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Heng Zhang

Publications and source records attributed to Heng Zhang.

At least 91 records · Page 5Linked to original sources
arXiv2026

The Cauchy problem for the improved Boussinesq equation with spatially quasi-periodic initial data

We study the Cauchy problem for the improved Boussinesq equation \[ u_{tt}-u_{xx}-u_{xxtt}-(u^2)_{xx}=0 \] on the real line with spatially quasi-periodic initial data. For a non-resonant frequency vector $ω\in\mathbb R^ν$, we prove local existence and uniqueness of classical spatially quasi-periodic solutions with the same frequency vector $ω$ in two Fourier-side classes. First, for exponentially decaying initial Fourier coefficients, we obtain a spatially quasi-periodic solution whose Fourier coefficients remain exponentially decaying on an explicit time interval. Second, for initial Fourier coefficients $c(n)$ and $d(n)$ satisfying the polynomial decay $ |c(n)|+|d(n)|\lesssim (1+|n|)^{-r}, \; r>ν+2, $ we prove that the corresponding spatially quasi-periodic solution preserves the same polynomial decay rate as the initial data. We also extend these results to the nonlinearity $u^p$ with integer $p \geq 3$.

math.AP↗
arXiv2026

Semantic-Contact Fields for Category-Level Generalizable Tactile Tool Manipulation

Generalizing tool manipulation requires both semantic planning and precise physical control. Modern generalist robot policies, such as Vision-Language-Action (VLA) models, often lack the physical grounding required for contact-rich tool manipulation. Conversely, existing contact-aware policies that leverage tactile or haptic sensing are typically instance-specific and fail to generalize across diverse tool geometries. Bridging this gap requires learning representations that are both semantically transferable and physically grounded, yet a fundamental barrier remains: diverse real-world tactile data are prohibitive to collect at scale, while direct zero-shot sim-to-real transfer is challenging due to the complex nonlinear deformation of soft tactile sensors. To address this, we propose Semantic-Contact Fields (SCFields), a unified 3D representation that fuses visual semantics with dense extrinsic contact estimates, including contact probability and force. SCFields is learned through a two-stage Sim-to-Real Contact Learning Pipeline: we first pre-train on large-scale simulation to learn geometry-aware contact priors, then fine-tune on a small set of real data pseudo-labeled via geometric heuristics and force optimization to align real tactile signals. The resulting force-aware representation serves as the dense observation input to a diffusion policy, enabling physical generalization to unseen tool instances. Experiments on scraping, crayon drawing, and peeling demonstrate robust category-level generalization, significantly outperforming vision-only and raw-tactile baselines. Project page: https://kevinskwk.github.io/SCFields/.

cs.RO↗
arXiv2026

Dispersive estimates for discrete Klein-Gordon equations on one-dimensional lattice with quasi-periodic potentials

We prove $\ell^{1}\!\to\!\ell^{\infty}$ dispersive estimates for the discrete Klein--Gordon equation on $\mathbb Z$ with small real-analytic quasi-periodic potentials, showing that the time-decay rate persists as $(\tfrac13)^{-}$. As applications, we derive the corresponding Strichartz estimates and establish small-data global well-posedness for the associated nonlinear discrete Klein--Gordon equation.

math.AP↗
arXiv2026

Higher odd-order nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4

The nonlinear Hall effect is a new member of the Hall effect family, which attracts intense research interests, and it is closely related to the quantum geometry of quantum materials. The previous studies primarily concentrate on the second-order and third-order nonlinear Hall effect. However, the experimental study of higher-order nonlinear Hall effect is scarce at present. In this work, we report the observations of the higher odd-order (third-, fifth-, seventh-order) nonlinear Hall effect in magnetic topological insulator Mn(Bi1-xSbx)2Te4 thin flakes. The higher odd-order nonlinear Hall voltage exhibits a twofold angular dependence and exists only below the Néel temperature. It reaches its maximum near the charge neutral point and decays exponentially as the order of the nonlinear Hall effect increases. Furthermore, such higher odd-order nonlinear Hall effect is observed in both odd- and even-layer samples with comparable magnitudes. Theoretical analysis indicates that the higher odd-order nonlinear Hall effect responses may arise from the Berry curvature multipoles. Our work paves the way for the study of the higher-order nonlinear transport phenomena.

cond-mat.mes-hall↗
arXiv2026

Room-temperature third-order nonlinear anomalous Hall effect in ferromagnetic metal Fe3GaTe2

Berry curvature, as the imaginary component of quantum geometry, plays a crucial role in condensed matter physics. The spatial distribution of Berry curvature can be characterized by its dipole and multipole moments, which can induce the nonlinear anomalous Hall effect (NLAHE). To date, the NLAHE has been demonstrated in various materials, yet reports on room-temperature NLAHE are still limited. In this work, we report the observation of the third-order NLAHE in ferromagnetic metal Fe3GaTe2. The third-order NLAHE shows hysteretic behavior with the variation of magnetic field, where the coercive field is the same as that of the anomalous Hall effect, and the third-order NLAHE remains observable up to the Curie temperature (~350 K). The scaling analysis suggests that the third-order NLAHE may be attributed to the Berry curvature quadrupole. Our work not only provides an approach to study magnetic materials through nonlinear electric transports, but also opens up possibilities for the future development of room-temperature third-order nonlinear electronic devices.

cond-mat.mtrl-sci↗
arXiv2026

Framelet-Based Blind Image Restoration with Minimax Concave Regularization

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this problem, both the point spread function (PSF) and the underlying latent sharp image must be estimated simultaneously. This problem cannot be solved directly due to its ill-posed nature. One powerful tool for solving such problems is total variation (TV) regularization. The $\ell_0$-norm regularization within the TV framework has been widely adopted to promote sparsity in image gradients or transform domains, leading to improved preservation of edges and fine structures. However, the use of the $\ell_0$-norm results in a highly nonconvex and computationally intractable optimization problem, which limits its practical applicability. To overcome these difficulties, we employ the minimax concave penalty (MCP), which promotes enhanced sparsity and provides a closer approximation to the $\ell_0$-norm. In addition, a reweighted $\ell_1$-norm regularization is incorporated to further reduce estimation bias and improve the preservation of fine image details and textures. After introducing the proposed model, a numerical algorithm is developed to solve the resulting optimization problem. The effectiveness of the proposed approach is then demonstrated through experimental evaluations on several test images.

cs.CV↗
arXiv2026

Large Language Models for Market Research: A Data-augmentation Approach

Large Language Models (LLMs) have transformed artificial intelligence by excelling in complex natural language processing tasks. Their ability to generate human-like text has opened new possibilities for market research, particularly in conjoint analysis, where understanding consumer preferences is essential but often resource-intensive. Traditional survey-based methods face limitations in scalability and cost, making LLM-generated data a promising alternative. However, while LLMs have the potential to simulate real consumer behavior, recent studies highlight a significant gap between LLM-generated and human data, with biases introduced when substituting between the two. In this paper, we address this gap by proposing a novel statistical data augmentation approach that efficiently integrates LLM-generated data with real data in conjoint analysis. This results in statistically robust estimators with consistent and asymptotically normal properties, in contrast to naive approaches that simply substitute human data with LLM-generated data, which can exacerbate bias. We further present a finite-sample performance bound on the estimation error. We validate our framework through an empirical study on COVID-19 vaccine preferences, demonstrating its superior ability to reduce estimation error and save data and costs by 24.9% to 79.8%. In contrast, naive approaches fail to save data due to the inherent biases in LLM-generated data compared to human data. Another empirical study on sports car choices validates the robustness of our results. Our findings suggest that while LLM-generated data is not a direct substitute for human responses, it can serve as a valuable complement when used within a robust statistical framework.

cs.AI↗
arXiv2026

MO-RiskVAE: A Multi-Omics Variational Autoencoder for Survival Risk Modeling in Multiple MyelomaMO-RiskVAE

Multimodal variational autoencoders (VAEs) have emerged as a powerful framework for survival risk modeling in multiple myeloma by integrating heterogeneous omics and clinical data. However, when trained under survival supervision, standard latent regularization strategies often fail to preserve prognostically relevant variation, leading to unstable or overly constrained representations. Despite numerous proposed variants, it remains unclear which aspects of latent design fundamentally govern performance in this setting. In this work, we conduct a controlled investigation of latent modeling choices for multimodal survival prediction within a unified extension of the MyeVAE framework. By systematically isolating regularization scale, posterior geometry, and latent space structure under identical architectures and optimization protocols, we show that survival-driven training is primarily sensitive to the magnitude and structure of latent regularization rather than the specific divergence formulation. In particular, moderate relaxation of KL regularization consistently improves survival discrimination, while alternative divergence mechanisms such as MMD and HSIC provide limited benefit without appropriate scaling. We further demonstrate that structuring the latent space can improve alignment between learned representations and survival risk gradients. A hybrid continuous--discrete formulation based on Gumbel--Softmax enhances global risk ordering in the continuous latent subspace, even though stable discrete subtype discovery does not emerge under survival supervision. Guided by these findings, we instantiate a robust multimodal survival model, termed MO-RiskVAE, which consistently improves risk stratification over the original MyeVAE without introducing additional supervision or complex training heuristics.

cs.LG↗
arXiv2026

CompliantVLA-adaptor: VLM-Guided Variable Impedance Action for Safe Contact-Rich Manipulation

We propose a CompliantVLA-adaptor that augments the state-of-the-art Vision-Language-Action (VLA) models with vision-language model (VLM)-informed context-aware variable impedance control (VIC) to improve the safety and effectiveness of contact-rich robotic manipulation tasks. Existing VLA systems (e.g., RDT, Pi0.5, OpenVLA-oft) typically output position, but lack force-aware adaptation, leading to unsafe or failed interactions in physical tasks involving contact, compliance, or uncertainty. In the proposed CompliantVLA-adaptor, a VLM interprets task context from images and natural language to adapt the stiffness and damping parameters of a VIC controller. These parameters are further regulated using real-time force/torque feedback to ensure interaction forces remain within safe thresholds. We demonstrate that our method outperforms the VLA baselines on a suite of complex contact-rich tasks, both in simulation and the real world, with improved success rates and reduced force violations. This work presents a promising path towards a safe foundation model for physical contact-rich manipulation. We release our code, prompts, and force-torque-impedance-scenario context datasets at https://sites.google.com/view/compliantvla.

cs.RO↗
arXiv2026

MLFCIL: A Multi-Level Forgetting Mitigation Framework for Federated Class-Incremental Learning in LEO Satellites

Low-Earth-orbit (LEO) satellite constellations are increasingly performing on-board computing. However, the continuous emergence of new classes under strict memory and communication constraints poses major challenges for collaborative training. Federated class-incremental learning (FCIL) enables distributed incremental learning without sharing raw data, but faces three LEO-specific challenges: non-independent and identically distributed data heterogeneity caused by orbital dynamics, amplified catastrophic forgetting during aggregation, and the need to balance stability and plasticity under limited resources. To tackle these challenges, we propose MLFCIL, a multi-level forgetting mitigation framework that decomposes catastrophic forgetting into three sources and addresses them at different levels: class-reweighted loss to reduce local bias, knowledge distillation with feature replay and prototype-guided drift compensation to preserve cross-task knowledge, and class-aware aggregation to mitigate forgetting during federation. In addition, we design a dual-granularity coordination strategy that combines round-level adaptive loss balancing with step-level gradient projection to further enhance the stability-plasticity trade-off. Experiments on the NWPU-RESISC45 dataset show that MLFCIL significantly outperforms baselines in both accuracy and forgetting mitigation, while introducing minimal resource overhead.

cs.NI↗
arXiv2026

Reward-Zero: Language Embedding Driven Implicit Reward Mechanisms for Reinforcement Learning

We introduce Reward-Zero, a general-purpose implicit reward mechanism that transforms natural-language task descriptions into dense, semantically grounded progress signals for reinforcement learning (RL). Reward-Zero serves as a simple yet sophisticated universal reward function that leverages language embeddings for efficient RL training. By comparing the embedding of a task specification with embeddings derived from an agent's interaction experience, Reward-Zero produces a continuous, semantically aligned sense-of-completion signal. This reward supplements sparse or delayed environmental feedback without requiring task-specific engineering. When integrated into standard RL frameworks, it accelerates exploration, stabilizes training, and enhances generalization across diverse tasks. Empirically, agents trained with Reward-Zero converge faster and achieve higher final success rates than conventional methods such as PPO with common reward-shaping baselines, successfully solving tasks that hand-designed rewards could not in some complex tasks. In addition, we develop a mini benchmark for the evaluation of completion sense during task execution via language embeddings. These results highlight the promise of language-driven implicit reward functions as a practical path toward more sample-efficient, generalizable, and scalable RL for embodied agents. Code will be released after peer review.

cs.LG↗
arXiv2026

ActivePose: Active 6D Object Pose Estimation and Tracking for Robotic Manipulation

Accurate 6-DoF object pose estimation and tracking are critical for reliable robotic manipulation. However, zero-shot methods often fail under viewpoint-induced ambiguities and fixed-camera setups struggle when objects move or become self-occluded. To address these challenges, we propose an active pose estimation pipeline that combines a Vision-Language Model (VLM) with "robotic imagination" to dynamically detect and resolve ambiguities in real time. In an offline stage, we render a dense set of views of the CAD model, compute the FoundationPose entropy for each view, and construct a geometric-aware prompt that includes low-entropy (unambiguous) and high-entropy (ambiguous) examples. At runtime, the system: (1) queries the VLM on the live image for an ambiguity score; (2) if ambiguity is detected, imagines a discrete set of candidate camera poses by rendering virtual views, scores each based on a weighted combination of VLM ambiguity probability and FoundationPose entropy, and then moves the camera to the Next-Best-View (NBV) to obtain a disambiguated pose estimation. Furthermore, since moving objects may leave the camera's field of view, we introduce an active pose tracking module: a diffusion-policy trained via imitation learning, which generates camera trajectories that preserve object visibility and minimize pose ambiguity. Experiments in simulation and real-world show that our approach significantly outperforms classical baselines.

cs.RO↗
arXiv2026

MachaGrasp: Morphology-Aware Cross-Embodiment Dexterous Hand Articulation Generation for Grasping

Dexterous grasping with multi-fingered hands remains challenging due to high-dimensional articulations and the cost of optimization-based pipelines. Existing end-to-end methods require training on large-scale datasets for specific hands, limiting their ability to generalize across different embodiments. We propose MachaGrasp, an eigengrasp-based, end-to-end framework for cross-embodiment grasp generation. From a hand's morphology description, we derive a morphology embedding and an eigengrasp set. Conditioned on these, together with the object point cloud and wrist pose, an amplitude predictor regresses articulation coefficients in a low-dimensional space, which are decoded into full joint articulations. Articulation learning is supervised with a Kinematic-Aware Articulation Loss (KAL) that emphasizes fingertip-relevant motions and injects morphology-specific structure. In simulation on unseen objects across three dexterous hands, MachaGrasp attains a 91.9% average grasp success rate with less than 0.4 seconds inference per grasp. With few-shot adaptation to an unseen hand, it achieves 85.6% success on unseen objects in simulation, and real-world experiments on this few-shot-generalized hand achieve an 87% success rate. The code and additional materials are available on our project website https://connor-zh.github.io/MachaGrasp.

cs.RO↗
arXiv2026

Decision-dependent distributionally robust standard quadratic optimization with Wasserstein ambiguity

The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting applications ranging from portfolio optimization to machine learning. Sometimes, the data matrix is uncertain but some information about its distribution can be inferred, e.g. a distance to a reference distribution (typically, the empirical distribution after sampling). In distributionally robust optimization, the goal is to hedge against the worst case of all possible distributions in an ambiguity set, defined by above mentioned distance. In this paper we will focus on distributionally robust StQPs under Wasserstein distance, and show equivalence to an accordingly modified deterministic instance of an StQP. This blends well into recent findings for other approaches of StQPs under uncertainty. We will also address out-of-sample performance guarantees. Carefully designed experiments shall complement and illustrate the approach.

math.OC↗
arXiv2026

D3MAS: Decompose, Deduce, and Distribute for Enhanced Knowledge Sharing in Multi-Agent Systems

Multi-agent systems powered by large language models exhibit strong capabilities in collaborative problem-solving. However, these systems suffer from substantial knowledge redundancy. Agents duplicate efforts in retrieval and reasoning processes. This inefficiency stems from a deeper issue: current architectures lack mechanisms to ensure agents share minimal sufficient information at each operational stage. Empirical analysis reveals an average knowledge duplication rate of 47.3\% across agent communications. We propose D3MAS (Decompose, Deduce, and Distribute), a hierarchical coordination framework addressing redundancy through structural design rather than explicit optimization. The framework organizes collaboration across three coordinated layers. Task decomposition filters irrelevant sub-problems early. Collaborative reasoning captures complementary inference paths across agents. Distributed memory provides access to non-redundant knowledge. These layers coordinate through structured message passing in a unified heterogeneous graph. This cross-layer alignment ensures information remains aligned with actual task needs. Experiments on four challenging datasets show that D3MAS consistently improves reasoning accuracy by 8.7\% to 15.6\% and reduces knowledge redundancy by 46\% on average.

cs.GR↗
arXiv2026

HyperAgent: Leveraging Hypergraphs for Topology Optimization in Multi-Agent Communication

Recent advances in large language model-powered multi-agent systems have demonstrated remarkable collective intelligence through effective communication. However, existing approaches face two primary challenges: (i) \textit{Ineffective group collaboration modeling}, as they rely on pairwise edge representations in graph structures, limiting their ability to capture relationships among multiple agents; and (ii) \textit{Limited task-adaptiveness in communication topology design}, leading to excessive communication cost for simple tasks and insufficient coordination for complex scenarios. These issues restrict the scalability and practical deployment of adaptive collaboration frameworks. To address these challenges, we propose \textbf{HyperAgent}, a hypergraph-based framework that optimizes communication topologies and effectively captures group collaboration patterns using direct hyperedge representations. Unlike edge-based approaches, HyperAgent uses hyperedges to link multiple agents within the same subtask and employs hypergraph convolutional layers to achieve one-step information aggregation in collaboration groups. Additionally, it incorporates a variational autoencoder framework with sparsity regularization to dynamically adjust hypergraph topologies based on task complexity. Experiments highlight the superiority of HyperAgent in both performance and efficiency. For instance, on GSM8K, HyperAgent achieves 95.07\% accuracy while reducing token consumption by 25.33\%, demonstrating the potential of hypergraph-based optimization for multi-agent communication.

cs.MA↗
arXiv2026

RECAP: Local Hebbian Prototype Learning as a Self-Organizing Readout for Reservoir Dynamics

Robust perception in brains is often attributed to high-dimensional population activity together with local plasticity mechanisms that reinforce recurring structure. In contrast, most modern image recognition systems are trained by error backpropagation and end-to-end gradient optimization, which are not naturally aligned with local computation and local plasticity. We introduce RECAP (Reservoir Computing with Hebbian Co-Activation Prototypes), a bio-inspired learning strategy for robust image classification that couples untrained reservoir dynamics with a self-organizing Hebbian prototype readout. RECAP discretizes time-averaged reservoir responses into activation levels, constructs a co-activation mask over reservoir unit pairs, and incrementally updates class-wise prototype matrices via a Hebbian-like potentiation-decay rule. Inference is performed by overlap-based prototype matching. The method avoids error backpropagation and is naturally compatible with online prototype updates. We illustrate the resulting robustness behavior on MNIST-C, where RECAP remains robust under diverse corruptions without exposure to corrupted training samples.

cs.NE↗
arXiv2026

Curvature and local matchings of conference graphs and extensions

We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters $(4γ+1,2γ,γ-1,γ)$. Our method depends only on the parameter relations and applies to broader classes of amply regular graphs. In particular, we develop a new combinatorial approach to show the existence of local perfect matchings. A key observation is that counting common neighbors leads to useful quadratic polynomials. As a corollary, we derive an interesting number-theoretic result concerning quadratic residues.

math.CO↗