arXiv subjects

Wen Huang

Publications and source records attributed to Wen Huang.

At least 37 records · Page 2Linked to original sources

arXiv2026

MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research

Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.

cs.AI↗

arXiv2026

Diffeomorphic Logarithm of Special Orthogonal Matrices

The special orthogonal group $\mathbb{SO}_n$ is a Lie group whose geometry and local structure are encoded by the exponential map in its Lie algebra $\mathbf{Skew}_n$, the set of skew-symmetric matrices. The associated multi-valued inverse problem -- the matrix logarithm -- in $\mathbb{SO}_n$ exhibits a highly nontrivial local diffeomorphism structure, which differs from the matrix logarithm for invertible matrices. This work characterizes the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices where its derivative is invertible. We show that this set with an invertible derivative can be organized into diffeomorphic regions, using a canonical alignment of Schur decompositions. In particular, the region that contains the principal logarithm has a special multiplicity structure: each matrix in $\mathbb{SO}_n$ admits at most two skew-symmetric preimages in this region. Based on this geometric framework, we introduce the diffeomorphic logarithm of special orthogonal matrices together with an efficient and stable algorithm. Moreover, it is applied to the Karcher mean problem in $\mathbb{SO}_n$, demonstrating continuous behavior of the mean under perturbations of the data, which is not captured by the principal logarithm.

math.DG↗

arXiv2026

RelayFormer: A Unified Local-Global Attention Framework for Scalable Image and Video Manipulation Localization

Visual manipulation localization (VML) aims to identify tampered regions in images and videos, a task that has become increasingly challenging with the rise of advanced editing tools. Existing methods face two central issues. The first is resolution diversity. Resizing or padding can distort subtle forensic cues and introduce unnecessary computational cost. The second is the difficulty of extending spatial models for images to spatio-temporal inputs in videos, which often results in maintaining separate architectures for the two data types. To address these challenges, we propose RelayFormer, a unified framework that adapts to varying resolutions and naturally handles both static and temporal visual data. RelayFormer partitions inputs into fixed-size sub-images and introduces Global Local Relay (GLR) tokens that propagate structured context through a relay-based attention mechanism. This design enables efficient exchange of global cues, such as semantic or temporal consistency, while preserving fine-grained manipulation artifacts. Unlike prior approaches that depend on uniform resizing or sparse attention, RelayFormer scales to variable resolutions and video sequences with minimal overhead. Experiments across diverse benchmarks demonstrate superior performance and strong efficiency, combining resolution adaptivity without interpolation or excessive padding, unified processing for images and videos, and a favorable balance between accuracy and computational cost. Code is available at~\href{https://github.com/WenOOI/RelayFormer}{https://github.com/WenOOI/RelayFormer}.

cs.CV↗

arXiv2026

The Exponential of Skew-Symmetric Matrices: A Nearby Inverse and Efficient Computation of Derivatives

The matrix exponential restricted to skew-symmetric matrices has numerous applications, notably in view of its interpretation as the Lie group exponential and Riemannian exponential for the special orthogonal group. We characterize the invertibility of the derivative of the skew-restricted exponential, thereby providing a simple expression of the tangent conjugate locus of the orthogonal group. In view of the skew restriction, this characterization differs from the classic result on the invertibility of the derivative of the exponential of real matrices. Based on this characterization, for every skew-symmetric matrix $A$ outside the (zero-measure) tangent conjugate locus, we explicitly construct the domain and image of a smooth inverse -- which we term \emph{nearby logarithm} -- of the skew-restricted exponential around $A$. This nearby logarithm reduces to the classic principal logarithm of special orthogonal matrices when $A=\mathbf{0}$. The symbolic formulae for the differentiation and its inverse are derived and implemented efficiently. The extensive numerical experiments show that the proposed formulae are up to $3.9$-times and $3.6$-times faster than the current state-of-the-art robust formulae for the differentiation and its inversion, respectively.

math.DG↗

arXiv2026

ARBOR: Online Process Rewards via a Reusable Rubric Buffer for Search Agents

LLM-based search agents are trained predominantly with outcome-only reward, leaving the search process itself unsupervised. This signal degenerates on outcome-homogeneous groups where all sampled trajectories share the same correctness, yielding zero within-group advantage and no gradient. Existing process supervision either trains a costly verifier or generates per-query rubrics that are inconsistent across queries and discarded after one use. We propose ARBOR (Adaptive Rubric Buffer for Online Reward), a reusable process-reward framework that maintains a rubric memory shared across queries. Query-local drafts induced from contrastive trajectories are admitted, consolidated into cross-query common rubrics, and retired as the policy evolves. A small active subset of common rubrics scores trajectories via sparse pairwise judging, and the resulting scores are added to the base reward, providing process-level gradient even when outcome reward is uniform. ARBOR consistently outperforms GRPO and DAPO baselines on four multi-hop QA benchmarks, raising average LLM-judge accuracy by up to 4.2 points and converting up to 42% of otherwise-zero-gradient training groups into informative ones.

cs.CL↗

arXiv2026

Membership Reference Attack against Laplace Mechanism of Differential Privacy

The differential privacy is a widely accepted conception of privacy protection and the Laplace mechanism is a famous instance of differential privacy mechanisms to deal with numerical data. In this paper, we point out that the differential privacy does not take liner property of queries into account, resulting in information leakage. In order to show the information leakage, we construct a membership reference attacks against the Laplace mechanism. Concretely, we propose a method to obtain multiple independent identical distribution samples of linear query's answer under constrains of the Laplace mechanism. The proposed method is based on linear property of linear query and some background knowledge. Based on obtained samples, a hypothesis test method is used to determine whether a targert record is in data set.

cs.CR↗

arXiv2026

Retractions by Alternating Projections

Alternating projections and their variants are classical tools for computing points in intersections of sets. Existing analyses for smooth manifolds mainly focus on local convergence rates under transversality or related regularity conditions. In this work, we develop a unified framework for a broad class of (possibly inexact) alternating-projection-type methods on intersections of smooth manifolds. Specifically, under the assumption that two $C^{2,1}$ embedded submanifolds $\mathcal{M}_1, \mathcal{M}_2 \subset \mathbb{R}^n$ intersect cleanly, we show that the associated alternating mapping admits a well-defined local limiting map $ψ$ on the intersection manifold $\mathcal{M}=\mathcal{M}_1\cap \mathcal{M}_2$, and that $ψ$ is a retraction on $\mathcal{M}$. If, in addition, $\mathcal{M}_1$ and $\mathcal{M}_2$ are $C^{3,1}$, then $ψ$ is a second-order retraction. Furthermore, the standard NewtonSLRA scheme, which exhibits quadratic local behavior under transversality, can be understood as inducing a second-order retraction on $\M$. This framework thus provides new retraction-based optimization tools for problems constrained to the intersection manifold.

math.OC↗

arXiv2026

AdaptiveLoad: Towards Efficient Video Diffusion Transformer Training

In video generation models, particularly world models, training large-scale video diffusion Transformers (such as DiT and MMDiT) poses significant computational challenges due to the extreme variance in sequence lengths within mixed-mode datasets. Existing bucket-based data loading strategies typically rely on "equal token length" constraints. This approach fails to account for the quadratic complexity of self-attention mechanisms, leading to severe load imbalance and underutilization of GPU resources. This paper proposes \textit{AdaptiveLoad}, an integrated optimization framework consisting of two core components: (1) A dual-constraint adaptive load balancing system, which eliminates long-sequence bottlenecks by simultaneously limiting memory consumption and computational load ($B \times S^p \le M_{\text{comp}}$); (2) A fused LayerNorm-Modulate CUDA kernel, which utilizes a D-tile coalesced reduction strategy to increase throughput and alleviate memory pressure. Experimental results on the Wan 2.1 world model demonstrate that our method reduces the computational imbalance rate from 39\% to 18.9\%, improves peak VRAM utilization efficiency by 22.7\%, and achieves an overall training throughput increase of 27.2\%.

cs.DC↗

arXiv2026

D-VLA: A High-Concurrency Distributed Asynchronous Reinforcement Learning Framework for Vision-Language-Action Models

The rapid evolution of Embodied AI has enabled Vision-Language-Action (VLA) models to excel in multimodal perception and task execution. However, applying Reinforcement Learning (RL) to these massive models in large-scale distributed environments faces severe systemic bottlenecks, primarily due to the resource conflict between high-fidelity physical simulation and the intensive VRAM/bandwidth demands of deep learning. This conflict often leaves overall throughput constrained by execution-phase inefficiencies. To address these challenges, we propose D-VLA, a high-concurrency, low-latency distributed RL framework for large-scale embodied foundation models. D-VLA introduces "Plane Decoupling," physically isolating high-frequency training data from low-frequency weight control to eliminate interference between simulation and optimization. We further design a four-thread asynchronous "Swimlane" pipeline, enabling full parallel overlap of sampling, inference, gradient computation, and parameter distribution. Additionally, a dual-pool VRAM management model and topology-aware replication resolve memory fragmentation and optimize communication efficiency. Experiments on benchmarks like LIBERO show that D-VLA significantly outperforms mainstream RL frameworks in throughput and sampling efficiency for billion-parameter VLA models. In trillion-parameter scalability tests, our framework maintains exceptional stability and linear speedup, providing a robust system for high-performance general-purpose embodied agents.

cs.AI↗

arXiv2026

Sword: Style-Robust World Models as Simulators via Dynamic Latent Bootstrapping for VLA Policy Post-Training

The integration of Vision-Language-Action (VLA) models with World Models has gained increasing attention. One representative approach treats learned World Models as generative simulators, enabling policy optimization entirely within "imagination." However, when deployed as simulators for specific environments such as the LIBERO benchmark, existing World Models often suffer from poor generalization and long-horizon error accumulation. During closed-loop rollouts, these models are highly sensitive to initial-state perturbations; minor changes in color, illumination, and other visual factors can trigger cascading hallucinations, leading to severe blurriness or overexposure. Moreover, long-horizon error accumulation further degrades the quality and fidelity of predicted future states. These issues limit the reliability of World Models as simulators. To mitigate these problems, we propose Sword, a robust World Model framework. Our method introduces Structure-Guided Style Augmentation to disentangle the visual textures of interactive environments from task-relevant dynamics, thereby improving generalization. We further propose Dynamic Latent Bootstrapping, which maintains consistency between training and inference while keeping memory consumption low. Extensive experiments on the LIBERO benchmark show that our method significantly outperforms the baseline WoVR in terms of generalization, generation quality, robustness, fidelity, and the success rate of reinforcement-learning post-training for VLA models.

cs.CV↗

arXiv2026

NoiseGate: Learning Per-Latent Timestep Schedules as Information Gating in World Action Models

World Action Models (WAMs) are an emerging family of policies that tie robot action generation to future-observation modeling. In this work, we focus on the joint video--action modeling paradigm, where actions and imagined future observations are co-generated along a shared denoising or flow trajectory, so that perception, prediction, and control are coupled within one generative process. Existing WAMs typically realize this paradigm with a Mixture-of-Transformers (MoT), where video and action tokens interact through shared self-attention. This architecture can in principle assign a separate timestep $t_f$ to each predicted latent frame, yet current systems collapse this degree of freedom onto a single shared scalar $t$. Under the noise-as-masking view of Diffusion Forcing, this shared schedule imposes the unjustified prior that every predicted latent is equally reliable for action generation. We instead view the per-latent schedule as a \emph{learnable information-gating policy}: by changing a latent frame's noise level, the policy modulates the reliability of its Key/Value contribution to the action tokens. We propose \textbf{NoiseGate}, which combines independent per-latent timestep sampling during backbone training, a lightweight Gating Policy Network that emits per-latent time increments during denoising, and task-reward optimization that trains the schedule policy without hand-crafted shape priors. Built on a joint video--action MoT backbone, NoiseGate delivers consistent gains on diverse RoboTwin random-scene manipulation tasks.

cs.RO↗

arXiv2026

A restricted memory quasi-Newton bundle method for nonsmooth optimization on Riemannian manifolds

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a Riemannian version of the quasi-Newton updating formulas. A Riemannian subgradient aggregation technique is proposed and used to significantly reduce the computations in the quadratic programming subproblem when calculating the candidate descent direction. Moreover, a Riemannian line-search procedure is proposed to generate the stepsizes, and the process is finitely terminated under the assumption of a newly proposed Riemannian semismoothness. Global convergence of the proposed method is established: if the serious iteration steps are finite, then the last serious iterate is stationary; otherwise, every accumulation point of the serious iteration sequence is stationary. In addition, a modified algorithm with limited-memory quasi-Newton updates is presented to further reduce the computational cost. Finally, numerical experiments demonstrate that (i) the quasi-Newton updates accelerate the convergence of the bundle method, (ii) the aggregation technique significantly reduces the computational cost for solving the quadratic programming subproblem, and (iii) the proposed methods outperform the compared state-of-the-art Riemannian optimization methods for locally Lipschitz continuous functions.

math.OC↗

arXiv2026

DPDSyn: Improving Differentially Private Dataset Synthesis for Model Training by Downstream Task Guidance

How to synthesize a dataset while achieving differential privacy for AI model training is a meaningful but challenging problem. To address this problem, state-of-the-art methods first select original private dataset's multiple low-dimensional distributions that have the potential to approximate the distribution of original private dataset with high precision, and then synthesize a dataset obeying all selected low-dimensional distributions as the synthetic dataset. However, it is difficult to select suitable low-dimensional distributions, which in turn degrades the data utility of resulting synthetic dataset. To improve differentially private dataset synthesis, we propose to train a differentially private AI model for downstream tasks on the original private dataset and utilize the trained model to synthesize datasets. In particular, on the one hand, the AI model satisfies differential privacy so no matter how to use the model does not disclose private information of original private dataset. On the other hand, the AI model is trained to complete the downstream task so the AI model preserves critical information for completing downstream tasks. We utilize the AI model to synthesize datasets to achieve the goal of improving data utility while preserving privacy. Empirical evaluations on four benchmark datasets demonstrate that our proposed DPDSyn consistently outperforms eight state-of-the-art baselines with a maximum improvement of 2.40x in accuracy and 333.73x in synthesis efficiency. Further experiments also validate that DPDSyn has strong scalability across varying data scales.

cs.CR↗

arXiv2026

Thousand-GPU Large-Scale Training and Optimization Recipe for AI-Native Cloud Embodied Intelligence Infrastructure

Embodied intelligence is a key step towards Artificial General Intelligence (AGI), yet its development faces multiple challenges including data, frameworks, infrastructure, and evaluation systems. To address these issues, we have, for the first time in the industry, launched a cloud-based, thousand-GPU distributed training platform for embodied intelligence, built upon the widely adopted LeRobot framework, and have systematically overcome bottlenecks across the entire pipeline. At the data layer, we have restructured the data pipeline to optimize the flow of embodied training data. In terms of training, for the GR00T-N1.5 model, utilizing thousand-GPU clusters and data at the scale of hundreds of millions, the single-round training time has been reduced from 15 hours to just 22 minutes, achieving a 40-fold speedup. At the model layer, by combining variable-length FlashAttention and Data Packing, we have moved from sample redundancy to sequence integration, resulting in a 188% speed increase; π-0.5 attention optimization has accelerated training by 165%; and FP8 quantization has delivered a 140% speedup. On the infrastructure side, relying on high-performance storage, a 3.2T RDMA network, and a Ray-driven elastic AI data lake, we have achieved deep synergy among data, storage, communication, and computation. We have also built an end-to-end evaluation system, creating a closed loop from training to simulation to assessment. This framework has already been fully validated on thousand-GPU clusters, laying a crucial technical foundation for the development and application of next-generation autonomous intelligent robots, and is expected to accelerate the arrival of the era of human-machine integration.

cs.RO↗

arXiv2026

Frequency-resolved N-photon correlations in the ultra-strong coupling regime

Frequency-resolved photon emission is central to applications from quantum information encoding to high-resolution spectroscopy, and then studying their correlations is therefore essential for revealing the underlying emission pathways and multiphoton statistics. Here, we investigate frequency-resolved N-photon correlations in an ultrastrongly coupled cavity QED system where a qubit interacts with a single-mode cavity. Owing to counter-rotating interactions, the eigenstates and energy spectrum are strongly modified, giving rise to rich spectral and statistical properties in the emitted frequency-resolved photons. Through frequency-selective detection, we reveal pronounced multiphoton antibunching, as well as multiphoton bunching originating from cascade transitions among dressed eigenstates. In particular, we show that parity symmetry plays a decisive role in shaping these correlations. The symmetry-breaking opens additional transition channels and dramatically enhances the generation of correlated photon pairs and even photon triplets of different frequencies. Our work extends frequency-resolved correlations to the ultra-strong coupling regime and demonstrates their potential as a sensitive probe of symmetry in light-matter interaction systems.

quant-ph↗

arXiv2026

Typical periodic optimization for dynamical systems: symbolic dynamics

We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Mañé cohomology lemma does not hold. This leads to new solutions of the Typical Periodic Optimization problem in the Lipschitz category: existence of an open dense set of Lipschitz functions such that each member has a unique maximizing measure and this measure is periodic (an equi-distribution on a single periodic orbit). The theory yields a structural theorem, that isolates the part of the system responsible for any robust non-periodic optimization. The structural theorem is developed further in the setting of symbolic dynamics: given any shift space, for typical Lipschitz functions the maximizing measure is shown to be either periodic or supported on the Markov boundary of the shift space. It follows that Contreras' Typical Periodic Optimization theorem for shifts of finite type can be extended to a wide class of shift spaces, including every sofic shift. The structural theorem is used to provide the first known example of a shift space where Typical Periodic Optimization fails despite periodic measures being dense in the set of all invariant measures.

math.DS↗

arXiv2026

ATA: Bridging Implicit Reasoning with Attention-Guided and Action-Guided Inference for Vision-Language Action Models

Vision-Language-Action (VLA) models rely on current observations, including images, language instructions, and robot states, to predict actions and complete tasks. While accurate visual perception is crucial for precise action prediction and execution, recent work has attempted to further improve performance by introducing explicit reasoning during inference. However, such approaches face significant limitations. They often depend on data-intensive resources such as Chain-of-Thought (CoT) style annotations to decompose tasks into step-by-step reasoning, and in many cases require additional visual grounding annotations (e.g., bounding boxes or masks) to highlight relevant image regions. Moreover, they involve time-consuming dataset construction, labeling, and retraining, which ultimately results in longer inference sequences and reduced efficiency. To address these challenges, we propose ATA, a novel training-free framework that introduces implicit reasoning into VLA inference through complementary attention-guided and action-guided strategies. Unlike CoT or explicit visual-grounding methods, ATA formulates reasoning implicitly by integrating attention maps with an action-based region of interest (RoI), thereby adaptively refining visual inputs without requiring extra training or annotations. ATA is a plug-and-play implicit reasoning approach for VLA models, lightweight yet effective. Extensive experiments show that it consistently improves task success and robustness while preserving, and even enhancing, inference efficiency.

cs.CV↗

arXiv2026

Localizing Speech Deepfakes Beyond Transitions via Segment-Aware Learning

Localizing partial deepfake audio, where only segments of speech are manipulated, remains challenging due to the subtle and scattered nature of these modifications. Existing approaches typically rely on frame-level predictions to identify spoofed segments, and some recent methods improve performance by concentrating on the transitions between real and fake audio. However, we observe that these models tend to over-rely on boundary artifacts while neglecting the manipulated content that follows. We argue that effective localization requires understanding the entire segments beyond just detecting transitions. Thus, we propose Segment-Aware Learning (SAL), a framework that encourages models to focus on the internal structure of segments. SAL introduces two core techniques: Segment Positional Labeling, which provides fine-grained frame supervision based on relative position within a segment; and Cross-Segment Mixing, a data augmentation method that generates diverse segment patterns. Experiments across multiple deepfake localization datasets show that SAL consistently achieves strong performance in both in-domain and out-of-domain settings, with notable gains in non-boundary regions and reduced reliance on transition artifacts. The code is available at https://github.com/SentryMao/SAL.

cs.SD↗