arXiv subjects

Bohan Wang

Publications and source records attributed to Bohan Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants

In this paper, we are concerned with the optimal asymptotic lower bound for the stability of Sobolev inequality on the Heisenberg group. We first establish the optimal local stability of Sobolev inequality on the CR sphere through bispherical harmonics and complicated orthogonality technique ( see Lemma 3.1). The loss of rearrangement inequality in the CR setting makes it impossible to use any rearrangement flow technique (either differential rearrangement flow or integral rearrangement flow) to derive the optimal stability of Sobolev inequality on the CR sphere from corresponding optimal local stability. To circumvent this, we will use the CR Yamabe flow to establish the optimal stability of Sobolev inequality on the Heisenberg group with the dimension-dependent constants (see Theorem 1.1). As an application, we also establish the optimal stability of the Hardy-Littlewood-Sobolev (HLS) inequality for special conformal index with the dimension-dependent constants (see Theorem 1.3). Our approach is rearrangement-free and can be used to study the optimal stability problem for fractional Sobolev inequality or HLS inequality on the Heisenberg group once the corresponding continuous flow is established.

math.AP↗

arXiv2025

Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs. This survey serves as a resource for researchers and practitioners seeking to understand and contribute to the fusion of GNNs and DEs

cs.LG↗

arXiv2025

RobotSmith: Generative Robotic Tool Design for Acquisition of Complex Manipulation Skills

Endowing robots with tool design abilities is critical for enabling them to solve complex manipulation tasks that would otherwise be intractable. While recent generative frameworks can automatically synthesize task settings, such as 3D scenes and reward functions, they have not yet addressed the challenge of tool-use scenarios. Simply retrieving human-designed tools might not be ideal since many tools (e.g., a rolling pin) are difficult for robotic manipulators to handle. Furthermore, existing tool design approaches either rely on predefined templates with limited parameter tuning or apply generic 3D generation methods that are not optimized for tool creation. To address these limitations, we propose RobotSmith, an automated pipeline that leverages the implicit physical knowledge embedded in vision-language models (VLMs) alongside the more accurate physics provided by physics simulations to design and use tools for robotic manipulation. Our system (1) iteratively proposes tool designs using collaborative VLM agents, (2) generates low-level robot trajectories for tool use, and (3) jointly optimizes tool geometry and usage for task performance. We evaluate our approach across a wide range of manipulation tasks involving rigid, deformable, and fluid objects. Experiments show that our method consistently outperforms strong baselines in terms of both task success rate and overall performance. Notably, our approach achieves a 50.0\% average success rate, significantly surpassing other baselines such as 3D generation (21.4%) and tool retrieval (11.1%). Finally, we deploy our system in real-world settings, demonstrating that the generated tools and their usage plans transfer effectively to physical execution, validating the practicality and generalization capabilities of our approach.

cs.RO↗

arXiv2025

Selftok: Discrete Visual Tokens of Autoregression, by Diffusion, and for Reasoning

We completely discard the conventional spatial prior in image representation and introduce a novel discrete visual tokenizer: Self-consistency Tokenizer (Selftok). At its design core, we compose an autoregressive (AR) prior -- mirroring the causal structure of language -- into visual tokens by using the reverse diffusion process of image generation. The AR property makes Selftok fundamentally distinct from traditional spatial tokens in the following two key ways: - Selftok offers an elegant and minimalist approach to unify diffusion and AR for vision-language models (VLMs): By representing images with Selftok tokens, we can train a VLM using a purely discrete autoregressive architecture -- like that in LLMs -- without requiring additional modules or training objectives. - We theoretically show that the AR prior satisfies the Bellman equation, whereas the spatial prior does not. Therefore, Selftok supports reinforcement learning (RL) for visual generation with effectiveness comparable to that achieved in LLMs. Besides the AR property, Selftok is also a SoTA tokenizer that achieves a favorable trade-off between high-quality reconstruction and compression rate. We use Selftok to build a pure AR VLM for both visual comprehension and generation tasks. Impressively, without using any text-image training pairs, a simple policy gradient RL working in the visual tokens can significantly boost the visual generation benchmark, surpassing all the existing models by a large margin. Therefore, we believe that Selftok effectively addresses the long-standing challenge that visual tokens cannot support effective RL. When combined with the well-established strengths of RL in LLMs, this brings us one step closer to realizing a truly multimodal LLM. Project Page: https://selftok-team.github.io/report/.

cs.CV↗

arXiv2025

AdamS: Momentum Itself Can Be A Normalizer for LLM Pretraining and Post-training

We introduce AdamS, a simple yet effective alternative to Adam for large language model (LLM) pretraining and post-training. By leveraging a novel denominator, i.e., the root of weighted sum of squares of the momentum and the current gradient, AdamS eliminates the need for second-moment estimates. Hence, AdamS is efficient, matching the memory and compute footprint of SGD with momentum while delivering superior optimization performance. Moreover, AdamS is easy to adopt: it can directly inherit hyperparameters of AdamW, and is entirely model-agnostic, integrating seamlessly into existing pipelines without modifications to optimizer APIs or architectures. The motivation behind AdamS stems from the observed $(L_0, L_1)$ smoothness properties in transformer objectives, where local smoothness is governed by gradient magnitudes that can be further approximated by momentum magnitudes. We establish rigorous theoretical convergence guarantees and provide practical guidelines for hyperparameter selection. Empirically, AdamS demonstrates strong performance in various tasks, including pre-training runs on GPT-2 and Llama2 (up to 13B parameters) and reinforcement learning in post-training regimes. With its efficiency, simplicity, and theoretical grounding, AdamS stands as a compelling alternative to existing optimizers.

cs.LG↗

arXiv2025

Project-and-Fuse: Improving RGB-D Semantic Segmentation via Graph Convolution Networks

Most existing RGB-D semantic segmentation methods focus on the feature level fusion, including complex cross-modality and cross-scale fusion modules. However, these methods may cause misalignment problem in the feature fusion process and counter-intuitive patches in the segmentation results. Inspired by the popular pixel-node-pixel pipeline, we propose to 1) fuse features from two modalities in a late fusion style, during which the geometric feature injection is guided by texture feature prior; 2) employ Graph Neural Networks (GNNs) on the fused feature to alleviate the emergence of irregular patches by inferring patch relationship. At the 3D feature extraction stage, we argue that traditional CNNs are not efficient enough for depth maps. So, we encode depth map into normal map, after which CNNs can easily extract object surface tendencies.At projection matrix generation stage, we find the existence of Biased-Assignment and Ambiguous-Locality issues in the original pipeline. Therefore, we propose to 1) adopt the Kullback-Leibler Loss to ensure no missing important pixel features, which can be viewed as hard pixel mining process; 2) connect regions that are close to each other in the Euclidean space as well as in the semantic space with larger edge weights so that location informations can been considered. Extensive experiments on two public datasets, NYU-DepthV2 and SUN RGB-D, have shown that our approach can consistently boost the performance of RGB-D semantic segmentation task.

cs.CV↗

arXiv2025

TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents 3D shapes by deforming a collection of tetrahedral spheres, with geometric regularizations and constraints that effectively resolve common mesh issues such as irregular triangles, non-manifoldness, and floating artifacts. Experimental results on multi-view and single-view reconstruction highlight TetSphere splatting's superior mesh quality while maintaining competitive reconstruction accuracy compared to state-of-the-art methods. Additionally, TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation.

cs.CV↗

arXiv2025

Synthetic Video Enhances Physical Fidelity in Video Synthesis

We investigate how to enhance the physical fidelity of video generation models by leveraging synthetic videos derived from computer graphics pipelines. These rendered videos respect real-world physics, such as maintaining 3D consistency, and serve as a valuable resource that can potentially improve video generation models. To harness this potential, we propose a solution that curates and integrates synthetic data while introducing a method to transfer its physical realism to the model, significantly reducing unwanted artifacts. Through experiments on three representative tasks emphasizing physical consistency, we demonstrate its efficacy in enhancing physical fidelity. While our model still lacks a deep understanding of physics, our work offers one of the first empirical demonstrations that synthetic video enhances physical fidelity in video synthesis. Website: https://kevinz8866.github.io/simulation/

eess.IV↗

arXiv2024

Physically Compatible 3D Object Modeling from a Single Image

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

cs.CV↗

arXiv2024

Volume Rendering of Human Hand Anatomy

We study the design of transfer functions for volumetric rendering of magnetic resonance imaging (MRI) datasets of human hands. Human hands are anatomically complex, containing various organs within a limited space, which presents challenges for volumetric rendering. We focus on hand musculoskeletal organs because they are volumetrically the largest inside the hand, and most important for the hand's main function, namely manipulation of objects. While volumetric rendering is a mature field, the choice of the transfer function for the different organs is arguably just as important as the choice of the specific volume rendering algorithm; we demonstrate that it significantly influences the clarity and interpretability of the resulting images. We assume that the hand MRI scans have already been segmented into the different organs (bones, muscles, tendons, ligaments, subcutaneous fat, etc.). Our method uses the hand MRI volume data, and the geometry of its inner organs and their known segmentation, to produce high-quality volume rendering images of the hand, and permits fine control over the appearance of each tissue. We contribute two families of transfer functions to emphasize different hand tissues of interest, while preserving the visual context of the hand. We also discuss and reduce artifacts present in standard volume ray-casting of human hands. We evaluate our volumetric rendering on five challenging hand motion sequences. Our experimental results demonstrate that our method improves hand anatomy visualization, compared to standard surface and volume rendering techniques.

cs.GR↗

arXiv2024

Medial Skeletal Diagram: A Generalized Medial Axis Approach for 3D Shape Representation

We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous elements in the medial axis representation to effectively shift the complexity away from the discrete elements. To that end, we introduce generalized enveloping primitives, an enhancement over the standard primitives in the medial axis, which ensure efficient coverage of intricate local features of the input shape and substantially reduce the number of discrete elements required. Moreover, we present a computational framework for constructing a medial skeletal diagram from an arbitrary closed manifold mesh. Our optimization pipeline ensures that the resulting medial skeletal diagram comprehensively covers the input shape with the fewest primitives. Additionally, each optimized primitive undergoes a post-refinement process to guarantee an accurate match with the source mesh in both geometry and tessellation. We validate our approach on a comprehensive benchmark of 100 shapes, demonstrating the sparsity of the discrete elements and superior reconstruction accuracy across a variety of cases. Finally, we exemplify the versatility of our representation in downstream applications such as shape generation, mesh decomposition, shape optimization, mesh alignment, mesh compression, and user-interactive design.

cs.GR↗

arXiv2024

Texture-AD: An Anomaly Detection Dataset and Benchmark for Real Algorithm Development

Anomaly detection is a crucial process in industrial manufacturing and has made significant advancements recently. However, there is a large variance between the data used in the development and the data collected by the production environment. Therefore, we present the Texture-AD benchmark based on representative texture-based anomaly detection to evaluate the effectiveness of unsupervised anomaly detection algorithms in real-world applications. This dataset includes images of 15 different cloth, 14 semiconductor wafers and 10 metal plates acquired under different optical schemes. In addition, it includes more than 10 different types of defects produced during real manufacturing processes, such as scratches, wrinkles, color variations and point defects, which are often more difficult to detect than existing datasets. All anomalous areas are provided with pixel-level annotations to facilitate comprehensive evaluation using anomaly detection models. Specifically, to adapt to diverse products in automated pipelines, we present a new evaluation method and results of baseline algorithms. The experimental results show that Texture-AD is a difficult challenge for state-of-the-art algorithms. To our knowledge, Texture-AD is the first dataset to be devoted to evaluating industrial defect detection algorithms in the real world. The dataset is available at https://XXX.

cs.CV↗

arXiv2024

Adapted-MoE: Mixture of Experts with Test-Time Adaption for Anomaly Detection

Most unsupervised anomaly detection methods based on representations of normal samples to distinguish anomalies have recently made remarkable progress. However, existing methods only learn a single decision boundary for distinguishing the samples within the training dataset, neglecting the variation in feature distribution for normal samples even in the same category in the real world. Furthermore, it was not considered that a distribution bias still exists between the test set and the train set. Therefore, we propose an Adapted-MoE which contains a routing network and a series of expert models to handle multiple distributions of same-category samples by divide and conquer. Specifically, we propose a routing network based on representation learning to route same-category samples into the subclasses feature space. Then, a series of expert models are utilized to learn the representation of various normal samples and construct several independent decision boundaries. We propose the test-time adaption to eliminate the bias between the unseen test sample representation and the feature distribution learned by the expert model. Our experiments are conducted on a dataset that provides multiple subclasses from three categories, namely Texture AD benchmark. The Adapted-MoE significantly improves the performance of the baseline model, achieving 2.18%-7.20% and 1.57%-16.30% increase in I-AUROC and P-AUROC, which outperforms the current state-of-the-art methods. Our code is available at https://github.com/.

cs.CV↗

arXiv2024

RAVSS: Robust Audio-Visual Speech Separation in Multi-Speaker Scenarios with Missing Visual Cues

While existing Audio-Visual Speech Separation (AVSS) methods primarily concentrate on the audio-visual fusion strategy for two-speaker separation, they demonstrate a severe performance drop in the multi-speaker separation scenarios. Typically, AVSS methods employ guiding videos to sequentially isolate individual speakers from the given audio mixture, resulting in notable missing and noisy parts across various segments of the separated speech. In this study, we propose a simultaneous multi-speaker separation framework that can facilitate the concurrent separation of multiple speakers within a singular process. We introduce speaker-wise interactions to establish distinctions and correlations among speakers. Experimental results on the VoxCeleb2 and LRS3 datasets demonstrate that our method achieves state-of-the-art performance in separating mixtures with 2, 3, 4, and 5 speakers, respectively. Additionally, our model can utilize speakers with complete audio-visual information to mitigate other visual-deficient speakers, thereby enhancing its resilience to missing visual cues. We also conduct experiments where visual information for specific speakers is entirely absent or visual frames are partially missing. The results demonstrate that our model consistently outperforms others, exhibiting the smallest performance drop across all settings involving 2, 3, 4, and 5 speakers.

cs.SD↗

arXiv2024

Provable Adaptivity of Adam under Non-uniform Smoothness

Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Adam rely on the bounded smoothness assumption, referred to as the \emph{L-smooth condition}. Unfortunately, this assumption does not hold for many deep learning tasks. Moreover, we believe that this assumption obscures the true benefit of Adam, as the algorithm can adapt its update magnitude according to local smoothness. This important feature of Adam becomes irrelevant when assuming globally bounded smoothness. This paper studies the convergence of randomly reshuffled Adam (RR Adam) with diminishing learning rate, which is the major version of Adam adopted in deep learning tasks. We present the first convergence analysis of RR Adam without the bounded smoothness assumption. We demonstrate that RR Adam can maintain its convergence properties when smoothness is linearly bounded by the gradient norm, referred to as the \emph{$(L_0, L_1)$-smooth condition. We further compare Adam to SGD when both methods use diminishing learning rate. We refine the existing lower bound of SGD and show that SGD can be slower than Adam. To our knowledge, this is the first time that Adam and SGD are rigorously compared in the same setting and the advantage of Adam is revealed.

cs.LG↗

arXiv2024

Gradient Descent with Polyak's Momentum Finds Flatter Minima via Large Catapults

Although gradient descent with Polyak's momentum is widely used in modern machine and deep learning, a concrete understanding of its effects on the training trajectory remains elusive. In this work, we empirically show that for linear diagonal networks and nonlinear neural networks, momentum gradient descent with a large learning rate displays large catapults, driving the iterates towards much flatter minima than those found by gradient descent. We hypothesize that the large catapult is caused by momentum "prolonging" the self-stabilization effect (Damian et al., 2023). We provide theoretical and empirical support for our hypothesis in a simple toy example and empirical evidence supporting our hypothesis for linear diagonal networks.

cs.LG↗

arXiv2024

Learning Multi-dimensional Human Preference for Text-to-Image Generation

Current metrics for text-to-image models typically rely on statistical metrics which inadequately represent the real preference of humans. Although recent work attempts to learn these preferences via human annotated images, they reduce the rich tapestry of human preference to a single overall score. However, the preference results vary when humans evaluate images with different aspects. Therefore, to learn the multi-dimensional human preferences, we propose the Multi-dimensional Preference Score (MPS), the first multi-dimensional preference scoring model for the evaluation of text-to-image models. The MPS introduces the preference condition module upon CLIP model to learn these diverse preferences. It is trained based on our Multi-dimensional Human Preference (MHP) Dataset, which comprises 918,315 human preference choices across four dimensions (i.e., aesthetics, semantic alignment, detail quality and overall assessment) on 607,541 images. The images are generated by a wide range of latest text-to-image models. The MPS outperforms existing scoring methods across 3 datasets in 4 dimensions, enabling it a promising metric for evaluating and improving text-to-image generation.

cs.CV↗

arXiv2024

On the Convergence of Adam under Non-uniform Smoothness: Separability from SGDM and Beyond

This paper aims to clearly distinguish between Stochastic Gradient Descent with Momentum (SGDM) and Adam in terms of their convergence rates. We demonstrate that Adam achieves a faster convergence compared to SGDM under the condition of non-uniformly bounded smoothness. Our findings reveal that: (1) in deterministic environments, Adam can attain the known lower bound for the convergence rate of deterministic first-order optimizers, whereas the convergence rate of Gradient Descent with Momentum (GDM) has higher order dependence on the initial function value; (2) in stochastic setting, Adam's convergence rate upper bound matches the lower bounds of stochastic first-order optimizers, considering both the initial function value and the final error, whereas there are instances where SGDM fails to converge with any learning rate. These insights distinctly differentiate Adam and SGDM regarding their convergence rates. Additionally, by introducing a novel stopping-time based technique, we further prove that if we consider the minimum gradient norm during iterations, the corresponding convergence rate can match the lower bounds across all problem hyperparameters. The technique can also help proving that Adam with a specific hyperparameter scheduler is parameter-agnostic, which hence can be of independent interest.

cs.LG↗