arXiv subjects

Lu Zhang

Publications and source records attributed to Lu Zhang.

At least 145 records · Page 8Linked to original sources

arXiv2025

A discontinuous Galerkin method for one-dimensional nonlocal wave problems

This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the gradient field in local discontinuous Galerkin (DG) methods for classical partial differential equations (PDEs) and reformulate the equation into a system of equations. The proposed scheme then uses a DG method for spatial discretization and the Crank-Nicolson method for time integration. We prove optimal L2 error convergence for both the solution and the auxiliary variable under a special class of radial kernels at the semi-discrete level. In addition, for general kernels, we demonstrate the asymptotic compatibility of the scheme, ensuring that it recovers the classical DG approximation of the local wave equation in the zero-horizon limit. Furthermore, we prove that the fully discrete scheme preserves the energy of the nonlocal wave equation. A series of numerical experiments are presented to validate the theoretical findings.

math.NA↗

arXiv2025

MUVOD: A Novel Multi-view Video Object Segmentation Dataset and A Benchmark for 3D Segmentation

The application of methods based on Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3D GS) have steadily gained popularity in the field of 3D object segmentation in static scenes. These approaches demonstrate efficacy in a range of 3D scene understanding and editing tasks. Nevertheless, the 4D object segmentation of dynamic scenes remains an underexplored field due to the absence of a sufficiently extensive and accurately labelled multi-view video dataset. In this paper, we present MUVOD, a new multi-view video dataset for training and evaluating object segmentation in reconstructed real-world scenarios. The 17 selected scenes, describing various indoor or outdoor activities, are collected from different sources of datasets originating from various types of camera rigs. Each scene contains a minimum of 9 views and a maximum of 46 views. We provide 7830 RGB images (30 frames per video) with their corresponding segmentation mask in 4D motion, meaning that any object of interest in the scene could be tracked across temporal frames of a given view or across different views belonging to the same camera rig. This dataset, which contains 459 instances of 73 categories, is intended as a basic benchmark for the evaluation of multi-view video segmentation methods. We also present an evaluation metric and a baseline segmentation approach to encourage and evaluate progress in this evolving field. Additionally, we propose a new benchmark for 3D object segmentation task with a subset of annotated multi-view images selected from our MUVOD dataset. This subset contains 50 objects of different conditions in different scenarios, providing a more comprehensive analysis of state-of-the-art 3D object segmentation methods. Our proposed MUVOD dataset is available at https://volumetric-repository.labs.b-com.com/#/muvod.

cs.CV↗

arXiv2025

Domain-Adaptive Diagnosis of Lewy Body Disease with Transferability Aware Transformer

Lewy Body Disease (LBD) is a common yet understudied form of dementia that imposes a significant burden on public health. It shares clinical similarities with Alzheimer's disease (AD), as both progress through stages of normal cognition, mild cognitive impairment, and dementia. A major obstacle in LBD diagnosis is data scarcity, which limits the effectiveness of deep learning. In contrast, AD datasets are more abundant, offering potential for knowledge transfer. However, LBD and AD data are typically collected from different sites using different machines and protocols, resulting in a distinct domain shift. To effectively leverage AD data while mitigating domain shift, we propose a Transferability Aware Transformer (TAT) that adapts knowledge from AD to enhance LBD diagnosis. Our method utilizes structural connectivity (SC) derived from structural MRI as training data. Built on the attention mechanism, TAT adaptively assigns greater weights to disease-transferable features while suppressing domain-specific ones, thereby reducing domain shift and improving diagnostic accuracy with limited LBD data. The experimental results demonstrate the effectiveness of TAT. To the best of our knowledge, this is the first study to explore domain adaptation from AD to LBD under conditions of data scarcity and domain shift, providing a promising framework for domain-adaptive diagnosis of rare diseases.

cs.LG↗

arXiv2025

Leveraging Transformer Models to Capture Multi-Scale Dynamics in Biomolecules by nano-GPT

Long-term biomolecular dynamics are critical for understanding key evolutionary transformations in molecular systems. However, capturing these processes requires extended simulation timescales that often exceed the practical limits of conventional models. To address this, shorter simulations, initialized with diverse perturbations, are commonly used to sample phase space and explore a wide range of behaviors. Recent advances have leveraged language models to infer long-term behavior from short trajectories, but methods such as long short-term memory (LSTM) networks are constrained to low-dimensional reaction coordinates, limiting their applicability to complex systems. In this work, we present nano-GPT, a novel deep learning model inspired by the GPT architecture, specifically designed to capture long-term dynamics in molecular systems with fine-grained conformational states and complex transitions. The model employs a two-pass training mechanism that incrementally replaces molecular dynamics (MD) tokens with model-generated predictions, effectively mitigating accumulation errors inherent in the training window. We validate nano-GPT on three distinct systems: a four-state model potential, the alanine dipeptide, a well-studied simple molecule, and the Fip35 WW domain, a complex biomolecular system. Our results show that nano-GPT effectively captures long-timescale dynamics by learning high-order dependencies through attention mechanism, offering a novel perspective for interpreting biomolecular processes.

q-bio.QM↗

arXiv2025

A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems

The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. We characterize the impact of learning uncertainty on the joint inversion results for two typical inverse problems. Numerical evidence is provided to demonstrate the feasibility of using data-driven models to improve the joint inversion of multiple coefficients in PDEs.

math.NA↗

arXiv2025

Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the numerical flux function and a corresponding entropy, the proposed method ensures conservation and entropy dissipation, critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.

math.NA↗

arXiv2025

GoIRL: Graph-Oriented Inverse Reinforcement Learning for Multimodal Trajectory Prediction

Trajectory prediction for surrounding agents is a challenging task in autonomous driving due to its inherent uncertainty and underlying multimodality. Unlike prevailing data-driven methods that primarily rely on supervised learning, in this paper, we introduce a novel Graph-oriented Inverse Reinforcement Learning (GoIRL) framework, which is an IRL-based predictor equipped with vectorized context representations. We develop a feature adaptor to effectively aggregate lane-graph features into grid space, enabling seamless integration with the maximum entropy IRL paradigm to infer the reward distribution and obtain the policy that can be sampled to induce multiple plausible plans. Furthermore, conditioned on the sampled plans, we implement a hierarchical parameterized trajectory generator with a refinement module to enhance prediction accuracy and a probability fusion strategy to boost prediction confidence. Extensive experimental results showcase our approach not only achieves state-of-the-art performance on the large-scale Argoverse & nuScenes motion forecasting benchmarks but also exhibits superior generalization abilities compared to existing supervised models.

cs.CV↗

arXiv2025

Attention-based Adversarial Robust Distillation in Radio Signal Classifications for Low-Power IoT Devices

Due to great success of transformers in many applications such as natural language processing and computer vision, transformers have been successfully applied in automatic modulation classification. We have shown that transformer-based radio signal classification is vulnerable to imperceptible and carefully crafted attacks called adversarial examples. Therefore, we propose a defense system against adversarial examples in transformer-based modulation classifications. Considering the need for computationally efficient architecture particularly for Internet of Things (IoT)-based applications or operation of devices in environment where power supply is limited, we propose a compact transformer for modulation classification. The advantages of robust training such as adversarial training in transformers may not be attainable in compact transformers. By demonstrating this, we propose a novel compact transformer that can enhance robustness in the presence of adversarial attacks. The new method is aimed at transferring the adversarial attention map from the robustly trained large transformer to a compact transformer. The proposed method outperforms the state-of-the-art techniques for the considered white-box scenarios including fast gradient method and projected gradient descent attacks. We have provided reasoning of the underlying working mechanisms and investigated the transferability of the adversarial examples between different architectures. The proposed method has the potential to protect the transformer from the transferability of adversarial examples.

cs.LG↗

arXiv2025

A Neural Rejection System Against Universal Adversarial Perturbations in Radio Signal Classification

Advantages of deep learning over traditional methods have been demonstrated for radio signal classification in the recent years. However, various researchers have discovered that even a small but intentional feature perturbation known as adversarial examples can significantly deteriorate the performance of the deep learning based radio signal classification. Among various kinds of adversarial examples, universal adversarial perturbation has gained considerable attention due to its feature of being data independent, hence as a practical strategy to fool the radio signal classification with a high success rate. Therefore, in this paper, we investigate a defense system called neural rejection system to propose against universal adversarial perturbations, and evaluate its performance by generating white-box universal adversarial perturbations. We show that the proposed neural rejection system is able to defend universal adversarial perturbations with significantly higher accuracy than the undefended deep neural network.

cs.LG↗

arXiv2025

Vision Transformer with Adversarial Indicator Token against Adversarial Attacks in Radio Signal Classifications

The remarkable success of transformers across various fields such as natural language processing and computer vision has paved the way for their applications in automatic modulation classification, a critical component in the communication systems of Internet of Things (IoT) devices. However, it has been observed that transformer-based classification of radio signals is susceptible to subtle yet sophisticated adversarial attacks. To address this issue, we have developed a defensive strategy for transformer-based modulation classification systems to counter such adversarial attacks. In this paper, we propose a novel vision transformer (ViT) architecture by introducing a new concept known as adversarial indicator (AdvI) token to detect adversarial attacks. To the best of our knowledge, this is the first work to propose an AdvI token in ViT to defend against adversarial attacks. Integrating an adversarial training method with a detection mechanism using AdvI token, we combine a training time defense and running time defense in a unified neural network model, which reduces architectural complexity of the system compared to detecting adversarial perturbations using separate models. We investigate into the operational principles of our method by examining the attention mechanism. We show the proposed AdvI token acts as a crucial element within the ViT, influencing attention weights and thereby highlighting regions or features in the input data that are potentially suspicious or anomalous. Through experimental results, we demonstrate that our approach surpasses several competitive methods in handling white-box attack scenarios, including those utilizing the fast gradient method, projected gradient descent attacks and basic iterative method.

cs.LG↗

arXiv2025

A Causal Lens for Learning Long-term Fair Policies

Fairness-aware learning studies the development of algorithms that avoid discriminatory decision outcomes despite biased training data. While most studies have concentrated on immediate bias in static contexts, this paper highlights the importance of investigating long-term fairness in dynamic decision-making systems while simultaneously considering instantaneous fairness requirements. In the context of reinforcement learning, we propose a general framework where long-term fairness is measured by the difference in the average expected qualification gain that individuals from different groups could obtain.Then, through a causal lens, we decompose this metric into three components that represent the direct impact, the delayed impact, as well as the spurious effect the policy has on the qualification gain. We analyze the intrinsic connection between these components and an emerging fairness notion called benefit fairness that aims to control the equity of outcomes in decision-making. Finally, we develop a simple yet effective approach for balancing various fairness notions.

cs.LG↗

arXiv2025

Towards Explicit Geometry-Reflectance Collaboration for Generalized LiDAR Segmentation in Adverse Weather

Existing LiDAR semantic segmentation models often suffer from decreased accuracy when exposed to adverse weather conditions. Recent methods addressing this issue focus on enhancing training data through weather simulation or universal augmentation techniques. However, few works have studied the negative impacts caused by the heterogeneous domain shifts in the geometric structure and reflectance intensity of point clouds. In this paper, we delve into this challenge and address it with a novel Geometry-Reflectance Collaboration (GRC) framework that explicitly separates feature extraction for geometry and reflectance. Specifically, GRC employs a dual-branch architecture designed to independently process geometric and reflectance features initially, thereby capitalizing on their distinct characteristic. Then, GRC adopts a robust multi-level feature collaboration module to suppress redundant and unreliable information from both branches. Consequently, without complex simulation or augmentation, our method effectively extracts intrinsic information about the scene while suppressing interference, thus achieving better robustness and generalization in adverse weather conditions. We demonstrate the effectiveness of GRC through comprehensive experiments on challenging benchmarks, showing that our method outperforms previous approaches and establishes new state-of-the-art results.

cs.CV↗

arXiv2025

Unifying Language Agent Algorithms with Graph-based Orchestration Engine for Reproducible Agent Research

Language agents powered by large language models (LLMs) have demonstrated remarkable capabilities in understanding, reasoning, and executing complex tasks. However, developing robust agents presents significant challenges: substantial engineering overhead, lack of standardized components, and insufficient evaluation frameworks for fair comparison. We introduce Agent Graph-based Orchestration for Reasoning and Assessment (AGORA), a flexible and extensible framework that addresses these challenges through three key contributions: (1) a modular architecture with a graph-based workflow engine, efficient memory management, and clean component abstraction; (2) a comprehensive suite of reusable agent algorithms implementing state-of-the-art reasoning approaches; and (3) a rigorous evaluation framework enabling systematic comparison across multiple dimensions. Through extensive experiments on mathematical reasoning and multimodal tasks, we evaluate various agent algorithms across different LLMs, revealing important insights about their relative strengths and applicability. Our results demonstrate that while sophisticated reasoning approaches can enhance agent capabilities, simpler methods like Chain-of-Thought often exhibit robust performance with significantly lower computational overhead. AGORA not only simplifies language agent development but also establishes a foundation for reproducible agent research through standardized evaluation protocols.

cs.CL↗

arXiv2025

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving

Large Language Models (LLMs) have demonstrated formidable capabilities in solving mathematical problems, yet they may still commit logical reasoning and computational errors during the problem-solving process. Thus, this paper proposes a framework, MATH-VF, which includes a Formalizer and a Critic, for formally verifying the correctness of the solutions generated by large language models. Our framework first utilizes a Formalizer which employs an LLM to translate a natural language solution into a formal context. Afterward, our Critic (which integrates various external tools such as a Computer Algebra System and an SMT solver) evaluates the correctness of each statement within the formal context, and when a statement is incorrect, our Critic provides corrective feedback. We empirically investigate the effectiveness of MATH-VF in two scenarios: 1) Verification: MATH-VF is utilized to determine the correctness of a solution to a given problem. 2) Refinement: When MATH-VF identifies errors in the solution generated by an LLM-based solution generator for a given problem, it submits the corrective suggestions proposed by the Critic to the solution generator to regenerate the solution. We evaluate our framework on widely used mathematical benchmarks: MATH500 and ProcessBench, demonstrating the superiority of our approach over existing approaches.

cs.AI↗

arXiv2025

Bootstraping Clustering of Gaussians for View-consistent 3D Scene Understanding

Injecting semantics into 3D Gaussian Splatting (3DGS) has recently garnered significant attention. While current approaches typically distill 3D semantic features from 2D foundational models (e.g., CLIP and SAM) to facilitate novel view segmentation and semantic understanding, their heavy reliance on 2D supervision can undermine cross-view semantic consistency and necessitate complex data preparation processes, therefore hindering view-consistent scene understanding. In this work, we present FreeGS, an unsupervised semantic-embedded 3DGS framework that achieves view-consistent 3D scene understanding without the need for 2D labels. Instead of directly learning semantic features, we introduce the IDentity-coupled Semantic Field (IDSF) into 3DGS, which captures both semantic representations and view-consistent instance indices for each Gaussian. We optimize IDSF with a two-step alternating strategy: semantics help to extract coherent instances in 3D space, while the resulting instances regularize the injection of stable semantics from 2D space. Additionally, we adopt a 2D-3D joint contrastive loss to enhance the complementarity between view-consistent 3D geometry and rich semantics during the bootstrapping process, enabling FreeGS to uniformly perform tasks such as novel-view semantic segmentation, object selection, and 3D object detection. Extensive experiments on LERF-Mask, 3D-OVS, and ScanNet datasets demonstrate that FreeGS performs comparably to state-of-the-art methods while avoiding the complex data preprocessing workload. Our code is publicly available at https://github.com/wb014/FreeGS.

cs.CV↗

arXiv2025

Shallow AutoEncoding Recommender with Cold Start Handling via Side Features

User and item cold starts present significant challenges in industrial applications of recommendation systems. Supplementing user-item interaction data with metadata is a common solution-but often at the cost of introducing additional biases. In this work, we introduce an augmented EASE model that seamlessly integrates both user and item side information to address these cold start issues. Our straightforward, autoencoder-based method produces a closed-form solution that leverages rich content signals for cold items while refining user representations in data-sparse environments. Importantly, our method strikes a balance by effectively recommending cold start items and handling cold start users without incurring extra bias, and it maintains strong performance in warm settings. Experimental results demonstrate improved recommendation accuracy and robustness compared to previous collaborative filtering approaches. Moreover, our model serves as a strong baseline for future comparative studies.

cs.IR↗

arXiv2025

Antidote: A Unified Framework for Mitigating LVLM Hallucinations in Counterfactual Presupposition and Object Perception

Large Vision-Language Models (LVLMs) have achieved impressive results across various cross-modal tasks. However, hallucinations, i.e., the models generating counterfactual responses, remain a challenge. Though recent studies have attempted to alleviate object perception hallucinations, they focus on the models' response generation, and overlooking the task question itself. This paper discusses the vulnerability of LVLMs in solving counterfactual presupposition questions (CPQs), where the models are prone to accept the presuppositions of counterfactual objects and produce severe hallucinatory responses. To this end, we introduce "Antidote", a unified, synthetic data-driven post-training framework for mitigating both types of hallucination above. It leverages synthetic data to incorporate factual priors into questions to achieve self-correction, and decouple the mitigation process into a preference optimization problem. Furthermore, we construct "CP-Bench", a novel benchmark to evaluate LVLMs' ability to correctly handle CPQs and produce factual responses. Applied to the LLaVA series, Antidote can simultaneously enhance performance on CP-Bench by over 50%, POPE by 1.8-3.3%, and CHAIR & SHR by 30-50%, all without relying on external supervision from stronger LVLMs or human feedback and introducing noticeable catastrophic forgetting issues.

cs.CV↗

arXiv2025

Scanning-free three-dimensional fluorescent dipoles imaging by polarization self-interference digital holography (pSIDH)

Polarization microscopy provides insights into the structure and orientational organization of biomolecules and their architectures in cells. The above key functional signatures, which are natively 3D, can be only detected in 2D for a single measurement in conventional polarization microscopy. It is so far a challenging task to capture simultaneously the 3D structure and molecular orientation in a single frame of far-field intensity distribution, within the timescale of rapid-happened spatial organization events of bio-complexes. We report an optical imaging method called pSIDH, to encode multidimensional sample information includes 3D structures and dipole orientations, in their far-field fluorescence-self-interference pattern. The computational reconstruction from the holographic extracted complex-valued light field provides optical-aberration-corrected 3D polarization images of the sample. In pSIDH microscope incorporating planar liquid crystal lens and high numerical aperture objective, we demonstrate scanning-free 3D volumetric polarization imaging of fluorescently-labelled sample, with simultaneously computational-improved system measuring accuracy on the 3D spatial and polarization dimensions. The pSIDH imaging on phalloidin-fluorophore labelling U2OS cells provides rapid tools of capturing simultaneous the 3D structural details and spatial-averaged molecular orientation distributions of biological complex architectures such as actin filaments.

physics.optics↗