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Lei Zhang

Publications and source records attributed to Lei Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Re4: Scientific Computing Agent with Rewriting, Resolution, Review and Revision

Large language models (LLMs) have demonstrated abilities to perform complex tasks in multiple domains, including mathematical and scientific reasoning. In this work, we construct a novel agent framework for solving representative problems in scientific computing. The proposed agent incorporates a "rewriting-resolution-review-revision" logical chain via three reasoning LLMs (the Consultant, Reviewer, and Programmer) in a collaborative and interactive manner. The Consultant module enables knowledge transfer to link problems to professional domain insights, thereby rewriting problem descriptions through text augmentation. The Programmer module generates and executes well-structured code to solve problems. The Reviewer module enables self-debugging and self-refinement through interactive feedback with code runtime outputs. Through the end-to-end review mechanism, the Programmer's executable code undergoes iterative revision. We comprehensively evaluate the framework on typical partial differential equations (PDEs), engineering-oriented flow past a cylinder, ill-conditioned linear systems, and data-driven physical analysis problems. Compared with a single-model approach, this collaborative framework significantly improves the bug-free code generation rate and reduces non-physical solutions, establishing a reliable framework for autonomous code generation from natural language descriptions. The review mechanism improved the average execution success (bug-free code and non-NaN solutions) rate of DeepSeek R1 from 59% to 82%, while ChatGPT 4.1-mini improved from 66% to 87% and Gemini-2.5 improved from 60% to 84%. Automatic code generation and review provide a promising workflow for scientific computing; analysis of solver-development trajectories further reveals recurring implementation difficulties in boundary treatment, array indexing, and the preservation of numerical constraints.

cs.AI↗
arXiv2026

Memorize When Needed: Decoupled Memory Control for Spatially Consistent Long-Horizon Video Generation

Spatially consistent long-horizon video generation aims to maintain temporal and spatial consistency along predefined camera trajectories. Existing methods mostly entangle memory modeling with video generation, leading to inconsistent content during scene revisits and diminished generative capacity when exploring novel regions, even when trained on extensive annotated data. To address these limitations, we propose a decoupled framework that separates memory conditioning from generation. Our approach significantly reduces training costs while simultaneously enhancing spatial consistency and preserving the generative capacity for novel scene exploration. Specifically, we employ a lightweight, independent memory branch to learn precise spatial consistency from historical observations. We first introduce a hybrid memory representation to capture complementary temporal and spatial cues from generated frames, then leverage a per-frame cross-attention mechanism to ensure each frame is conditioned exclusively on the most spatially relevant historical information, which is injected into the generative model to ensure spatial consistency. When generating new scenes, a camera-aware gating mechanism is proposed to mediate the interaction between memory and generation modules, enabling memory conditioning only when meaningful historical references exist. Compared with the existing method, our method is highly data-efficient, yet the experiments demonstrate that our approach achieves state-of-the-art performance in terms of both visual quality and spatial consistency. Project page can be found at https://iguoyanjun.github.io/memorize-when-needed-project-page/.

cs.CV↗
arXiv2026

SWE-Bench ProMax: Benchmarking Agents on Large-Scale Multilingual Code Refactoring

As AI coding agents take on increasingly complex, long-horizon software engineering tasks, existing benchmarks are rapidly saturating and their evaluation quality has come under serious scrutiny: a recent audit found that nearly 60% of unsolved SWE-bench Verified instances contain flawed tests -- either overly narrow tests that reject correct solutions or overly broad tests that check unstated requirements -- and that frontier models can verbatim reproduce gold patches from training data. Code refactoring, which requires coordinated, behavior-preserving changes across many files, offers a substantially harder and more realistic test of agent capability, yet remains underserved by current benchmarks. We introduce SWE-Bench ProMax, an expert-curated, multilingual code refactoring benchmark of 170 instances drawn from real commits across seven programming languages (Python, Java, TypeScript, Go, C, C++, and Rust). Every instance undergoes rigorous, multi-stage curation that directly addresses the quality problems identified in prior benchmarks: issue descriptions are rewritten from scratch to provide precise, unambiguous specifications, and test suites are manually reviewed to remove overly narrow and overly broad tests. Tasks with insufficient complexity or limited cross-file scope are filtered out, yielding a benchmark of challenging, large-scale refactoring tasks that average 11.5 modified files and 261.6 lines of code per instance, substantially exceeding the scale of existing benchmarks. Experiments with frontier models under two agent scaffolds show that the best model achieves only 41.2% resolve rate, confirming that SWE-Bench ProMax presents a meaningful and unsaturated challenge for current AI coding agents. Our benchmark is available at https://huggingface.co/datasets/swe-bench-promax/SWE-Bench-ProMax.

cs.CL↗
arXiv2026

A $B_{1g}$ phonon unlocks $d$-wave superconductivity in the repulsive Hubbard model

Using numerically exact finite-temperature quantum Monte Carlo, we demonstrate that a $B_{1g}$ phonon coupled to the doped $t$-$t'$ repulsive Hubbard model produces genuine $d$-wave superconductivity at a substantial transition temperature, in excess of either interaction alone. The observed trends suggest that stronger Hubbard repulsion may cooperate with the phonon to further raise the pairing scale. The enhancement persists at stronger repulsion within the accessible window, limited by the fermion sign problem, and follows a common trend across phonon frequencies $Ω$ when organized by a retardation scale $2πT/Ω$. We also find a well-defined superconducting dome in doping, echoing a characteristic feature of correlated superconductors. Our results identify the $B_{1g}$ phonon as a plausible microscopic ingredient for robust $d$-wave superconductivity in the Hubbard model and suggest a concrete, physically motivated route toward materials with higher superconducting transition temperatures.

cond-mat.supr-con↗
arXiv2026

S$^2$-RL: Sample-Set Dual Reinforcement Learning for Generative Semantic Segmentation Dataset Distillation

While dataset distillation has witnessed significant advances in image classification, its extension to dense prediction tasks such as semantic segmentation is plagued by two core bottlenecks: bi-level optimization-based approaches suffer from prohibitive computational costs stemming from pixel-wise gradient unrolling, whereas proxy-based generative methods merely infuse visual textures into fixed semantic masks derived from real data, thus failing to condense rich semantic knowledge into a compact set of informative, novel scene generations. To address both bottlenecks simultaneously, we propose a novel Sample-Set Reinforcement Learning (S$^2$-RL) framework for generative semantic segmentation dataset distillation (SSDD). Specifically, S$^2$-RL formulates SSDD as a diffusion model based text-to-image generation paradigm, enabling flexible generation of images with informative, novel semantic distributions via a concise text prompt. Furthermore, we fine-tune a diffusion policy via Group Relative Policy Optimization (GRPO), leveraging a sample-set dual reward paradigm: for individual samples, it enforces semantic alignment with input text prompts and intra-class feature diversity; for sample sets, it maximizes inter-sample semantic distribution diversity by solving a contextual multi-armed bandit problem. These design choices enable S$^2$-RL to distill large-scale semantic segmentation datasets into a compact set of generated samples that encapsulate diverse, informative semantic knowledge without the need of pixel-wise gradient unrolling. Extensive experiments on the ADE20K and COCO datasets demonstrate that S$^2$-RL achieves substantial and consistent improvements over state-of-the-art baselines, establishing a new benchmark for SSDD.

cs.CV↗
arXiv2026

OSWAM: An Effective World Action Model with One-Step Action Generation

Direct-policy World Action Models (WAM) have demonstrated the benefits of decoupling action generation from explicit future visual prediction for efficient inference in autonomous driving and embodied control. However, they still require tens of denoising steps to achieve competitive action quality, incurring substantial latency and hindering real-time deployment. Simply reducing the number of denoising steps will collapse the nonlinear multi-step denoising trajectory into coarse updates, substantially degrading action quality. To reduce the denoising steps while enabling real-time action generation, we present an effective world action model with one-step action generation, namely OSWAM, for autonomous driving and embodied control. We argue that it is the absence of structured action priors in random noise initialization that forces direct-policy WAMs to recover coherent action sequences through iterative denoising. Hence, we construct imagination tokens to initialize the diffusion process, providing physical priors and action-conditioned representations. We further introduce privileged information distillation with future conditioning to enhance future-aware action generation. As a result, OSWAM can efficiently and effectively generate high quality actions in just one diffusion step. Our experiments demonstrate that OSWAM achieves comparable or even better results in both autonomous driving and embodied control than direct-policy WAM and Joint-WAM that require tens of steps. It obtains approximately $3\times$ speedup over direct-policy WAM baselines and supports real-time compiled inference with latency as low as 40ms on an NVIDIA RTX 5090 GPU. The project page is available at https://gwenzhang.github.io/OSWAM/

cs.CV↗
arXiv2026

Semantic-Aware Deformable Feature Alignment for Thyroid Nodule Segmentation in Ultrasound

Accurate segmentation of thyroid nodules in ultrasound images is essential for clinical diagnosis yet remains challenging due to boundary ambiguity, speckle noise, and complex geometric variability. Existing methods often fail to reconcile global semantic understanding with precise local boundary delineation, leading to errors in irregular cases. To address this, we propose SDFA-Net, a framework built on semantic-aware deformable feature alignment that explicitly decouples the learning of robust global semantics and detailed local geometry. Our approach integrates three main components: a clustered linear context aggregation module for efficient long-range dependency modeling, an affinity-driven token modulation mechanism using dynamic prototypes to suppress background interference, and a cascaded spatially-aligned feature fusion strategy that achieves sub-pixel geometric alignment across multiple resolution stages. By filtering and aligning multi-scale features, SDFA-Net ensures robust fusion that is both semantically meaningful and geometrically accurate. We validate our method through extensive experiments on three public thyroid ultrasound datasets, TN3K, TUCC, and DDTI, where it demonstrates superior performance over state-of-the-art methods. The proposed framework offers a generalizable solution for precise medical image segmentation in boundary-ambiguous scenarios.

eess.IV↗
arXiv2026

Isolated singularities of solutions to the Yamabe equation in higher dimensions I

We complete, in the general Riemannian setting, the classification of isolated singularities of positive solutions to the Yamabe equation for dimensions \(3\le n\le29\), initiated in the flat case by Caffarelli, Gidas, and Spruck in 1989. Precisely, every isolated singularity is either removable or the solution is asymptotic to a Fowler solution. The sharpness of this range is established by counterexamples for every dimension \(n\ge30\) in our companion paper.

math.AP↗
arXiv2026

ForceDelta-VLA: Distilling Force-Conditioned Action Corrections for Contact-Rich Manipulation

Force-aware Vision-Language-Action (VLA) policies improve contact-rich manipulation, but typically combine task-level motion and contact-dependent adjustment in a single action prediction. Demonstrations provide no explicit labels for decomposing that prediction into a reusable reference action and a correction. We present ForceDelta-VLA, a correction-distillation framework that constructs an explicit force-correction target using paired predictions from a frozen teacher's force-conditioned and learned force-agnostic modes. A separate delay-correction target accounts for reference-action mismatch and the change in reference state. Training uses asynchronous schedule replay with the cached task context available during execution. The resulting lightweight policy adjusts the reference actions using recent force history and robot state, responding to contact changes between reference-action updates without regenerating complete action chunks. Across nine single-arm and bimanual contact-rich tasks, ForceDelta-VLA achieves an 82.2% mean success rate, compared with 54.4% for the original ForceVLA baseline. Direct execution of our Stage-1 Temporal Teacher achieves 70.6%. Relative to ForceVLA, the complete system reduces mean peak contact force over successful trials by approximately 26% on both platforms.

cs.RO↗
arXiv2026

Lean-QuantumAlg: A Framework for AI Agents to Produce Quantum Algorithms that Humans Can Trust

AI agents are increasingly capable of constructing quantum algorithms and proofs, yet machine-checked proofs alone cannot guarantee that the intended problem is solved or that resource claims match the verified computation. Here we introduce Lean-QuantumAlg, a Lean 4 framework for trustworthy AI-assisted development of quantum algorithms. Its Algorithm-Solves-Problem contract binds correctness, success probability, borrowed-state restoration and quantum and classical resource bounds to a single execution, while separating the guarantees that Lean checks from the problem specifications and execution models that humans review. We demonstrate the framework on nine AI-formalized quantum algorithms, from Grover search to quantum attacks on RSA-2048 and P-256, with less than 1% of each algorithm's imported source code requiring statement-level human review once the shared framework has been audited. By integrating reusable mathematical foundations, certified algorithmic primitives and execution-grounded verification, Lean-QuantumAlg provides a basis for AI agents to construct and certify quantum algorithms, opening a path toward scalable AI-driven discovery of quantum algorithms.

quant-ph↗
arXiv2026

A domain-decomposition reduced-order model for two-phase CO$_2$ sequestration with moving wells

We present a domain-decomposition reduced-order model for two-phase geological CO$_2$ storage with fixed and moving wells. The approach builds on a nonoverlapping Schur formulation of a conservative RT0--P0 discretization solved by a sequential pressure--transport algorithm. The distinctive feature of the formulation is that local reduced models are coupled through physically meaningful interface variables: pressure traces for the pressure solve and inflow saturation traces for the transport solve. To address moving wells, we introduce a well-aware strategy that combines source-response enrichment, HAPOD-based far-field compression, and hybrid full-order/reduced-order treatment of well and near-well subdomains. We also formulate conservation-oriented hyper-reduction rules where interface fluxes, boundary terms and source terms are protected. Numerical results are presented to demonstrate accuracy, computational efficiency, robustness of the overall methodology.

math.NA↗
arXiv2026

Preserving Operator Intent Under Actuation Constraints: Teleoperation of Manipulators with Coupled Transmissions

Teleoperation enables intuitive control of remote engineering robots for precision tasks. Existing direct joint-mapping methods have two limitations: independent motor saturation disrupts pitch-roll coordination in differential wrists, while fixed mappings struggle with abrupt tracking changes caused by gravitational loads and actuation constraints. We propose an actuator-constraint-aware leader-follower teleoperation method that jointly models leader gravity compensation, leader-follower joint mapping, and follower differential-wrist control. Specifically, we perform coordinated saturation in motor space according to the available gravity margin and integrate continuous angle unwrapping, feedback-state monitoring, and feasible-reference updates. This preserves the operator's motion direction, reduces coordination distortion, and suppresses recovery transients during saturation or brief communication failures. Real-robot experiments demonstrate smoother wrist trajectories and more continuous recovery than direct mapping.

cs.RO↗
arXiv2026

Foundation4D: Towards a unified perception and reconstruction model for autonomous vehicles

We introduce Foundation4D, a unified feed-forward model for geometry estimation, 3D detection, semantic occupancy, and Gaussian reconstruction from multi-camera driving video. A shared backbone uses factorized spatiotemporal attention to efficiently combine observations across cameras and time. Our video inference pipeline uses pose graph optimization to refine camera trajectories and assembles object tracks across input windows. We also develop a data annotation pipeline and release PAI-Foundation4D, a benchmark with dense depth and semantic occupancy labels for 1,253 driving clips. With benchmark-specific fine-tuning, Foundation4D achieves the lowest depth AbsRel on Waymo and nuScenes, the highest detection mAP on nuScenes, and the highest occupancy mIoU on OpenOccupancy among the compared methods. Our task-combination study shows benefits for both detection and geometry: co-training detection with geometry and occupancy improves top-class mAP by 1.2 points over detection-only training, while co-training geometry with detection reduces camera-to-rig translation error by $13.4\%$ relative to geometry-only training. We further use the predicted geometry and trajectories as priors for lidarless NuRec, supporting reconstruction of driving scenes for simulation.

cs.CV↗
arXiv2026

MBTI: A Multi-Branch Efficient Fine-Tuning Framework for Hyperspectral Image Classification with Foundation Models

Hyperspectral foundation models learn transferable spectral-spatial representations from large-scale unlabeled data. They provide an effective paradigm for adapting to downstream hyperspectral image (HSI) classification tasks with limited labeled samples. However, spectral band configurations vary substantially across sensors, which makes direct model transfer difficult. Existing adaptation strategies often compress, select, or reshape the original spectra to match model-specific input requirements. These operations may discard useful spectral information and weaken local spectral continuity. To address this problem, we propose MBTI, a Multi-Branch efficient fine-tuning framework for Hyperspectral Image classification. MBTI adapts hyperspectral foundation models to downstream classification tasks while preserving full-band spectral information. First, we introduce a spectral-continuity-preserving multi-branch preprocessing strategy. The original HSI is divided into multiple continuous spectral subsets, and a band reuse mechanism is used when the remaining bands cannot form a complete branch. This avoids invalid padding and unnecessary spectral loss. Second, independent Low-Rank Adaptation (LoRA) modules are inserted into each branch. They enable different spectral intervals to learn task-specific discriminative features while keeping most pre-trained parameters frozen. Finally, a multi-branch channel attention fusion module adaptively recalibrates and integrates features from all spectral branches. Experiments on three public hyperspectral datasets show that MBTI achieves competitive and superior performance compared with representative classification methods. Under the final rank-8 configuration, only about 2.33\%--2.36\% of the parameters are trainable. The code will be available at https://github.com/Azhenmiddleblock/MBTI/tree/main.

cs.CV↗
arXiv2026

TRCM: Topology-Aware Route-Consistency Modeling for Robust Neural Vehicle Routing

Neural combinatorial optimization has enabled fast constructive solvers for the Capacitated Vehicle Routing Problem (CVRP), yet most autoregressive models still construct solutions through sequential node selection and represent route organization only implicitly. We investigate whether route-level customer co-assignment can be modeled explicitly and used to guide this node-level decision process. To this end, we propose TopologyAware RouteConsistency Modeling (TRCM), which reuses node representations from a standard autoregressive construction pipeline to predict pairwise same-route probabilities and injects them into customer selection as a route-consistency signal. Because sameroute supervision is both class-imbalanced and structurally uneven, TRCM combines structure-preserving augmentation with Topological Entropy (TE)- based reweighting to emphasize locally ambiguous customer pairs. Under matched decoding budgets, TRCM reduces the optimality gap from 3.67% to 3.28% on CVRP50 and from 2.11% to 1.99% on CVRP100; under 8-fold augmented inference, it reduces the CVRP100 gap from 1.61% to 1.49%. On XML100, TRCM*8Aug improves the average objective by 0.24%, with larger gains on several structurally informative factors. A controlled demand-reassignment test over 500 variants further shows more concentrated objective fluctuations. These results support explicit route-consistency modeling as an effective structural principle for autoregressive neural routing.

cs.LG↗
arXiv2026

Vanishing transport noise enhances stability of stratified Couette flow in the 3D Boussinesq system

In this paper, we study the enhanced nonlinear stability of stably stratified Couette flow in the three-dimensional Boussinesq system driven by a common affine Stratonovich transport noise. Our main result shows that, for fixed $β>1/2$, suitably chosen noise amplitudes enlarge the range of perturbations for which we prove stability, even as they vanish with viscosity. For each fixed deterministic Sobolev perturbation satisfying the sufficient smallness conditions, the strong solution is global and obeys stability estimates on an event of prescribed high probability. No spatial localization or vanishing initial double means are required. The proof combines noise-induced mixing with coupled energy estimates to control nonlinear feedback and preserve the physical damping of the fast vertical velocity and temperature.

math.AP↗
arXiv2026

Global exact controllability for Schrödinger equations with Lipschitz and logarithmic nonlinearities

In this paper, we study global exact controllability of semilinear Schrödinger equations by localized internal additive controls. For every globally Lipschitz nonlinearity in arbitrary dimensions, we prove that any two $L^2$ states can be connected in any prescribed positive time, without smallness assumptions on the states or the Lipschitz constant. The result holds on smooth bounded Euclidean domains under a local convex-phase condition, and on an interval with any nonempty open control region. It also extends to compact Riemannian manifolds under the corresponding phase condition. In one dimension, we further establish controllability for logarithmic nonlinearities of the form \[ f(z)=zϕ(|z|)+\mathfrak g(z), \] where $ϕ$ is real-valued, $\mathfrak g$ is globally Lipschitz, and $r|ϕ'(r)|\leq D(1+|\log r|)^γ$ with $0\leqγ<1/2$. For the endpoint case $γ=1/2$, we achieve the result by assuming the leading coefficient is sufficiently small. These results resolve the global Lipschitz controllability question raised by Zuazua \cite[Section~3]{Zuazua2003} in the stated geometric settings and establish its logarithmic extension within the specified one-dimensional classes.

math.OC↗