 is a heteroscedastic mixture of Gaussian. As currently written in the paper, it feels that all the points of the distribution are convolved with the Gaussian noise (which is coherent with the proposed setting). Following Shah (2023), shouldn't a heteroscedastic mixture of Gaussian write $X_i \\\\sim \\\\\\\\mathcal{N}(\\\\mu_i, \\\\sigma_i)$.\\nIn other words, IMO maths matches the setting, but I am not sure of the ¨heteroscedastic mixture of Gaussian¨ terminology.\\n\\n- Regarding the cost of the augmentation, are all models trained with the augmentation, do you confirm that all models are trained with the same budget? (i.e., with the same number of images seen, since the datasets are different) I guess yes since EDM code takes ¨million number of images¨ as input\\n\\n\\nTheorem 4.2:\\n- what are $c_1$ and $c_2$? Absolute constants as defined in Vershynin (2018)?\\n- \\\"Discussion\\\" I did not understand the discussion after Theorem 4.2, could you elaborate on the \\\"error in estimating the low-dimensional sub-space\\\" and the \\\"low-dimensional estimation procedures\\\"\\n- \\\"Then, there is a procedure which when given n independent ....\\\" could you give a word on the procedure?\\n\\n- Algorithm 1: is the noise level of each sample require in Algorithm 1?\"\n },\n {\n \"id\": \"N2ABe9tw9u\",\n \"initial_rating\": 5,\n \"confidence\": 2,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper studies data scaling laws for ambient diffusion. The authors find that training on a small set of clean data and a large set of noisy data significantly outperforms training solely on either one of these sets. The paper provides both theoretical analysis and empirical results to verify their findings.\",\n \"strengths\": \"1. The studied problem is interesting and important.\\n2. The authors provide theoretical results to support their findings.\",\n \"weaknesses\": \"1. I'm a bit confused about the relationship between thm 4.2 and alg 1. The thm 4.2 states that there exists a procedure which can return a good estimate of D. Is Algorithm 1 the procedure referenced in this theorem?\\n2. Alg 1 need to know whether each data is clean or noisy. Is it possible to generalize the proposed algorithm to handle cases where clean and noisy data are mixed?\\n3. In the experiments, The paper only presents the empirical results of the proposed method and does not compare it with previous work. (Daras et al., 2024; 2023b).\",\n \"questions\": \"see weakness\"\n },\n {\n \"id\": \"l7W7fHy7UY\",\n \"initial_rating\": 8,\n \"confidence\": 3,\n \"soundness\": 4,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"Quick summary: This paper studies the performance of the diffusion model in the ambient diffusion scenario. Previous work shows that the diffusion model trained by noisy data is inferior to the model trained on clean data, and the consistent diffusion model requires the noisy samples to be infinity from the asymptotic view. This paper proposes to use the mixture of clean data (high-frequency feature) and corrupted data (low-frequency feature) to assist the ambient diffusion model to obtain a very close performance to the state-of-the-art and provide the theoretic analysis to support the experiment and evaluate the corresponding value of noise image using the inspiring sampling bounds from the theoretical results.\\nQuality: The paper is well-written and well-motivated, and the proposed method is good with a theoretical foundation albeit a bit simple.\\nOriginality: The theoretical analysis of the two sampling bounds is inspiring with practical meaning. \\nSignificance: This is an important research direction because noise data is common in the real world.\\nPros: * Important problem * theoretical foundation * nice results and sufficient experiments\\nCons: * The solution is a bit simple and kind of engineering consideration. \\nSummary: This is a nice paper that gives a simple solution to the ambient diffusion models with theoretic analysis and while not groundbreaking, certainly merits a publication.\",\n \"strengths\": \"The theoretical analysis of the two sampling bounds is inspiring with practical meaning.\",\n \"weaknesses\": \"The solution is a bit simple and kind of engineering consideration.\",\n \"questions\": \"What's the exact number of samples or dimensions in your settings in line 93, page 2?\"\n },\n {\n \"id\": \"IB58uNafYK\",\n \"initial_rating\": 8,\n \"confidence\": 3,\n \"soundness\": 3,\n \"contribution\": 4,\n \"presentation\": 3,\n \"summary\": \"First, the paper empirically shows that training on entire noisy data will lead to bad performance, but as long as a few clean data (~10%) are available, models trained by the proposed algorithm are comparable to models trained on clean data. Second, the paper derives minimax optimal estimation bounds to explain the phenomenon. Third, the paper pinpoints the price of noisy images for different datasets and noise levels, which has practical implications.\",\n \"strengths\": \"1. The paper is written clearly.\\n2. In practice, we have small sets of clean data and large sets of noisy data, so the paper considers an important setting.\\n3. The experiments on different realistic image datasets are sufficient to support the claim in the paper.\\n4. The established estimation bounds are minimax optimal and discussed clearly. \\n5. The price of noisy images is interesting.\",\n \"weaknesses\": \"1. The obtained $\\\\hat{D}$ is the ERM result for the Wasserstein distance loss, which is mismatched with the loss of diffusion models. Thus, there exists a gap between theory and practice.\\n2. The proposed algorithm and proof technique are mainly based on existing works, which may decrease the novelty of this paper.\",\n \"questions\": \"1. How can we know the value $\\\\sigma_{t_n}$ in the inputs of Algorithm 1?\"\n },\n {\n \"id\": \"l7rTrHkltw\",\n \"initial_rating\": 6,\n \"confidence\": 3,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 4,\n \"summary\": \"This paper tackles a critical issue in training diffusion models with corrupted data when clean data is scarce or costly. The authors explore the effectiveness of a combination of a small clean dataset and a large noisy dataset, demonstrating that this approach can yield performance close to models trained solely on clean data. Theoretical analysis based on Gaussian Mixture Models (GMMs) with heterogeneous variances and experimental validation across multiple datasets support these claims. Additionally, the paper proposes a budget allocation mechanism for more efficient dataset curation by balancing the use of noisy and clean data.\",\n \"strengths\": \"* The paper is well-written and logically structured, making the content easy to follow.\\n* The theoretical analysis is rigorous and provides good intuition behind the proposed methods. The experiments are thorough, involving the training of more than 80 models across various datasets and noise levels.\\n* The paper’s conclusions offer significant practical value for dataset curation and budget allocation strategies in real-world applications, where collecting clean data can be expensive.\",\n \"weaknesses\": \"* The analysis is limited to Gaussian noise corruption and discrete distributions with finite support. Expanding this framework to continuous distributions and non-Gaussian noise would increase its impact.\\n* The proposed method assumes that the noise level is known in advance, which may not be the case in real-world scenarios. Incorporating techniques and analysis to handle unknown noise levels would make the approach more practical.\",\n \"questions\": \"It remains unclear why an exponentially larger amount of corrupted data is necessary to compensate for the lack of clean data. Can the authors provide more clarification for this point?\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"5;6;6;8;8\",\n \"rating_avg\": 6.6,\n \"confidence\": \"2;3;3;3;3\",\n \"confidence_avg\": 2.8,\n \"soundness\": \"2;3;3;3;4\",\n \"soundness_avg\": 3,\n \"contribution\": \"2;3;3;4;3\",\n \"contribution_avg\": 3,\n \"presentation\": \"3;4;3;3;3\",\n \"presentation_avg\": 3.2\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"ICLR 2025 Poster\",\n \"venueid\": \"ICLR.cc/2025/Conference\",\n \"processed_at\": \"2026-01-14T22:16:03.716901\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"DxFFYZ6kUr\",\n \"metareview\": \"The paper explores the challenge of training generative models when access to large-scale, high-quality datasets is limited. The authors demonstrate that a small subset of clean data (e.g., 10% of the total dataset) combined with a larger set of highly noisy data is sufficient to achieve performance comparable to models trained solely on similar-sized clean datasets, reaching near state-of-the-art results. To support these findings, the paper provides theoretical evidence through novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. The theoretical analysis reveals that, for sufficiently large datasets, the effective marginal utility of a noisy sample is exponentially lower than that of a clean sample. This insight is further corroborated by experiments showing that a small clean subset significantly reduces the sample size requirements for noisy data.\\n\\n\\nPros:\\n+ Important Problem Setting: The paper addresses the practical challenge of training diffusion models with noisy data, which is common in real-world applications.\\n+ Combination of Theory and Empirical Results: The work provides theoretical insights into sample complexity for Gaussian Mixture Models (GMMs) with heterogeneous variances, alongside extensive experiments demonstrating the effectiveness of using a small clean subset with a large noisy dataset.\\n+ Clear Presentation: The paper is well-written and logically structured, making the arguments and findings easy to follow.\\n+ Practical Utility: The findings offer significant implications for dataset curation strategies, balancing the use of noisy and clean data to achieve near state-of-the-art results.\\n+ Thorough Experiments: The study involves training over 80 models across datasets of varying noise levels, providing empirical validation of the claims.\\n\\nCons:\\n- Limited Novelty: The proposed algorithm and proof techniques are largely based on existing works, which raises questions about the paper's novelty.\\n- Narrow Scope of Analysis: The theoretical analysis is restricted to Gaussian noise and discrete distributions with finite support, limiting the applicability to more general noise models or continuous distributions.\\n- Gap Between Theory and Practice: The theoretical results focus on the Wasserstein loss, which does not perfectly align with the actual loss used in diffusion models, creating a disconnect between theory and implementation.\\n- Assumption of Known Noise Levels: The proposed method assumes that the noise level is known, which may not hold in practical scenarios. Addressing unknown noise levels would improve the method’s applicability.\\n- Simplistic Solution: While effective, the proposed solution is considered by some reviewers as overly simple and primarily engineering-driven.\\n\\nAfter the revision as discussed below all reviewers recommend acceptance. I concur.\",\n \"additional_comments\": \"The discussion primarily revolved around the following points:\\n\\n- Theoretical Contributions: Some reviewers raised concerns about the clarity and novelty of the theoretical results (Theorems 4.2–4.4). The authors clarified their significance and addressed ambiguities but acknowledged that they rely on existing techniques.\\n\\n- Real-World Applications: Reviewers asked for concrete examples of where noisy data might arise and how it could be leveraged. The authors provided examples from protein design and experimental imaging methods, strengthening the paper's practical motivation.\\n\\n- Experimental Comparisons: A few reviewers highlighted the lack of comparisons with previous works (e.g., Daras et al.). The authors argued that their method generalizes earlier work by introducing clean data into the mix, demonstrating superior performance.\\n\\n- Noise Level Assumptions: The assumption of known noise levels was questioned. The authors responded that noise levels can be estimated, but reviewers suggested incorporating this into the theoretical analysis.\\n\\nThe discussion led to a slight convergence of opinions, with some reviewers increasing their scores and all reviewers recommending acceptance.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Accept (Poster)\"\n}"}}},{"rowIdx":3398,"cells":{"paper_id":{"kind":"string","value":"qazJfAmgOt"},"arxiv_id":{"kind":"string","value":"2410.10922v1"},"title":{"kind":"string","value":"A few-shot Label Unlearning in Vertical Federated Learning"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract This paper addresses the critical challenge of unlearning in Vertical Federated Learning (VFL), an area that has received limited attention compared to horizontal federated learning. We introduce the first approach specifically designed to tackle label unlearning in VFL, focusing on scenarios where the active party aims to mitigate the risk of label leakage. Our method leverages a limited amount of labeled data, utilizing manifold mixup to augment the forward embedding of insufficient data, followed by gradient ascent on the augmented embeddings to erase label information from the models. This combination of augmentation and gradient ascent enables high unlearning effectiveness while maintaining efficiency, completing the unlearning procedure within seconds. Extensive experiments conducted on diverse datasets, including MNIST, CIFAR10, CIFAR100, and ModelNet, validate the efficacy and scalability of our approach. This work represents a significant advancement in federated learning, addressing the unique challenges of unlearning in VFL while preserving both privacy and computational efficiency.\\n\\n## 1 Introduction\\n\\nFigure: Figure 1: Illustration of risk of label leakage in vertical federated unlearning.\\nRefer to caption: x1.png\\n\\nVertical Federated Learning (VFL) (Yang et al., ) allows multiple organizations to collaboratively utilize their private datasets in a privacy-preserving manner, even when they share some sample IDs but differ significantly in terms of features. In VFL, there are typically two types of parties: (i) the passive party, which holds the features, and (ii) the active party, which possesses the labels. VFL has seen widespread application, especially in sensitive domains like banking, healthcare, and e-commerce, where organizations benefit from joint modeling without exposing their raw data (Yang et al., ; Li et al., ).\\n\\nA fundamental requirement in Vertical Federated Learning (VFL) is the necessity for unlearning, which is driven by participants’ ”right to be forgotten” as mandated by regulations such as the General Data Protection Regulation (GDPR)(^1^11[https://gdpr-info.eu/art-17-gdpr/](https://gdpr-info.eu/art-17-gdpr/)) and the California Consumer Privacy Act (CCPA)(^2^22[https://oag.ca.gov/privacy/ccpa](https://oag.ca.gov/privacy/ccpa)). While unlearning has been explored in the context of Horizontal Federated Learning (HFL), there has been limited attention to its application in vertical settings. Existing studies on vertical federated unlearning (Zhang et al., ; Wang et al., ; Deng et al., ) primarily focus on the unlearning process for individual clients, often addressing the removal of all features from the passive party upon their exit. In contrast, this paper emphasizes the unlearning of labels, which is a critical aspect in VFL, particularly in scenarios such as Credit Risk Assessment where the determination of a loan applicant’s likelihood of default is essential. Moreover, the active party aims to eliminate label information not only from the active model but also from the passive models, as the passive models may retain label information (Fu et al., ).\\n\\nA significant challenge in directly applying traditional machine unlearning methods, such as retraining (Bourtoule et al., ; Foster et al., ) or Boundary unlearning (Chen et al., ), in this context pose a risk of leaking unlearned labels during the unlearning process. Typically, the active party, which retains the labels, must either inform the passive party about the samples that require unlearning or transfer the gradients associated with the unlearned label. This practice may inadvertently expose sensitive label information to the passive party (see Figure 1 and Sect. 3.2).\\n\\nTo address this challenge, we propose a few-shot unlearning method that effectively erases labels from both the active model and passive model in vertical federated learning by leveraging a limited amount of private data (see Sect. 4). Specifically, our method employs manifold mixup (Verma et al., ) to augment the forward embeddings of each passive party. The active party then performs gradient ascent on the mixed embeddings to unlearn the active model and subsequently transfers the inverse gradients to the passive party to facilitate the unlearning of the passive model independently. This approach offers three key advantages: first, it necessitates only labels from a small amount of private data, significantly reducing the risk of label privacy leakage; second, by utilizing the manifold mixup technique, it enhances unlearning effectiveness with minimal data; and third, it is highly efficient, completing the unlearning process within seconds. The primary contributions of this work are as follows:\\n\\n- 1.\\nTo the best of our knowledge, this is the first work to address the unlearning of labels in vertical federated learning.\\n- 2.\\nWe systematically elucidate the label privacy leakage that may occur when directly applying traditional machine unlearning methods in Sect. 3.2.\\n- 3.\\nWe propose a few-shot label unlearning method that effectively erases labels from both the active and passive models in vertical federated learning, utilizing a limited amount of private data. Moreover, this approach leverages only a small number of data to mitigate the risk of label privacy leakage while employing manifold mixup to enhance unlearning effectiveness.\\n- 4.\\nWe conduct extensive experiments on multiple benchmark datasets, including MNIST, CIFAR-10, CIFAR-100, and ModelNet, demonstrating that our method rapidly and effectively unlearns target labels compared to other machine unlearning methods.\\n\\n## 2 Related Works\\n\\n##### Machine Unlearning & Horizontal Federated Unlearning.\\n\\nMachine unlearning was initially introduced by (Cao & Yang, ) to selectively remove some data from model without retrain the model from scratch (Garg et al., ; Chen et al., ). Machine unlearning can be categorized into exact unlearning and approximate unlearning. Exact unlearning methods such as SISA (Bourtoule et al., ) and ARCANE (Yan et al., ) split data into sections and train sub-models for each data section and merge all sub-models. During unlearning, retrain the affected data section and merge all sub-models again. In approximate unlearning, techniques such as fine tuning(Golatkar et al., ; Jia et al., ) (fine tune with $\\\\mathcal{D}_{r}$), random label(Graves et al., ; Chen et al., ) (fine tune with incorrect random label of $\\\\mathcal{D}_{u}$), noise introducing(Tarun et al., ; Huang et al., ), gradient ascent(Goel et al., ; Choi & Na, ; Abbasi et al., ; Hoang et al., ; Golatkar et al., )(maximise loss associate with $\\\\mathcal{D}_{u}$), knowledge distillation(Chundawat et al., ; Zhang et al., ; Kurmanji et al., ) (train a student model) and weights scrubbing (Golatkar et al., ; ; ; Guo et al., ; Foster et al., ) (discarding heavily influenced weights) are used.\\n\\nMost of the existing research works in federated unlearning are horizontal federated unlearning (Wu et al., ; Gu et al., ; Zhao et al., ; Romandini et al., ; Liu et al., ; Zhang et al., ; Su & Li, ; Ye et al., ; Gao et al., ; Cao et al., ; Yuan et al., ; Alam et al., ; Li et al., ; Halimi et al., ; Xia et al., ; Wang et al., ; Dhasade et al., ; Liu et al., ; Zhao et al., ; Wang et al., ; Gu et al., ). Only these three research works focus in vertical federated unlearning (Zhang et al., ; Wang et al., ; Deng et al., ). (Zhang et al., ) introduce vertical federated unlearning in gradient boosting tree. (Wang et al., ) introduce passive party unlearning on deep learning model with fast retraining on remaining parties. (Deng et al., ) introduce passive party unlearning on logistic regression model.\\n\\nExisting literature on VFU primarily focus on passive parties unlearning (Zhang et al., ; Wang et al., ; Deng et al., ). Significant gap arise when active party seek for a collaboration from passive parties for a single class unlearning while all parties remaining engaged in VFL. Unfortunately, current VFU approaches do not address this specific scenario, as they do not explore class unlearning within VFL setting. In contrast to prior works focusing on class unlearning in centralise machine unlearning and horizontal federated unlearning settings, this study uniquely addresses class unlearning of classification model within the VFL paradigm. This distinction arises because traditional class unlearning methods in centralised and HFL setting are impractical for VFL settings, where all parties have different features of data and different computational power.\\n\\n##### Vertical Federated Learning & Privacy Leakage\\n\\nVertical Federated Learning (VFL) is introduced to meet the needs of enterprises looking to utilize features distributed across multiple parties for improved model performance, compared to models trained by a single entity, all while preserving data privacy (Yang et al., ). In VFL, privacy is of utmost importance because the participants are typically companies that handle valuable and sensitive user information. Hence, privacy protection during VFU is also an important criteria. We explain the risk of label leakage during VFU in section 3.2.\\n\\n## 3 Label Leakage during Vertical Federated Unlearning\\n\\nThis section illustrates the risk of label during the label unlearning process.\\n\\n### 3.1 General Setup\\n\\nVFL Training.\\nWe assume that a vertical federated learning setting consists of one active party $P_{0}$ and $K$ passive parties $\\\\{P_{1},\\\\cdots,P_{K}\\\\}$ who collaboratively train a VFL model $\\\\Theta=(\\\\theta,\\\\omega)$ to optimize the following objective:\\n\\n$$ $\\\\begin{split}\\\\min_{\\\\omega,\\\\theta_{1},\\\\cdots,\\\\theta_{K}}&\\\\frac{1}{n}\\\\sum_{i=1}^ {n}\\\\ell(F_{\\\\omega}\\\\circ(G_{\\\\theta_{1}}(x_{1,i}),G_{\\\\theta_{2}}(x_{2,i}),\\\\\\\\ &\\\\cdots,G_{\\\\theta_{K}}(x_{K,i})),y_{i}),\\\\end{split}$ (1) $$\\n\\nin which Party $P_{k}$ owns features $\\\\mathbf{x}_{k}=(x_{k,1},\\\\cdots,x_{k,n})$ and the passive model $G_{\\\\theta_{k}}$, the active party owns the labels $\\\\mathbf{y}=\\\\{y_{1},\\\\cdots,y_{m}\\\\}$ and active model $F_{\\\\omega}$. Each passive party $k$ transfers its forward embedding $H_{k}$ to the active party to compute the loss. The active model $F_{\\\\omega}$ and passive models $G_{\\\\theta_{k}},k\\\\in\\\\{1,\\\\dots,K\\\\}$ are trained based on backward gradients. Note that, before training, all parties leverage Private Set Intersection (PSI) protocols to align data records with the same IDs.\\n\\nUnlearning Label in VFL.\\nWhen the active party requests to unlearn some sensitive labels $\\\\mathbf{y}^{u}$, where the corresponding feature is $\\\\{\\\\mathbf{x}^{u}_{k}\\\\}_{k=1}^{K}:=\\\\{\\\\{x_{k,i}^{u}\\\\}_{i=1}^{n_{u}}\\\\}_{k=1}^{K}$. The active party aims to remove the influence of $\\\\mathbf{y}^{u}$ on both the active model $F_{\\\\omega}$ and $K$ passive models $\\\\{G_{\\\\theta_{k}}\\\\}_{k=1}^{K}$.\\n\\nThreat Model.\\nWe assume all participating parties are semi-honest and do not collude with each other. An adversary (i.e., the passive party) faithfully executes the training protocol but may launch privacy attacks to infer the private labels of the active party.\\n\\nAssumption.\\nWe assume that the passive party possesses corresponding labels for a limited number of features, defined as $\\\\mathcal{D}^{p}=\\\\{(\\\\mathbf{x}_{k}^{p},\\\\mathbf{y}^{p})\\\\}_{k=1}^{K}=\\\\{\\\\{(x_{k,i}\\n^{p},y_{i})\\\\}_{i=1}^{n_{p}}\\\\}_{k=1}^{K}$, where $n_{p}<<n_{u}$. This assumption is reasonable, as the active party must convey some label information to the passive party in order to effectively remove that information. Furthermore, this assumption is widely employed in prior works (Fu et al., ; Gu et al., ; Zou et al., ).\\n\\nFigure: Figure 2: Illustration of label leakage accuracy during Boundary unlearning in VFL in ResNet18 model with different number of classes.\\nRefer to caption: x2.png\\n\\n### 3.2 Label leakage during unlearning\\n\\nTo remove the influence of the passive models $\\\\{G_{\\\\theta_{k}}\\\\}_{k=1}^{K}$, there exists a risk of unlearning label leakage ($\\\\mathbf{y}_{u}=\\\\{y_{1}^{u},\\\\ldots,y_{m_{u}}^{u}\\\\}$)\\nto the passive parties. During the unlearning process, the active party is required to transfer information to the passive party, e.g., gradients $\\\\mathbf{g}_{u}=\\\\{g_{1}^{u},\\\\ldots,g_{n_{u}}^{u}\\\\}$, in order to effectively unlearn the label associated with the passive model. Consequently, the passive party may infer the label based on this information.\\n\\nIn particular, when unlearning a single class $y_{u,1}$, we consider two representative unlearning methods: retraining (Foster et al., ) and Boundary unlearning (Chen et al., ). For retraining methods, the active party must inform the passive party regarding which features do not require training, thus, the label is leaked. In the case of Boundary unlearning, the gradients transferred to the passive party correspond to the features associated with the label $y_{u,1}$ may leak the label.\\n\\nFurthermore, when multiple labels ($m_{u}$) are targeted for unlearning, we consider the Boundary unlearning as an example. This method illustrates that the passive party can infer label information from the gradients $\\\\mathbf{g}_{u}$ transmitted by the active party during the unlearning process. Specifically, the passive party employs clustering on $\\\\mathbf{g}_{u}$ to derive $m_{u}$ clusters by optimizing the following objective function:\\n\\n$$ $\\\\min\\\\sum_{g_{i}\\\\in\\\\mathcal{C}_{j}}\\\\sum_{j=1}^{m_{u}}|g_{u,i}-\\\\bar{g}_{u,j}|,$ (2) $$\\n\\nwhere $\\\\mathcal{C}_{j}$ denotes the set of points assigned to cluster $j$, and $\\\\bar{g}_{u,j}$ represents the centroid of cluster $j$. Consequently, the passive party can deduce the labels of the features in $\\\\mathcal{X}$. Figure 2 presents the label leakage accuracy during unlearning in vertical federated learning for varying numbers of unlearning classes. For instance, even with four classes from CIFAR-100, the passive party achieves a clustering accuracy of 62.45%.\\n\\nFigure: Figure 3: Overview of our proposed VFU framework.\\nRefer to caption: x3.png\\n\\n## 4 The Proposed few-shot label unlearning methods\\n\\nThis section introduces the proposed methods few-shot label unlearning methods, utilizing a limited amount of labeled data. Figure 3 shows the overview of our proposed solution. The methods comprise two primary steps: first, augmenting the forward embedding through manifold mixup to address the scarcity of labeled data for unlearning, as discussed in Section 4.1. Second, employing gradient ascent on the augmented embedding to influence both the passive and active models, thereby facilitating the removal of the specified class, as elaborated in Section 4.2.\\n\\n### 4.1 Vertical Manifold Mixup\\n\\nDue to the label privacy leakage described in Section 3.2, directly applying traditional machine unlearning methods poses challenges. We assume that the active party discloses a limited number of labels to the passive party to facilitate the unlearning of a specific class. However, this small labeled dataset, denoted as $\\\\mathcal{D}_{p}$, is insufficient for effective unlearning (see Appendix). Consequently, this scenario can be framed as a few-shot unlearning problem, wherein a minimal set of labels is employed to unlearn all associated labels.\\n\\nFigure: Algorithm 1 Our Method\\n\\nDrawing inspiration from few-shot learning principles, we adopt the manifold mixup mechanism (Verma et al., ) by interpolating hidden embeddings rather than directly mixing the features. We propose a manifold mixup framework for Vertical Federated Learning (VFL) by optimizing the following loss function:\\n\\n$$ $\\\\begin{split}&\\\\min_{\\\\omega,\\\\theta_{1},\\\\cdots,\\\\theta_{K}}\\\\frac{1}{n_{p}^{2}} \\\\sum_{i,j=1}^{n_{p}}\\\\ell(F_{\\\\omega}\\\\circ(\\\\text{Mix}_{\\\\lambda}(G_{\\\\theta_{1}}(x _{1,i}^{p}),G_{\\\\theta_{1}}(x_{1,j}^{p})),\\\\\\\\ &\\\\quad\\\\cdots,\\\\text{Mix}_{\\\\lambda}(G_{\\\\theta_{K}}(x_{K,i}^{p}),G_{\\\\theta_{K}}(x _{K,j}^{p})),\\\\text{Mix}_{\\\\lambda}(y_{i}^{p},y_{j}^{p})),\\\\end{split}$ $$\\n\\nwhere\\n\\n$$ $\\\\text{Mix}_{\\\\lambda}(a,b)=\\\\lambda\\\\cdot a+(1-\\\\lambda)\\\\cdot b.$ (3) $$\\n\\nThe mixed coefficient $\\\\lambda$ ranges from 0 to 1. The advantage of the manifold mixup approach lies in its ability to flatten the state distributions (Verma et al., ). Specifically, for each passive party $k$, mixup is applied to the forward embeddings $\\\\{{H}^{p}_{k}=G_{\\\\theta}(x_{k,i}^{p})\\\\}$ to generate numerous mixed embeddings $H_{k}^{\\\\prime}$. Subsequently, all passive parties transfer their respective mixed embeddings $H_{k}^{\\\\prime}$ to the active party.\\n\\n### 4.2 Vertical Label Unlearning via Gradient Ascent\\n\\nOnce the augmented embeddings $\\\\{H_{1}^{\\\\prime},\\\\ldots,H_{K}^{\\\\prime}\\\\}$ for the representative unlearned data $\\\\mathcal{D}_{p}$ (label is known) are generated, a straightforward yet effective strategy is to implement gradient ascent for both the active and passive models using these augmented embeddings. Specifically, the active party concatenates all embeddings $\\\\{H_{k}^{\\\\prime}\\\\}_{k=1}^{K}$ into a single tensor $H^{\\\\prime}=[H_{1}^{\\\\prime},\\\\ldots,H_{K}^{\\\\prime}]$, and optimizes it according to the following formulation:\\n\\n$$ $\\\\min_{\\\\omega}\\\\ell(F_{\\\\omega}(H^{\\\\prime}),y^{\\\\prime})=\\\\ell(F_{\\\\omega}([H_{1}^{ \\\\prime},\\\\ldots,H_{K}^{\\\\prime}]),y^{\\\\prime}),$ (4) $$\\n\\nwhere $y^{\\\\prime}$ represents the mixture of the representative unlearned labels and $\\\\eta$ is the learning rate.\\n\\nUnlearning for active model $F_{\\\\omega}$. On one hand, the active model undergoes unlearning for active model $F_{\\\\omega}$ via gradient ascent as follows:\\n\\n$$ $\\\\omega=\\\\omega+\\\\eta\\\\nabla_{\\\\omega}\\\\ell(F_{\\\\omega}(H^{\\\\prime}),y^{\\\\prime}).$ (5) $$\\n\\nUnlearning for passive model $G_{\\\\omega_{k}}$. Subsequently, the active party computes the gradients $g_{k}^{\\\\prime}=\\\\frac{\\\\partial\\\\ell}{\\\\partial H_{k}^{\\\\prime}}$ in accordance with equation 4 and transmits these gradients to the corresponding passive party $k$. Finally, the passive party $k$ updates the passive model $G_{\\\\theta_{k}}$ using the following expression:\\n\\n$$ $\\\\theta_{k}=\\\\theta_{k}+\\\\eta\\\\nabla_{H_{k}^{\\\\prime}}\\\\ell(F_{\\\\omega}(H^{\\\\prime}),y ^{\\\\prime})\\\\cdot\\\\nabla_{\\\\theta_{k}}H_{k}^{\\\\prime}.$ (6) $$\\n\\nIt is important to note that gradient ascent may lead to significant degradation in model utility or even result in vanishing gradients if the parameters are not appropriately tuned. Therefore, employing a small learning rate $\\\\eta$ and a limited number of unlearning epochs can mitigate these issues while achieving effective unlearning results (see experimental details in Appendix A).\\n\\n## 5 Experimental Result\\n\\nThis section presents the empirical analysis of the proposed method in terms of utility, unlearning effectiveness, time efficiency and some ablation studies.\\n\\n### 5.1 Experiment Setup\\n\\n##### Unlearning Scenarios\\n\\nSingle-class unlearning: We forget a single class from all datasets. Two-classes unlearning: We forget two classes from CIFAR10 and CIFAR100. Multi-classes unlearning: We forget four classes from CIFAR100.\\n\\n##### VFL Setting & Datasets & Models\\n\\nWe stimulate a VFL scenario by splitting a neural network into two bottom models and a top model and assigning the two bottom models to each two passive parties and the top model to the active party. We conduct experiments on four datasets: MNIST(Lecun et al., ), CIFAR10, CIFAR100(Krizhevsky et al., ) and ModelNet(Wu et al., ). We adopt Resnet18(He et al., ) on dataset MNIST, CIFAR10, CIFAR100 and ModelNet. We do extend our experiments with Vgg16(Simonyan & Zisserman, ) on dataset CIFAR10 and CIFAR100. Experiments are repeated over five random trials, and results are reported as mean and standard deviation. Further details are in Appendix A.1.\\n\\n##### Evaluations Metrics\\n\\nWe evaluate the utility of unlearning by measuring accuracy of $\\\\mathcal{D}_{r}$ before and after unlearning. The higher accuracy on $\\\\mathcal{D}_{r}$ indicates stronger utility. To evaluate the unlearning effectiveness, we construct a simple MIA from (Shokri et al., ) to test Attack Success Rate (ASR) and measuring the accuracy of $\\\\mathcal{D}_{u}$ before and after unlearning. MIA seeks to determine if a specific data record was included in the training of a target machine learning model. Time efficiency is evaluated by comparing the runtime of each baseline.\\n\\n##### Baselines\\n\\nWe compare our method with the following baselines: Retrain, Fine Tuning(Golatkar et al., ; Jia et al., ), Fisher Forgetting(Golatkar et al., ), Amnesiac Unlearning(Graves et al., ), UNSIR(Tarun et al., ) and Boundary Unlearning (Chen et al., ). Additional details are available in Appendix A.1.\\n\\n### 5.2 Experimental Results\\n\\n#### 5.2.1 Utility Guarantee\\n\\nTo assess the utility of our proposed unlearning method, we evaluate accuracy on $\\\\mathcal{D}_{r}$ before and after unlearning (Tab 1, 2, 3). An effective unlearning method should retain as much information as possible from $\\\\mathcal{D}_{r}$.\\n\\nFrom tab 1, 2, 3, we observe that: 1) Fine-tuning achieve good preservation on $\\\\mathcal{D}_{r}$, but its unlearning effectiveness is low (see Section 5.2.2). 2) Fisher forgetting badly preserve the information of $\\\\mathcal{D}_{r}$, resulting in huge degradation on $\\\\mathcal{D}_{r}$ accuracy. 3) Random incorrect labeling of $\\\\mathcal{D}_{u}$ from Amnesiac Unlearning causes the decision boundaries for $\\\\mathcal{D}_{r}$ to shift unpredictably, resulting in a drop in accuracy on $\\\\mathcal{D}_{r}$. This degradation is more pronounced in datasets with a large number of classes, such as CIFAR100 and ModelNet. 4) The repair step from UNSIR fails to fully retain the information in $\\\\mathcal{D}_{r}$, leading to some performance degradation on $\\\\mathcal{D}_{r}$. 5) Boundary unlearning exhibit inconsistencies across different datasets, models, and scenarios. In some cases, they show huge degradation on $\\\\mathcal{D}_{r}$, while in other instances, they preserve $\\\\mathcal{D}_{r}$ well.\\n\\nOur solution show good unlearning utility in all experiments.\\n\\nTable: Table 1: Accuracy of $\\\\mathcal{D}_{r}$ and $\\\\mathcal{D}_{u}$ for each unlearning method across Resnet18 and Vgg16 model in single-class unlearning\\n\\nTable: Table 2: Accuracy of $\\\\mathcal{D}_{r}$ and $\\\\mathcal{D}_{u}$ for each unlearning method across Resnet18 and Vgg16 model in two-classes unlearning\\n\\nTable: Table 3: Accuracy of $\\\\mathcal{D}_{r}$ and $\\\\mathcal{D}_{u}$ for each unlearning method across Resnet18 and Vgg16 model in multi-classes unlearning.\\n\\n#### 5.2.2 Unlearning Effectiveness\\n\\nFor unlearning effectiveness, we run MIA to evaluate if the unlearned model leaks any information about the $\\\\mathcal{D}_{u}$ and measure the accuracy of $\\\\mathcal{D}_{u}$ before and after unlearning. We present the MIA graph of single-class unlearning in Resnet18 (fig 4(a)) and Vgg16 (fig 4(b)). Additional MIA figures are available in figure 11.\\n\\nFrom tab 1, 2, 3, we observe that: 1) Fine-tuning show bad unlearning effectiveness on CIFAR10 and CIFAR100 datasets. The unlearning effectiveness of fine tuning is worse on two-classes (Tab 2) and multi-classes unlearning scenarios (Tab 3); 2) Fisher forgetting, Amnesiac Unlearning and UNSIR shows strong unlearning effectiveness, reducing accuracy of $\\\\mathcal{D}_{u}$ to 0.00%; 3) Boundary unlearning exhibit inconsistencies across different datasets, models, and scenarios. In some cases, they show good unlearning effectiveness on $\\\\mathcal{D}_{u}$, while in other instances, they show bad unlearning effectiveness.\\n\\nOur solution demonstrates strong effectiveness across all models, datasets, and scenarios. It achieving successful unlearning of $\\\\mathcal{D}_{u}$. From fig 4(a), 4(b), we observe that: 1) Fine tuning shows consistent ASR score in experiments. 2) Fisher forgetting show high ASR score in many experiments. 3) Amnesiac unlearning show inconsistencies in ASR score such as very high ASR score and very low ASR score on different experiments. 4) UNSIR show high ASR score on almost all experiments. 5) Boundary unlearning show relatively consistent ASR scores.\\n\\nOur solution show consistent ASR performance across all datasets, models and scenarios.\\n\\nFigure: (a) Resnet18\\nRefer to caption: x4.png\\n\\n#### 5.2.3 Time Efficiency\\n\\nFigure: Figure 5: The runtime(s) of each unlearning method.\\nRefer to caption: x6.png\\n\\nFor computational complexity, we measure the execution time of unlearning methods in seconds. We present an execution time graph of single-class unlearning in the Resnet18 model CIFAR10 dataset in figure 5. Our solution has the lowest execution time on all experiments.\\n\\nFrom fig 5, we observe that : 1) The standard gold retrain model takes the highest execution time in all experiments. 2) Unlearning methods that utilise full dataset or $\\\\mathcal{D}_{r}$ such as Fine Tuning, Amnesiac Unlearning and Fisher forgetting have high execution time in all the experiments. 3) Unlearning methods that utilise only $\\\\mathcal{D}_{u}$ such as Boundary Unlearning shows a lower execution time. Our solution has the lowest execution time on all experiments.\\n\\n### 5.3 Ablation Study\\n\\nIn this section, we conduct an ablation study on the effectiveness of our method for different number of passive parties and different privacy-preserving VFL mechanishm.\\n\\n#### 5.3.1 Evaluation for different number of passive parties\\n\\nTable 4 shows the accuracy of $\\\\mathcal{D}_{r}$ and $\\\\mathcal{D}_{u}$ on 1 passive party, 2 passive parties and 4 passive parties. Figure 7 shows the ASR score along different numbers of passive parties. Both two results show that our method can perform well in unlearning effectiveness and utility.\\n\\nTable: Table 4: Accuracy of $\\\\mathcal{D}_{r}$ and $\\\\mathcal{D}_{u}$ for each unlearning method across Resnet18 model in single-class unlearning on different number of passive parties.\\n\\nFigure: Figure 6: Comparison of the utility and unlearning effectiveness on different size of $D_{p}$.\\nRefer to caption: x7.png\\n\\n#### 5.3.2 Evaluation on different size of D p subscript 𝐷 𝑝 D_{p} italic_D start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT\\n\\nWe apply the gradient ascent with different size $D_{p}$ to achieve unlearning in Figure 6, e.g, three methods (GA-s using 40 samples, GA-A using 5000 samples and ours). It shows that 1) 40 samples is not enough to unlearn since the unlearning result on $D_{u}$ is only 40.48% while 5000 samples is 0%; 2) our methods only use 40 samples but achieve the 0% unlearning effectiveness on $D_{u}$.\\n\\nFigure: Figure 7: Comparison of different unlearning methods evaluated on MIA attacks for different number of passive parties on CIFAR10.\\nRefer to caption: x8.png\\n\\n#### 5.3.3 Evaluation for different privacy preserving VFL methods\\n\\nWe evaluate our unlearning methods under two privacy preserving VFL methods, Differential Privacy (Fu et al., ) and Gradient Compression (Fu et al., ).\\nFigures 8 and 9 show the effectiveness of our solution on the Differential Privacy and Gradient Compression model across different levels of variance Gaussian noise and compression ratio respectively. It shows that even for the large compression ratio and noise level, the proposed method still unlearn effectively while the utility of the vertical training decreases a lot.\\n\\nFigure: (a)\\nRefer to caption: x9.png\\n\\nFigure: (a)\\nRefer to caption: x11.png\\n\\n## 6 Conclusions\\n\\nIn conclusion, this paper presents a pioneering approach to label unlearning within Vertical Federated Learning, addressing a critical gap in the existing literature. By introducing a few-shot unlearning method that leverages manifold mixup, we effectively mitigate the risk of label privacy leakage while ensuring efficient unlearning from both active and passive models. Our systematic exploration of potential label privacy risks and extensive experimental validation on benchmark datasets underscores the method’s efficacy and rapid performance. Ultimately, this work not only advances the understanding of unlearning in VFL but also sets the stage for further innovations in privacy-preserving collaborative machine learning practices.\\n\\n## Appendix A Appendix\\n\\nThis section provides detailed informations on our experimental settings and additional experimental results.\\n\\n### A.1 Experimental Setup\\n\\n##### Datasets\\n\\nMNIST(Lecun et al., ) datasets contain images of handwritten digits. MNIST dataset comprises 60,000 training examples and 10,000 test examples. Each example is represented as a single-channel image with dimensions of 28x28 pixels, categorised into one of 10 classes. CIFAR10 (Krizhevsky et al., ) dataset comprises 60,000 images, each with dimensions of 32x32 pixels and three colour channels, distributed across 10 classes. This dataset includes 6,000 images per class and is partitioned into 50,000 training examples and 10,000 test examples. Within each class, there are 5000 training images and 1000 test images. Similarly, the CIFAR100 (Krizhevsky et al., ) dataset shares the same image dimensions and structure as CIFAR10 but extends to 100 classes, with each class containing 600 images. Within each class, there are 500 training images and 100 test images. ModelNet (Wu et al., ) dataset is a widely-used 3D shape classification and shape retrieval benchmark, which currently contains 127,915 3D CAD models from 662 object categories. We created 2 2D multi-view images per 3D mesh model by placing 2 virtual cameras evenly distributed around the centroid and partitioned the images into 2 parties by their angles, which contains 19662 images to train and 4930 images to test.\\n\\n##### Baselines\\n\\nThe baseline methods in this study:\\n\\nBaseline: Original model before unlearning.\\n\\nRetrain: Retrain the model from scratch with $\\\\mathcal{D}_{r}$ with the same hyper-parameters to baseline.\\n\\nFine Tuning(Golatkar et al., ; Jia et al., ): The baseline model is fine-tuned using $\\\\mathcal{D}_{r}$ for 5 epochs with 0.01 learning rate.\\n\\nFisher Forgetting(Golatkar et al., ): We use fisher information matrix(FIM) to inject noise into the parameters proportional to their relative importance to the $\\\\mathcal{D}_{f}$ compared to the $\\\\mathcal{D}_{r}$.\\n\\nAmnesiac(Graves et al., ): We retrain the model for 3 epochs with relabeled $\\\\mathcal{D}_{f}$ with incorrect random label and $\\\\mathcal{D}_{r}$.\\n\\nUnsir(Tarun et al., ): We introduce noise matrix on $\\\\mathcal{D}_{f}$ to impair the model with noise generated and repair the model with $\\\\mathcal{D}_{r}$.\\n\\nBoundary Unlearning(Chen et al., ): We create adversarial examples from $\\\\mathcal{D}_{f}$ and assign new nearest incorrect adversarial label to shrink the $\\\\mathcal{D}_{f}$ to nearest incorrect decision boundary.\\n\\nGradient Ascent(Golatkar et al., ): We maximise the loss of $\\\\mathcal{D}_{f}$ on the model for small number of epochs.\\n\\n##### Model Architecture\\n\\nTable 5 summarise our VFL framework setting.\\n\\n**Table 5: Models in experiments. FC: Fully-connected layer. Conv: convolutional layer**\\n| Model name | Model of Passive Party | Model of Active Party |\\n| --- | --- | --- |\\n| Resnet18 | 20 Conv | 1 FC |\\n| Vgg16 | 13 Conv | 3 FC |\\n\\n##### Implementation Details\\n\\nTable 6 and 7 summarises the hyper-parameters for our unlearning method.\\n\\nTable: Table 6: Hyper-parameters use for unlearning in our solution in Single-class unlearning.\\n\\nTable: Table 7: Hyper-parameters use for unlearning in our solution in two-classes and multi-classes unlearning.\\n\\nTable 8 summarise the model name and datasets involve in each unlearning scenarios.\\n\\n**Table 8: Models and datasets involve in each unlearning scenarios.**\\n| Scenarios | Models | Datasets |\\n| --- | --- | --- |\\n| Single-class Unlearning | Resnet18 | MNIST, CIFAR10, CIFAR100, ModelNet |\\n| Vgg16 | CIFAR10, CIFAR100 | |\\n| Two-classes Unlearning | Resnet18 | CIFAR10, CIFAR100 |\\n| Vgg16 | CIFAR10, CIFAR100 | |\\n| Multi-classes Unlearning | Resnet18 | CIFAR100 |\\n| Vgg16 | CIFAR100 | |\\n\\nFigure: Figure 10: PMC resnet18 cifar10 single class\\nRefer to caption: x13.png\\n\\n### A.2 Additional Experiments Result\\n\\nFigure11 shows MIA graphs for various number of passive parties. Moreover, Figure 10 shows the PMC attack (one strongest label privacy attack in (Fu et al., )) before and after unlearning methods. It demonstrates that our methods achieve beyond 40% drops for the model accuracy on $D_{u}$.\\n\\nFigure: (a)\\nRefer to caption: x14.png\",\n \"metadata\": {\n \"authors\": [\n \"Hanlin Gu\",\n \"Hong Xi Tae\",\n \"Chee Seng Chan\",\n \"Lixin Fan\",\n \"AI Lab, Webank, PR China\"\n ],\n \"title\": \"A few-shot Label Unlearning in Vertical Federated Learning\",\n \"total_chars\": 31997,\n \"total_lines\": 284,\n \"updated_at\": \"2026-01-25T15:02:50.969609\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"cE8s1M4dlt","initial_rating":5,"confidence":2,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper aims to address the label unlearning problem in vertical federated learning (VFL). It demonstrates the lable leakage issue with applying traditional techniques in lable unlearning in VFL and proposes a few shot unlearning method to address mitigate this issue. Extensive experiments on 4 datasets and 2 model architectures show that the proposed method is effective and effcient while preserving good utility.","strengths":"- The paper is well structured and generally easy to follow\n- The proposed method is intuitive and seems to be technically sound\n- Extensive experiments on 4 datasets and 2 model architectures demonstrate the effectiveness of the proposed method","weaknesses":"- As mentioned in the introduction, VFL is mostly used in finance, healthcare, or ecommerce scenarios, but this work mostly validated the proposed method on simple vision datasets.\n- The discussion and presentation of experiment results can be improved. e.g., the paper discusses utility in Sec 5.2.1 but also mentioning effectiveness in Figure 4 in Sec 5.2.2. It is not intuitive to compare different methods on these two aspects easily. \n- Figure 1 is not easy to understand and interpret the label leakage risk.\n- VFU seems to be used without definition","questions":"- Can the proposed method be applied to non-vision datasets or other vision tasks other than classification?"},{"id":"M3Kn2S233D","initial_rating":6,"confidence":4,"soundness":4,"contribution":4,"presentation":4,"summary":"This paper focuses on the unlearning problem in vertical federated learning (VFL). The authors leverage a limited amount of data for unlearning to mitigate the label leakage risk of existing unlearning methods. In particular, the authors propose to mixup feature embeddings during the learning process. Then during the unlearning process, the mixup scheme can be utilized to augment the limited data. The unlearning is finally achieved by gradient ascent on the augmented data. Experiments conducted on diverse datasets validate the performance of the proposed framework.","strengths":"* The discussed topic, unlearning in VFL, is important.\n* The writing is clear.\n* The proposed mixup augmentation is simple yet effective.\n* The empirical results demonstrate the effectiveness of the proposed framework. The model after unlearning demonstrate high accuracy and low attack success rate.\n* The ablation is extensive and helpful.","weaknesses":"As shown in Equation (3), the feature size of the active party increases quadratically as the number of clients increases. Therefore, the scalability of the framework is relatively limited.\n\nThe effeciency of the proposed method is still doubted.\nThe authors did not correct their submission.\nI will maintain my score.","questions":"As shown in Figure 4, the ASR of Amnesiac is abnormally high (up to 96.1) on CIFAR-100 with Resnet 18 architecture while ASR of Amnesiac on other datasets or architectures is only up to 3.1. Could the authors provide more explanations?"},{"id":"apb2q8ABHc","initial_rating":5,"confidence":4,"soundness":3,"contribution":3,"presentation":2,"summary":"This paper proposes a few-shot label unlearning method specifically designed for Vertical Federated Learning (VFL) to mitigate privacy leakage risks associated with traditional unlearning approaches. In VFL, multiple organizations collaborate on model training by sharing some sample IDs while differing in feature sets, making it particularly suitable for sensitive fields such as banking and healthcare. This method leverages a small amount of private data and manifold mixup to augment embeddings, employing gradient ascent to remove labels from the active party’s model and transferring inverse gradients to the passive party to ensure independent label removal from both models. Experimental results demonstrate that this approach achieves rapid and effective label unlearning across various datasets, significantly reducing privacy leakage risks.","strengths":"1. **Introducing the first method for label unlearning in Vertical Federated Learning (VFL)**: This paper pioneers a novel approach specifically tailored for the removal of label information in VFL settings, addressing a critical gap in existing federated learning literature. Unlike prior work focused on feature-based unlearning, this method uniquely targets the secure and efficient unlearning of labels across collaborative models, enhancing data protection compliance in sensitive domains.\n\n2. **Detailing potential privacy leaks in traditional unlearning methods**: The paper systematically examines the vulnerabilities of conventional unlearning techniques when applied to VFL, especially the risk of sensitive label information being inadvertently exposed to other parties during the unlearning process. By identifying specific points of leakage, this study highlights the importance of secure information flow between the active and passive parties in VFL.\n\n3. **Proposing an effective few-shot unlearning approach that uses limited data and enhances unlearning with manifold mixup**: To minimize data exposure, this approach relies on a small subset of private data, significantly reducing privacy risks. Through manifold mixup, the method augments data embeddings, allowing for robust and efficient unlearning with minimal information. This few-shot strategy achieves a balance between privacy preservation and computational efficiency, making it practical for real-world applications.\n\n4. **Demonstrating superior unlearning performance on benchmark datasets like MNIST, CIFAR-10, CIFAR-100, and ModelNet**: Extensive experiments validate the method's effectiveness and speed in removing target labels, outperforming traditional unlearning techniques on widely used datasets. The results illustrate the approach’s scalability and adaptability across diverse data types, affirming its potential for high-performance unlearning in federated settings.","weaknesses":"1. The paper lacks a preliminary section to help readers understand the meaning of each mathematical symbol. Some symbols are not explained, making it difficult for me to follow the methodology. Please clarify the definition of each variable in the paper.\n\n2. While the paper’s motivation is clear and innovative, it lacks explanations regarding specific methods, such as why gradient ascent and inverse gradient can remove label information. Additionally, I am uncertain whether the proposed method guarantees convergence. Please provide an analysis or discussion on the forgetting functionality and convergence of this method.\n(1). provide a theoretical justification for why gradient ascent and inverse gradients are effective for label removal\n(2). Include a convergence analysis or discussion of the conditions under which convergence is guaranteed\n(3). Offer more detailed explanations of the forgetting mechanism and how it ensures complete removal of label information\n\n3. The experimental setup lacks sufficient detail, including which categories were selected for forgetting in each dataset, the number of clients, and how data attributes were assigned. Please add a more detailed description of the experimental setup.\n(1). A table or list of the exact categories chosen for forgetting in each dataset\n(2). The number of clients/parties involved in each experiment\n(3). A description of how data attributes were distributed among the parties This level of detail would allow for better reproducibility and understanding of the experimental conditions.","questions":"See weakness"},{"id":"Xc3u2jWPSk","initial_rating":8,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper explores the unlearning process in vertical federated learning (VFL), a topic that has been relatively underexplored in prior research. The authors highlight the risk of label leakage during the unlearning phase and propose a solution to address this issue. Their method utilizes a small set of labeled data, combined with feature mixup and gradient ascent, to mitigate the leakage of label information from VFL systems.","strengths":"1. The proposed method is simple and intuitive, approaching the unlearning process from a few-shot perspective and utilizing feature mixup to handle limited sample sizes.\n2. The method demonstrates broad applicability.\n3. Extensive experimental results indicate that the method not only performs consistently across various datasets and models with different numbers of clients but can also be effectively integrated with differential privacy and gradient compression methods. Furthermore, the proposed method exhibits the lowest unlearning cost compared to its competitors.","weaknesses":"1. The label leakage described in Sec. 3.2 would only occur if both active and passive clients share the same label space. However, in most VFL scenarios, clients have distinct label spaces. Therefore, this assumption of label leakage is questionable.\n2. In the introduction, the statement that \"... the passive party holds the features, ... the active party possesses the labels.\" is inaccurate. The active party also holds its own features.\n3. Some notations are unclear. For instance, in line 152, \"{x^u_k}\" is used, but the variable \"u\" is not defined. I assume it refers to samples for unlearning.\n4. The figures are difficult to interpret, particularly Fig. 1 and Fig. 6.\n5. The mix rate lambda is crucial to the method. However, the authors neither provide a thorough analysis of this hyperparameter nor clarify whether lambda remains consistent across different clients.","questions":"Please check the weakness part for details."}],"string":"[\n {\n \"id\": \"cE8s1M4dlt\",\n \"initial_rating\": 5,\n \"confidence\": 2,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper aims to address the label unlearning problem in vertical federated learning (VFL). It demonstrates the lable leakage issue with applying traditional techniques in lable unlearning in VFL and proposes a few shot unlearning method to address mitigate this issue. Extensive experiments on 4 datasets and 2 model architectures show that the proposed method is effective and effcient while preserving good utility.\",\n \"strengths\": \"- The paper is well structured and generally easy to follow\\n- The proposed method is intuitive and seems to be technically sound\\n- Extensive experiments on 4 datasets and 2 model architectures demonstrate the effectiveness of the proposed method\",\n \"weaknesses\": \"- As mentioned in the introduction, VFL is mostly used in finance, healthcare, or ecommerce scenarios, but this work mostly validated the proposed method on simple vision datasets.\\n- The discussion and presentation of experiment results can be improved. e.g., the paper discusses utility in Sec 5.2.1 but also mentioning effectiveness in Figure 4 in Sec 5.2.2. It is not intuitive to compare different methods on these two aspects easily. \\n- Figure 1 is not easy to understand and interpret the label leakage risk.\\n- VFU seems to be used without definition\",\n \"questions\": \"- Can the proposed method be applied to non-vision datasets or other vision tasks other than classification?\"\n },\n {\n \"id\": \"M3Kn2S233D\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 4,\n \"contribution\": 4,\n \"presentation\": 4,\n \"summary\": \"This paper focuses on the unlearning problem in vertical federated learning (VFL). The authors leverage a limited amount of data for unlearning to mitigate the label leakage risk of existing unlearning methods. In particular, the authors propose to mixup feature embeddings during the learning process. Then during the unlearning process, the mixup scheme can be utilized to augment the limited data. The unlearning is finally achieved by gradient ascent on the augmented data. Experiments conducted on diverse datasets validate the performance of the proposed framework.\",\n \"strengths\": \"* The discussed topic, unlearning in VFL, is important.\\n* The writing is clear.\\n* The proposed mixup augmentation is simple yet effective.\\n* The empirical results demonstrate the effectiveness of the proposed framework. The model after unlearning demonstrate high accuracy and low attack success rate.\\n* The ablation is extensive and helpful.\",\n \"weaknesses\": \"As shown in Equation (3), the feature size of the active party increases quadratically as the number of clients increases. Therefore, the scalability of the framework is relatively limited.\\n\\nThe effeciency of the proposed method is still doubted.\\nThe authors did not correct their submission.\\nI will maintain my score.\",\n \"questions\": \"As shown in Figure 4, the ASR of Amnesiac is abnormally high (up to 96.1) on CIFAR-100 with Resnet 18 architecture while ASR of Amnesiac on other datasets or architectures is only up to 3.1. Could the authors provide more explanations?\"\n },\n {\n \"id\": \"apb2q8ABHc\",\n \"initial_rating\": 5,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"This paper proposes a few-shot label unlearning method specifically designed for Vertical Federated Learning (VFL) to mitigate privacy leakage risks associated with traditional unlearning approaches. In VFL, multiple organizations collaborate on model training by sharing some sample IDs while differing in feature sets, making it particularly suitable for sensitive fields such as banking and healthcare. This method leverages a small amount of private data and manifold mixup to augment embeddings, employing gradient ascent to remove labels from the active party’s model and transferring inverse gradients to the passive party to ensure independent label removal from both models. Experimental results demonstrate that this approach achieves rapid and effective label unlearning across various datasets, significantly reducing privacy leakage risks.\",\n \"strengths\": \"1. **Introducing the first method for label unlearning in Vertical Federated Learning (VFL)**: This paper pioneers a novel approach specifically tailored for the removal of label information in VFL settings, addressing a critical gap in existing federated learning literature. Unlike prior work focused on feature-based unlearning, this method uniquely targets the secure and efficient unlearning of labels across collaborative models, enhancing data protection compliance in sensitive domains.\\n\\n2. **Detailing potential privacy leaks in traditional unlearning methods**: The paper systematically examines the vulnerabilities of conventional unlearning techniques when applied to VFL, especially the risk of sensitive label information being inadvertently exposed to other parties during the unlearning process. By identifying specific points of leakage, this study highlights the importance of secure information flow between the active and passive parties in VFL.\\n\\n3. **Proposing an effective few-shot unlearning approach that uses limited data and enhances unlearning with manifold mixup**: To minimize data exposure, this approach relies on a small subset of private data, significantly reducing privacy risks. Through manifold mixup, the method augments data embeddings, allowing for robust and efficient unlearning with minimal information. This few-shot strategy achieves a balance between privacy preservation and computational efficiency, making it practical for real-world applications.\\n\\n4. **Demonstrating superior unlearning performance on benchmark datasets like MNIST, CIFAR-10, CIFAR-100, and ModelNet**: Extensive experiments validate the method's effectiveness and speed in removing target labels, outperforming traditional unlearning techniques on widely used datasets. The results illustrate the approach’s scalability and adaptability across diverse data types, affirming its potential for high-performance unlearning in federated settings.\",\n \"weaknesses\": \"1. The paper lacks a preliminary section to help readers understand the meaning of each mathematical symbol. Some symbols are not explained, making it difficult for me to follow the methodology. Please clarify the definition of each variable in the paper.\\n\\n2. While the paper’s motivation is clear and innovative, it lacks explanations regarding specific methods, such as why gradient ascent and inverse gradient can remove label information. Additionally, I am uncertain whether the proposed method guarantees convergence. Please provide an analysis or discussion on the forgetting functionality and convergence of this method.\\n(1). provide a theoretical justification for why gradient ascent and inverse gradients are effective for label removal\\n(2). Include a convergence analysis or discussion of the conditions under which convergence is guaranteed\\n(3). Offer more detailed explanations of the forgetting mechanism and how it ensures complete removal of label information\\n\\n3. The experimental setup lacks sufficient detail, including which categories were selected for forgetting in each dataset, the number of clients, and how data attributes were assigned. Please add a more detailed description of the experimental setup.\\n(1). A table or list of the exact categories chosen for forgetting in each dataset\\n(2). The number of clients/parties involved in each experiment\\n(3). A description of how data attributes were distributed among the parties This level of detail would allow for better reproducibility and understanding of the experimental conditions.\",\n \"questions\": \"See weakness\"\n },\n {\n \"id\": \"Xc3u2jWPSk\",\n \"initial_rating\": 8,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper explores the unlearning process in vertical federated learning (VFL), a topic that has been relatively underexplored in prior research. The authors highlight the risk of label leakage during the unlearning phase and propose a solution to address this issue. Their method utilizes a small set of labeled data, combined with feature mixup and gradient ascent, to mitigate the leakage of label information from VFL systems.\",\n \"strengths\": \"1. The proposed method is simple and intuitive, approaching the unlearning process from a few-shot perspective and utilizing feature mixup to handle limited sample sizes.\\n2. The method demonstrates broad applicability.\\n3. Extensive experimental results indicate that the method not only performs consistently across various datasets and models with different numbers of clients but can also be effectively integrated with differential privacy and gradient compression methods. Furthermore, the proposed method exhibits the lowest unlearning cost compared to its competitors.\",\n \"weaknesses\": \"1. The label leakage described in Sec. 3.2 would only occur if both active and passive clients share the same label space. However, in most VFL scenarios, clients have distinct label spaces. Therefore, this assumption of label leakage is questionable.\\n2. In the introduction, the statement that \\\"... the passive party holds the features, ... the active party possesses the labels.\\\" is inaccurate. The active party also holds its own features.\\n3. Some notations are unclear. For instance, in line 152, \\\"{x^u_k}\\\" is used, but the variable \\\"u\\\" is not defined. I assume it refers to samples for unlearning.\\n4. The figures are difficult to interpret, particularly Fig. 1 and Fig. 6.\\n5. The mix rate lambda is crucial to the method. However, the authors neither provide a thorough analysis of this hyperparameter nor clarify whether lambda remains consistent across different clients.\",\n \"questions\": \"Please check the weakness part for details.\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"5;5;5;6\",\n \"rating_avg\": 5.25,\n \"confidence\": \"4;4;2;4\",\n \"confidence_avg\": 3.5,\n \"soundness\": \"2;3;3;4\",\n \"soundness_avg\": 3,\n \"contribution\": \"3;3;3;4\",\n \"contribution_avg\": 3.25,\n \"presentation\": \"2;2;3;4\",\n \"presentation_avg\": 2.75\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"Submitted to ICLR 2025\",\n \"venueid\": \"ICLR.cc/2025/Conference/Rejected_Submission\",\n \"processed_at\": \"2026-01-14T22:16:03.718241\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"7C4AiPk3D5\",\n \"metareview\": \"This paper received two positive and two negative reviews. Positive reviews highlighted its clear structure and effective mixup augmentation method for unlearning in Vertical Federated Learning (VFL). Empirical results show improved accuracy and reduced attack success rates, with the method being practical for few-shot settings and applicable across datasets and models. It integrates well with techniques like differential privacy and gradient compression, achieving the lowest unlearning cost compared to existing methods. However, the negative reviews raised several concerns. The lack of a section explaining mathematical symbols makes the methodology hard to follow, and definitions for variables are needed. While the use of gradient ascent and inverse gradients is justified, the paper does not explain why these methods are effective for label removal or discuss the convergence conditions. An analysis of the forgetting mechanism would strengthen the paper. The experimental setup lacks detail, such as categories for forgetting, client numbers, and data distribution, which hinders reproducibility. A table summarizing this information is recommended. Furthermore, while VFL is used in fields like finance and healthcare, the experiments focus on simple vision datasets, which may not capture real-world complexities. The presentation of results could be clearer, particularly in comparing utility and effectiveness. The authors have made considerable efforts in their response, the Area Chair (AC) believes that the paper requires significant revisions for ICLR publication, particularly in terms of experimental analysis.\",\n \"additional_comments\": \"Two negative reviewers did not participate in the review discussion, two positive reviewer have recognized the rebuttal and revision.\\n\\n1. Motivation/problem definition issues. Motivation is privacy such as GDPR & CCPA, for which instance-wise unlearning is the relevant goal. However, the method and experiments are designed for class-wise unlearning. Class-wise unlearning is not the mainstream, and it’s not explained why it’s important. \\n2. The data used in the main experiments is not reflective of the typical finance or healthcare settings where VFL is used. A little bit of this is added in the rebuttal, but this is a too major late revision.\\n3. Lots of unclear details, including lack of clarity on how the baselines are adapted to VFL setting (besides missing details mentioned by others). \\n4. Methodological Novelty. In the end the solution is to use a fairly standard few-shot learning augmentation.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Reject\"\n}"}}},{"rowIdx":3399,"cells":{"paper_id":{"kind":"string","value":"qdOIkeZ5e4"},"arxiv_id":{"kind":"string","value":"2307.02869v2"},"title":{"kind":"string","value":"Generalized Video Moment Retrieval"},"markdown":{"kind":"string","value":"{\n \"content\": \"## Abstract\\n\\nAbstract Video moment retrieval pursues an efficient and generalized solution to identify the specific temporal segments within an untrimmed video that correspond to a given language description.\\nTo achieve this goal, we provide a generative diffusion-based framework called MomentDiff, which simulates a typical human retrieval process from random browsing to gradual localization.\\nSpecifically, we first diffuse the real span to random noise, and learn to denoise the random noise to the original span with the guidance of similarity between text and video.\\nThis allows the model to learn a mapping from arbitrary random locations to real moments, enabling the ability to locate segments from random initialization.\\nOnce trained, MomentDiff could sample random temporal segments as initial guesses and iteratively refine them to generate an accurate temporal boundary.\\nDifferent from discriminative works ( e.g., based on learnable proposals or queries), MomentDiff with random initialized spans could resist the temporal location biases from datasets.\\nTo evaluate the influence of the temporal location biases, we propose two “anti-bias” datasets with location distribution shifts, named Charades-STA-Len and Charades-STA-Mom.\\nThe experimental results demonstrate that our efficient framework consistently outperforms state-of-the-art methods on three public benchmarks, and exhibits better generalization and robustness on the proposed anti-bias datasets.\\nThe code, model, and anti-bias evaluation datasets are available at https://github.com/IMCCretrieval/MomentDiff .\\n\\n## 1 Introduction\\n\\nVideo understanding [, , , , , , , , ] is a crucial problem in machine learning [, , , , , , ], which covers various video analysis tasks, such as video classification and action detection.\\nBut both tasks above are limited to predicting predefined action categories.\\nA more natural and elaborate video understanding process is the ability for machines to match human language descriptions to specific activity segments in a complex video.\\nHence, a series of studies [, , , , ] are conducted on Video Moment Retrieval (VMR), with the aim of identifying the moment boundaries ( i.e., the start and end time) within a given video that best semantically correspond to the text query.\\n\\nFigure: Figure 1: (a) Proposal-predefined methods. Yellow highlights in the timeline represent frequently occurring moments in the dataset. (b) Proposal-learnable methods. (c) Our generative method. (d) We model the VMR task as a process of gradually generating real temporal span from random noise.\\nRefer to caption: /html/2307.02869/assets/x1.png\\n\\nAs shown in Fig. [1](#S1.F1)(a), early works address the VMR task by designing predefined dense video proposals ( i.e., sliding windows [, , ], anchors [] and 2D map [] ).\\nThen, the prediction segment is determined based on the maximum similarity score between dense proposals and the query text.\\nHowever, these methods have a large redundancy of proposals and the numbers of positive and negative proposals are unbalanced, which limits the learning efficiency [].\\nTo deal with this problem, a series of VMR works [, , , , , , , ] have recently emerged, mainly discussing how to reduce the number of proposals and improve the quality of proposals.\\nAmong them, a promising scheme (Fig. [1](#S1.F1)(b)) is to use sparse and learnable proposals [, , ] or queries [, ] (i.e., soft proposals) to model the statistics of the entire dataset and adaptively predict video segments.\\nHowever, these proposal-learnable methods rely on a few specific proposals or queries to fit the location distribution of ground truth moments.\\nFor example, these proposals or queries may tend to focus on video segments where locations in the dataset occur more often (i.e., yellow highlights in Fig. [1](#S1.F1)(b)).\\nThus, these methods potentially disregard significant events that transpire in out-of-sample situations.\\nRecent studies [, ] indicate that VMR models [, , ] may exploit the location biases present in dataset annotations [], while downplaying multimodal interaction content.\\nThis leads to the limited generalization of the model, especially in real-world scenarios with location distribution shifts.\\n\\nTo tackle the above issues, we propose a generative perspective for the VMR task.\\nAs shown in Fig. [1](#S1.F1) (c) and (d), given an untrimmed video and the corresponding text query, we first introduce several random spans as the initial prediction, then employ a diffusion-based denoiser to iteratively refine the random spans by conditioning on similarity relations between the text query and video frames.\\nA heuristic explanation of our method is that, it can be viewed as a way for humans to quickly retrieve moments of interest in a video.\\nSpecifically, given an unseen video, instead of watching the entire video from beginning to end (which is too slow), humans may first glance through random contents to identify a rough location, and finally iteratively focus on key semantic moments and generate temporal coordinates.\\nIn this way, we do not rely on distribution-specific proposals or queries (as mentioned in the above discriminative approaches) and exhibit more generalization and robustness (Tab. [5](#S4.T5) and Fig. [4](#S4.F4)) when the ground truth location distributions of training and test sets are different.\\n\\nTo implement our idea, we introduce a generative diffusion-based framework, named MomentDiff.\\nFirstly, MomentDiff extracts feature embeddings for both the input text query and video frames. Subsequently, these text and video embeddings are fed into a similarity-aware condition generator.\\nThis generator modulates the video embeddings with text embeddings to produce text-video fusion embeddings.\\nThe fusion embeddings contain rich semantic information about the similarity relations between the text query and each video frame, so we can use them as a guide to help us generate predictions.\\nFinally, we develop a Video Moment Denoiser (VMD) that enhances noise perception and enables efficient generation with only a small number of random spans and flexible embedding learning.\\nSpecifically, VMD directly maps randomly initialized spans into the multimodal space, taking them as input together with noise intensities.\\nThen, VMD iteratively refines spans according to the similarity relations of fusion embeddings, thereby generating true spans from random to real.\\n\\nOur main contributions are summarized as follows.\\n1) To the best of our knowledge, we are the first to tackle video moment retrieval from a generative perspective, which does not rely on predefined or learnable proposals and mitigates temporal location biases from datasets.\\n2) We propose a new framework, MomentDiff, which utilizes diffusion models to iteratively denoise random spans to the correct results.\\n3) We propose two “anti-bias” datasets with location distribution shifts to evaluate the influence of location biases, named Charades-STA-Len and Charades-STA-Mom.\\nExtensive experiments demonstrate that MomentDiff is more efficient and transferable than state-of-the-art methods on three public datasets and two anti-bias datasets.\\n\\n## 2 Related Work\\n\\nVideo Moment Retrieval.\\nVideo moment retrieval [, , , , , , , , ] is a newly researched subject that emphasizes retrieving correlated moments in a video, given a natural language query.\\nPioneering works are proposal-based approaches, which employ a \\\"proposal-rank\\\" two-stage pipeline.\\nEarly methods [, , , , ] usually use handcrafted predefined proposals to retrieve moments.\\nFor example, CTRL [] and MCN [] aim to generate video proposals by using sliding windows of different scales.\\nTGN [] emphasizes temporal information and develops multi-scale candidate solutions through predefined anchors.\\n2DTAN [] designs a 2D temporal map to enumerate proposals.\\nHowever, these dense proposals introduce redundant computation with a large number of negative samples [, ].\\nTherefore, two types of methods are proposed:\\n1) Proposal-free methods [, , ] do not use any proposals and are developed to directly regress start and end boundary values or probabilities based on ground-truth segments.\\nThese methods are usually much faster than proposal-based methods.\\n2) Proposal-learnable methods that use proposal prediction networks [, , ] or learnable queries [, ] to model dataset statistics and adaptively predict video segments.\\nQSPN [] and APGN [] adaptively obtain discriminative proposals without handcrafted design.\\nLPNet [] uses learnable proposals to alleviate the redundant calculations in dense proposals.\\nMomentDETR [] can predict multiple segments using learnable queries.\\nSince proposal-learnable methods adopt a two-stage prediction [, , ] or implicit iterative [] design, the performance is often better than that of proposal-free methods.\\nHowever, proposal-learnable methods explicitly fit the location distribution of target moments.\\nThus, models are likely to be inclined to learn location bias in datasets [, ], resulting in limited generalization.\\nWe make no assumptions about the location and instead use random inputs to alleviate this problem.\\n\\nDiffusion models.\\nDiffusion Models [, , , ] are inspired by stochastic diffusion processes in non-equilibrium thermodynamics.\\nThe model first defines a Markov chain of diffusion steps to slowly add random noise to the data, and then learns the reverse diffusion process to construct the desired data samples from the noise.\\nThe diffusion-based generation has achieved disruptive achievements in tasks such as vision generation [, , , , , , ] and text generation [].\\nMotivated by their great success in generative tasks [], diffusion models have been used in image perception tasks such as object detection [] and image segmentation [].\\nHowever, diffusion models are less explored for video-text perception tasks.\\nThis paper models similarity-aware multimodal information as coarse-grained cues, which can guide the diffusion model to generate the correct moment boundary from random noise in a gradual manner.\\nUnlike DiffusionDet [], we avoid a large number of Region of Interest (ROI) features and do not require additional post-processing techniques.\\nTo our knowledge, this is the first study to adapt the diffusion model for video moment retrieval.\\n\\n## 3 Method\\n\\nIn this section, we first define the problem in Sec. [3.1](#S3.SS1), introduce our framework in Sec. [3.2](#S3.SS2), and describe the inference process in Sec. [3.3](#S3.SS3).\\n\\n### 3.1 Problem Definition\\n\\nSuppose an untrimmed video $\\\\mathcal{V}=\\\\{\\\\boldsymbol{v}_{i}\\\\}_{i=1}^{N_{v}}$ is associated with a natural text description $\\\\mathcal{T}=\\\\{\\\\boldsymbol{t}_{i}\\\\}_{i=1}^{N_{t}}$, where $N_{v}$ and $N_{t}$ represent the frame number and word number, respectively.\\nUnder this notation definition,\\nVideo Moment Retrieval (VMR) aims to learn a model $\\\\boldsymbol{\\\\Omega}$ to effectively predict the moment $\\\\hat{\\\\boldsymbol{x}}_{0}=(\\\\hat{\\\\boldsymbol{c}}_{0},\\\\hat{\\\\boldsymbol{w}}_{0})$ that is most relevant to the given text description: $\\\\hat{\\\\boldsymbol{x}}_{0}=\\\\boldsymbol{\\\\Omega}(\\\\mathcal{T},\\\\mathcal{V})$, where $\\\\hat{\\\\boldsymbol{c}}_{0}$ and $\\\\hat{\\\\boldsymbol{w}}_{0}$ represent the center time and duration length of the temporal moments, i.e., predicted spans.\\n\\nFigure: Figure 2: Our MomentDiff framework, which includes a Similarity-aware Condition Generator (SCG) and a Video Moment Denoiser (VMD). The diffusion process is conducted progressively in VMD.\\nRefer to caption: /html/2307.02869/assets/x2.png\\n\\n### 3.2 The MomentDiff Framework\\n\\nFig. [2](#S3.F2) sheds light on the generation modeling architecture of our proposed MomentDiff.\\nConcretely, we first extract frame-level and word-level features by utilizing pre-trained video and text backbone networks.\\nAfterward, we employ a similarity-aware condition generator to interact text and visual features into fusion embeddings.\\nFinally, combined with the fusion embeddings, the video moment denoiser can progressively produce accurate temporal targets from random noise.\\n\\n#### 3.2.1 Visual and Textual Representations.\\n\\nBefore performing multimodal interaction, we should convert the raw data into a continuous feature space.\\nTo demonstrate the generality of our model, we use three distinct visual extractors [, ] to obtain video features $\\\\mathcal{V}$:\\n1) 2D visual encoder, the VGG model [].\\n2) 3D visual encoder, the C3D model [].\\n3) Cross-modal pre-train encoder, the CLIP visual model [].\\nHowever, due to the absence of temporal information in CLIP global features, we additionally employ the SlowFast model [] to extract features, which concatenate CLIP features.\\nBesides, to take full advantage of the video information [], we try to incorporate audio features, which are extracted using a pre-trained PANN model [].\\nTo obtain text features, we try two feature extractors: the Glove model [] and the CLIP textual model to extract 300-d and 512-d text features $\\\\mathcal{T}$, respectively.\\n\\n#### 3.2.2 Similarity-aware Condition Generator\\n\\nUnlike generation tasks [] that focus on the veracity and diversity of results, the key to the VMR task is to fully understand the video and sentence information and to mine the similarities between text queries and video segments.\\nTo this end, we need to provide multimodal information to cue the denoising network to learn the implicit relationships in the multimodal space.\\n\\nA natural idea is to interact and aggregate information between video and text sequences with a multi-layer Transformer [].\\nSpecifically, we first use two multilayer perceptron (MLP) networks to map feature sequences into the common multimodal space:\\n$\\\\boldsymbol{V}\\\\in\\\\mathbb{R}^{N_{v}\\\\times D}$ and $\\\\boldsymbol{T}\\\\in\\\\mathbb{R}^{N_{t}\\\\times D}$, where $D$ is the embedding dimension.\\nThen, we employ two cross-attention layers to perform interactions between multiple modalities, where video embeddings $\\\\boldsymbol{V}$ are projected as the query $\\\\boldsymbol{Q}_{v}$, text embeddings $\\\\boldsymbol{T}$ are projected as key $\\\\boldsymbol{K}_{t}$ and value $\\\\boldsymbol{V}_{t}$:\\n$\\\\boldsymbol{\\\\hat{V}}=\\\\operatorname{softmax}\\\\left(\\\\boldsymbol{Q}_{v}\\\\boldsymbol{K}_{t}^{\\\\mathrm{T}}\\\\right)\\\\boldsymbol{V}_{t}+\\\\boldsymbol{Q}_{v},$\\nwhere $\\\\boldsymbol{\\\\hat{V}}\\\\in\\\\mathbb{R}^{N_{v}\\\\times D}$.\\nTo help the model better understand the video sequence relations, we feed $\\\\boldsymbol{\\\\hat{V}}$ into a 2-layer self-attention network, and the final similarity-aware fusion embedding is $\\\\boldsymbol{F}=\\\\operatorname{softmax}\\\\left(\\\\boldsymbol{Q}_{\\\\hat{v}}\\\\boldsymbol{K}_{\\\\hat{v}}^{\\\\mathrm{T}}\\\\right)\\\\boldsymbol{V}_{\\\\hat{v}}+\\\\boldsymbol{Q}_{\\\\hat{v}}$, where $\\\\boldsymbol{Q}_{\\\\hat{v}},\\\\boldsymbol{K}_{\\\\hat{v}},\\\\boldsymbol{V}_{\\\\hat{v}}$ is the matrix obtained from $\\\\boldsymbol{\\\\hat{V}}$ after three different projections respectively.\\n\\nIn the span generation process, even for the same video, the correct video segments corresponding to different text queries are very different.\\nSince the fusion embedding $\\\\boldsymbol{F}$ serves as the input condition of the denoiser, the quality of $\\\\boldsymbol{F}$ directly affects the denoising process.\\nTo learn similarity relations for $\\\\boldsymbol{F}$ in the multimodal space,\\nwe design the similarity loss $\\\\mathcal{L}_{sim}$,\\nwhich contains the pointwise cross entropy loss and the pairwise margin loss:\\n\\n$$ $\\\\mathcal{L}_{sim}=-\\\\frac{1}{N_{v}}\\\\sum_{i=1}\\\\boldsymbol{y}_{i}*log(\\\\boldsymbol{s}_{i})+(1-\\\\boldsymbol{y}_{i})*log(1-\\\\boldsymbol{s}_{i})+\\\\frac{1}{N_{s}}\\\\sum_{j=1}\\\\max\\\\left(0,\\\\beta+\\\\boldsymbol{s}_{n_{j}}-\\\\boldsymbol{s}_{p_{j}}\\\\right),$ (1) $$\\n\\nwhere $\\\\boldsymbol{s}\\\\in\\\\mathbb{R}^{N_{v}}$ is the similarity score, which is obtained by predicting the fusion embedding $\\\\boldsymbol{F}$ through the MLP network.\\n$\\\\boldsymbol{y}\\\\in\\\\mathbb{R}^{N_{v}}$ is the similarity label, where $\\\\boldsymbol{y}_{i}=1$ if the $i$-th frame is within the ground truth temporal moment and $\\\\boldsymbol{y}_{i}=0$ otherwise.\\n$\\\\boldsymbol{s}_{p_{j}}$ and $\\\\boldsymbol{s}_{n_{j}}$ are the randomly sampled positive and negative frames.\\n$N_{s}$ is the number of samples and the margin $\\\\beta=0.2$.\\nAlthough $\\\\mathcal{L}_{sim}$ may only help the fusion embedding retain some coarse-grained similarity semantics, this still provides indispensable multimodal information for the denoiser.\\n\\n#### 3.2.3 Video Moment Denoiser\\n\\nRecent works [, ] have revealed that previous models [, , ] may rely on the presence of location bias in annotations to achieve seemingly good predictions.\\nTo alleviate this problem, instead of improving distribution-specific proposals or queries, we use random location spans to iteratively obtain real spans from a generative perspective.\\nIn this section, we first introduce the principle of the forward and reverse processes in diffusion models.\\nThen, we build the diffusion generation process in the video moment denoiser with model distribution $p_{\\\\theta}(\\\\boldsymbol{x}_{0})$ to learn the data distribution $q(\\\\boldsymbol{x}_{0})$.\\n\\nFigure: Figure 3: Video moment denoiser. For simplicity, we only draw the intensity-aware attention structure that is different from the general Transformer.\\nRefer to caption: /html/2307.02869/assets/x3.png\\n\\nForward process.\\nDuring training, we first construct a forward process that corrupts real segment spans $\\\\boldsymbol{x}_{0}\\\\sim q(\\\\boldsymbol{x}_{0})$ to noisy data $\\\\boldsymbol{x}_{m}$, where $m$ is the noisy intensity.\\nSpecifically, the Gaussian noise process of any two consecutive intensities [] can be defined as:\\n$q\\\\left(\\\\boldsymbol{x}_{m}\\\\mid\\\\boldsymbol{x}_{m-1}\\\\right)=\\\\mathcal{N}\\\\left(\\\\boldsymbol{x}_{m};\\\\sqrt{1-\\\\beta_{m}}\\\\boldsymbol{x}_{m-1},\\\\beta_{m}\\\\mathrm{I}\\\\right),$\\nwhere $\\\\beta$ is the variance schedule.\\nIn this way, $\\\\boldsymbol{x}_{m}$ can be constructed by $\\\\boldsymbol{x}_{0}$:\\n$q\\\\left(\\\\boldsymbol{x}_{1:m}\\\\mid\\\\boldsymbol{x}_{0}\\\\right)=\\\\prod_{i=1}^{m}q\\\\left(\\\\boldsymbol{x}_{i}\\\\mid\\\\boldsymbol{x}_{i-1}\\\\right).$\\nBenefiting from the reparameterization technique, the final forward process is simplified to:\\n\\n$$ $\\\\boldsymbol{x}_{m}=\\\\sqrt{\\\\bar{\\\\alpha}_{m}}\\\\boldsymbol{x}_{0}+\\\\sqrt{1-\\\\bar{\\\\alpha}_{m}}\\\\boldsymbol{\\\\epsilon}_{m},$ (2) $$\\n\\nwhere the noise $\\\\boldsymbol{\\\\epsilon}_{m}\\\\sim\\\\mathcal{N}(0,\\\\mathrm{I})$ and $\\\\bar{\\\\alpha}_{m}=\\\\prod_{i=1}^{m}(1-\\\\beta_{i})$.\\n\\nReverse process.\\nThe denoising process is learning to remove noise asymptotically from $\\\\boldsymbol{x}_{m}$ to $\\\\boldsymbol{x}_{0}$, and its traditional single-step process can be defined as:\\n\\n$$ $p_{\\\\theta}\\\\left(\\\\mathrm{\\\\boldsymbol{x}}_{m-1}\\\\mid\\\\boldsymbol{x}_{m}\\\\right)=\\\\mathcal{N}\\\\left(\\\\boldsymbol{x}_{m-1};\\\\boldsymbol{\\\\mu}_{\\\\theta}\\\\left(\\\\boldsymbol{x}_{m},m\\\\right),\\\\sigma_{m}^{2}\\\\boldsymbol{I}\\\\right)$ (3) $$\\n\\nwhere $\\\\sigma_{m}^{2}$is associated with $\\\\beta_{m}$ and $\\\\boldsymbol{\\\\mu}_{\\\\theta}\\\\left(\\\\boldsymbol{x}_{m},m\\\\right)$ is the predicted mean.\\nIn this paper, we train the Video Moment Denoiser (VMD) to reverse this process.\\nThe difference is that we predict spans from the VMD network $f_{\\\\theta}(\\\\boldsymbol{x}_{m},m,\\\\boldsymbol{F})$ instead of $\\\\boldsymbol{\\\\mu}_{\\\\theta}\\\\left(\\\\boldsymbol{x}_{m},m\\\\right)$.\\n\\nDenoiser network.\\nAs shown in Fig. [3](#S3.F3), the VMD network mainly consists of 2-layer cross-attention Transformer layers.\\nNext, we walk through how VMD works step by step.\\nFor clarity, the input span and output prediction presented below are a single vector.\\n\\n❶ Span normalization.\\nUnlike generation tasks,\\nour ground-truth temporal span $\\\\boldsymbol{x}_{0}$ is defined by two parameters $\\\\boldsymbol{c}_{0}$ and $\\\\boldsymbol{w}_{0}$ that have been normalized to $[0,1]$, where $\\\\boldsymbol{c}_{0}$ and $\\\\boldsymbol{w}_{0}$ are the center and length of the span $\\\\boldsymbol{x}_{0}$.\\nTherefore, in the above forward process, we need to extend its scale to $[-\\\\lambda,\\\\lambda]$ to stay close to the Gaussian distribution [, ].\\nAfter the noise addition is completed, we need to clamp $\\\\boldsymbol{x}_{m}$ to $[-\\\\lambda,\\\\lambda]$ and then transform the range to $[0,1]$: $\\\\boldsymbol{x}_{m}=(\\\\boldsymbol{x}_{m}/\\\\lambda+1)/2$, where $\\\\lambda=2$.\\n\\n❷ Span embedding.\\nTo model the data distribution in multimodal space, we directly project the discrete span to the embedding space through the Fully Connected (FC) layer: $\\\\boldsymbol{x}^{\\\\prime}_{m}=\\\\text{FC}(\\\\boldsymbol{x}_{m})\\\\in\\\\mathbb{R}^{D}$.\\nCompared to constructing ROI features in DiffusionDet [], linear projection is very flexible and decoupled from conditional information (i.e., fusion embeddings), avoiding more redundancy.\\n\\n❸ Intensity-aware attention.\\nThe denoiser needs to understand the added noise intensity $m$ during denoising, so we design the intensity-aware attention to perceive the intensity magnitude explicitly.\\nIn Fig. [3](#S3.F3), we use sinusoidal mapping for the noise intensity $m$ to obtain $\\\\boldsymbol{e}_{m}\\\\in\\\\mathbb{R}^{D}$ in the multimodal space and add it to the span embedding.\\nWe project $\\\\boldsymbol{x}^{\\\\prime}_{m}+\\\\boldsymbol{e}_{m}$ as query embedding and\\nthe positional embedding $\\\\boldsymbol{pos}_{m}\\\\in\\\\mathbb{R}^{D}$ is obtained by sinusoidal mapping of $\\\\boldsymbol{x}_{m}$.\\nWe can obtain the input query: $\\\\boldsymbol{Q}_{m}=\\\\text{Concat}(\\\\text{Proj}(\\\\boldsymbol{x}^{\\\\prime}_{m}+\\\\boldsymbol{e}_{m}),\\\\boldsymbol{pos}_{m})$.\\nSimilarly,\\nThe input key is $\\\\boldsymbol{K}_{f}=\\\\text{Concat}(\\\\text{Proj}(\\\\boldsymbol{F}),\\\\boldsymbol{pos}_{f})$\\nand the input value is $\\\\boldsymbol{V}_{f}=\\\\text{Proj}(\\\\boldsymbol{F})$, where $\\\\text{Proj}(\\\\cdot)$ is the projection function and $\\\\boldsymbol{pos}_{f}\\\\in\\\\mathbb{R}^{D}$ is the standard position embedding in Transformer [].\\nThus, the intensity-aware attention is:\\n\\n$$ $\\\\boldsymbol{{Q}}_{m}=\\\\operatorname{softmax}\\\\left(\\\\boldsymbol{Q}_{m}\\\\boldsymbol{K}_{f}^{\\\\mathrm{T}}\\\\right)\\\\boldsymbol{V}_{f}+\\\\boldsymbol{Q}_{m}.$ (4) $$\\n\\n❹ Denoising training.\\nFinally, the generated transformer output is transformed into predicted spans $\\\\boldsymbol{\\\\hat{x}}_{m-1}=(\\\\boldsymbol{\\\\hat{c}}_{m-1},\\\\boldsymbol{\\\\hat{w}}_{m-1})$ and confidence scores $\\\\boldsymbol{\\\\hat{z}}_{m-1}$, which are implemented through a simple FC layer, respectively.\\nFollowing [], the network prediction should be as close to ground truth $\\\\boldsymbol{x}_{0}$ as possible.\\nIn addition, inspired by [, ], we define the denoising loss as:\\n\\n$$ $\\\\mathcal{L}_{\\\\text{vmr}}\\\\left(\\\\boldsymbol{x}_{0},f_{\\\\theta}(\\\\boldsymbol{x}_{m},m,\\\\boldsymbol{F})\\\\right)=\\\\lambda_{\\\\mathrm{L}1}\\\\left\\\\|\\\\boldsymbol{x}_{0}-\\\\boldsymbol{\\\\hat{x}}_{m-1}\\\\right\\\\|+\\\\lambda_{\\\\text{iou }}\\\\mathcal{L}_{\\\\text{iou }}\\\\left(\\\\boldsymbol{x}_{0},\\\\boldsymbol{\\\\hat{x}}_{m-1}\\\\right)+\\\\lambda_{\\\\text{ce}}\\\\mathcal{L}_{ce}(\\\\boldsymbol{\\\\hat{z}}_{m-1}),$ (5) $$\\n\\nwhere $\\\\lambda_{\\\\mathrm{L}1}$, $\\\\lambda_{\\\\text{iou}}$ and $\\\\lambda_{\\\\text{ce}}$ are hyperparameters, $\\\\mathcal{L}_{\\\\text{iou}}$ is a generalized IoU loss [], $\\\\mathcal{L}_{\\\\text{ce}}$ is\\na cross-entropy loss.\\nNote that the above procedure is a simplification of training.\\nConsidering that there may be more than one ground truth span in the dataset [], we set the number of input and output spans to $N_{r}$.\\nFor the input, apart from the ground truth, the extra spans are padded with random noise.\\nFor the output,\\nwe calculate the matching cost of each predicted span and ground truth according to $\\\\mathcal{L}_{vmr}$ (i.e., the Hungarian match []), and find the span with the smallest cost to calculate the loss.\\nIn $\\\\mathcal{L}_{\\\\text{ce}}$, we set the confidence label to 1 for the best predicted span and 0 for the remaining spans.\\n\\n### 3.3 Inference\\n\\nAfter training, MomentDiff can be applied to generate temporal moments for video-text pairs including unseen pairs during training.\\nSpecifically, we randomly sample noise $\\\\boldsymbol{\\\\hat{x}}_{m}$ from a Gaussian distribution $\\\\mathcal{N}(0,\\\\mathrm{I})$, the model can remove noise according to the update rule of diffusion models []:\\n\\n$$ $\\\\displaystyle\\\\boldsymbol{\\\\hat{x}}_{m-1}=$ $\\\\displaystyle\\\\sqrt{\\\\bar{\\\\alpha}_{m-1}}f_{\\\\theta}(\\\\boldsymbol{\\\\hat{x}}_{m},m,\\\\boldsymbol{F})+\\\\sqrt{1-\\\\bar{\\\\alpha}_{m-1}-\\\\sigma_{m}^{2}}\\\\frac{\\\\boldsymbol{\\\\hat{x}}_{m}-\\\\sqrt{\\\\bar{\\\\alpha}_{m}}f_{\\\\theta}(\\\\boldsymbol{\\\\hat{x}}_{m},m,\\\\boldsymbol{F})}{\\\\sqrt{1-\\\\bar{\\\\alpha}_{m}}}+\\\\sigma_{m}\\\\boldsymbol{\\\\epsilon}_{m}.$ (6) $$\\n\\nAs shown in Fig [1](#S1.F1)(d), we iterate this process continuously to obtain $\\\\boldsymbol{\\\\hat{x}}_{0}$ from coarse to fine.\\nNote that in the last step we directly use $f_{\\\\theta}(\\\\boldsymbol{\\\\hat{x}}_{1},1,\\\\boldsymbol{F})$ as $\\\\boldsymbol{\\\\hat{x}}_{0}$.\\nIn $\\\\boldsymbol{\\\\hat{x}}_{0}$, we choose the span with the highest confidence score in $\\\\boldsymbol{\\\\hat{z}}_{0}$ as the final prediction.\\nTo reduce inference overhead, we do not employ any post-processing techniques, such as box renewal in DiffusionDet [] and self-condition [].\\n\\n## 4 Experiments\\n\\n### 4.1 Datasets, Metrics and Implementation Details\\n\\nDatasets. We evaluate the efficacy of our model by conducting experiments on three representative datasets: Charades-STA [], QVHighlights [] and TACoS [].\\nThe reason is that the above three datasets exhibit diversity.\\nCharades-STA comprises intricate daily human activities.\\nQVHighlights contains a broad spectrum of themes, ranging from everyday activities and travel in lifestyle vlogs to social and political events in news videos.\\nTACoS mainly presents long-form videos featuring culinary activities.\\nThe training and testing divisions are consistent with existing methods [, ].\\n\\nMetrics. To make fair comparisons, we adopt the same evaluation metrics as those used in previous works [, , , , , , ], namely R1@n, MAP@n, and $\\\\text{MAP}_{avg}$.\\nSpecifically, R1@n is defined as the percentage of testing queries that have at least one correct retrieved moment (with an intersection over union (IoU) greater than n) within the top-1 results.\\nSimilarly, MAP@n is defined as the mean average precision with an IoU greater than n, while $\\\\text{MAP}_{avg}$ is determined as the average MAP@n across multiple IoU thresholds [0.5: 0.05: 0.95].\\n\\nImplementation details.\\nFor a fair comparison [, , ], we freeze the video encoder and text encoder and use only the extracted features.\\nFor VGG [], C3D [] or SlowFast+CLIP (SF+C) [, ], we extract video features every 1/6s, 1s or 2s.\\nSo the frame number $N_{v}$ is related to the length of the video, while the max text length $N_{t}$ is set to 32.\\nNote that since the videos in TACoS are long, we uniformly sample the video frame features and set the max frame number $N_{v}$ to 100 in TACoS.\\nWe set the hidden size $D=256$ in all Transformer layers.\\nIn SCG, we also use a variant of the pairwise margin loss called InfoNCE loss [].\\nThe number of random spans $N_{r}$ is set to 10 for QVHighlights, 5 for Charades-STA and TACoS.\\nWe use the cosine schedule for $\\\\beta$.\\nFor all datasets, we optimize MomentDiff for 100 epochs on one NVIDIA Tesla A100 GPU,\\nemploy Adam optimizer [] with 1e-4 weight decay and fix the batch size as 32.\\nThe learning rate is set to 1e-4.\\nBy default, the loss hyperparameters $\\\\lambda_{\\\\mathrm{L}1}=10$, $\\\\lambda_{\\\\text{iou}}=1$ and $\\\\lambda_{\\\\text{ce}}=4$.\\nThe weight values for $\\\\mathcal{L}_{sim}$ and $\\\\mathcal{L}_{vmr}$ are 4 and 1.\\nTo speed up the sampling process during inference, we follow DDIM [] and iterate 50 times.\\n\\n**Table 1: Performance comparisons (%) on the Charades-STA dataset. \\\"${\\\\star}$\\\" denotes that we re-implement the method under the same training scheme. \\\"A\\\" stands for using audio data.**\\n| Method | Type | Charades-STA | | | | |\\n| --- | --- | --- | --- | --- | --- | --- |\\n| R1@0.5 | R1@0.7 | MAP@0.5 | MAP@0.75 | $\\\\text{MAP}_{avg}$ | | |\\n| MAN [] | VGG, Glove | 41.21 | 20.54 | - | - | - |\\n| RaNet^⋆[] | VGG, Glove | 42.91 | 25.82 | 53.28 | 24.41 | 28.55 |\\n| 2DTAN^⋆[] | VGG, Glove | 41.34 | 23.91 | 54.68 | 24.15 | 29.26 |\\n| DORi [] | VGG, Glove | 43.47 | 26.37 | - | - | - |\\n| CBLN [] | VGG, Glove | 47.94 | 28.22 | - | - | - |\\n| DCM [] | VGG, Glove | 47.80 | 28.00 | - | - | - |\\n| MMN^⋆ [] | VGG, Glove | 46.93 | 27.07 | 58.85 | 28.16 | 31.58 |\\n| MomentDETR^⋆ [] | VGG, Glove | 50.54 | 28.01 | 57.39 | 25.62 | 29.87 |\\n| MomentDiff | VGG, Glove | 51.94 | 28.25 | 59.86 | 29.11 | 31.66 |\\n| UMT [] | VGG+A, Glove | 48.44 | 29.76 | 58.03 | 27.46 | 30.37 |\\n| MomentDiff | VGG+A, Glove | 52.62 | 29.93 | 60.69 | 29.74 | 31.81 |\\n| DEBUG[] | C3D, Glove | 37.39 | 17.69 | - | - | - |\\n| LPNet[] | C3D, Glove | 40.94 | 21.13 | - | - | - |\\n| VSLNet^⋆[] | C3D, Glove | 48.67 | 30.33 | 56.88 | 25.79 | 30.16 |\\n| MomentDETR^⋆[] | C3D, Glove | 50.49 | 29.95 | 56.27 | 26.08 | 29.92 |\\n| MomentDiff | C3D, Glove | 53.79 | 30.18 | 59.32 | 29.85 | 31.89 |\\n| MomentDETR^⋆ [] | SF+C, C | 53.22 | 30.87 | 58.86 | 26.43 | 30.43 |\\n| MomentDiff | SF+C, Glove | 55.42 | 32.17 | 60.93 | 32.47 | 32.59 |\\n| MomentDiff | SF+C, C | 55.57 | 32.42 | 61.07 | 32.51 | 32.85 |\\n\\n### 4.2 Performance Comparisons\\n\\nComparison with state-of-the-art methods.\\nTo prove the effectiveness of MomentDiff, we compare the retrieval performance with 17 discriminative VMR methods.\\nTab. [1](#S4.T1), Tab. [4.2](#S4.SS2), and Tab. [4.2](#S4.SS2) show the R1@n, MAP@n, and $\\\\text{MAP}_{avg}$ results on Charades-STA, QVHighlights and TACoS.\\nCompared with SOTA methods [, , , , , ], MomentDiff achieves significant improvements on Charades-STA regardless of whether 2D features (VGG), multimodal features (VGG+A), 3D features (C3D), or multimodal pre-trained features (SF+C) are used.\\nThis proves that MomentDiff is a universal generative VMR method.\\nIn the other two datasets (QVHighlights and TACoS), we still have highly competitive results.\\nSpecifically, compared to MomentDETR [], MomentDiff obtains 2.35%, 3.86%, and 13.13% average gains in R1@0.5 on three datasets.\\nIt is worth noting that TACoS contains long videos of cooking events where different events are only slightly different in terms of cookware, food and other items.\\nThe learnable queries in MomentDETR may not cope well with such fine-grained dynamic changes.\\nWe attribute the great advantage of MomentDiff over these methods to fully exploiting similarity-aware condition information and progressive refinement denoising.\\n\\nFigure: Table 2: Performance comparisons (%) on QVHighlights with SF+C video features and CLIP text features. \\\"${\\\\star}$\\\" denotes that we re-implement the method with only segment moment labels. \\\"${\\\\dagger}$\\\" stands for using audio data. MDE is the abbreviation of MomentDETR [].\\n\\nFigure: Table 3: Performance comparisons (%) on TACoS. We adopt C3D features to encode videos. MDE is the abbreviation of MomentDETR [].\\n\\n**Table 4: Transfer experiments (%) on Charades-CD (VGG, Glove) and ActivityNet-CD (C3D, Glove).**\\n| Method | Charades-CD | ActivityNet-CD | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| R1@0.3 | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | R1@0.3 | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | |\\n| 2DTAN [] | 49.71 | 28.95 | 12.78 | 12.60 | 40.04 | 22.07 | 10.29 | 12.77 |\\n| MMN [] | 55.91 | 34.56 | 15.84 | 15.73 | 44.13 | 24.69 | 12.22 | 15.06 |\\n| MomentDETR [] | 57.34 | 41.18 | 19.31 | 18.95 | 39.98 | 21.30 | 10.58 | 12.19 |\\n| MomentDiff | 67.73 | 47.17 | 22.98 | 22.76 | 45.54 | 26.96 | 13.69 | 16.38 |\\n\\n**Table 5: Transfer experiments (%) on anti-bias datasets with VGG and Glove video-text features.**\\n| Method | Charades-STA-Len | Charades-STA-Mom | | | | | | |\\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\\n| R1@0.3 | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | R1@0.3 | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | |\\n| 2DTAN [] | 39.68 | 28.68 | 17.72 | 22.79 | 27.81 | 20.44 | 10.84 | 17.23 |\\n| MMN [] | 43.58 | 34.31 | 19.94 | 26.85 | 33.58 | 27.20 | 14.12 | 19.18 |\\n| MomentDETR [] | 42.73 | 34.39 | 16.12 | 24.02 | 29.94 | 22.16 | 11.56 | 18.66 |\\n| MomentDiff | 51.25 | 38.32 | 23.38 | 28.19 | 48.39 | 33.59 | 15.71 | 21.37 |\\n\\nFigure: Figure 4: Statistical distributions on anti-bias datasets with location distribution shifts. We count the length or moment of each video-text pair, and finally normalize the counts ($\\\\#$ Samples) for clarity. Train/Test: the count distribution of true spans on the training or test set. MDE: the count distribution of top-1 predicted spans by using MomentDETR on the test set.\\nRefer to caption: /html/2307.02869/assets/x4.png\\n\\nTransfer experiments.\\nTo explore the location bias problem, we first organize the Out of Distribution (OOD) experiment following [], which repartitions Charades-STA [] and ActivityNet-Captions [] datasets according to moment annotation density values [].\\nIn Tab. [4](#S4.T4), we exceed MomentDETR by a large margin on Charades-CD and ActivityNet-CD.\\nThese results prove the robustness of the model in dealing with OOD scenarios.\\n\\nTo further explore the impact of a single factor ($\\\\boldsymbol{w}_{0}$ or $\\\\boldsymbol{c}_{0}$ ) on the location bias problem,\\nwe organize moment retrieval on two anti-bias datasets with location distribution shifts:\\n❶ Charades-STA-Len.\\nWe collect all video-text pairs with $\\\\boldsymbol{w}_{0}\\\\leq 10s$ and randomly sample pairs with $\\\\boldsymbol{w}_{0}>10s$ in the original training set of Charades-STA, which account for 80% and 20% of the new training set, respectively.\\nOn the contrary, we collect all pairs with $\\\\boldsymbol{w}_{0}>10s$ and randomly sample pairs with $\\\\boldsymbol{w}_{0}\\\\leq 10s$ from the original test set, accounting for 80% and 20% of the new test set.\\n❷ Charades-STA-Mom.\\nSimilarly, we collect all video-text pairs with the end time $\\\\boldsymbol{c}_{0}+\\\\boldsymbol{w}_{0}/2\\\\leq 15s$ and sample pairs with the start time $\\\\boldsymbol{c}_{0}-\\\\boldsymbol{w}_{0}/2>15s$ as the training set, which accounts for 80% and 20%, respectively.\\nLikewise, the construction rules for the test set are the opposite of those for the training set.\\nDataset statistics can refer to Train/Test in Fig. [4](#S4.F4) and the supplementary material.\\n\\nIn Tab. [5](#S4.T5), the proposed MomentDiff shows much more robustness than previous state-of-the-art method MomentDETR [].\\nConcretely, compared with the experiment in Tab. [1](#S4.T1), the performance gap between MomentDiff and MomentDETR gets larger on Charades-STA-Len and Charades-STA-Mom.\\nFig. [4](#S4.F4) also demonstrates that the distribution of our prediction is closer to the one of the test set.\\nWe conjecture that it is because MomentDiff discards the learnable proposals that fit the prior distribution of the training set.\\nMoreover, 2DTAN [] and MMN [] perform worse than MomentDETR on the original Charades-STA dataset, but they achieve better or comparable results than MomentDETR in Tab. [5](#S4.T5).\\nThis shows that predefined proposals [, ] may be better than learnable proposals in dealing with the location bias problem, but they take up more time and space overhead.\\nDifferently, our method performs well on both public datasets and anti-bias datasets.\\n\\n**Table 6: Ablation study (%) on the Charades-STA dataset with SF+C video features and CLIP text features. We report R1@0.5, R1@0.7 and $\\\\text{MAP}_{avg}$. Default settings are marked in blue.**\\n| Type | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ |\\n| --- | --- | --- | --- |\\n| ROI | 50.21 | 28.85 | 29.12 |\\n| FC | 55.57 | 32.42 | 32.85 |\\n\\nFigure: Figure 5: Visualization of the diffusion process on Charades-STA (Left) and QVHighlights (Right). For clarity, we show 3 random spans ($\\\\boldsymbol{x}_{50}$) with Gaussian initialization, and progressively get the top-1 result ($\\\\boldsymbol{x}_{0}$) according to the confidence score. Green box: right segment. MDE: MomentDETR [].\\nRefer to caption: /html/2307.02869/assets/x5.png\\n\\n### 4.3 Ablation Study\\n\\nTo provide further insight into MomentDiff, we conduct critical ablation studies on Charades-STA.\\n\\nSpan embedding type.\\nRegarding the way discrete spans are mapped to the embedding space,\\nwe compare the ROI strategy [] with our linear projection (FC) in Tab. [6](#S4.T6)(a).\\nFor the ROI strategy, we slice the fusion embeddings $\\\\boldsymbol{F}$ corresponding to random spans, followed by mean pooling on the sliced features.\\nTab. [6](#S4.T6)(a) shows that ROI does not work well.\\nThis may be due to two points:\\n1) ROI is a hard projection strategy, while the importance of each video frame is quite different.\\nFC is similar to soft ROI, and its process can be trained end-to-end.\\n2) FC is decoupled from $\\\\boldsymbol{F}$, which allows the model to focus on modeling the diffusion process and avoid over-dependence on $\\\\boldsymbol{F}$.\\n\\nScale $\\\\lambda$.\\n$\\\\lambda$ is the signal-to-noise ratio [] of the diffusion process, and its effect is shown in Tab. [6](#S4.T6)(b).\\nWe find that the effect of larger $\\\\lambda$ drops significantly,\\nwhich may be due to the lack of more hard samples for denoising training when the proportion of noise is small, resulting in poor generalization.\\n\\nVideo Moment Denoiser (VMD) and noise intensity $m$.\\nIn Tab. [6](#S4.T6)(c), we first remove the denoiser and the diffusion process (w/o VMD).\\nAfter training with the same losses, we find that predicting with only fusion embeddings $\\\\boldsymbol{F}$ leads to a drastic drop in results, which reveals the effectiveness of denoising training.\\nThen we remove the noise intensity $m$ (w/o $m$), and the result is reduced by 5.16% on R1@0.5. This shows that explicitly aggregating noise intensity with random spans improves noise modeling.\\nCombined with VMD and $m$, the diffusion mechanism can fully understand the data distribution and generate the real span from coarse to fine.\\n\\nLoss designs.\\nIn Tab. [6](#S4.T6)(d), we show the impact of loss functions.\\nIn $\\\\mathcal{L}_{sim}$, we use pointwise and pairwise constraints to guide token-wise interactions between multimodal features, while ensuring reliable conditions for subsequent denoising.\\nIn $\\\\mathcal{L}_{vmr}$, the model can learn to accurately localize exact segments.\\nAdequate multimodal interaction and denoising training procedures are complementary.\\n\\nSpan number.\\nIn Tab. [6](#S4.T6)(e), we only need 5 random spans to achieve good results.\\nUnlike object detection [], the number of correct video segments corresponding to text query is small.\\nTherefore, a large number of random inputs may make the model difficult to train and deteriorate the performance.\\n\\nModel performance vs. speed.\\nIn Tab. [6](#S4.T6)(f), we explore the effects of different diffusion steps.\\nWhen step=2, good results and fast inference speed have been achieved.\\nSubsequent iterations can improve the results of high IoU (i.e., R1@0.7), which shows the natural advantages of diffusion models.\\n\\n### 4.4 Qualitative Results\\n\\nWe show two examples of the diffusion process in Fig. [5](#S4.F5).\\nWe can find that the retrieved moments by MomentDiff are closer to the ground truth than those by MomentDETR.\\nThe diffusion process can gradually reveal the similarity between text and video frames, thus achieving better results.\\nBesides, the final predictions corresponding to spans with multiple random initial locations are close to the ground truth.\\nThis shows that our model achieves a mapping from arbitrary locations to real segments.\\n\\n## 5 Limitation and Conclusion\\n\\nLimitation.\\nCompared to existing methods [, ], the diffusion process requires multiple rounds of iterations, which may affect the inference speed.\\nAs shown in Tab. [6](#S4.T6)(f), we reduce the number of iterations, with only a small sacrifice in performance.\\nIn practical usage, we suggest choosing a reasonable step number for a better trade-off between performance and speed.\\n\\nConclusion.\\nThis paper proposes a novel generative video moment retrieval framework, MomentDiff, which simulates a typical human retrieval style via diffusion models.\\nBenefiting from the denoising diffusion process from random noise to temporal span, we achieve the refinement of prediction results and alleviate the location bias problem existing in discriminative methods.\\nMomentDiff demonstrates efficiency and generalization on multiple diverse and anti-bias datasets.\\nWe aim to stimulate further research on video moment retrieval by addressing the inadequacies in the framework design, and firmly believe that this work provides fundamental insights into the multimodal domain.\\n\\n## 6 Acknowledgement\\n\\nThis work is supported by the National Key Research and Development Program of China (2022YFB3104700), the National Nature Science Foundation of China (62121002, 62022076, 62232006).\\n\\n## Appendix A Implementation details\\n\\n### A.1 Datasets\\n\\nPublic datasets.\\nCharades-STA [] serves as a benchmark dataset for the video moment retrieval task and is built upon the Charades dataset, originally collected for video action recognition and video captioning.\\nThe Charades-STA dataset comprises 6,672 videos and 16,128 video-query pairs, allocated for training (12,408 pairs) and testing (3,720 pairs).\\nOn average, the videos in this dataset have a duration of 29.76 seconds.\\nEach video is annotated with an average of 2.4 moments, with each moment lasting approximately 8.2 seconds.\\nQVHighlights [] contains 10,148 videos, each 150 seconds long and annotated with at least one text query describing its relevant content.\\nThese videos are from three main categories, daily vlogs, travel vlogs, and news events.\\nOn average, there are approximately 1.8 non-overlapping moments per query, annotated on 2s non-overlapping clips.\\nThe dataset contains a total of 10,310 queries with 18,367 annotated moments.\\nThe training set, validation set and test set include 7,218, 1,550 and 1,542 video-text pairs, respectively.\\nTACoS [] is compiled specifically for video moment retrieval and dense video captioning tasks.\\nIt is comprised of 127 videos that depict cooking activities, with an average duration of 4.79 minutes. TACoS contains a total of 18,818 video-query pairs.\\nIn comparison to the Charades-STA dataset, TACoS has more video segments that are temporally annotated with queries per video.\\nOn average, each video contains 148 queries.\\nAdditionally, the TACoS dataset is known for its difficulty, as the queries it contains are limited to only a few seconds or even just a few frames.\\nTo ensure impartial comparisons, we use the same dataset split [], which consists of 10,146, 4,589, and 4,083 video-query pairs for the training, validation, and testing sets, respectively.\\nActivityNet-Captions [] comprises of 20,000 videos and 100,000 descriptions that encompass a wide range of contexts.\\nSimilar to [], we designate val 1 as the validation set and val 2 as the testing set. The dataset contains 37,417, 17,505, and 17,031 pairs of moments and corresponding sentences for training, validation, and testing respectively.\\n\\n**Table 7: Training and test sets on two anti-bias datasets.**\\n| Dataset | Charades-STA-Len | Charades-STA-Mom | | | | |\\n| --- | --- | --- | --- | --- | --- | --- |\\n| $\\\\boldsymbol{w}_{0}\\\\leq 10s$ | $\\\\boldsymbol{w}_{0}>10s$ | Total | $\\\\boldsymbol{c}_{0}+\\\\boldsymbol{w}_{0}/2\\\\leq 15s$ | $\\\\boldsymbol{c}_{0}-\\\\boldsymbol{w}_{0}/2>15s$ | Total | |\\n| Training | 9307 | 2326 | 11633 | 5330 | 1332 | 6662 |\\n| Test | 197 | 788 | 985 | 259 | 1038 | 1297 |\\n\\nAnti-bias datasets.\\nTo explore the location bias problem, we construct two anti-bias datasets with location distribution shifts based on the Charades-STA dataset.\\nIn video moment retrieval, length and position are important parameters of spans.\\n\\nTherefore, we first investigate the effect of span length $\\\\boldsymbol{w}_{0}$.\\nAs shown in Tab. [7](#A1.T7), in the training set of Charades-STA-Len, we collect 9,307 video-text pairs with span length $\\\\boldsymbol{w}_{0}\\\\leq 10s$ and 2,326 video-text pairs with $\\\\boldsymbol{w}_{0}>10s$, accounting for 80% and 20% of the total training set.\\nIn contrast, in the test set, we select 197 video-text pairs with $\\\\boldsymbol{w}_{0}\\\\leq 10s$ and 788 video-text pairs with $\\\\boldsymbol{w}_{0}>10s$, accounting for 20% and 80% of the total test set.\\n\\nThen, we design the dataset Charades-STA-Mom based on the span’s end time $\\\\boldsymbol{c}_{0}+\\\\boldsymbol{w}_{0}/2$ and start time $\\\\boldsymbol{c}_{0}-\\\\boldsymbol{w}_{0}/2$.\\nIn the training set of Charades-STA-Mom, we collect 5,330 video-text pairs with $\\\\boldsymbol{c}_{0}+\\\\boldsymbol{w}_{0}/2\\\\leq 15s$ and 1,332 video-text pairs with $\\\\boldsymbol{c}_{0}-\\\\boldsymbol{w}_{0}/2>15s$, accounting for 80% and 20% of the total training set.\\nIn contrast, in the test set, we select 259 video-text pairs with $\\\\boldsymbol{c}_{0}+\\\\boldsymbol{w}_{0}/2\\\\leq 15s$ and 788 video-text pairs with $\\\\boldsymbol{c}_{0}-\\\\boldsymbol{w}_{0}/2>15s$, accounting for 20% and 80% of the total test set.\\n\\nFigure: Algorithm 1 MomentDiff Training in a PyTorch-like style.\\n\\n### A.2 Pseudo Code of MomentDiff\\n\\nAlgorithm [1](#algorithm1) provides the pseudo-code of MomentDiff Training in a PyTorch-like style.\\n\\nThe inference procedure of MomentDiff is a denoising sampling process from noise to temporal spans.\\nStarting from spans sampled in Gaussian distribution, the model progressively refines its predictions, as shown in Algorithm [2](#algorithm2).\\n\\nFigure: Algorithm 2 MomentDiff inference in a PyTorch-like style.\\n\\n## Appendix B Inference Efficiency of MomentDiff\\n\\n**Table 8: The inference time of 2DTAN [], MMN [], MomentDETR [] and MomentDiff on Charades-STA with VGG video features and Glove text features. We report R1@0.5, R1@0.7 and $\\\\text{MAP}_{avg}$. Default settings are marked in blue.**\\n| Method | Charades-STA | Inference time | | |\\n| --- | --- | --- | --- | --- |\\n| R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | (second) | |\\n| 2DTAN [] | 41.34 | 23.91 | 29.26 | 42.18 |\\n| MMN [] | 46.93 | 27.07 | 31.58 | 53.42 |\\n| MomentDETR [] | 50.54 | 28.01 | 29.87 | 12.42 |\\n| MomentDiff (Step=1) | 49.17 | 26.39 | 29.12 | 7.56 |\\n| MomentDiff (Step=2) | 50.81 | 27.84 | 31.27 | 8.23 |\\n| MomentDiff (Step=10) | 52.36 | 28.08 | 31.75 | 11.01 |\\n| MomentDiff (Step=50) | 51.94 | 28.25 | 31.66 | 20.74 |\\n| MomentDiff (Step=100) | 52.21 | 28.84 | 31.01 | 34.35 |\\n\\nInference time.\\nInference efficiency is critical for machine learning models.\\nWe test 2DTAN [], MMN [], MomentDETR [] and MomentDiff on the Pytorch framework [] in Tab. [8](#A2.T8).\\nWe test all models with one NVIDIA Tesla A100 GPU.\\n\\nCompared with 2DTAN [] and MMN [], MomentDiff (Step=1) not only achieves the best results on recall, but also improves the inference speed by 5-7 times.\\nThis is because 2DTAN and MMN predefine a large number of proposals, which may be redundant and increase computational overhead.\\nCompared to MomentDETR [], MomentDiff (Step=10) achieves better results with similar inference time.\\nThe possible reasons are that we adopt fewer random spans, very simple network structures, and avoid post-processing.\\n\\n## Appendix C More Experiment Results\\n\\n### C.1 Experiment on ActivityNet-Captions\\n\\nThe results of our method on ActivityNet-Captions are shown in Tab. [9](#A3.T9).\\nWe record the 1 epoch training time and the inference time for all test samples in one NVIDIA Tesla A100 GPU.\\nOur model has been improved compared with baseline (MomentDETR).\\nCompared to SOTAs, we still have competitive results.\\nCompared with MMN, our method is 25 times faster in training time and 7.24 times faster in testing time.\\n\\n### C.2 Error bars\\n\\nFig. [6](#A3.F6) shows the performance fluctuation of the model on the Charades-STA dataset.\\nWe use different random seeds (seed= 2023, 2022, 2021, 2020, 2019) and different features (VGG, Glove; C3D, Glove; SF+C, C;) to organize experiments.\\nThis shows that the model always converges and achieves stable results for different initializations.\\nThis phenomenon demonstrates the ability of the model to learn to generate real spans from arbitrary random spans.\\n\\n**Table 9: Performance comparisons (%) on ActivityNet-Captions with C3D video features and Glove text features.**\\n| Method | R1@0.3 | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ | Training time | Inference time |\\n| --- | --- | --- | --- | --- | --- | --- |\\n| 2DTAN [] | 59.92 | 44.63 | 27.53 | 27.26 | 1.1h | 523.74s |\\n| MMN [] | 65.21 | 48.26 | 28.95 | 28.74 | 1.5h | 662.12s |\\n| MomentDETR [] | 61.87 | 43.19 | 25.74 | 25.63 | 0.05h | 52.72s |\\n| MomentDiff | 62.79 | 46.52 | 28.43 | 28.19 | 0.06h | 91.43s |\\n\\nFigure: Figure 6: Performance fluctuations (%) corresponding to different features and multiple random seeds on the Charades-STA dataset.\\nRefer to caption: /html/2307.02869/assets/x6.png\\n\\n**Table 10: Ablation study (%) on the Charades-STA dataset with SF+C video features and CLIP text features. We report R1@0.5, R1@0.7 and $\\\\text{MAP}_{avg}$. Default settings are marked in blue.**\\n| Sampling | R1@0.5 | R1@0.7 | $\\\\text{MAP}_{avg}$ |\\n| --- | --- | --- | --- |\\n| DDPM [] | 55.62 | 32.37 | 32.48 |\\n| DDIM [] | 55.57 | 32.42 | 32.85 |\\n\\n### C.3 Ablation study\\n\\nDifferent sampling strategies.\\nDenoising Diffusion Probabilistic Models (DDPM) [] and Denoising Diffusion Implicit Models (DDIM) [] are popular and classic diffusion models.\\nWe show the results of both strategies in Tab. [10](#A3.T10)(a).\\nWe find that DDIM and DDPM perform similarly, but DDIM samples faster.\\nTherefore we adopt DDIM as the default technology.\\n\\nEffect of the schedule of $\\\\beta$.\\nThe schedule of $\\\\beta$ determines the weighting ratio of different intensity noises.\\nIn Tab. [10](#A3.T10)(b), we find that the cosine schedule works better in our experiment.\\nThe cosine schedule makes the noisy spans change slowly at the beginning and end during the diffusion process, and the generation effect is more stable.\\nSo we set the cosine schedule as the default.\\n\\nEffect of the Box Renewal.\\nBox Renewal is a post-processing technique in DiffusionDet [].\\nTab. [10](#A3.T10)(c) shows that Box Renewal can indeed slightly improve the results.\\nTo keep the inference process as simple as possible, we do not use Box Renewal by default.\\n\\nEffect of the batch size.\\nAs shown in Tab. [10](#A3.T10)(d), we set the batch size to 32 to achieve the best results.\\n\\nEffect of the layer number.\\nIn Tab. [10](#A3.T10)(e), we show the effect of the layer number of Similarity-aware Condition Generator (SCG) and Video Moment Denoiser (VMD). The default setting (2+2:2): SCG contains 2 cross-attention and 2 self-attention layers and VMD contains 2 cross-attention layers.\\nThe default setting works best.\\n\\nEffect of the weight value on $\\\\mathcal{L}_{sim}$.\\nWe set the weight values of $\\\\mathcal{L}_{sim}$ and $\\\\mathcal{L}_{vmr}$ to 4 and 1, respectively.\\nKeeping the weight value of $\\\\mathcal{L}_{vmr}$ unchanged, we organize the weight influence experiment of $\\\\mathcal{L}_{sim}$, as shown in Tab. [10](#A3.T10)(f).\\nThe default setting works best.\\n\\nEffect of the number of spans on R1@0.5.\\nOur training and inference are decoupled.\\nOur simple framework allows us to input any number of random noises.\\nTab. [10](#A3.T10)(g) shows that there is a slight improvement when testing with more noise boxes.\\n\\n## Appendix D Broader Impacts\\n\\nFirst, our work does not involve private data.\\nSecond, we believe that AI is a double-edged sword, and our model is no exception.\\nFor example, when users or websites use our model, only natural language is needed to locate video moments and collect desired video material, which improves the productivity of society.\\nHowever, this may have a negative impact if the natural language entered by the user contains words related to violence, pornography, etc.\\nWe will consider these scenarios and implement a more secure VMR model.\",\n \"metadata\": {\n \"authors\": [\n \"Lei Zhang\",\n \", Yun Zheng\",\n \", Deli Zhao\",\n \", Yongdong Zhang\"\n ],\n \"title\": \"MomentDiff: Generative Video Moment Retrieval from Random to Real\",\n \"total_chars\": 51106,\n \"total_lines\": 577,\n \"updated_at\": \"2026-01-25T15:02:53.785321\"\n }\n}"},"reviews":{"kind":"list like","value":[{"id":"MPehAL5waJ","initial_rating":6,"confidence":4,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper first introduce a novel GVMR framework that significantly expands the scope of traditional VMR, catering to a wider range of query types and enhancing the model’s practical nutility and present a meticulously curated dataset. To deal with GVMR, they propose the BCANet model. Totally speaking, the contributions about extend task and new dataset is valuable.","strengths":"1. This paper introduces a extend task about TVG which covers more situations about video localiztion.\n2. They build a new dataset for their introduced dataset which helps the deeper researches in future.\n3. They propose a model based on LLM generate queries in fine-grain semantic, to benefit the video content understanding to the next stage","weaknesses":"1. The boundary awareness is a common question in this field and many works like[1] focus on this problem. The author didn't analyse the differences between them to show their novelty.\n\n\n*[1]J. Wang, L. Ma, and W. Jiang, “Temporally grounding language queries in videos by contextual boundary-aware prediction,” in AAAI, 2020.","questions":"1. The model relies on the LLaVa to generate scene captions to divide the backgrounds and foregrounds. Will it brings noisy due to the diversity of generated samples?\n2. Did you compare your model with the finetuinng model based on multimodal LLM ?\n3. With using the LLM to generate captions , what about the time cost and memory usage?\n4. Will the dataset be open source? If so ,it will be an important contribution."},{"id":"aMPEIbURhB","initial_rating":6,"confidence":5,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper introduces the Generalized Video Moment Retrieval (GVMR) framework, which extends traditional Video Moment Retrieval (VMR) to handle a wider range of query types. To support this expanded task, it presents the NExT-VMR dataset, derived from the YFCC100M collection, featuring diverse query scenarios to enable more robust model evaluation. Additionally, a novel transformer-based model named BCANet is proposed and achieves outperforms when compared with traditional VMR approaches.","strengths":"1. A novel GVMR framework is first introduced that significantly expands the scope of traditional VMR, catering to a wider range of query types and enhancing the model's practical utility.\n\n2. A meticulously curated dataset, NExT-VMR, is presented. The dataset is specifically designed for GVMR task, which includes a variety of query types and scenarios, thereby enabling more robust and versatile model training and evaluation.","weaknesses":"1. As mentioned in the paper, \"GVMR aspires to deliver a robust and flexible solution for video moment retrieval, significantly enhancing the model's interpretative prowess, precision, and retrieval efficiency.\" Would the enhancement of the model on interpretative prowess, precision, and retrieval efficiency be proved and presented in experiments?\n\n2. More statistics of the proposed dataset are needed to be listed in Table 1, such as the entire/average lengths of videos and queries and the number of one-to-multi and no-target samples in the dataset.\n\n3. Is it possible to demonstrate the evaluation of this method on traditional VMR datasets (e.g., Charades, ActivityNet, and TACoS) for one-to-one (different from the mentioned one-to-multi or no-target) VMR tasks? \n\n4. The BCANet pipeline presented in Figure 1 is confusing and difficult to interpret. The respective variable symbols should be labeled in Figure 1. Moreover, the processes for the BCL and QCA modules, along with query-text cross-attention, are also not clearly depicted in the figure. Moreover, what's the meaning of the \"region\" and \"region features\" in this paper? Dose the \"region\" mean a video clip?\n\n5. The BCANet proposed in this paper does not seem to include specific designs for handling one-to-multi cases. Compared to traditional VMR methods, what advantages does BCANet offer in dealing with such data?\n\n6. Since the retrieval speed is also an important metric in VMR, for example, [a] analyze the speed of various VMR approaches. I recommend the authors conducting speed analysis in this paper. In addition, is GVMR slower than traditional VMR?\n[a] Fast video moment retrieval, ICCV 2021.","questions":"Please refer to the weakness part."},{"id":"9HvlIWs5s1","initial_rating":5,"confidence":5,"soundness":2,"contribution":3,"presentation":2,"summary":"This paper introduces the Generalized Video Moment Retrieval framework, which expands traditional VMR to handle complex, non-target, and multi-target queries. To support this, the authors present the NExT-VMR dataset and BCANet, a transformer-based model with a Boundary-aware Cross Attention module that improves boundary detection and query understanding. \nThe results show that GVMR, NExT-VMR, and BCANet significantly enhance VMR performance, setting a new benchmark for future research in multimedia information retrieval.","strengths":"The problem the authors solve is interesting.\n\nThis paper provides a good moment retrieval dataset.\n\nThe paper is clearly written and the method can be understood.","weaknesses":"- The NExT-VMR dataset is not large enough to be used for large-scale training. In addition, why not divide the test set on NExT-VMR for experiments?\n\n- Figure 3 is confusing. There are many colored blocks around the Query-Text Cross Attention module. I don't understand what it wants to express? Lack of technical details.","questions":"- Can't the previous model achieve multi-target query well after training on the standard dataset? Lack of relevant experiments to prove the author's motivation.\n\n- Can the model in this paper use a single query to query multiple related clips in the video? This is a more worthy of attention.\n\n- YFCC100M is an excellent large-scale video dataset, but why did the author only select 9957 videos from YFCC100M? How was it selected?\n- Will the author open source the dataset and code?"},{"id":"Dx7CG8IfID","initial_rating":6,"confidence":5,"soundness":3,"contribution":3,"presentation":3,"summary":"This paper introduces the Generalized Video Moment Retrieval (GVMR) framework, which expands traditional Video Moment Retrieval (VMR) to accommodate both non-target and multi-target queries, moving beyond the usual single-target focus. To support this, the authors present the NExT-VMR dataset, derived from the YFCC100M collection, featuring diverse query scenarios for robust model evaluation. They also propose BCANet, a transformer-based model that incorporates the Boundary-aware Cross Attention (BCA) module to enhance boundary detection and improve understanding of video content in relation to queries. Experiments demonstrate the potential of the NExT-VMR dataset and BCANet to advance VMR capabilities.","strengths":"- This paper introduces a new task called Generalized Video Moment Retrieval (GVMR), which is designed to adeptly handle the complexities of various query types, extending the traditional Video Moment Retrieval (VMR) paradigm to include both multiple-target and no-target queries.\n- This paper presents a specialized dataset, NExT-VMR, which is meticulously constructed and analyzed from the YFCC100M dataset. Tailored specifically for GVMR, this dataset features a diverse range of query types, including one-to-multiple and no-target queries.\n- This paper introduces a model called BCANet, aimed at improving performance on the challenging task of GVMR, where the model must accurately predict a variable number of temporal timestamps based on natural language descriptions.","weaknesses":"- Why does the paper utilize the YFCC100M dataset as the primary data source instead of existing VMR datasets such as TACoS, Charades-STA, MAD, or ActivityNet-Captions?\n- From the statistics in Table 1, it can be seen that the average number of segments corresponding to a query is less than 2, which contradicts the paper's motivation for creating multiple-target queries. Additionally, the proportion of non-target queries is very low. Based on the dataset statistics, it is unclear where the challenges of this new dataset compared to existing ones lie.\n- From Table 2, it can be seen that BCANet shows a significant advantage only in the single-moment retrieval task, while its performance in multi-target and non-target scenarios is not as pronounced. This raises questions about the overall effectiveness of the method.","questions":"- BCANet is a supervised learning framework. How does it address the issue of inconsistent target quantities for each query in a batch during the training process? Additionally, if a query corresponds to three moments, are all three segments' timestamp information used in the loss function calculation?\n- For queries labeled as non-target, what information do they provide during training?\n- Why does the paper utilize the YFCC100M dataset as the primary data source instead of existing VMR datasets such as TACoS, Charades-STA, MAD, or ActivityNet-Captions?\n- From the statistics in Table 1, it can be seen that the average number of segments corresponding to a query is less than 2, which contradicts the paper's motivation for creating multiple-target queries. Additionally, the proportion of non-target queries is very low. Based on the dataset statistics, it is unclear where the challenges of this new dataset compared to existing ones lie.\n- From Table 2, it can be seen that BCANet shows a significant advantage only in the single-moment retrieval task, while its performance in multi-target and non-target scenarios is not as pronounced. This raises questions about the overall effectiveness of the method."}],"string":"[\n {\n \"id\": \"MPehAL5waJ\",\n \"initial_rating\": 6,\n \"confidence\": 4,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper first introduce a novel GVMR framework that significantly expands the scope of traditional VMR, catering to a wider range of query types and enhancing the model’s practical nutility and present a meticulously curated dataset. To deal with GVMR, they propose the BCANet model. Totally speaking, the contributions about extend task and new dataset is valuable.\",\n \"strengths\": \"1. This paper introduces a extend task about TVG which covers more situations about video localiztion.\\n2. They build a new dataset for their introduced dataset which helps the deeper researches in future.\\n3. They propose a model based on LLM generate queries in fine-grain semantic, to benefit the video content understanding to the next stage\",\n \"weaknesses\": \"1. The boundary awareness is a common question in this field and many works like[1] focus on this problem. The author didn't analyse the differences between them to show their novelty.\\n\\n\\n*[1]J. Wang, L. Ma, and W. Jiang, “Temporally grounding language queries in videos by contextual boundary-aware prediction,” in AAAI, 2020.\",\n \"questions\": \"1. The model relies on the LLaVa to generate scene captions to divide the backgrounds and foregrounds. Will it brings noisy due to the diversity of generated samples?\\n2. Did you compare your model with the finetuinng model based on multimodal LLM ?\\n3. With using the LLM to generate captions , what about the time cost and memory usage?\\n4. Will the dataset be open source? If so ,it will be an important contribution.\"\n },\n {\n \"id\": \"aMPEIbURhB\",\n \"initial_rating\": 6,\n \"confidence\": 5,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper introduces the Generalized Video Moment Retrieval (GVMR) framework, which extends traditional Video Moment Retrieval (VMR) to handle a wider range of query types. To support this expanded task, it presents the NExT-VMR dataset, derived from the YFCC100M collection, featuring diverse query scenarios to enable more robust model evaluation. Additionally, a novel transformer-based model named BCANet is proposed and achieves outperforms when compared with traditional VMR approaches.\",\n \"strengths\": \"1. A novel GVMR framework is first introduced that significantly expands the scope of traditional VMR, catering to a wider range of query types and enhancing the model's practical utility.\\n\\n2. A meticulously curated dataset, NExT-VMR, is presented. The dataset is specifically designed for GVMR task, which includes a variety of query types and scenarios, thereby enabling more robust and versatile model training and evaluation.\",\n \"weaknesses\": \"1. As mentioned in the paper, \\\"GVMR aspires to deliver a robust and flexible solution for video moment retrieval, significantly enhancing the model's interpretative prowess, precision, and retrieval efficiency.\\\" Would the enhancement of the model on interpretative prowess, precision, and retrieval efficiency be proved and presented in experiments?\\n\\n2. More statistics of the proposed dataset are needed to be listed in Table 1, such as the entire/average lengths of videos and queries and the number of one-to-multi and no-target samples in the dataset.\\n\\n3. Is it possible to demonstrate the evaluation of this method on traditional VMR datasets (e.g., Charades, ActivityNet, and TACoS) for one-to-one (different from the mentioned one-to-multi or no-target) VMR tasks? \\n\\n4. The BCANet pipeline presented in Figure 1 is confusing and difficult to interpret. The respective variable symbols should be labeled in Figure 1. Moreover, the processes for the BCL and QCA modules, along with query-text cross-attention, are also not clearly depicted in the figure. Moreover, what's the meaning of the \\\"region\\\" and \\\"region features\\\" in this paper? Dose the \\\"region\\\" mean a video clip?\\n\\n5. The BCANet proposed in this paper does not seem to include specific designs for handling one-to-multi cases. Compared to traditional VMR methods, what advantages does BCANet offer in dealing with such data?\\n\\n6. Since the retrieval speed is also an important metric in VMR, for example, [a] analyze the speed of various VMR approaches. I recommend the authors conducting speed analysis in this paper. In addition, is GVMR slower than traditional VMR?\\n[a] Fast video moment retrieval, ICCV 2021.\",\n \"questions\": \"Please refer to the weakness part.\"\n },\n {\n \"id\": \"9HvlIWs5s1\",\n \"initial_rating\": 5,\n \"confidence\": 5,\n \"soundness\": 2,\n \"contribution\": 3,\n \"presentation\": 2,\n \"summary\": \"This paper introduces the Generalized Video Moment Retrieval framework, which expands traditional VMR to handle complex, non-target, and multi-target queries. To support this, the authors present the NExT-VMR dataset and BCANet, a transformer-based model with a Boundary-aware Cross Attention module that improves boundary detection and query understanding. \\nThe results show that GVMR, NExT-VMR, and BCANet significantly enhance VMR performance, setting a new benchmark for future research in multimedia information retrieval.\",\n \"strengths\": \"The problem the authors solve is interesting.\\n\\nThis paper provides a good moment retrieval dataset.\\n\\nThe paper is clearly written and the method can be understood.\",\n \"weaknesses\": \"- The NExT-VMR dataset is not large enough to be used for large-scale training. In addition, why not divide the test set on NExT-VMR for experiments?\\n\\n- Figure 3 is confusing. There are many colored blocks around the Query-Text Cross Attention module. I don't understand what it wants to express? Lack of technical details.\",\n \"questions\": \"- Can't the previous model achieve multi-target query well after training on the standard dataset? Lack of relevant experiments to prove the author's motivation.\\n\\n- Can the model in this paper use a single query to query multiple related clips in the video? This is a more worthy of attention.\\n\\n- YFCC100M is an excellent large-scale video dataset, but why did the author only select 9957 videos from YFCC100M? How was it selected?\\n- Will the author open source the dataset and code?\"\n },\n {\n \"id\": \"Dx7CG8IfID\",\n \"initial_rating\": 6,\n \"confidence\": 5,\n \"soundness\": 3,\n \"contribution\": 3,\n \"presentation\": 3,\n \"summary\": \"This paper introduces the Generalized Video Moment Retrieval (GVMR) framework, which expands traditional Video Moment Retrieval (VMR) to accommodate both non-target and multi-target queries, moving beyond the usual single-target focus. To support this, the authors present the NExT-VMR dataset, derived from the YFCC100M collection, featuring diverse query scenarios for robust model evaluation. They also propose BCANet, a transformer-based model that incorporates the Boundary-aware Cross Attention (BCA) module to enhance boundary detection and improve understanding of video content in relation to queries. Experiments demonstrate the potential of the NExT-VMR dataset and BCANet to advance VMR capabilities.\",\n \"strengths\": \"- This paper introduces a new task called Generalized Video Moment Retrieval (GVMR), which is designed to adeptly handle the complexities of various query types, extending the traditional Video Moment Retrieval (VMR) paradigm to include both multiple-target and no-target queries.\\n- This paper presents a specialized dataset, NExT-VMR, which is meticulously constructed and analyzed from the YFCC100M dataset. Tailored specifically for GVMR, this dataset features a diverse range of query types, including one-to-multiple and no-target queries.\\n- This paper introduces a model called BCANet, aimed at improving performance on the challenging task of GVMR, where the model must accurately predict a variable number of temporal timestamps based on natural language descriptions.\",\n \"weaknesses\": \"- Why does the paper utilize the YFCC100M dataset as the primary data source instead of existing VMR datasets such as TACoS, Charades-STA, MAD, or ActivityNet-Captions?\\n- From the statistics in Table 1, it can be seen that the average number of segments corresponding to a query is less than 2, which contradicts the paper's motivation for creating multiple-target queries. Additionally, the proportion of non-target queries is very low. Based on the dataset statistics, it is unclear where the challenges of this new dataset compared to existing ones lie.\\n- From Table 2, it can be seen that BCANet shows a significant advantage only in the single-moment retrieval task, while its performance in multi-target and non-target scenarios is not as pronounced. This raises questions about the overall effectiveness of the method.\",\n \"questions\": \"- BCANet is a supervised learning framework. How does it address the issue of inconsistent target quantities for each query in a batch during the training process? Additionally, if a query corresponds to three moments, are all three segments' timestamp information used in the loss function calculation?\\n- For queries labeled as non-target, what information do they provide during training?\\n- Why does the paper utilize the YFCC100M dataset as the primary data source instead of existing VMR datasets such as TACoS, Charades-STA, MAD, or ActivityNet-Captions?\\n- From the statistics in Table 1, it can be seen that the average number of segments corresponding to a query is less than 2, which contradicts the paper's motivation for creating multiple-target queries. Additionally, the proportion of non-target queries is very low. Based on the dataset statistics, it is unclear where the challenges of this new dataset compared to existing ones lie.\\n- From Table 2, it can be seen that BCANet shows a significant advantage only in the single-moment retrieval task, while its performance in multi-target and non-target scenarios is not as pronounced. This raises questions about the overall effectiveness of the method.\"\n }\n]","isConversational":false},"scores":{"kind":"string","value":"{\n \"rating\": \"5;5;6;6\",\n \"rating_avg\": 5.5,\n \"confidence\": \"5;5;5;4\",\n \"confidence_avg\": 4.75,\n \"soundness\": \"3;2;3;3\",\n \"soundness_avg\": 2.75,\n \"contribution\": \"3;3;3;3\",\n \"contribution_avg\": 3,\n \"presentation\": \"3;2;3;3\",\n \"presentation_avg\": 2.75\n}"},"metadata":{"kind":"string","value":"{\n \"primary_area\": \"\",\n \"track\": \"main\",\n \"venue\": \"ICLR 2025 Poster\",\n \"venueid\": \"ICLR.cc/2025/Conference\",\n \"processed_at\": \"2026-01-14T22:16:03.719106\"\n}"},"meta_review":{"kind":"string","value":"{\n \"id\": \"Dh3GdP2Fu5\",\n \"metareview\": \"This paper proposed a new Generalized Video Moment Retrieval framework, which expands traditional VMR to handle complex, non-target, and multi-target queries. To facilitate research on this task, a new dataset named NExT-VMR dataset, is derived from the YFCC100M collection, featuring diverse query scenarios to enable more robust model evaluation. The advantage of the method is that it defines a new task and establishes a relevant dataset, proposing a effective baseline model. The weakness is that some references, which were already published in some conference, were cited in arxiv format. Since all reviewers leaned to accept this paper, I recommend accept to it if there is not ethic problem.\",\n \"additional_comments\": \"The concerns raised by reviewers include insufficient details about dataset construction, lack of complexity analysis and some statistic information about dataset, lack of comparison with some related works etc. The authors’ rebuttals addressed these concerns well. Two reviewers raised their ratings, one reviewer maintained his positive ratings, and one reviewer didn’t provide final rating.\"\n}"},"decision":{"kind":"string","value":"{\n \"decision\": \"Accept (Poster)\"\n}"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":33,"numItemsPerPage":100,"numTotalItems":4011,"offset":3300,"length":100}},"jwt":"eyJhbGciOiJFZERTQSIsImtpZCI6Im1sR1pFYktIVHRVSGRhX1RRdEczQ0N1S3k5ME9Qd25DNHY5elRjM3FVYzgifQ.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc4MzYxODE4OCwianRpIjoiZjhjMGU4NmMtNmQzZS00MTNjLThmODEtZGY1OWQwYjI0ZGQ0Iiwic3ViIjoiL2RhdGFzZXRzL1VLUExhYi9Qcm9SZXZpZXdlci1EYXRhc2V0IiwiZXhwIjoxNzgzNjIxNzg4LCJpc3MiOiJodHRwczovL2h1Z2dpbmdmYWNlLmNvIn0.5FbSQMNKST1PSf-835TaYFX98SAqDrvrA4OAy7hG4Q86-pq5-XseBgppn7z6Si0ZrhU7iaEq7QIkNJyi7DB2Bw","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"train","numRows":4011,"numBytesParquet":144344024},{"config":"default","split":"test","numRows":1000,"numBytesParquet":45705060}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
paper_id string | arxiv_id string | title string | markdown dict | reviews list | scores dict | metadata dict | meta_review dict | decision dict |
|---|---|---|---|---|---|---|---|---|
p74CpDzw1Y | 2410.11055v1 | Varying Shades of Wrong: Aligning LLMs with Wrong Answers Only | {
"content": "## Abstract\n\nAbstract In the absence of abundant reliable annotations for challenging tasks and contexts, how can we expand the frontier of LLM capabilities with potentially wrong answers? We focus on two research questions: (1) Can LLMs generate reliable preferences among wrong options? And if so, (2... | [
{
"id": "Imxy4bVWT7",
"initial_rating": 8,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper presents a creative approach to solving alignment problem in large language models (LLMs) especially in resource constraint settings by proposing a met... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "4;4;2;4",
"confidence_avg": 3.5,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "2;3;3;3",
"contribution_avg": 2.75,
"presentation": "2;3;2;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.619098"
} | {
"id": "pSDlBZ9MZ3",
"metareview": "This paper introduces a novel solution to the alignment problem in large language models (LLMs), particularly for resource-constrained scenarios, through a method called \"wrong-over-wrong alignment.\" The key concept involves training LLMs to distinguish between varying levels ... | {
"decision": "Accept (Poster)"
} |
p8qhVIo980 | 2402.03038v1 | Automatic Combination of Sample Selection Strategies for Few-Shot Learning | {
"content": "## Abstract\n\nAbstract In few-shot learning, such as meta-learning, few-shot fine-tuning or in-context learning, the limited number of samples used to train a model have a significant impact on the overall success. Although a large number of sample selection strategies exist, their impact on the perfor... | [
{
"id": "QT0xAasldB",
"initial_rating": 5,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 2,
"summary": "This paper explores 20 sample selection strategies in few-shot learning, introducing the Automatic Combination of Sample Selection Strategies (ACSESS) method. ACS... | {
"rating": "5;5;5;6;6",
"rating_avg": 5.4,
"confidence": "4;4;3;4;5",
"confidence_avg": 4,
"soundness": "3;2;3;3;3",
"soundness_avg": 2.8,
"contribution": "4;2;2;3;3",
"contribution_avg": 2.8,
"presentation": "2;3;2;3;3",
"presentation_avg": 2.6
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.620615"
} | {
"id": "71tU3WMcSS",
"metareview": "The paper empirically explores the question of the impact of sample selection on the performance of few-shot learning and presents a scheme: ACSESS, that can automatically combine strategies for selecting data samples towards improved performance. The key idea is to identify a s... | {
"decision": "Reject"
} |
p8sr9kfUbQ | 2407.06390v1 | JANET: Joint Adaptive predictioN-region Estimation for Time-series | {
"content": "## Abstract\n\nAbstract Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead predic... | [
{
"id": "WLG8TAgj2Z",
"initial_rating": 3,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "The paper presents a promising framework, JANET, for joint prediction regions in time-series analysis, but it falls short in critical areas that limit its contrib... | {
"rating": "3;3;3;5",
"rating_avg": 3.5,
"confidence": "3;4;4;4",
"confidence_avg": 3.75,
"soundness": "3;2;3;3",
"soundness_avg": 2.75,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "2;2;3;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.621646"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
p9OsTj0nMP | 2406.08973v1 | XLand-100B: A Large-Scale Multi-Task Dataset for In-Context Reinforcement Learning | {
"content": "## Abstract\n\nAbstract Following the success of the in-context learning paradigm in large-scale language and computer vision models, the recently emerging field of in-context reinforcement learning is experiencing a rapid growth. However, its development has been held back by the lack of challenging be... | [
{
"id": "wgJYLREXmW",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper introduces a dataset, XLand-100B, for training and testing in-context RL algorithms. In-context RL is the problem of predicting how to act in a task, gi... | {
"rating": "5;6;6;8",
"rating_avg": 6.25,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "2;3;3;4",
"contribution_avg": 3,
"presentation": "2;4;3;4",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.622500"
} | {
"id": "fTWdIpIp20",
"metareview": "The authors present a new dataset for training and testing in-context RL algorithms that goes beyond existing tasks in simple environments and on small-scale datasets. They also provide results from running common baselines, showing that existing methods struggle to generalize t... | {
"decision": "Accept (Poster)"
} |
pA8oI8a00l | 2409.17601v2 | CleanerCLIP: Fine-grained Counterfactual Semantic Augmentation for Backdoor Defense in Contrastive Learning | {
"content": "## Abstract\n\nAbstract Pre-trained large models for multimodal contrastive learning, such as CLIP, have been widely recognized in the industry as highly susceptible to data-poisoned backdoor attacks. This poses significant risks to downstream model training. In response to such potential threats, finet... | [
{
"id": "QzAqnHZpQE",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "This paper introduces a fine-tuning-based backdoor defense, CleanerCLIP, targeting, as claimed, more stealthy backdoor attacks. CleanerCLIP introduces a sub-text ... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "4;4;3;2",
"confidence_avg": 3.25,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "2;2;2;2",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.623212"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pAQzEY7M03 | 2410.02761v3 | FakeShield: Explainable Image Forgery Detection and Localization via Multi-modal Large Language Models | {
"content": "## Abstract\n\nAbstract The rapid development of generative AI is a double-edged sword, which not only facilitates content creation but also makes image manipulation easier and more difficult to detect. Although current image forgery detection and localization (IFDL) methods are generally effective, the... | [
{
"id": "OAgOViiNVY",
"initial_rating": 8,
"confidence": 5,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper designs a multimodal framework called FakeShield, which uses the power of large language models to train the model by building a Multi-Modal Tamper Desc... | {
"rating": "5;6;8",
"rating_avg": 6.333333333333333,
"confidence": "5;5;5",
"confidence_avg": 5,
"soundness": "3;4;3",
"soundness_avg": 3.3333333333333335,
"contribution": "3;3;3",
"contribution_avg": 3,
"presentation": "2;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.624071"
} | {
"id": "pmiiFVzrP7",
"metareview": "1x accept, 2x borderline accept. This paper introduces a multimodal large-language-model-based approach to detect, localize, and explain image forgeries by constructing and leveraging a new multimodal dataset enriched with GPT-generated textual descriptions. The reviewers agree ... | {
"decision": "Accept (Poster)"
} |
pAkQhhn4vB | 2408.16204v1 | Revisit Micro-batch Clipping: Adaptive Data Pruning via Gradient Manipulation | {
"content": "## Abstract\n\nAbstract Micro-batch clipping, a gradient clipping method, has recently shown potential in enhancing auto-speech recognition (ASR) model performance.\nHowever, the underlying mechanism behind this improvement remains mysterious, particularly the observation that only certain micro-batch s... | [
{
"id": "dzi9buYQfY",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper revisits micro-batch clipping, an optimization technique initially proposed for memory efficiency in differentially private stochastic gradient descent... | {
"rating": "5;6;6",
"rating_avg": 5.666666666666667,
"confidence": "4;3;4",
"confidence_avg": 3.6666666666666665,
"soundness": "3;3;3",
"soundness_avg": 3,
"contribution": "2;3;3",
"contribution_avg": 2.6666666666666665,
"presentation": "2;3;3",
"presentation_avg": 2.6666666666666665
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.624765"
} | {
"id": "aG3MieoQg3",
"metareview": "This paper revisits micro-batch clipping, an optimization technique initially introduced for improving memory efficiency in differentially private stochastic gradient descent. The authors conceptualize micro-batch clipping as a form of data pruning, proposing that certain \"drag... | {
"decision": "Accept (Poster)"
} |
pB1XSj2y4X | 2410.04542v1 | Generative Flows on Synthetic Pathway for Drug Design | {
"content": "## Abstract\n\nAbstract Generative models in drug discovery have recently gained attention as efficient alternatives to brute-force virtual screening. However, most existing models do not account for synthesizability, limiting their practical use in real-world scenarios. In this paper, we propose RxnFlo... | [
{
"id": "wmf38eSgtw",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This paper introduces RXNFLOW, a generative framework that integrates synthesizability considerations into molecular generation for drug design. Following previou... | {
"rating": "5;5;5;5;6",
"rating_avg": 5.2,
"confidence": "3;4;4;4;3",
"confidence_avg": 3.6,
"soundness": "2;3;3;2;3",
"soundness_avg": 2.6,
"contribution": "2;3;2;2;3",
"contribution_avg": 2.4,
"presentation": "2;3;3;3;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.625532"
} | {
"id": "EgOHA6Zd5o",
"metareview": "The paper proposes RxnFlow, a model based on generative flow networks that is shown to scale to large compound spaces. \n\nThe main contribution of the work is in scaling up GFlowNets to handle very realistic and comprehensive molecular spaces defined by 71 reaction templates an... | {
"decision": "Accept (Poster)"
} |
pBqOH2g6K1 | 2410.01933v1 | TAEGAN: Generating Synthetic Tabular Data for Data Augmentation | {
"content": "## Abstract\n\nAbstract Synthetic tabular data generation has gained significant attention for its potential in data augmentation, software testing and privacy-preserving data sharing.\nHowever, most research has primarily focused on larger datasets and evaluating their quality in terms of metrics like ... | [
{
"id": "C1wmiz0Y4I",
"initial_rating": 5,
"confidence": 2,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "The paper presents TAEGAN, a GAN-based framework for generating synthetic tabular data for effective data augmentation. It introduces a masked auto-encoder genera... | {
"rating": "3;3;3;5;5;8",
"rating_avg": 4.5,
"confidence": "4;2;4;3;2;4",
"confidence_avg": 3.1666666666666665,
"soundness": "2;2;2;2;2;3",
"soundness_avg": 2.1666666666666665,
"contribution": "2;2;1;2;2;3",
"contribution_avg": 2,
"presentation": "1;1;1;2;2;3",
"presentation_avg": 1.666666666666666... | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.626371"
} | {
"id": "0RaGbstrnQ",
"metareview": "This paper proposed a GAN-based tabular data synthesis method after observing recent LLM-based tabular data synthesis methods are too large when considering their target tabular data size small. This paper's GAN design is outdated (as pointed by some reviewers) and they did not ... | {
"decision": "Reject"
} |
pCX1kZ0qHL | 2402.04550v3 | Riemann-Lebesgue Forest for Regression | {
"content": "## Abstract\n\nAbstract We propose a novel ensemble method called Riemann-Lebesgue Forest (RLF) for regression. The core idea in RLF is to mimic the way how a measurable function can be approximated by partitioning its range into a few intervals. With this idea in mind, we develop a new tree learner nam... | [
{
"id": "zkaWm0L9Ud",
"initial_rating": 5,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 1,
"summary": "The paper introduces a new ensemble regression method called the Riemann-Lebesgue Forest (RLF), which leverages a novel tree structure, the Riemann-Lebesgue Tree ... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "4;3;4;3",
"confidence_avg": 3.5,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "2;1;2;3",
"contribution_avg": 2,
"presentation": "2;2;1;3",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.627439"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pD6TiCpyDR | 2410.07761v1 | Jump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models | {
"content": "## Abstract\n\nAbstract Diffusion models have seen notable success in continuous domains, leading to the development of discrete diffusion models (DDMs) for discrete variables. Despite recent advances, DDMs face the challenge of slow sampling speeds. While parallel sampling methods like τ 𝜏 \\tau itali... | [
{
"id": "cj6FAg12DR",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This paper proposes a method, Jump Your Steps, to optimize the discretization schedule of discrete diffusion models, by minimizing the compounding decoding error ... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "4;3;4;4",
"confidence_avg": 3.75,
"soundness": "2;2;3;4",
"soundness_avg": 2.75,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.630138"
} | {
"id": "v8nETO33Ln",
"metareview": "This work addresses the challenge of slow sampling speeds in discrete diffusion models (DDMs) by introducing Jump Your Steps (JYS), a novel method to optimize discrete sampling timesteps. JYS minimizes Compounding Decoding Error (CDE), a key issue in parallel sampling methods li... | {
"decision": "Accept (Poster)"
} |
pE0UM18TQh | 2405.13396v1 | Fine-tuned In-Context Learning Transformers are Excellent Tabular Data Classifiers. | {
"content": "## Abstract\n\nAbstract The recently introduced TabPFN pretrains an In-Context Learning (ICL) transformer on synthetic data to perform tabular data classification. As synthetic data does not share features or labels with real-world data, the underlying mechanism that contributes to the success of this m... | [
{
"id": "bH5kRgXALg",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "This paper studies in-context learning (ICL) for tabular data, building upon TabPFN. The authors showed that fine-tuning leads to better downstream performance, a... | {
"rating": "3;5;5",
"rating_avg": 4.333333333333333,
"confidence": "3;3;4",
"confidence_avg": 3.3333333333333335,
"soundness": "3;2;2",
"soundness_avg": 2.3333333333333335,
"contribution": "2;3;2",
"contribution_avg": 2.3333333333333335,
"presentation": "2;3;2",
"presentation_avg": 2.33333333333333... | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.633757"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pH543jrbe8 | 2405.19950v1 | Multimodal Lego: Model Merging and Fine-Tuning Across Topologies and Modalities in Biomedicine | {
"content": "## Abstract\n\nAbstract Learning holistic computational representations in physical, chemical or biological systems requires the ability to process information from different distributions and modalities within the same model.\nThus, the demand for multimodal machine learning models has sharply risen fo... | [
{
"id": "eiIZh1gbes",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 4,
"presentation": 3,
"summary": "The authors study the multimodal learning problem and propose a novel method that can merge encoders from different modalities freely. This is achieved through th... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "3;2;4;4",
"contribution_avg": 3.25,
"presentation": "3;2;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.634663"
} | {
"id": "74qLKSN6QC",
"metareview": "Key Strengths:\n1. The paper presents a novel approach to multimodal data fusion using frequency-domain processing, with promising results across multiple datasets\n2. The \"wrapper\" nature of LegoBlocks makes it adaptable to various tasks and architectures\n3. The paper includ... | {
"decision": "Accept (Poster)"
} |
pHOH8FVrTp | 2410.03529v1 | No Need to Talk: Asynchronous Mixture of Language Models | {
"content": "## Abstract\n\nAbstract We introduce SmallTalk LM , an innovative method for training a mixture of language models in an almost asynchronous manner. Each model of the mixture specializes in distinct parts of the data distribution, without the need of high-bandwidth communication between the nodes traini... | [
{
"id": "iTjZBORNAM",
"initial_rating": 8,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 4,
"summary": "Large language models at modern scale are typically trained by means of distributed, synchronous model-parallel algorithms that rely on bespoke compute clusters w... | {
"rating": "5;8;8",
"rating_avg": 7,
"confidence": "3;3;4",
"confidence_avg": 3.3333333333333335,
"soundness": "3;4;3",
"soundness_avg": 3.3333333333333335,
"contribution": "2;4;3",
"contribution_avg": 3,
"presentation": "3;4;4",
"presentation_avg": 3.6666666666666665
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Spotlight",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.635428"
} | {
"id": "x5pd9vCNQf",
"metareview": "This paper introduces a more parallelizable MoE system. The approach is very simple, introducing a single router to make asynchronous operation possible.\n\nPros: Appears to significant improve efficiency of an MoE. Very simple approach, can be further modified.\n\nCons: Longer ... | {
"decision": "Accept (Spotlight)"
} |
pHe4P1IVnb | 2406.03199v2 | Bayesian WeakS-to-Strong from Text Classification to Generation | {
"content": "## Abstract\n\nAbstract Advances in large language models raise the question of how alignment techniques will adapt as models become increasingly complex and humans will only be able to supervise them weakly. Weak-to-Strong mimics such a scenario where weak model supervision attempts to harness the full... | [
{
"id": "DmJ4L0kC11",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper extends work in Weak-to-Strong generalization in two notable ways: (1) considering the setting in which there is an ensemble of multiple weak teachers;... | {
"rating": "3;3;6;8",
"rating_avg": 5,
"confidence": "3;3;3;3",
"confidence_avg": 3,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.636132"
} | {
"id": "YXhx6g7f4e",
"metareview": "This paper seeks to improve weak-to-strong generalization. This phenomenon, which has been known for quite a long time, has recently become popularized due to its theorized application to superalignment. In weak-to-strong generalization, a weak model produces outputs that a stro... | {
"decision": "Accept (Poster)"
} |
pISLZG7ktL | 2410.18647v1 | Data Scaling Laws in Imitation Learning for Robotic Manipulation | {
"content": "## Abstract\n\nAbstract Data scaling has revolutionized fields like natural language processing and computer vision, providing models with remarkable generalization capabilities. In this paper, we investigate whether similar data scaling laws exist in robotics, particularly in robotic manipulation, and ... | [
{
"id": "ABNtQgdjuI",
"initial_rating": 8,
"confidence": 5,
"soundness": 3,
"contribution": 3,
"presentation": 4,
"summary": "The authors in this work construct zero-shot generalizable policies with imitation learning and propose some scaling rules that determines the performance of such... | {
"rating": "5;8;8;8",
"rating_avg": 7.25,
"confidence": "4;4;3;5",
"confidence_avg": 4,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "3;4;3;3",
"contribution_avg": 3.25,
"presentation": "4;4;4;4",
"presentation_avg": 4
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Oral",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.636989"
} | {
"id": "7rD9YzMtoZ",
"metareview": "The paper investigated data scaling laws in the case of behavior cloning in robot manipulation. They specifically try diffusion policy as the algorithm and UMI as the data collection device. During this work, many demos were collected in real (40K), and many real robot roll-outs... | {
"decision": "Accept (Oral)"
} |
pJhgMNKEV3 | 2408.15565v1 | SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models | {
"content": "## Abstract\n\nAbstract There is a growing trend of teaching large language models (LLMs) to solve mathematical problems through coding. Existing studies primarily focus on prompting powerful, closed-source models to generate seed training data followed by in-domain data augmentation, equipping LLMs wit... | [
{
"id": "Y1qxy3mduS",
"initial_rating": 5,
"confidence": 5,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "The paper introduces a novel approach to enhancing large language models (LLMs) for solving mathematical problems via coding. The authors propose using large-scal... | {
"rating": "3;5;5",
"rating_avg": 4.333333333333333,
"confidence": "4;3;5",
"confidence_avg": 4,
"soundness": "2;3;2",
"soundness_avg": 2.3333333333333335,
"contribution": "2;2;2",
"contribution_avg": 2,
"presentation": "2;2;2",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.637760"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pK3oe2bubc | 2407.04513v1 | LayerShuffle: Enhancing Robustness in Vision Transformers by Randomizing Layer Execution Order | {
"content": "## Abstract\n\nAbstract Due to their architecture and how they are trained, artificial neural networks are typically not robust toward pruning, replacing, or shuffling layers at test time. However, such properties would be desirable for different applications, such as distributed neural network architec... | [
{
"id": "U4Fjkl1L3X",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 1,
"presentation": 2,
"summary": "This paper investigates alternative training approaches for vision transformers where the layers are permuted randomly to make them robust to pruning and shufflin... | {
"rating": "1;5;5;6",
"rating_avg": 4.25,
"confidence": "5;5;4;4",
"confidence_avg": 4.5,
"soundness": "2;3;2;3",
"soundness_avg": 2.5,
"contribution": "2;3;1;3",
"contribution_avg": 2.25,
"presentation": "2;3;2;4",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.638717"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pKMpmbuKnd | 2410.12652v1 | Constrained Posterior Sampling: Time Series Generation with Hard Constraints | {
"content": "## Abstract\n\nAbstract Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by ph... | [
{
"id": "cXeUBVFWJv",
"initial_rating": 3,
"confidence": 5,
"soundness": 3,
"contribution": 2,
"presentation": 4,
"summary": "The paper introduces Constrained Posterior Sampling, a diffusion-based method for generating time series that adhere to hard constraints. The approach is theoreti... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "5;4;4;3",
"confidence_avg": 4,
"soundness": "3;2;4;4",
"soundness_avg": 3.25,
"contribution": "1;2;3;4",
"contribution_avg": 2.5,
"presentation": "4;4;3;4",
"presentation_avg": 3.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.639790"
} | {
"id": "hb5Sqx8gQl",
"metareview": "This paper considers the constrained sampling problem from a diffusion model. It has two orthogonal components, the development of the constrained posterior sampling (CPS) algorithm and its application to time series. The proposed CPS algorithm leverages proximal optimization al... | {
"decision": "Reject"
} |
pMp5njgeLx | 2405.20267v4 | Auto-Arena: Automating LLM Evaluations with Agent Peer Battles and Committee Discussions | {
"content": "## Abstract\n\nAbstract As LLMs continuously evolve, there is an urgent need for a reliable evaluation method that delivers trustworthy results promptly. Currently, static benchmarks suffer from inflexibility and unreliability, leading users to prefer human voting platforms like Chatbot Arena. However, ... | [
{
"id": "RdsRLy15sw",
"initial_rating": 6,
"confidence": 3,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This paper proposes a novel framework for automatically evaluating LLMs using LLM-powered agents. The framework consists of three main components: question genera... | {
"rating": "3;5;6;6",
"rating_avg": 5,
"confidence": "4;4;3;3",
"confidence_avg": 3.5,
"soundness": "2;3;4;2",
"soundness_avg": 2.75,
"contribution": "2;2;3;2",
"contribution_avg": 2.25,
"presentation": "3;3;4;3",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.640741"
} | {
"id": "9zOSnhKwyM",
"metareview": "This paper introduces Auto-Arena, an automated evaluation framework for large language models (LLMs) that utilizes a multi-stage process comprising question generation, peer battles, and committee discussions. By emulating human-like evaluation, Auto-Arena overcomes the limitati... | {
"decision": "Reject"
} |
pNdPJACSLB | 2410.02438v1 | Learning K-U-Net in Constant Complexity with Application to Time Series Forecasting | {
"content": "## Abstract\n\nAbstract Training deep models for time series forecasting is a critical task with an inherent challenge of time complexity. While current methods generally ensure linear time complexity, our observations on temporal redundancy show that high-level features are learned 98.44% slower than l... | [
{
"id": "t3eij0fCal",
"initial_rating": 3,
"confidence": 3,
"soundness": 2,
"contribution": 2,
"presentation": 1,
"summary": "The authors propose a constant complexity method for time series forecasting. The motivation for forecasting is not so clear though.",
"strengths": "- Clear t... | {
"rating": "1;3;3;3",
"rating_avg": 2.5,
"confidence": "4;3;3;3",
"confidence_avg": 3.25,
"soundness": "1;1;2;2",
"soundness_avg": 1.5,
"contribution": "1;2;2;2",
"contribution_avg": 1.75,
"presentation": "1;1;2;1",
"presentation_avg": 1.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.641417"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pNgyXuGcx4 | 2405.18710v1 | To FP8 and Back Again: Quantifying Reduced Precision Effects on LLM Training Stability | {
"content": "## Abstract\n\nAbstract The massive computational costs associated with large language model (LLM) pretraining have spurred great interest in reduced-precision floating-point representations to accelerate the process. As a result, the BrainFloat16 (BF16) precision has become the de facto standard for LL... | [
{
"id": "Pjm5zmoBp4",
"initial_rating": 5,
"confidence": 2,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "The authors explores what happens when large language models (LLMs) are trained using FP8 precision, meaning only 8 bits are used for floating-point numbers. FP8 ... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "4;3;2;2",
"confidence_avg": 2.75,
"soundness": "2;2;2;2",
"soundness_avg": 2,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "2;2;2;2",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.642020"
} | {
"id": "DxsMAC0tOc",
"metareview": "The paper addresses the important problem of training LLMs in reduced-precision floating-point representations. The scope is to find if the available methods for training in FP8 precision are robust enough. In this context, the paper proposes new evaluation strategies for the sh... | {
"decision": "Reject"
} |
pPQPQ7Yd58 | 2410.05063v2 | Control-oriented Clustering of Visual Latent Representation | {
"content": "## Abstract\n\nAbstract We initiate a study of the geometry of the visual representation space –the information channel from the vision encoder to the action decoder– in an image-based control pipeline learned from behavior cloning. Inspired by the phenomenon of neural collapse (NC) in image classificat... | [
{
"id": "s49TP0Lh3o",
"initial_rating": 8,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper studies neural collapse for control tasks. To facilitate this study, the authors learn policies with behavior cloning end-to-end. To probe the learned ... | {
"rating": "3;5;5;8",
"rating_avg": 5.25,
"confidence": "3;4;3;4",
"confidence_avg": 3.5,
"soundness": "3;2;2;4",
"soundness_avg": 2.75,
"contribution": "2;3;2;4",
"contribution_avg": 2.75,
"presentation": "1;3;2;4",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Spotlight",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.642762"
} | {
"id": "RjtP9FS3jo",
"metareview": "The reviewers are generally enthusiastic about this work, highlighting several strengths and providing positive ratings. Notable strengths include being the first paper to study neural collapse in control, employing a unique, creative, and insightful experimental approach, and c... | {
"decision": "Accept (Spotlight)"
} |
pPyJyeLriR | 2408.09212v2 | Scalable and Certifiable Graph Unlearning: Overcoming the Approximation Error Barrier | {
"content": "## Abstract\n\nAbstract Graph unlearning has emerged as a pivotal research area for ensuring privacy protection, given the widespread adoption of Graph Neural Networks (GNNs) in applications involving sensitive user data. Among existing studies, certified graph unlearning is distinguished by providing r... | [
{
"id": "j0cRQFlTSK",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 4,
"summary": "This paper studies the certified graph unlearning problem with controlled propagation approximation to accelerate the unlearning speed over large-scale datasets. ... | {
"rating": "5;5;6;8",
"rating_avg": 6,
"confidence": "3;4;4;4",
"confidence_avg": 3.75,
"soundness": "3;3;3;3",
"soundness_avg": 3,
"contribution": "2;2;3;4",
"contribution_avg": 2.75,
"presentation": "2;3;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Spotlight",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.644138"
} | {
"id": "BCz8k1EYzO",
"metareview": "This paper introduces ScaleGUN, a scalable and certifiable graph unlearning model. It overcomes scalabilit challenges by integrating approximate graph propagation (a la forward push), while ensuring bounded approximation errors. The authors tackle various unlearning scenarios, i... | {
"decision": "Accept (Spotlight)"
} |
pQqeQpMkE7 | 2406.18533v1 | On Scaling Up 3D Gaussian Splatting Training | {
"content": "## Abstract\n\nAbstract 3D Gaussian Splatting (3DGS) is increasingly popular for 3D reconstruction due to its superior visual quality and rendering speed. However, 3DGS training currently occurs on a single GPU, limiting its ability to handle high-resolution and large-scale 3D reconstruction tasks due t... | [
{
"id": "xXHag3Zl0t",
"initial_rating": 8,
"confidence": 5,
"soundness": 3,
"contribution": 4,
"presentation": 4,
"summary": "This paper, named Grendel, presents a system to enable the distributed training of 3DGS. By leveraging the spatial locality and discovering the Gaussian intersect... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "5;4;4;5",
"confidence_avg": 4.5,
"soundness": "3;2;3;3",
"soundness_avg": 2.75,
"contribution": "3;2;4;4",
"contribution_avg": 3.25,
"presentation": "2;2;2;4",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Oral",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.645759"
} | {
"id": "TwVrj0iYOx",
"metareview": "This paper presents a parallel training method for 3D Gaussian splatting, which significantly improves the training speed and working scene scale. The paper is strongly motivated for scaling the 3DGS. Although the quality improvement is rather limited, the method has a strong me... | {
"decision": "Accept (Oral)"
} |
pRCOZllZdT | 2410.10605v1 | Boltzmann priors for Implicit Transfer Operators | {
"content": "## Abstract\n\nAbstract Accurate prediction of thermodynamic properties is essential in drug discovery and materials science. Molecular dynamics (MD) simulations provide a principled approach to this task, yet they typically rely on prohibitively long sequential simulations. Implicit Transfer Operator (... | [
{
"id": "5AYR4gYE7f",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This work looks at predicting molecular dynamics simulations quickly over time, using longer time steps. The authors introduce a method using diffusion models to ... | {
"rating": "5;5;6;6",
"rating_avg": 5.5,
"confidence": "3;4;4;4",
"confidence_avg": 3.75,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "2;2;4;3",
"contribution_avg": 2.75,
"presentation": "2;3;2;4",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.646632"
} | {
"id": "QVL5rTwPv0",
"metareview": "As positives for this paper, reviewers have mentioned the importance of the topic of this paper, focusing on enabling temporal coarse grained molecular dynamics. Making use of cheaply obtainable off-equilibrium data was seen as a promising approach to train more scalable models.... | {
"decision": "Accept (Poster)"
} |
pTyEnkuSQ0 | 2406.15673v1 | Large Language Models have Intrinsic Self-Correction Ability | {
"content": "## 1 Proof on why SC is effective\n\nLet’s assume that for a benchmark $Q$ where each question $q\\in Q$ has $k>=2$ possible answers, some LLM has the true ability of $correct(A\\in Q)=\\lambda>\\frac{1}{k}$. Theoretically speaking, such true ability could be achieved when the LLM is performing a beam s... | [
{
"id": "SM0XPUmFX9",
"initial_rating": 10,
"confidence": 3,
"soundness": 4,
"contribution": 4,
"presentation": 3,
"summary": "The paper claims to demonstrate the intrinsic self-correction capabilities of LLMs. Motivated from examples where bias in the prompts can interfere with the corr... | {
"rating": "3;3;5;10",
"rating_avg": 5.25,
"confidence": "4;3;4;3",
"confidence_avg": 3.5,
"soundness": "1;2;3;4",
"soundness_avg": 2.5,
"contribution": "1;2;1;4",
"contribution_avg": 2,
"presentation": "1;2;3;4",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.647391"
} | {
"id": "9gnCaD5rkO",
"metareview": "This paper studies intrinsic self-correction in large language models (LLMs) – their ability to revise previous answers without external input. looking at how temperature and the bias of prompts affect their performance. The paper’s core claim is that with carefully chosen “fair... | {
"decision": "Reject"
} |
pUbbLHjCPM | 2410.13413v1 | Think Thrice Before You Act: Progressive Thought Refinement in Large Language Models | {
"content": "## Abstract\n\nAbstract Recent advancements in large language models (LLMs) have demonstrated that progressive refinement,\nrather than providing a single answer, results in more accurate and thoughtful outputs.\nHowever, existing methods often rely heavily on supervision signals to evaluate previous re... | [
{
"id": "ktjpbpmxyl",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "Previous methods of self-improvement tried to enhance performance within specific domains, because supervision signals are vague and hard to define and evaluate r... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "3;4;3;3",
"confidence_avg": 3.25,
"soundness": "3;3;2;3",
"soundness_avg": 2.75,
"contribution": "2;3;2;2",
"contribution_avg": 2.25,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.647991"
} | {
"id": "xhJdNCqm1E",
"metareview": "The paper proposes Progressive Thought Refinement (PTR), a two-phase framework enabling LLMs to self-refine responses iteratively. Phase one constructs thought-data via weak-strong model cooperation, and phase two employs weighted thought-mask fine-tuning for multi-iteration res... | {
"decision": "Accept (Poster)"
} |
pVL4bYKOGM | 2407.03094v2 | Conformal prediction for causal effects of continuous treatments | {
"content": "## Abstract\n\nAbstract Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods... | [
{
"id": "QgCvBhMdHS",
"initial_rating": 6,
"confidence": 2,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper proposes a conformal prediction method for continuous treatments, addressing the challenge of unknown propensity scores. It derives finite-sample predi... | {
"rating": "3;5;6;6",
"rating_avg": 5,
"confidence": "3;4;4;2",
"confidence_avg": 3.25,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "3;3;3;3",
"contribution_avg": 3,
"presentation": "2;2;3;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.649207"
} | {
"id": "FLx1ybANMs",
"metareview": "This paper proposed a conformal prediction method for continuous treatments, addressing the challenge of unknown propensity scores. The problem is well motivated and the extension of conformal inference to continuous treatments is important. However, some main concerns remain:\n... | {
"decision": "Reject"
} |
pWdUcV5axb | 2410.11242v1 | Automatically Generating Visual Hallucination Test Cases for Multimodal Large Language Models | {
"content": "## Abstract\n\nAbstract Visual hallucination (VH) occurs when a multimodal large language model (MLLM) generates responses with incorrect visual details for prompts. Existing methods for generating VH test cases primarily rely on human annotations, typically in the form of triples: (image, question, ans... | [
{
"id": "Cp7Ys6MtHW",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This paper introduces VHExpansion, an automated framework for generating additional visual hallucination (VH) test cases based on existing ones to evaluate multim... | {
"rating": "3;5;5;5",
"rating_avg": 4.5,
"confidence": "4;3;5;4",
"confidence_avg": 4,
"soundness": "2;2;3;2",
"soundness_avg": 2.25,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "2;2;3;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.650046"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pWrCiFpm3L | 2406.14265v1 | VeriFlow: Modeling Distributions for Neural Network Verification | {
"content": "## Abstract\n\nAbstract Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks.\nNaively verifying a safety property amounts to ensuring the safety of a neural network for the whole input space irrespective of any training or test set.\nHowever, thi... | [
{
"id": "5VVHiTcwot",
"initial_rating": 8,
"confidence": 3,
"soundness": 3,
"contribution": 4,
"presentation": 4,
"summary": "This paper introduces a methodology to verify semantically meaning properties using a neuro-symbolic approach, in which the input to the neural network under veri... | {
"rating": "3;3;6;8",
"rating_avg": 5,
"confidence": "3;4;4;3",
"confidence_avg": 3.5,
"soundness": "3;2;4;3",
"soundness_avg": 3,
"contribution": "3;2;4;4",
"contribution_avg": 3.25,
"presentation": "2;1;2;4",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.650885"
} | {
"id": "rUDWTwytrl",
"metareview": "The submission proposes the VeriFlow architecture as a flow based density model tailored to allow any verification approach to restrict its search to the some data distribution of interest.\n\n+ The topic is of interest as more meaningful specifications are important to showcase... | {
"decision": "Reject"
} |
pXIbcRPxWR | 2410.14198v1 | Supervised Chain of Thought | {
"content": "## Abstract\n\nAbstract Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs—the Transformer—has inherent limitations in computational depth, rendering them th... | [
{
"id": "DT76cCnkG8",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 1,
"summary": "This paper examines the limitations of Transformer-based Large Language Models (LLMs) in handling complex reasoning tasks, due to their limited computational dept... | {
"rating": "1;3;3;5",
"rating_avg": 3,
"confidence": "3;4;4;4",
"confidence_avg": 3.75,
"soundness": "1;3;2;3",
"soundness_avg": 2.25,
"contribution": "1;2;2;2",
"contribution_avg": 1.75,
"presentation": "2;2;1;3",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.651671"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pXUAiJshdh | 2406.09098v3 | SciKnowEval: Evaluating Multi-level Scientific Knowledge of Large Language Models | {
"content": "## Abstract\n\nAbstract Large language models (LLMs) have gained increasing prominence in scientific research, but there is a lack of comprehensive benchmarks to fully evaluate their proficiency in understanding and mastering scientific knowledge.\nTo address this need, we introduce the SciKnowEval benc... | [
{
"id": "6qJiuNkVZu",
"initial_rating": 5,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper constructs a benchmark to evaluate LLM's scientific knowledge and tests many LLM's performance on the benchmark.\nSpecifically, the benchmark is design... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "3;2;3;3",
"soundness_avg": 2.75,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "3;3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.652415"
} | {
"id": "Z3XrWAjzf9",
"metareview": "Summary:\n\nThis paper introduces the SciKnowEval benchmark to evaluate LLMs across five progressive levels of scientific knowledge (studying extensively, inquiring earnestly, thinking profoundly, discerning clearly, and practicing assiduously), which aim to assess the breadth a... | {
"decision": "Reject"
} |
pZISppZSTv | 2410.03441v1 | CLoSD: Closing the Loop between Simulation and Diffusion for multi-task character control | {
"content": "## Abstract\n\nAbstract Motion diffusion models and Reinforcement Learning (RL) based control for physics-based simulations have complementary strengths for human motion generation.\nThe former is capable of generating a wide variety of motions, adhering to intuitive control such as text, while the latt... | [
{
"id": "G5fTiHKSTX",
"initial_rating": 8,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper presents CLoSD, a text-driven reinforcement learning (RL) controller for character motion, merging the generative capabilities of diffusion models with... | {
"rating": "6;6;8;8",
"rating_avg": 7,
"confidence": "4;4;4;3",
"confidence_avg": 3.75,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;3;3;3",
"contribution_avg": 2.75,
"presentation": "3;3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Spotlight",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.653126"
} | {
"id": "hOyIwwU5cM",
"metareview": "The paper presents CLoSD, method combining motion diffusion models with RL-based control for physics-based character motion generation. The key contribution is a closed-loop framework integrating a Diffusion Planner (DiP) and tracking controller for real-time text-driven motion... | {
"decision": "Accept (Spotlight)"
} |
pZiyCaVuti | 2410.10813v1 | LongMemEval: Benchmarking Chat Assistants on Long-Term Interactive Memory | {
"content": "## Abstract\n\nAbstract Recent large language model (LLM)-driven chat assistant systems have integrated memory components to track user-assistant chat histories, enabling more accurate and personalized responses. However, their long-term memory capabilities in sustained interactions remain underexplored... | [
{
"id": "wPzynD6sce",
"initial_rating": 8,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "the paper proposes LONGMEMEVAL, a comprehensive benchmark designed to evaluate five core long-term memory abilities of chat assistants: information extraction, mu... | {
"rating": "3;6;8;8",
"rating_avg": 6.25,
"confidence": "4;4;4;4",
"confidence_avg": 4,
"soundness": "2;3;2;3",
"soundness_avg": 2.5,
"contribution": "3;3;3;3",
"contribution_avg": 3,
"presentation": "1;3;2;3",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.653911"
} | {
"id": "M8ntT0agYk",
"metareview": "Summary: \n\nLong-term memory capabilities of LLM-based chat assistants in sustained interactions remain underexplored. This paper introduces LongMemEval, a new benchmark designed to evaluate five core long-term memory abilities: information extraction, multi-session reasoning, ... | {
"decision": "Accept (Poster)"
} |
pZz0nOroGv | 2410.06234v1 | TEOChat: A Large Vision-Language Assistant for Temporal Earth Observation Data | {
"content": "## Abstract\n\nAbstract Large vision and language assistants have enabled new capabilities for interpreting natural images. These approaches have recently been adapted to earth observation data, but they are only able to handle single image inputs, limiting their use for many real-world tasks. In this w... | [
{
"id": "dP63HiznTj",
"initial_rating": 1,
"confidence": 5,
"soundness": 2,
"contribution": 1,
"presentation": 3,
"summary": "The work attempts to develop the first vision-language model for temporal earth observation data (EOD). When an EOD is prompted with temporal images and NLP, the ... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;3;5;5",
"confidence_avg": 4.25,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;2;3;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.654863"
} | {
"id": "KqKpcbYa3c",
"metareview": "The manuscript received ratings of 5, 8, 6, and 1. Reviewers appreciated that the manuscript introduces a model tailored for temporal Earth observation (EO) data along with tailored instruction set for tempora domain in remote sensing, thereby addressesing an important gap in ex... | {
"decision": "Accept (Poster)"
} |
pbre0HKsfE | 2410.02486v1 | Encryption-Friendly LLM Architecture | {
"content": "## Abstract\n\nAbstract Large language models (LLMs) offer personalized responses based on user interactions, but this use case raises serious privacy concerns. Homomorphic encryption (HE) is a cryptographic protocol supporting arithmetic computations in encrypted states and provides a potential solutio... | [
{
"id": "EVfJurbM9L",
"initial_rating": 6,
"confidence": 3,
"soundness": 4,
"contribution": 3,
"presentation": 4,
"summary": "This paper presents optimizations to LLM architectures to make them more friendly towards Homomorphic Encryption evaluation. Concretely, first they propose to use... | {
"rating": "5;6;6",
"rating_avg": 5.666666666666667,
"confidence": "3;4;3",
"confidence_avg": 3.3333333333333335,
"soundness": "3;3;4",
"soundness_avg": 3.3333333333333335,
"contribution": "2;2;3",
"contribution_avg": 2.3333333333333335,
"presentation": "3;4;4",
"presentation_avg": 3.66666666666666... | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.656022"
} | {
"id": "6PAm6AdPXs",
"metareview": "All reviewers except one (EsSP) argued for accepting the paper. For this reviewer their main conerns were on #1 a lack of novelty, #2 incorrect descriptions, #3 insufficient model security considerations. Specifically for #1 the reviewer argued that (a) the topic is widely studi... | {
"decision": "Accept (Poster)"
} |
pdF86dyoS6 | 2407.14618v1 | SOREL: A Stochastic Algorithm for Spectral Risks Minimization | {
"content": "## Abstract\n\nAbstract The spectral risk has wide applications in machine learning, especially in real-world decision-making, where people are not only concerned with models’ average performance. By assigning different weights to the losses of different sample points, rather than the same weights as in... | [
{
"id": "QFYFk330Dl",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper proposes a stochastic algorithm for spectral risk minimization with trajectory stabilization for the primal variable. It is claimed that their approach... | {
"rating": "1;3;6;6",
"rating_avg": 4,
"confidence": "5;3;2;3",
"confidence_avg": 3.25,
"soundness": "1;1;3;3",
"soundness_avg": 2,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "4;3;3;3",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.657352"
} | {
"id": "1wJLRBigK8",
"metareview": "An algorithm called SOREL is proposed for spectral risk minimization, with convergence analysis for convex losses together with a strongly convex regularization. Experiments was limited to linear models in the original submission, but additional ones with nonlinear models are co... | {
"decision": "Accept (Poster)"
} |
pdjkikvCch | 2307.05772v2 | Random-Set Neural Networks | {
"content": "## Abstract\n\nAbstract Machine learning is increasingly deployed in safety-critical domains where robustness against adversarial attacks is crucial and erroneous predictions could lead to potentially catastrophic consequences. This highlights the need for learning systems to be equipped with the means ... | [
{
"id": "ipfFRX5AGG",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper focuses on a novel approach called Random-Set Neural Network (RS-NN) for classification tasks. The RS-NN approach aims to predict belief functions over... | {
"rating": "5;5;6",
"rating_avg": 5.333333333333333,
"confidence": "4;3;3",
"confidence_avg": 3.3333333333333335,
"soundness": "2;3;3",
"soundness_avg": 2.6666666666666665,
"contribution": "2;4;3",
"contribution_avg": 3,
"presentation": "4;4;3",
"presentation_avg": 3.6666666666666665
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.658460"
} | {
"id": "8X1sNFgSgu",
"metareview": "The paper introduces a novel method to augment neural networks with epistemic uncertainty estimates by providing distributions (belief functions) over the collection of sets of classes. The respective approach is referred to as random-set neural networks (RS-NN). The advantages ... | {
"decision": "Accept (Poster)"
} |
pf9J3GNxSe | 2406.05335v2 | Critical Phase Transition in Large Language Models | {
"content": "## Abstract\n\nAbstract Large Language Models (LLMs) have demonstrated impressive performance. To understand their behaviors, we need to consider the fact that LLMs sometimes show qualitative changes . The natural world also presents such changes called phase transitions , which are defined by singular,... | [
{
"id": "xO4p8C4Fpr",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "This paper proposes that qualitative changes in language model outputs can be analyzed as phase transitions—an analogy drawn from statistical physics. The authors... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "4;4;2;3",
"confidence_avg": 3.25,
"soundness": "3;2;2;3",
"soundness_avg": 2.5,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "3;2;2;4",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.659386"
} | {
"id": "FdA1bKtDaq",
"metareview": "This paper looks at the range of temperature values at which LLM-generated text mimics the statistical properties of natural language, framing it through the lens of phase transitions in physical systems. The authors hypothesize the existence of a singularity point on the temper... | {
"decision": "Reject"
} |
phAlw3JPms | 2407.04285v1 | Tackling Data Corruption in Offline Reinforcement Learning via Sequence Modeling | {
"content": "## Abstract\n\nAbstract Learning policies from offline datasets through offline reinforcement learning (RL) holds promise for scaling data-driven decision-making and avoiding unsafe and costly online interactions. However, real-world data collected from sensors or humans often contains noise and errors,... | [
{
"id": "JMJdJvouKH",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The work deals with the challenges posed by data corruption in offline RL and proposes a novel approach RDT. The primary contribution is the application of sequen... | {
"rating": "3;6;6;6",
"rating_avg": 5.25,
"confidence": "3;3;3;3",
"confidence_avg": 3,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "3;3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.660689"
} | {
"id": "Fv5JNi9mmH",
"metareview": "This paper proposes to use sequence models to tackle data corruption in offline RL with a limited dataset. It introduces Robust Decision Transformer with three componenets embedding dropout, Gaussian weighted learning, and iterative data correction. Extensive experiments on dive... | {
"decision": "Accept (Poster)"
} |
phWflQbLhu | 2409.15697v1 | dnaGrinder: a lightweight and high-capacity genomic foundation model | {
"content": "## Abstract\n\nAbstract The task of understanding and interpreting the complex information encoded within genomic sequences remains a grand challenge in biological research and clinical applications. In this context, recent advancements in large language model research have led to the development of bot... | [
{
"id": "KQHiU1nqPz",
"initial_rating": 3,
"confidence": 5,
"soundness": 1,
"contribution": 1,
"presentation": 2,
"summary": "This paper introduces the model dnaGrinder, a lightweight encoder-only genomic foundation model. dnaGrinder is engineered to handle long sequences (140k tokens wi... | {
"rating": "3;5;5;5",
"rating_avg": 4.5,
"confidence": "5;4;4;4",
"confidence_avg": 4.25,
"soundness": "1;3;3;2",
"soundness_avg": 2.25,
"contribution": "1;2;2;2",
"contribution_avg": 1.75,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.661549"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pjfrGVekwK | 2410.03592v1 | Variational Bayes Gaussian Splatting | {
"content": "## Abstract\n\nAbstract Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable rendering pipeline, which struggles with catas... | [
{
"id": "sBLdK0kGXz",
"initial_rating": 5,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper proposes Variational Bayes Gaussian Splatting (VBGS) for modeling 3D scenes by framing training of Gaussian Splats as variational inference. The formul... | {
"rating": "3;5;5;5",
"rating_avg": 4.5,
"confidence": "3;3;5;4",
"confidence_avg": 3.75,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "1;2;3;3",
"contribution_avg": 2.25,
"presentation": "2;3;2;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.663055"
} | {
"id": "5e74CsGzPX",
"metareview": "The paper proposes a variational Bayesian approach to learning Gaussian splats. The main claim is that the method matches state-of-the-art for static datasets but works much better for continual and streaming data. \n\nThe work shows promising results, especially in mitigating t... | {
"decision": "Reject"
} |
pk4YjZeevI | 2410.06273v1 | PREDICT: Preference Reasoning by Evaluating Decomposed preferences Inferred from Candidate Trajectories | {
"content": "## Abstract\n\nAbstract Accommodating human preferences is essential for creating AI agents that deliver personalized and effective interactions. Recent work has shown the potential for LLMs to infer preferences from user interactions, but they often produce broad and generic preferences, failing to cap... | [
{
"id": "GYjn8CLcIH",
"initial_rating": 5,
"confidence": 3,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "The paper introduces a method called PREDICT which is designed to infer individual user preferences from user interaction trajectories. The proposed approach is e... | {
"rating": "3;3;6;6",
"rating_avg": 4.5,
"confidence": "3;3;3;2",
"confidence_avg": 2.75,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;2;2;3",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.664738"
} | {
"id": "ZxIMQRKtWx",
"metareview": "This paper introduces PREDICT, a method that enhances the precision and adaptability of inferring human preferences in AI interactions by refining preferences iteratively, decomposing them into components, and validating them across multiple trajectories. Evaluated in both a gri... | {
"decision": "Reject"
} |
pl2c1PoiGO | 1912.08306v1 | Multi-Channel Graph Convolutions | {
"content": "## Abstract\n\nAbstract Graph neural networks (GNN) has been demonstrated to be effective in classifying graph structures. To further improve the graph representation learning ability, hierarchical GNN has been explored. It leverages the differentiable pooling to cluster nodes into fixed groups, and gen... | [
{
"id": "u2AwgWBlsO",
"initial_rating": 3,
"confidence": 3,
"soundness": 2,
"contribution": 2,
"presentation": 1,
"summary": "The authors propose a multi-channel graph convolution (MCGC) based on the convolution theorem and the graph Fourier transform, specifically designed for multi-cha... | {
"rating": "1;3;3;3;3;3;6",
"rating_avg": 3.142857142857143,
"confidence": "5;4;5;3;4;3;4",
"confidence_avg": 4,
"soundness": "1;2;3;2;2;2;3",
"soundness_avg": 2.142857142857143,
"contribution": "1;1;1;2;2;2;3",
"contribution_avg": 1.7142857142857142,
"presentation": "2;1;3;2;2;1;2",
"presentation_... | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.665912"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pl8OJhyArC | 2404.06091v1 | Hash3D: Training-free Acceleration for 3D Generation | {
"content": "## Abstract\n\nAbstract The evolution of 3D generative modeling has been notably propelled by the adoption of 2D diffusion models. Despite this progress,\nthe cumbersome optimization process per se\npresents a critical hurdle to efficiency.\nIn this paper,\nwe introduce Hash3D,\na universal acceleration... | [
{
"id": "AnLadMJZ1x",
"initial_rating": 5,
"confidence": 5,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "Hash3D proposed a novel feature reusing strategy for score distillation sampling.\nBy hashing and reusing these feature maps across nearby timesteps and camera an... | {
"rating": "5;5;5;5",
"rating_avg": 5,
"confidence": "2;1;4;5",
"confidence_avg": 3,
"soundness": "2;3;2;2",
"soundness_avg": 2.25,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "3;2;3;2",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.666674"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
pljYMCYDWJ | 2407.00075v2 | Logicbreaks: A Framework for Understanding Subversion of Rule-based Inference | {
"content": "## Abstract\n\nAbstract We study how to subvert large language models (LLMs) from following prompt-specified rules.\nWe model rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form “if P 𝑃 P italic_P and Q 𝑄 Q italic_Q , then R 𝑅 R italic_R ” for s... | [
{
"id": "V2eBAtWTVW",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 2,
"summary": "This manuscript explores the subversion of logical entailment in transformer-based LLMs, in three steps:\n1. a theoretical/mathematical representation of a single... | {
"rating": "5;6;6;6;8",
"rating_avg": 6.2,
"confidence": "3;3;2;3;3",
"confidence_avg": 2.8,
"soundness": "2;3;4;3;4",
"soundness_avg": 3.2,
"contribution": "2;3;3;3;3",
"contribution_avg": 2.8,
"presentation": "2;4;3;2;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.667584"
} | {
"id": "8wfXW3KiLA",
"metareview": "The paper considers the problem of manipulating LLMs so that they deviate from prompt-specified rules. Overall, the reviews lean towards acceptance, and I agree. The overall take-away message \"Language Models are Susceptible to Inference Subversions\" is important. The in-depth... | {
"decision": "Accept (Poster)"
} |
powufeT93G | 2409.18511v3 | Do We Need Domain-Specific Embedding Models? An Empirical Investigation | {
"content": "## Abstract\n\nAbstract Embedding models play a crucial role in representing and retrieving information across various NLP applications. Recent advancements in Large Language Models (LLMs) have further enhanced the performance of embedding models, which are trained on massive amounts of text covering al... | [
{
"id": "oenn5iMiyo",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper introduces FinMTEB, a massive text embedding benchmark specifically designed for the financial domain. Experimental results show that state-of-the-art ... | {
"rating": "3;5;6;6",
"rating_avg": 5,
"confidence": "3;3;3;4",
"confidence_avg": 3.25,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.668580"
} | {
"id": "tZ0BaBzePD",
"metareview": "The paper asks an intuitive question \"Do We Need Domain-Specific Embedding Models?\" and performed a case study in the financial domain, where the authors created a dataset. \n\nReviewers generally gave borderline or rejection scores. The biggest concern is an overclaim from on... | {
"decision": "Reject"
} |
pq1WUegkza | 2410.02321v1 | Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis | {
"content": "## Abstract\n\nAbstract Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis of the discrete-state counterparts remai... | [
{
"id": "ulhLqwm79I",
"initial_rating": 3,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 2,
"summary": "The paper presents a discrete-time sampling method using score estimators at fixed points in a multidimensional state space. It provides bounds on how closely the... | {
"rating": "3;6;8;8",
"rating_avg": 6.25,
"confidence": "4;5;3;3",
"confidence_avg": 3.75,
"soundness": "2;3;4;4",
"soundness_avg": 3.25,
"contribution": "3;3;4;3",
"contribution_avg": 3.25,
"presentation": "2;3;4;4",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.669460"
} | {
"id": "SnEBBGyhR8",
"metareview": "This paper offers a convergence analysis of score-based discrete diffusion model when the state space is $[S]^d$, generalizing the prior work of Chen and Ying that handles the case of $\\{0,1\\}^d$. The work leverages heavily the techniques from Chen and Ying, but also offers ne... | {
"decision": "Accept (Poster)"
} |
pq3RANvCZC | 2405.06003v1 | Binary Hypothesis Testing for Softmax Models and Leverage Score Models | {
"content": "## Abstract\n\nSoftmax distributions are widely used in machine learning, including Large Language Models (LLMs) where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the model produces an output drawn from the softmax distr... | [
{
"id": "os5VsN4ftV",
"initial_rating": 3,
"confidence": 4,
"soundness": 1,
"contribution": 2,
"presentation": 1,
"summary": "This paper studies the sample complexity of binary hypothesis testing in the context of softmax and leverage score models. First, the paper identifies the require... | {
"rating": "3;3;3;3",
"rating_avg": 3,
"confidence": "4;3;4;4",
"confidence_avg": 3.75,
"soundness": "2;2;2;1",
"soundness_avg": 1.75,
"contribution": "2;2;1;2",
"contribution_avg": 1.75,
"presentation": "2;2;2;1",
"presentation_avg": 1.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.670590"
} | {
"id": "gpyakF1K3V",
"metareview": "This paper considers the sample complexity of binary hypothesis testing for softmax models and leverage score models. Typically a statistical problem, the work is primarily motivated to improve understanding of the behavior of large language models. Reviewers found the work to b... | {
"decision": "Reject"
} |
pr37sbuhVa | 2408.04840v2 | mPLUG-Owl3: Towards Long Image-Sequence Understanding in Multi-Modal Large Language Models | {
"content": "#### \\thesubsubsection Pre-training\n\n#### \\thesubsubsection Multi-image Pre-training\n\n#### \\thesubsubsection Supervised-Finetuning\n\n### \\thesubsection High-resolution Image Processing\n\n### \\thesubsection Video Processing\n\n## 1 Experiments\n\n### \\thesubsection Visual Question Answering B... | [
{
"id": "cExQoz2kxe",
"initial_rating": 6,
"confidence": 5,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper introduces a multimodal large language model, mPLUG-Owl3, which is capable of processing multi-image and video understanding through interleaved traini... | {
"rating": "3;6;6;6",
"rating_avg": 5.25,
"confidence": "4;4;3;5",
"confidence_avg": 4,
"soundness": "3;3;3;3",
"soundness_avg": 3,
"contribution": "2;3;3;3",
"contribution_avg": 2.75,
"presentation": "3;3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.671256"
} | {
"id": "UXxBEQrUs6",
"metareview": "This paper presents mPLUG-Owl3, a new multimodal LLM that is able to efficiently processes long image sequences using the proposed hyper attention blocks. After rebuttal, it received scores of 5688. Reviewers are generally happy about the paper, commenting that (1) the proposed ... | {
"decision": "Accept (Poster)"
} |
ptTt8mhS7n | 2410.01548v2 | In-Context Transfer Learning: Demonstration Synthesis by Transferring Similar Tasks | {
"content": "## Abstract\n\nAbstract In-context learning (ICL) is an effective approach to help large language models (LLMs) adapt to various tasks by providing demonstrations of the target task.\nConsidering the high cost of labeling demonstrations, many methods propose synthesizing demonstrations from scratch usin... | [
{
"id": "w7zi3fwWKI",
"initial_rating": 5,
"confidence": 3,
"soundness": 2,
"contribution": 3,
"presentation": 3,
"summary": "The paper introduces In-Context Transfer Learning (ICTL), a method designed to improve demonstration synthesis for in-context learning (ICL) by leveraging labeled... | {
"rating": "1;5;5;5",
"rating_avg": 4,
"confidence": "4;4;3;3",
"confidence_avg": 3.5,
"soundness": "1;3;3;2",
"soundness_avg": 2.25,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "1;3;3;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.671911"
} | {
"id": "oesIRzsptq",
"metareview": "The paper presents a transfer learning method which synthesizes target task demonstrations by transferring labeled demonstrations from similar source tasks. The reviewers acknowledged the importance and potential of the problem addressed. However, they identified several limitat... | {
"decision": "Reject"
} |
ptjrpEGrGg | 2405.11204v2 | Learning from Imperfect Human Feedback: A Tale from Corruption-Robust Dueling | {
"content": "## Abstract\n\nAbstract This paper studies Learning from Imperfect Human Feedback (LIHF), addressing the potential irrationality or imperfect perception when learning from comparative human feedback. Building on evidences that human’s imperfection decays over time (i.e., humans learn to improve), we cas... | [
{
"id": "QchuBjlaGf",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper studied the dueling bandit problem with constraint corruption. It first proved that the problem is not easier with the constraint on the corruption wit... | {
"rating": "5;5;6;6;6",
"rating_avg": 5.6,
"confidence": "4;4;3;3;3",
"confidence_avg": 3.4,
"soundness": "3;3;3;3;3",
"soundness_avg": 3,
"contribution": "3;2;3;3;3",
"contribution_avg": 2.8,
"presentation": "3;3;3;2;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.672904"
} | {
"id": "2tytGg2J0m",
"metareview": "This paper addresses the concave-utility continuous-action dueling bandit problem, particularly focusing on a model that includes time-decaying corruption with an eye toward applications in Learning from Imperfect Human Feedback. The authors propose an algorithm for this problem... | {
"decision": "Accept (Poster)"
} |
puTxuiK2qO | 2405.16397v2 | AdaFisher: Adaptive Second Order Optimization via Fisher Information | {
"content": "## Abstract\n\nAbstract First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic gradient during the training. Despite their wid... | [
{
"id": "3Q9i5XrxSb",
"initial_rating": 5,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper proposes a new idea: using Kronecker factored preconditioners, with diagonal factors. The Kronecker product approximates empirical Fisher information ma... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "4;5;4;3",
"confidence_avg": 4,
"soundness": "3;2;3;3",
"soundness_avg": 2.75,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "3;2;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.674103"
} | {
"id": "Jm8rH62uyP",
"metareview": "This paper proposes AdaFisher, a new adaptive second-order optimization method, which offers a strong balance between convergence efficiency and computational feasibility. The authors introduce a novel diagonal block-Kronecker approximation to the Fisher Information Matrix (FIM)... | {
"decision": "Accept (Poster)"
} |
pudmhZdV78 | 2410.03140v1 | In-context learning in presence of spurious correlations | {
"content": "## Abstract\n\nAbstract Large language models exhibit a remarkable capacity for in-context learning, where they learn to solve tasks given a few examples.\nRecent work has shown that transformers can be trained to perform simple regression tasks in-context.\nThis work explores the possibility of trainin... | [
{
"id": "yWwFhk2zv6",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 2,
"summary": "This paper investigates the problem of in-context learning in the presence of spurious correlations. The authors first examine the single-task setting and demonst... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;3;2;3",
"confidence_avg": 3,
"soundness": "3;2;2;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;3;3;2",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.675099"
} | {
"id": "tpxgZwjHfx",
"metareview": "This paper explores how to make in-context learning (ICL) robust against spurious correlations in classification tasks. The authors find that standard ICL approaches are vulnerable to spurious features and tend to memorize tasks rather than truly learn from context. To address t... | {
"decision": "Reject"
} |
pwIGnH2LHJ | 2410.06992v2 | SWE-Bench+: Enhanced Coding Benchmark for LLMs | {
"content": "## Abstract\n\nAbstract Large Language Models (LLMs) in Software Engineering (SE) can offer assistance for coding. To facilitate a rigorous evaluation of LLMs in practical coding contexts, Carlos et al. introduced the SWE-bench dataset, which comprises 2,294 real-world GitHub issues and their correspond... | [
{
"id": "p7HCCt3yBn",
"initial_rating": 3,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 2,
"summary": "This paper analyzes the generation results of SWE-Agent+GPT-4 on SWE-bench, highlighting certain shortcomings within the original SWE-bench. For example, the auth... | {
"rating": "3;3;6",
"rating_avg": 4,
"confidence": "4;4;4",
"confidence_avg": 4,
"soundness": "3;2;4",
"soundness_avg": 3,
"contribution": "2;2;3",
"contribution_avg": 2.3333333333333335,
"presentation": "2;3;3",
"presentation_avg": 2.6666666666666665
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.675731"
} | {
"id": "XbuiviNq6z",
"metareview": "This paper presents SWE-Bench+, an extened evaluation of the original SWE-Bench dataset, to evaluate the real-world problem-solving capabilities of LLMs in software engineering. While valuable, the reviewers have raised key concerns. Firstly, SWE-Bench+ lacks broader comparisons... | {
"decision": "Reject"
} |
pwKokorglv | 2406.11818v1 | Embodied Instruction Following in Unknown Environments | {
"content": "## Abstract\n\nAbstract Enabling embodied agents to complete complex human instructions from natural language is crucial to autonomous systems in household services. Conventional methods can only accomplish human instructions in the known environment where all interactive objects are provided to the emb... | [
{
"id": "pLDthvTP4x",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 3,
"presentation": 2,
"summary": "The paper proposes a hierarchical approach for embodied instruction following in unknown environments where room configurations may change due to human activities... | {
"rating": "3;3;5;5",
"rating_avg": 4,
"confidence": "3;4;4;5",
"confidence_avg": 4,
"soundness": "1;2;1;3",
"soundness_avg": 1.75,
"contribution": "2;3;2;3",
"contribution_avg": 2.5,
"presentation": "2;2;3;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.676567"
} | {
"id": "WIW8eZXm92",
"metareview": "The paper received ratings that were all below the acceptance thresholds (5,5,3,3). The reviewers raised several concerns such as lack of a proper definition for unknown environments, lack of certain baselines, high cost of inference preventing real-world deployment, and unfair ... | {
"decision": "Reject"
} |
px1674Wp3C | 2312.11370v1 | G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model | {
"content": "## 1 Introduction\n\nLarge language models (LLMs) exhibit human-like proficiency in reasoning (Wei et al., ; Wang et al., ; Zhou et al., ) and generation (Ouyang et al., ; Touvron et al., ), which encourages extensive research on their application in mathematical problem solving (Fu et al., ; Gou et al.... | [
{
"id": "Epqk6S83ds",
"initial_rating": 5,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 4,
"summary": "Current Multi-Modal Language Models (MLLMs) struggle to solve geometry problems for lack of comprehension of geometry information. This paper generates a large-sc... | {
"rating": "5;5;5;5",
"rating_avg": 5,
"confidence": "4;5;4;3",
"confidence_avg": 4,
"soundness": "2;3;3;3",
"soundness_avg": 2.75,
"contribution": "2;3;2;3",
"contribution_avg": 2.5,
"presentation": "3;3;3;4",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.677432"
} | {
"id": "lsUzoupIRC",
"metareview": "This paper introduces G-LLaVA, a Multimodal Large Language Model fine-tuned with Geo170K, a dataset of 170,000 geometric image-caption and QA pairs. It is recognized as a pioneering effort in addressing geometric problem-solving in MLLMs, with an innovative data generation appro... | {
"decision": "Accept (Poster)"
} |
pxGucWt9vM | 2410.09426v1 | FlatQuant: Flatness Matters for LLM Quantization | {
"content": "## Abstract\n\nAbstract Recently, quantization has been widely used for the compression and acceleration of large language models (LLMs).\nDue to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with the equally spaced quantization points. Prior resea... | [
{
"id": "YkqUtm1bpx",
"initial_rating": 8,
"confidence": 5,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper introduces FlatQuant, a post-training quantization method for LLMs that focuses on flattening the distributions of weights and activations to reduce th... | {
"rating": "3;5;5;6;8",
"rating_avg": 5.4,
"confidence": "5;4;4;5;5",
"confidence_avg": 4.6,
"soundness": "2;2;3;3;3",
"soundness_avg": 2.6,
"contribution": "2;3;2;4;3",
"contribution_avg": 2.8,
"presentation": "3;2;3;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.678064"
} | {
"id": "BZ51nPnxQF",
"metareview": "This paper explores a post-training quantization method for LLMs. The main idea is to learn a linear transformation that can be applied to the weights and activations of LLMs, aiming to reduce activation outliers and improve flatness. Additionally, the authors propose a Kronecke... | {
"decision": "Reject"
} |
py34636XvR | 2410.02656v2 | Scalable Simulation-free Entropic Unbalanced Optimal Transport | {
"content": "## Abstract\n\nAbstract The Optimal Transport (OT) problem investigates a transport map that connects two distributions while minimizing a given cost function. Finding such a transport map has diverse applications in machine learning, such as generative modeling and image-to-image translation. In this p... | [
{
"id": "MjdLtVp9LT",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 2,
"summary": "The authors establish several new connections between entropic unbalanced optimal transport (EUOT), the Schrödinger Bridge (SB) problem, stochastic control (SOC),... | {
"rating": "3;5;5;6;6",
"rating_avg": 5,
"confidence": "3;4;4;2;4",
"confidence_avg": 3.4,
"soundness": "2;2;4;3;3",
"soundness_avg": 2.8,
"contribution": "2;2;3;3;3",
"contribution_avg": 2.6,
"presentation": "2;3;2;3;2",
"presentation_avg": 2.4
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.679030"
} | {
"id": "IH4Jy6kHEa",
"metareview": "This paper introduces Simulation-free Entropic Unbalanced Optimal Transport (SF-EUOT), a scalable approach to solving the EUOT problem, a generalization of the Schrödinger bridges problem. By deriving its dynamical form, dual formulation, and optimality conditions, the method av... | {
"decision": "Reject"
} |
pzmbxkCBiq | 2410.11677v2 | Understanding Likelihood Over-optimisation in Direct Alignment Algorithms | {
"content": "## Abstract\n\nAbstract Direct Alignment Algorithms (DAAs), such as Direct Preference Optimisation (DPO) and Identity Preference Optimisation (IPO), have emerged as alternatives to online Reinforcement Learning from Human Feedback (RLHF) algorithms such as Proximal Policy Optimisation (PPO) for aligning... | [
{
"id": "R5rViKunkN",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 4,
"summary": "* The paper studies how completion likelihood affects model performance in Direct Alignment Algorithms (DAAs) like DPO, IPO and Hinge loss, using 7B and 35B model... | {
"rating": "3;3;6;6",
"rating_avg": 4.5,
"confidence": "4;3;3;4",
"confidence_avg": 3.5,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;2",
"contribution_avg": 2.25,
"presentation": "1;3;2;4",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.680066"
} | {
"id": "vYfRtyWtbO",
"metareview": "This paper studies the relationship between completion likelihood and model performance in Direct Alignment Algorithms (DAAs), analyzing how increased likelihood of better completions and margins between better/worse completions affect performance. The paper claims that higher l... | {
"decision": "Reject"
} |
q2DmkZ1wVe | 2402.11924v5 | CofCA: A STEP-WISE Counterfactual Multi-hop QA benchmark | {
"content": "## Abstract\n\nAbstract While Large Language Models (LLMs) excel in question-answering (QA) tasks, their real reasoning abilities on multiple evidence retrieval and integration on Multi-hop QA tasks remain less explored. Firstly, LLMs sometimes generate answers that rely on internal memory rather than r... | [
{
"id": "lX1Pi0YX5r",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper proposed a new dataset, CofCA for evaluating LLM’s counterfactual multi-hop reasoning ability, which focuses on both final answer evaluation and reason... | {
"rating": "5;5;6;8",
"rating_avg": 6,
"confidence": "4;4;4;4",
"confidence_avg": 4,
"soundness": "3;3;3;3",
"soundness_avg": 3,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "3;2;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.681019"
} | {
"id": "XlGMYzgmzb",
"metareview": "There is a discrepancy among the review scores. Yet it is worthy to note that the two reviewers who gave 5 did not participant in the after-rebuttal discussion.\n\nI have personally read this paper and find it to be a valuable contribution. It tackles an important challenge in o... | {
"decision": "Accept (Poster)"
} |
q2VK1Z8XFo | 2410.15368v1 | Tighter Performance Theory of FedExProx | {
"content": "## Abstract\n\nAbstract We revisit FedExProx – a recently proposed distributed optimization method designed to enhance convergence properties of parallel proximal algorithms via extrapolation. In the process, we uncover a surprising flaw: its known theoretical guarantees on quadratic optimization tasks ... | [
{
"id": "ujY8APjWCp",
"initial_rating": 3,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This work revisited FedExProx, a recently proposed algorithm for FL, and furthered the convergence analysis. They first found the existing analysis of FedExProx i... | {
"rating": "3;5;6",
"rating_avg": 4.666666666666667,
"confidence": "4;4;1",
"confidence_avg": 3,
"soundness": "3;3;3",
"soundness_avg": 3,
"contribution": "2;2;2",
"contribution_avg": 2,
"presentation": "3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.682164"
} | {
"id": "aXtLmV5glG",
"metareview": "The paper presents notable theoretical advancements in federated optimization, particularly through its enhanced analysis of FedExProx. The theoretical contributions are seen as valuable additions to the field. The reviewers mostly concerned with the limited setting (quadratic c... | {
"decision": "Reject"
} |
q3Z2v2mt1R | 2411.05399v1 | Post-Hoc Robustness Enhancement in Graph Neural Networks with Conditional Random Fields | {
"content": "## Abstract\n\nAbstract Graph Neural Networks (GNNs), which are nowadays the benchmark approach in graph representation learning, have been shown to be vulnerable to adversarial attacks, raising concerns about their real-world applicability. While existing defense techniques primarily concentrate on the... | [
{
"id": "0YWgAm7nuL",
"initial_rating": 3,
"confidence": 5,
"soundness": 2,
"contribution": 1,
"presentation": 2,
"summary": "This work studies the adversarial robustness of Graph Neural Networks during inference (evasion attack) and propose a new defense method RobustCRF basde on Condit... | {
"rating": "3;3;5;5",
"rating_avg": 4,
"confidence": "4;5;3;3",
"confidence_avg": 3.75,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "2;1;3;2",
"contribution_avg": 2,
"presentation": "2;2;2;3",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.683309"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
q44uq3tc2D | 2410.13859v1 | $\gamma-$MoD: Exploring Mixture-of-Depth Adaptation for Multimodal Large Language Models | {
"content": "## Abstract\n\nAbstract Despite the significant progress in multimodal large language models (MLLMs), their high computational cost remains a barrier to real-world deployment. Inspired by the mixture of depths (MoDs) in natural language processing, we aim to address this limitation from the perspective ... | [
{
"id": "WxjBQlPQJE",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper proposes a novel Mixture-of-Depth (MoD) adaptation method, $\\gamma$-MoD, designed to improve computational efficiency for multimodal large language mo... | {
"rating": "5;6;6",
"rating_avg": 5.666666666666667,
"confidence": "5;4;3",
"confidence_avg": 4,
"soundness": "4;3;3",
"soundness_avg": 3.3333333333333335,
"contribution": "3;3;3",
"contribution_avg": 3,
"presentation": "3;3;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.683968"
} | {
"id": "Y6WRRBSMPx",
"metareview": "This paper proposes γ-MoD, a novel Mixture-of-Depth (MoD) adaptation strategy for multimodal large language models (MLLMs), aimed at improving computational efficiency. By introducing ARank to identify redundant layers, the method effectively reduces training and inference costs... | {
"decision": "Accept (Poster)"
} |
q5sOv4xQe4 | 2410.10812v1 | HART: Efficient Visual Generation with Hybrid Autoregressive Transformer | {
"content": "## Abstract\n\nAbstract We introduce Hybrid Autoregressive Transformer (HART), an autoregressive (AR) visual generation model capable of directly generating 1024 × \\times × 1024 images, rivaling diffusion models in image generation quality. Existing AR models face limitations due to the poor image reco... | [
{
"id": "WyvVsrWHkE",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 4,
"summary": "This paper addresses limitations in autoregressive models (AR models), particularly the challenges in image reconstruction due to discretized tokens and the high ... | {
"rating": "5;6;6;6;8",
"rating_avg": 6.2,
"confidence": "4;4;5;4;4",
"confidence_avg": 4.2,
"soundness": "3;3;3;3;3",
"soundness_avg": 3,
"contribution": "2;3;3;3;3",
"contribution_avg": 2.8,
"presentation": "3;3;2;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.684650"
} | {
"id": "GsOhXtSHzr",
"metareview": "The paper introduces Hybrid Autoregressive Transformer (HART), a novel approach to high-resolution (1024x1024) image generation that combines hybrid tokenization – discrete tokens for structure and continuous tokens for fine-grained details – achieving state-of-the-art performan... | {
"decision": "Accept (Poster)"
} |
q5zMyAUhGx | 2410.08026v1 | Generalization Bounds and Model Complexity for Kolmogorov–Arnold Networks | {
"content": "## Abstract\n\nAbstract Kolmogorov–Arnold Network (KAN) is a network structure recently proposed in Liu et al. ( 2024c ) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work provides a rigorous theoretical anal... | [
{
"id": "ZfIYNC9WEs",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This work addresses a gap in the current research on Kolmogorov–Arnold Networks (KANs) by (i) quantifying the complexity of KANs, and (ii) establishing high proba... | {
"rating": "5;5;5;6;6",
"rating_avg": 5.4,
"confidence": "3;2;4;3;4",
"confidence_avg": 3.2,
"soundness": "3;3;2;3;3",
"soundness_avg": 2.8,
"contribution": "2;2;2;3;3",
"contribution_avg": 2.4,
"presentation": "3;2;3;2;3",
"presentation_avg": 2.6
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.685430"
} | {
"id": "nQ2DJ3px3c",
"metareview": "Summary:\nThis paper provides a theoretical analysis of Kolmogorov–Arnold Networks (KANs), including generalization bounds for regression tasks and analysis of network complexity. The work addresses both bounded and unbounded loss functions and offers empirical validation of the... | {
"decision": "Accept (Poster)"
} |
q6TelS1z7N | 2402.03587v2 | Information-Theoretic Active Correlation Clustering | {
"content": "## Abstract\n\nAbstract We study correlation clustering where the pairwise similarities are not known in advance. For this purpose, we employ active learning to query pairwise similarities in a cost-efficient way. We propose a number of effective information-theoretic acquisition functions based on entr... | [
{
"id": "sYkEH0DLQG",
"initial_rating": 6,
"confidence": 3,
"soundness": 4,
"contribution": 2,
"presentation": 3,
"summary": "The paper presents a new approach to correlation clustering with a limited budget for similarity queries between pair objects. The main contribution is the design... | {
"rating": "3;6;6;6",
"rating_avg": 5.25,
"confidence": "2;4;4;3",
"confidence_avg": 3.25,
"soundness": "2;3;3;4",
"soundness_avg": 3,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.686364"
} | {
"id": "iPn6fe6MtQ",
"metareview": "This paper aims to design correlation clustering methods with a limited number of queries for pairwise similarities between objects. It introduces active learning and devises four information-theoretic acquisition functions. Specially, it utilizes mean-field approximation to ap... | {
"decision": "Reject"
} |
q6hEuC48Dk | 2410.04639v1 | Radial Basis Operator Networks | {
"content": "## Abstract\n\nAbstract Operator networks are designed to approximate nonlinear operators, which provide mappings between infinite-dimensional spaces such as function spaces. These networks are playing an increasingly important role in machine learning, with their most notable contributions in the field... | [
{
"id": "BN3JrTUP1z",
"initial_rating": 3,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 1,
"summary": "This paper deals with operator networks working with radial basis functions.\nTime and frequency domain are studied.\nA couple of experiments are carried out, mai... | {
"rating": "3;3;3;3;5",
"rating_avg": 3.4,
"confidence": "3;2;4;3;2",
"confidence_avg": 2.8,
"soundness": "2;3;2;3;3",
"soundness_avg": 2.6,
"contribution": "2;3;2;2;2",
"contribution_avg": 2.2,
"presentation": "2;3;1;1;3",
"presentation_avg": 2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.687213"
} | {
"id": "i1IwIHjD6I",
"metareview": "The paper proposes a novel (radial basis) operator network capable of learning nonlinear operators in both time and frequency domains, particularly when \nhandling complex-valued inputs.\nSeveral critical points (presentation, experiments, baselines,...) have been raised by the... | {
"decision": "Reject"
} |
q6pm9CObJn | 2405.11985v2 | MTVQA: Benchmarking Multilingual Text-Centric Visual Question Answering | {
"content": "## Abstract\n\nAbstract Text-Centric Visual Question Answering (TEC-VQA) in its proper format not only facilitates human-machine interaction in text-centric visual environments but also serves as a de facto gold proxy to evaluate AI models in the domain of text-centric scene understanding. Nonetheless, ... | [
{
"id": "mwrUXlsVPl",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper proposes a VQA dataset where models must contextualize multilingual text in the image to answer questions. The paper provides extensive benchmarking and... | {
"rating": "3;5;5;6;6",
"rating_avg": 5,
"confidence": "4;5;4;4;3",
"confidence_avg": 4,
"soundness": "2;2;3;3;3",
"soundness_avg": 2.6,
"contribution": "2;2;2;3;3",
"contribution_avg": 2.4,
"presentation": "3;3;2;3;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.688146"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
q6zrZbth1F | 2405.16696v1 | How many samples are needed to train a deep neural network? | {
"content": "## Abstract\n\nAbstract Neural networks have become standard tools in many areas, yet many important statistical questions remain open. This paper studies the question of how much data are needed to train a ReLU feed-forward neural network. Our theoretical and empirical results suggest that the generali... | [
{
"id": "Cyi2TmnPRC",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper proposes to bound by below the minimax risk of a sub-class of ReLU Multi-Layer Perceptrons (MLP). This sub-class, denoted by $\\mathcal{B}\\_{\\mathrm{... | {
"rating": "5;6;8;8",
"rating_avg": 6.75,
"confidence": "3;3;4;3",
"confidence_avg": 3.25,
"soundness": "2;3;4;3",
"soundness_avg": 3,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;3;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.690111"
} | {
"id": "6VcwXRWFGW",
"metareview": "**(a) Summary** \nThis paper investigates the sample complexity required to train deep ReLU feed-forward neural networks. By establishing minimax lower bounds and leveraging Fano's inequality, the authors demonstrate that the generalization error scales at a rate of \\(O(1/\\sq... | {
"decision": "Accept (Poster)"
} |
q7aROKohBZ | 2407.12833v2 | ESQA: Event Sequences Question Answering | {
"content": "## Abstract\n\nAbstract Event sequences (ESs) arise in many practical domains including finance, retail, social networks, and healthcare. In the context of machine learning, event sequences can be seen as a special type of tabular data with annotated timestamps. Despite the importance of ESs modeling an... | [
{
"id": "Serit5F1ZQ",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 2,
"summary": "The authors present a new approach to apply large language models to the task of event sequence prediction. This approach is a little fine-tuned and less expensiv... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "4;4;4;4",
"confidence_avg": 4,
"soundness": "2;3;2;3",
"soundness_avg": 2.5,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "3;2;2;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.692592"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qBpYqQUFPx | 2409.10516v2 | RetrievalAttention: Accelerating Long-Context LLM Inference via Vector Retrieval | {
"content": "## Abstract\n\nAbstract Transformer-based Large Language Models (LLMs) have become increasingly important. However, due to the quadratic time complexity of attention computation, scaling LLMs to longer contexts incurs extremely slow inference latency and high GPU memory consumption for caching key-value... | [
{
"id": "20zgiJFiYL",
"initial_rating": 8,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper introduces RetrievalAttention to improve inference speed and reduce memory usage for LLMs with long contexts by using Approximate Nearest Neighbor Searc... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "5;5;2;4",
"confidence_avg": 4,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.693358"
} | {
"id": "LMfAx7jceJ",
"metareview": "This paper introduces RetrievalAttention, a novel method that leverages Approximate Nearest Neighbor Search (ANNS) to accelerate attention computation and reduce GPU memory consumption in large language models (LLMs). Notably, RetrievalAttention employs an attention-aware vector... | {
"decision": "Reject"
} |
qDFpNXnuYK | 2403.15210v1 | Early Period of Training Impacts Adaptation for Out-of-Distribution Generalization: An Empirical Study | {
"content": "## Abstract\n\nAbstract Prior research has found that differences in the early period of neural network training significantly impact the performance of in-distribution (ID) tasks. However, neural networks are often sensitive to out-of-distribution (OOD) data, making them less reliable in downstream app... | [
{
"id": "pIfVw35lbC",
"initial_rating": 5,
"confidence": 3,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "This work investigates the impact of interventions by weight freezing during early stage of training on out of distribution generalization and reports empirical e... | {
"rating": "3;5;5;5;6",
"rating_avg": 4.8,
"confidence": "4;4;3;3;3",
"confidence_avg": 3.4,
"soundness": "2;3;3;2;2",
"soundness_avg": 2.4,
"contribution": "2;2;2;2;3",
"contribution_avg": 2.2,
"presentation": "1;3;3;3;3",
"presentation_avg": 2.6
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.694084"
} | {
"id": "h3jSSZu2ND",
"metareview": "This paper investigates the training dynamic of deep neural networks and how it impacts OOD generalization. In particular, this is the first paper that focuses on the impact of early training stages. They achieve this by gradually unfreezing, which is a method that existed befor... | {
"decision": "Reject"
} |
qDeEsfAb1j | 2212.02895v2 | Training Neural Networks on Data Sources with Unknown Reliability | {
"content": "## Abstract\n\nAbstract When data is generated by multiple sources, conventional training methods update models assuming equal reliability for each source and do not consider their individual data quality during training. However, in many applications, sources have varied levels of reliability that can ... | [
{
"id": "qdvOatnKPZ",
"initial_rating": 5,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 2,
"summary": "This paper studies learning with noisy labels in a particular setup, where the data consists of multiple sources and only some sources are noisy. The authors prop... | {
"rating": "3;3;5;5",
"rating_avg": 4,
"confidence": "3;4;4;3",
"confidence_avg": 3.5,
"soundness": "1;2;3;3",
"soundness_avg": 2.25,
"contribution": "2;1;3;2",
"contribution_avg": 2,
"presentation": "2;2;1;2",
"presentation_avg": 1.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.695174"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qFw2RFJS5g | 2410.18676v1 | Homomorphism Counts as Structural Encodings for Graph Learning | {
"content": "## Abstract\n\nAbstract Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use of positional encodings (e.g., Laplacian... | [
{
"id": "ylDxud1KuE",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "The paper proposes Motif Structural Encoding (MoSE), a novel structural encoding method based on homomorphism counts for graph learning tasks. MoSE leverages homo... | {
"rating": "5;6;6;6;8",
"rating_avg": 6.2,
"confidence": "4;5;3;3;4",
"confidence_avg": 3.8,
"soundness": "4;3;2;3;4",
"soundness_avg": 3.2,
"contribution": "3;3;3;2;3",
"contribution_avg": 2.8,
"presentation": "3;3;3;3;4",
"presentation_avg": 3.2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.696172"
} | {
"id": "VZTGIcvLc8",
"metareview": "(a) The paper proposes Motif Structural Encoding (MoSE), a novel structural encoding method for graph learning. It shows MoSE has greater expressive power than Random Walk Structural Encoding (RWSE) and is independent of the Weisfeiler-Lehman (WL) hierarchy. Empirically, MoSE ou... | {
"decision": "Accept (Poster)"
} |
qGL6fE1lqd | 2411.08027v1 | LLMPhy: Complex Physical Reasoning Using Large Language Models and World Models | {
"content": "## Abstract\n\nAbstract Physical reasoning is an important skill needed for robotic agents when operating in the real world. However, solving such reasoning problems often involves hypothesizing and reflecting over complex multi-body interactions under the effect of a multitude of physical forces and th... | [
{
"id": "noPEheBdPT",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 3,
"presentation": 4,
"summary": "This paper addresses the challenge of reasoning about the result of a complex multi-body physical interaction; specifically, the goal is to predict which objects ... | {
"rating": "3;3;3;5;5",
"rating_avg": 3.8,
"confidence": "4;4;4;4;4",
"confidence_avg": 4,
"soundness": "2;3;2;3;2",
"soundness_avg": 2.4,
"contribution": "1;2;2;2;3",
"contribution_avg": 2,
"presentation": "1;3;1;3;4",
"presentation_avg": 2.4
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.697060"
} | {
"id": "bwstCbfwZI",
"metareview": "This paper introduces LLMPhy, which integrates LLMs with a physics simulator to address physics reasoning tasks. The main claim is that LLMPhy can iteratively estimate the physical hyperparameters of a system using an analysis-by-synthesis approach and leverage the inferred prop... | {
"decision": "Reject"
} |
qH6pzxPZ0d | 2410.02845v1 | TOWARDS LAYER-WISE PERSONALIZED FEDERATED LEARNING: ADAPTIVE LAYER DISENTANGLEMENT VIA CONFLICTING GRADIENTS | {
"content": "## Abstract\n\nAbstract In personalized Federated Learning (pFL), high data heterogeneity can cause significant gradient divergence across devices, adversely affecting the learning process. This divergence, especially when gradients from different users form an obtuse angle during aggregation, can negat... | [
{
"id": "YG4B5XpieU",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 1,
"summary": "This paper presents a layer disentanglement mechanism to achieve personalized federated learning. Specifically, the paper distinguishes between personal layers an... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;3;2;3",
"soundness_avg": 2.5,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "1;1;2;3",
"presentation_avg": 1.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.698042"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qHVUdP1EEU | 2410.11816v1 | Jigsaw++: Imagining Complete Shape Priors for Object Reassembly | {
"content": "## Abstract\n\nAbstract The automatic assembly problem has attracted increasing interest due to its complex challenges that involve 3D representation. This paper introduces Jigsaw++, a novel generative method designed to tackle the multifaceted challenges of reconstruction for the reassembly problem. Ex... | [
{
"id": "OBPvG6Vucq",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "The paper introduces Jigsaw++, a generative method to improve automatic assembly tasks involving complex 3D reconstruction challenges. Unlike existing methods tha... | {
"rating": "3;6;6;8",
"rating_avg": 5.75,
"confidence": "4;3;4;5",
"confidence_avg": 4,
"soundness": "2;3;3;4",
"soundness_avg": 3,
"contribution": "2;3;3;3",
"contribution_avg": 2.75,
"presentation": "3;2;2;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.698999"
} | {
"id": "MMpqlpFKTK",
"metareview": "This paper introduces Jigsaw++, which handles object reassembly problems. The key idea is to propose a novel generative model, which is different from prior work focusing on piecewise part assembly that may overlook overall assembled shape. The authors demonstrated the effective... | {
"decision": "Reject"
} |
qIN5VDdEOr | 2410.14516v4 | Do LLMs ``know'' internally when they follow instructions? | {
"content": "## Abstract\n\nAbstract Instruction-following is crucial for building AI agents with large language models (LLMs), as these models must adhere strictly to user-provided constraints and guidelines.\nHowever, LLMs often fail to follow even simple and clear instructions.\nTo improve instruction-following b... | [
{
"id": "UW8hslAs4x",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 4,
"presentation": 3,
"summary": "This paper investigates the internal representation of LLMs and identifies a \"dimension\" that corresponds to their success in instrution-following. They show th... | {
"rating": "5;5;6;6;8",
"rating_avg": 6,
"confidence": "3;4;3;4;3",
"confidence_avg": 3.4,
"soundness": "3;2;3;3;4",
"soundness_avg": 3,
"contribution": "2;2;3;4;3",
"contribution_avg": 2.8,
"presentation": "2;3;3;3;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.699793"
} | {
"id": "Suf1hL1nRq",
"metareview": "The authors present a way to understand whether instructions will have the desired effect on instruction following behavior. There were concerns about how reliable these results are (relatively small effect) and applicability to modern models that are more robust. This is very m... | {
"decision": "Accept (Poster)"
} |
qJkCEcd50n | 2409.05208v4 | Influence-based Attributions can be Manipulated | {
"content": "## Abstract\n\nAbstract Influence Functions are a standard tool for attributing predictions to training data in a principled manner and are widely used in applications such as data valuation and fairness. In this work, we present realistic incentives to manipulate influence-based attributions and invest... | [
{
"id": "wXmeDnis1H",
"initial_rating": 3,
"confidence": 4,
"soundness": 2,
"contribution": 1,
"presentation": 2,
"summary": "The paper studied a setup in which the influence scores of training samples can be manipulated through a modified training procedure by changing the loss function... | {
"rating": "1;3;3;3;5",
"rating_avg": 3,
"confidence": "4;3;3;4;5",
"confidence_avg": 3.8,
"soundness": "1;1;2;2;3",
"soundness_avg": 1.8,
"contribution": "1;1;2;1;2",
"contribution_avg": 1.4,
"presentation": "2;2;3;2;2",
"presentation_avg": 2.2
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.700540"
} | {
"id": "G7Smcv0UCZ",
"metareview": "I have read all the materials of this paper including the manuscript, appendix, comments, and response. Based on collected information from all reviewers and my personal judgment, I can make the recommendation on this paper, reject. No objection from reviewers who participated i... | {
"decision": "Reject"
} |
qK3XElJUbq | 2405.21022v1 | You Only Scan Once: Efficient Multi-dimension Sequential Modeling with LightNet | {
"content": "## Abstract\n\nAbstract Linear attention mechanisms have gained prominence in causal language models due to their linear computational complexity and enhanced speed. However, the inherent decay mechanism in linear attention presents challenges when applied to multi-dimensional sequence modeling tasks, s... | [
{
"id": "FH3sVDa9UB",
"initial_rating": 5,
"confidence": 5,
"soundness": 4,
"contribution": 3,
"presentation": 4,
"summary": "1. The paper presents *LightNet*, a new variant of State Space Models (SSMs) incorporating an additive decay/selectivity parameter. Unlike Mamba or Linear Attenti... | {
"rating": "3;3;5;8",
"rating_avg": 4.75,
"confidence": "4;5;5;2",
"confidence_avg": 4,
"soundness": "2;2;4;3",
"soundness_avg": 2.75,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "1;1;4;3",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.701553"
} | {
"id": "lUOe5GZDHM",
"metareview": "The paper proposes a new form of additive linear attention to efficiently process multi-dimensional data. Further, the paper also proposes new forms of positional embeddings for the same. Empirical evaluations show performance improvements over linear attention on many multi-di... | {
"decision": "Reject"
} |
qK6U4Ahfms | 2410.21286v1 | OpenCity: A Scalable Platform to Simulate Urban Activities with Massive LLM Agents | {
"content": "## Abstract\n\nAbstract Agent-based models (ABMs) have long been employed to explore how individual behaviors aggregate into complex societal phenomena in urban space. Unlike black-box predictive models, ABMs excel at explaining the micro-macro linkages that drive such emergent behaviors. The recent ris... | [
{
"id": "56hzcoPF98",
"initial_rating": 3,
"confidence": 4,
"soundness": 1,
"contribution": 1,
"presentation": 2,
"summary": "The paper describes an approach\twhere LLM agents are used to simulate individual behaviour in large (city-scale) simulations of people.\tThe proposed platform us... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "4;4;4;3",
"confidence_avg": 3.75,
"soundness": "2;1;2;3",
"soundness_avg": 2,
"contribution": "2;1;2;2",
"contribution_avg": 1.75,
"presentation": "3;2;2;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.702247"
} | {
"id": "O3hX2Ha1wO",
"metareview": "The paper proposes OpenCity, a platform combining agent-based modeling (ABM) with large language models (LLMs) to simulate urban dynamics at scale. By leveraging techniques like the “group-and-distill” prompt optimization, the platform achieves significant computational efficien... | {
"decision": "Reject"
} |
qKgd7RaAem | 2411.05464v1 | Generalization, Expressivity, and Universality of Graph Neural Networks on Attributed Graphs | {
"content": "## Abstract\n\nAbstract We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained expressivity of GNNs. Namely, GNNs are bot... | [
{
"id": "jwiq4Twm19",
"initial_rating": 8,
"confidence": 4,
"soundness": 4,
"contribution": 3,
"presentation": 2,
"summary": "The authors propose a metric based on optimal transport distances between graph representations.\nUnder this metric, the authors show the MPNNs are Lipschitz and ... | {
"rating": "5;5;8;8",
"rating_avg": 6.5,
"confidence": "3;2;4;4",
"confidence_avg": 3.25,
"soundness": "3;3;4;4",
"soundness_avg": 3.5,
"contribution": "2;3;4;3",
"contribution_avg": 3,
"presentation": "2;2;3;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.703522"
} | {
"id": "mrnSofI4BE",
"metareview": "This paper proposes a new pseudo-metric on message passing GNNs on attributed graphs, based on the Wasserstein distance between distributions of computation tree analogs over graphons. The paper proves that message passing GNNs are universal approximations over attributed grapho... | {
"decision": "Accept (Poster)"
} |
qLRaPfDPXK | 2410.01064v1 | Truth or Deceit? A Bayesian Decoding Game Enhances Consistency and Reliability | {
"content": "## Abstract\n\nAbstract Large Language Models (LLMs) often produce outputs that – though plausible – can lack consistency and reliability, particularly in ambiguous or complex scenarios. Challenges arise from ensuring that outputs align with both factual correctness and human intent. This is problematic... | [
{
"id": "dGTipq5s1Y",
"initial_rating": 5,
"confidence": 2,
"soundness": 3,
"contribution": 3,
"presentation": 1,
"summary": "This work presents a novel approach to improving Large Language Model (LLM) outputs through game theory. Bayesian decoding game(BDG) structures the decoding proce... | {
"rating": "3;3;6",
"rating_avg": 4,
"confidence": "3;3;3",
"confidence_avg": 3,
"soundness": "3;2;3",
"soundness_avg": 2.6666666666666665,
"contribution": "2;3;3",
"contribution_avg": 2.6666666666666665,
"presentation": "1;1;2",
"presentation_avg": 1.3333333333333333
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.704791"
} | {
"id": "Gc4KG776xj",
"metareview": "This paper proposes a Bayesian decoding game to improve the consistency and reliability of model generations, by modeling the language model’s decoding as a game between a generator and a verifier. This work extends the framework by Jacob et al. (2024), by incorporating a new a... | {
"decision": "Reject"
} |
qNp86ByQlN | 2407.17396v1 | Systematic Relational Reasoning With Epistemic Graph Neural Networks | {
"content": "## Abstract\n\nAbstract Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work on reasoning with GNNs has shown that such models tend t... | [
{
"id": "LoWzQ4bLmX",
"initial_rating": 6,
"confidence": 2,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This work presents a representation-based method for predicting relationships between entities within a knowledge graph. The approach leverages Graph Neural Netwo... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;3;3;5",
"confidence_avg": 3.75,
"soundness": "3;2;2;3",
"soundness_avg": 2.5,
"contribution": "2;3;2;2",
"contribution_avg": 2.25,
"presentation": "3;3;2;4",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.705670"
} | {
"id": "XobnCJwVcL",
"metareview": "This paper introduces Epistemic GNN (EpiGNN), a novel GNN architecture designed for systematic reasoning in relational domains. EpiGNN overcomes the limitations of regular GNNs by treating node embeddings as epistemic states and using specialized message passing. It achieves sta... | {
"decision": "Accept (Poster)"
} |
qOqCXEXsX4 | 2406.16797v2 | Lottery Ticket Adaptation: Mitigating Destructive Interference in LLMs | {
"content": "## Abstract\n\nAbstract Existing methods for adapting large language models (LLMs) to new tasks are not suited to multi-task adaptation because they modify all the model weights–causing destructive interference between tasks. The resulting effects, such as catastrophic forgetting of earlier tasks, make ... | [
{
"id": "uaQ6d31EyE",
"initial_rating": 5,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 4,
"summary": "The paper proposes a fine-tuning method for adapting LLMs to enable multi-task learning and prevent catastrophic forgetting. The method uses a mask calibration st... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;1;3;3",
"soundness_avg": 2.25,
"contribution": "2;3;2;3",
"contribution_avg": 2.5,
"presentation": "3;2;4;3",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.706594"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qPTFzmXVLd | 2411.05001v1 | Analyzing the Language of Visual Tokens | {
"content": "## Abstract\n\nAbstract With the introduction of transformer-based models for vision and language tasks, such as LLaVA and Chameleon, there has been renewed interest in the discrete tokenized representation of images. These models often treat image patches as discrete tokens, analogous to words in natur... | [
{
"id": "KwvJklkaTB",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper looks at the statistical properties of \"visual languages,\" where images are broken into discrete tokens like words in a sentence, used in multimodal ... | {
"rating": "3;5;6;8",
"rating_avg": 5.5,
"confidence": "3;3;4;3",
"confidence_avg": 3.25,
"soundness": "2;2;3;3",
"soundness_avg": 2.5,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "3;3;3;4",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.707424"
} | {
"id": "xchfTWDsQW",
"metareview": "This paper tackles an interesting problem: that of analyzing the \"structure\" within sequential vision models, from a linguistic point of view. The main finding of the statistical evaluation is that visual tokens follow a Zipf distribution with higher entropy and lack cohesive ... | {
"decision": "Reject"
} |
qPZaTqLee4 | 2410.04190v1 | Harnessing Task Overload for Scalable Jailbreak Attacks on Large Language Models | {
"content": "## Abstract\n\nAbstract Large Language Models (LLMs) remain vulnerable to jailbreak attacks that bypass their safety mechanisms. Existing attack methods are fixed or specifically tailored for certain models and cannot flexibly adjust attack strength, which is critical for generalization when attacking m... | [
{
"id": "euUH6eIh4M",
"initial_rating": 5,
"confidence": 4,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "In this paper, the authors propose a method for conducting jailbreak attacks on LLM by strategically overloading their computational resources with preliminary lo... | {
"rating": "3;5;5;5",
"rating_avg": 4.5,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;2;3;2",
"soundness_avg": 2.25,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "2;3;2;3",
"presentation_avg": 2.5
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.708089"
} | {
"id": "l8fzf6UM85",
"metareview": "The paper introduces a jailbreak attack that exploits computational resource overload through character map lookup tasks. Based on the paper’s presentation, the method outperforms several baseline methods, such as GCG and FAIR.\n\nAll reviewers find the paper well-structured and... | {
"decision": "Reject"
} |
qPx3i9sMxv | 2410.10676v1 | Both Ears Wide Open: Towards Language-Driven Spatial Audio Generation | {
"content": "## Abstract\n\nAbstract Recently, diffusion models have achieved great success in mono-channel audio generation.\nHowever, when it comes to stereo audio generation, the soundscapes often have a complex scene of multiple objects and directions.\nControlling stereo audio with spatial contexts remains chal... | [
{
"id": "Zk1nEqvXjF",
"initial_rating": 6,
"confidence": 5,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper presents SpatialSonic, an innovative framework for generating controllable stereo audio driven by text and images. The proposed model leverages a new la... | {
"rating": "6;6;6;8",
"rating_avg": 6.5,
"confidence": "3;3;5;4",
"confidence_avg": 3.75,
"soundness": "3;3;3;3",
"soundness_avg": 3,
"contribution": "3;2;3;4",
"contribution_avg": 3,
"presentation": "2;3;3;4",
"presentation_avg": 3
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Spotlight",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.708883"
} | {
"id": "a336JGNSlW",
"metareview": "This paper proposes SpatialSonic, a spatial audio generation based on latent diffusion. The proposed model is trained by the newly proposed BEWO-1M dataset, a GPT-assisted dataset. The proposed SpatialSonic can generate stereo audio by using guidance by text instruction, image, ... | {
"decision": "Accept (Spotlight)"
} |
qPzYF2EpXb | 2409.20154v3 | GravMAD: Grounded Spatial Value Maps Guided Action Diffusion for Generalized 3D Manipulation | {
"content": "## Abstract\n\nAbstract Robots’ ability to follow language instructions and execute diverse 3D tasks is vital in robot learning. Traditional imitation learning-based methods perform well on seen tasks but struggle with novel, unseen ones due to variability. Recent approaches leverage large foundation mo... | [
{
"id": "Q1mbvzMjqD",
"initial_rating": 5,
"confidence": 5,
"soundness": 2,
"contribution": 2,
"presentation": 3,
"summary": "The paper proposes a pipeline of Grounded Spatial Value Maps-guided Action Diffusion (*GravMAD*), which is a subgoal-driven, language-conditioned action diffusion... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;4;5;3",
"confidence_avg": 4,
"soundness": "3;2;2;2",
"soundness_avg": 2.25,
"contribution": "2;2;2;3",
"contribution_avg": 2.25,
"presentation": "2;3;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.710040"
} | {
"id": "VYj4MonO4E",
"metareview": "The paper presents a framework for robotic manipulation that combines prior work on action diffusion and robotic control with foundation models. The approach demonstrates solid generalization capabilities and outperforms state-of-the-art baselines. \n\nStrengths:\n\n- Clear moti... | {
"decision": "Accept (Poster)"
} |
qQ5djlndm5 | 2312.02252v2 | StoryGPT-V: Large Language Models as Consistent Story Visualizers | {
"content": "## Abstract\n\nAbstract Recent generative models have demonstrated impressive capabilities in generating realistic and visually pleasing images grounded on textual prompts. Nevertheless, a significant challenge remains in applying these models for the more intricate task of story visualization. Since it... | [
{
"id": "NIh9KZr1zS",
"initial_rating": 5,
"confidence": 4,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "This paper focuses on the task of story visualization and proposes combining the advantages of LLMs and LDMs to generate a consistent story from a given long narr... | {
"rating": "3;3;5;6",
"rating_avg": 4.25,
"confidence": "3;5;4;4",
"confidence_avg": 4,
"soundness": "2;1;3;3",
"soundness_avg": 2.25,
"contribution": "2;2;2;2",
"contribution_avg": 2,
"presentation": "2;2;3;2",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.710991"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qTWDpbF47t | 2407.06182v1 | Compositional Video Generation as Flow Equalization | {
"content": "## Abstract\n\nAbstract Large-scale Text-to-Video (T2V) diffusion models\nhave recently demonstrated unprecedented\ncapability to transform natural language descriptions into stunning and photorealistic videos.\nDespite the promising results, a significant challenge remains:\nthese models struggle to fu... | [
{
"id": "TUJxAnaNhm",
"initial_rating": 8,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper introduces a novel approach for compositional video generation. The proposed method begins by analyzing the impact of input tokens on the video output,... | {
"rating": "3;5;8;8",
"rating_avg": 6,
"confidence": "5;4;4;3",
"confidence_avg": 4,
"soundness": "3;3;3;3",
"soundness_avg": 3,
"contribution": "2;2;3;3",
"contribution_avg": 2.5,
"presentation": "2;2;2;3",
"presentation_avg": 2.25
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.712093"
} | {
"id": "ly1iMA9YDP",
"metareview": "This paper introduces Vico, an inference-time method designed to enhance compositional video generation. Vico ensures equal influence for each textual token (verbs and nouns only) on the final video output through test-time optimization, dynamically assessing and rebalancing tok... | {
"decision": "Reject"
} |
qUJsX3XMBH | 2410.09335v1 | Rethinking Data Selection at Scale: Random Selection is Almost All You Need | {
"content": "## Abstract\n\nAbstract Supervised fine-tuning (SFT) is crucial for aligning Large Language Models (LLMs) with human instructions. The primary goal during SFT is to select a small yet representative subset of training data from the larger pool, such that fine-tuning with this subset achieves results com... | [
{
"id": "Cc2sPQljz6",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 2,
"presentation": 3,
"summary": "In this paper authors proposed a data filtration technique for the SFT (supervised fine-tuning phase) of LLM training.\nRigorously testing existing SOTA methods t... | {
"rating": "3;3;5;5;6",
"rating_avg": 4.4,
"confidence": "4;4;4;4;3",
"confidence_avg": 3.8,
"soundness": "2;2;3;2;3",
"soundness_avg": 2.4,
"contribution": "2;3;3;3;2",
"contribution_avg": 2.6,
"presentation": "2;2;3;2;3",
"presentation_avg": 2.4
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.712910"
} | {
"id": "DWQjqrz6vB",
"metareview": "The paper analyzes methods for selecting a high quality dataset for LLM supervised fine tuning (SFT). This task is highly motivated given that many papers show the crucial role of data quality in LLM training. An additional strength mentioned by the reviewers is the insights pro... | {
"decision": "Reject"
} |
qUZY7ymDPr | 2411.02327v2 | PPLLaVA: Varied Video Sequence Understanding With Prompt Guidance | {
"content": "## Abstract\n\nAbstract The past year has witnessed the significant advancement of video-based large language models. However, the challenge of developing a unified model for both short and long video understanding remains unresolved. Most existing video LLMs cannot handle hour-long videos, while method... | [
{
"id": "PYoXbUjM1T",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper proposes a new model that can handle short and long videos with state-of-the-art performance under comparable model sizes. By using DPO's fine-tuning st... | {
"rating": "3;3;5;6;6",
"rating_avg": 4.6,
"confidence": "4;5;4;5;4",
"confidence_avg": 4.4,
"soundness": "3;3;3;3;3",
"soundness_avg": 3,
"contribution": "2;3;2;4;3",
"contribution_avg": 2.8,
"presentation": "3;3;2;3;3",
"presentation_avg": 2.8
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.713531"
} | {
"id": "hhTjDBCYvW",
"metareview": "The paper proposes PPLLaVA, a video LLM utilizing prompt-guided pooling to efficiently process short and long videos. The method demonstrates strong performance across multiple video benchmarks. However, reviewers raised several concerns, including incremental novelty, CLIP dep... | {
"decision": "Reject"
} |
qVyjN01x4P | 2410.09836v1 | Learning Pattern-Specific Experts for Time Series Forecasting Under Patch-level Distribution Shift | {
"content": "## Abstract\n\nAbstract Time series forecasting, which aims to predict future values based on historical data, has garnered significant attention due to its broad range of applications.\nHowever, real-world time series often exhibit complex non-uniform distribution with varying patterns across segments,... | [
{
"id": "GMo5faOa1t",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper innovatively addresses the diversity of time series patterns by introducing a Mixture of Experts (MoE) approach for decoupled modeling. It leverages a u... | {
"rating": "3;5;5;5;6",
"rating_avg": 4.8,
"confidence": "4;4;2;4;4",
"confidence_avg": 3.6,
"soundness": "2;2;3;3;3",
"soundness_avg": 2.6,
"contribution": "2;2;2;3;3",
"contribution_avg": 2.4,
"presentation": "2;3;3;2;3",
"presentation_avg": 2.6
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.714271"
} | {
"id": "NucDEaNtDh",
"metareview": "This paper presents a pattern-based mixture of experts model for time series prediction. Reviewers agreed that this paper is well written and easy to follow, and the paper aims to address a critical problem, i.e., patch-level distributional shift in time series forecasting. Mean... | {
"decision": "Reject"
} |
qYniSDqk8a | 2409.17671v2 | Leveraging Anthropometric Measurements to Improve Human Mesh Estimation and Ensure Consistent Body Shapes | {
"content": "## Abstract\n\nAbstract The basic body shape of a person does not change within a single video. However, most SOTA human mesh estimation (HME) models output a slightly different body shape for each video frame, which results in inconsistent body shapes for the same person. In contrast, we leverage anthr... | [
{
"id": "cJ0IhFOM3t",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper proposes an intuitive way to improve the estimation of human body shape: learn a mapping model from easily observed spatial measurements, here using an... | {
"rating": "3;5;5;6",
"rating_avg": 4.75,
"confidence": "4;4;3;4",
"confidence_avg": 3.75,
"soundness": "2;3;2;3",
"soundness_avg": 2.5,
"contribution": "2;3;3;3",
"contribution_avg": 2.75,
"presentation": "2;4;4;3",
"presentation_avg": 3.25
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Conference Withdrawn Submission",
"venueid": "ICLR.cc/2025/Conference/Withdrawn_Submission",
"processed_at": "2026-01-14T22:16:03.715754"
} | {
"id": "",
"metareview": "",
"additional_comments": ""
} | {
"decision": ""
} |
qZwtPEw2qN | 2411.02780v1 | How Much is a Noisy Image Worth? Data Scaling Laws for Ambient Diffusion. | {
"content": "## Abstract\n\nAbstract The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or inst... | [
{
"id": "4FsSTwDBcu",
"initial_rating": 6,
"confidence": 3,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "The paper investigates the impact of noisy data on (ambient) diffusion models. The paper shows that noisy data can be leveraged to improve the performance of diff... | {
"rating": "5;6;6;8;8",
"rating_avg": 6.6,
"confidence": "2;3;3;3;3",
"confidence_avg": 2.8,
"soundness": "2;3;3;3;4",
"soundness_avg": 3,
"contribution": "2;3;3;4;3",
"contribution_avg": 3,
"presentation": "3;4;3;3;3",
"presentation_avg": 3.2
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.716901"
} | {
"id": "DxFFYZ6kUr",
"metareview": "The paper explores the challenge of training generative models when access to large-scale, high-quality datasets is limited. The authors demonstrate that a small subset of clean data (e.g., 10% of the total dataset) combined with a larger set of highly noisy data is sufficient t... | {
"decision": "Accept (Poster)"
} |
qazJfAmgOt | 2410.10922v1 | A few-shot Label Unlearning in Vertical Federated Learning | {
"content": "## Abstract\n\nAbstract This paper addresses the critical challenge of unlearning in Vertical Federated Learning (VFL), an area that has received limited attention compared to horizontal federated learning. We introduce the first approach specifically designed to tackle label unlearning in VFL, focusing... | [
{
"id": "cE8s1M4dlt",
"initial_rating": 5,
"confidence": 2,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper aims to address the label unlearning problem in vertical federated learning (VFL). It demonstrates the lable leakage issue with applying traditional te... | {
"rating": "5;5;5;6",
"rating_avg": 5.25,
"confidence": "4;4;2;4",
"confidence_avg": 3.5,
"soundness": "2;3;3;4",
"soundness_avg": 3,
"contribution": "3;3;3;4",
"contribution_avg": 3.25,
"presentation": "2;2;3;4",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "Submitted to ICLR 2025",
"venueid": "ICLR.cc/2025/Conference/Rejected_Submission",
"processed_at": "2026-01-14T22:16:03.718241"
} | {
"id": "7C4AiPk3D5",
"metareview": "This paper received two positive and two negative reviews. Positive reviews highlighted its clear structure and effective mixup augmentation method for unlearning in Vertical Federated Learning (VFL). Empirical results show improved accuracy and reduced attack success rates, wit... | {
"decision": "Reject"
} |
qdOIkeZ5e4 | 2307.02869v2 | Generalized Video Moment Retrieval | {
"content": "## Abstract\n\nAbstract Video moment retrieval pursues an efficient and generalized solution to identify the specific temporal segments within an untrimmed video that correspond to a given language description.\nTo achieve this goal, we provide a generative diffusion-based framework called MomentDiff, w... | [
{
"id": "MPehAL5waJ",
"initial_rating": 6,
"confidence": 4,
"soundness": 3,
"contribution": 3,
"presentation": 3,
"summary": "This paper first introduce a novel GVMR framework that significantly expands the scope of traditional VMR, catering to a wider range of query types and enhancing ... | {
"rating": "5;5;6;6",
"rating_avg": 5.5,
"confidence": "5;5;5;4",
"confidence_avg": 4.75,
"soundness": "3;2;3;3",
"soundness_avg": 2.75,
"contribution": "3;3;3;3",
"contribution_avg": 3,
"presentation": "3;2;3;3",
"presentation_avg": 2.75
} | {
"primary_area": "",
"track": "main",
"venue": "ICLR 2025 Poster",
"venueid": "ICLR.cc/2025/Conference",
"processed_at": "2026-01-14T22:16:03.719106"
} | {
"id": "Dh3GdP2Fu5",
"metareview": "This paper proposed a new Generalized Video Moment Retrieval framework, which expands traditional VMR to handle complex, non-target, and multi-target queries. To facilitate research on this task, a new dataset named NExT-VMR dataset, is derived from the YFCC100M collection, fea... | {
"decision": "Accept (Poster)"
} |
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