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Rui Gao

Publications and source records attributed to Rui Gao.

At least 19 recordsLinked to original sources
arXiv2026

Existence of disks with prescribed mean curvature and contact angle in arbitrary codimension

Under suitable relative homotopy and boundary admissibility assumptions, we establish a min-max theory in arbitrary codimension that produces nonconstant branched immersed disks or spheres in closed Riemannian manifolds, with controlled Morse index, where the prescribed mean curvature type tensor and the nonorthogonal, nonconstant contact angle condition of disks along a supporting submanifold are determined by the same differential 2-form. In Euclidean space, under suitable topological and convex barrier assumptions, we obtain such disks with free boundary on a closed supporting hypersurface and a Morse index bound depending only on the ambient dimension.

math.DG↗
arXiv2026

Few-Shot Open-Set Audio Classification via Transductive Prototype Refinement and Class Logit Enhancement

Few-shot Open-set audio classification requires classifying query samples from known classes with a few labeled support samples while rejecting query samples from unknown classes. Transductive inference jointly observes the full unlabeled query set to improve prototype estimation, yet standard transductive updates do not distinguish known from unknown query samples, leaving prototypes vulnerable to open-set contamination. Drawing on latent-inlierness weighting and decoupled scoring for unknown-class samples, we propose a two-phase transductive method operating over a frozen audio encoder. First, each query sample is assigned a latent inlierness score that down-weights likely unknown-class samples, so that prototype refinement is driven primarily by known-class evidence. The refined prototypes are then directly optimized on a transductive loss combining support cross-entropy, inlierness-weighted conditional entropy minimization, and inlierness-weighted marginal entropy maximization, while open-set rejection uses a prior-adaptive free-energy score that adjusts its threshold with the prior proportion of unknown-class samples, decoupling detection from classification. Experiments on three audio datasets show our method achieves state-of-the-art results for few-shot open-set audio classification under multiple experimental conditions.

cs.SD↗
arXiv2026

Outcome Disclosure and Temporal Refinement in Multi-Battle Team Contests

A team-contest designer values output rather than expenditure; nonlinear conversion makes the distinction consequential. We study two non-pecuniary instruments in majority-rule contests decided by pairwise all-pay battles with private abilities: disclosing resolved outcomes and splitting the battle schedule into finer blocks. Neither changes a battle's average pivotality; each only redistributes it across histories. Under nested information structures, this redistribution makes equilibrium ability-scaled expenditure weakly more dispersed player by player without changing its mean; expected aggregate expenditure is invariant across all designs considered. The resulting convex-order comparison ranks expected total output: convex output costs favor no disclosure and coarser temporal structures, concave costs favor full disclosure and finer ones, and linear costs make both comparisons neutral. The rankings hold for finite-support and smooth continuous-type ability distributions. The mechanism extends to degree-zero component contest technologies with a unique equilibrium outcome distribution. No and full disclosure bound every admissible public garbling.

econ.TH↗
arXiv2026

SRL-MPC: Shape-Aware Reinforcement Learned Model Predictive Control

Safe and efficient shape-aware navigation in heterogeneous crowds and robot fleets remains challenging. Traditional approaches often assume homogeneous robots, sparse workspaces, simplified geometry, offline computation, or handcrafted parameters to make the problem tractable, which limits their deployment in dense crowd scenarios. Toward this end, we propose Shape-Aware Reinforcement Learned Model Predictive Control (SRL-MPC), a method for safe, efficient, and adaptive navigation in crowds with heterogeneous shapes without geometry simplification. To encode shape-aware safety, we formulate high-order control barrier function (HOCBF) constraints from geometric separation features (GSFs) based on support function transformation. A reinforcement learning (RL) framework then learns a neural policy that reads GSFs and outputs real-time MPC parameter updates, enabling the MPC solver to adapt to neighboring crowd geometries. The key advantage of SRL-MPC is that it preserves the safety structure and generalizability of MPC while integrating the adaptability and intelligence of RL. Experiments in randomized crowd scenarios with arbitrary shaped robot fleets demonstrate the effectiveness, scalability, and robustness of SRL-MPC. The results show that SRL-MPC substantially outperforms representative baselines in safety and adaptability. Project website: https://hanruihua.github.io/srl_mpc_project/

cs.RO↗
arXiv2026

Wasserstein Policy Gradient for Entropy-Regularized Linear-Quadratic Control

Wasserstein policy gradient (WPG) updates state-conditional action laws by transport in the action space. We study entropy-regularized discounted linear-quadratic (LQ) control. A Bellman verification argument shows that the unrestricted problem has a linear-Gaussian optimal policy, and the discounted-occupancy-weighted statewise Wasserstein gradient is tangent to this policy class. WPG therefore reduces exactly to a finite-dimensional ODE for the feedback gain and action covariance. We prove that this ODE is globally well posed and converges exponentially from every admissible initialization. For each fixed LQ problem, the exponent has a positive limit as the entropy temperature tends to zero and contains no perturbative factor of the form $\exp(-c/τ)$, while retaining the usual dependence on the conditioning of the control problem.

math.OC↗
arXiv2026

SymStep: Symbolic Step Verification for Logical Reasoning

Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.

cs.AI↗
arXiv2026

Handwritten and Printed Text Segmentation via Region-Aware Human-Writing Descriptor Engineering

With the increasing demand for reusing paper documents in educational and office settings, accurate segmentation of handwritten and printed text has become a crucial step in document digitization. Although numerous deep learning models have been developed for this task, their high computational cost limits deployment on resource-constrained edge devices. To address this challenge, we present a lightweight framework optimized for efficient performance on devices with severely limited computational capacity. Our approach begins with the Sentence-level Connected Component Segmentation algorithm, aimed at extracting coherent sentence-level segments from document images. We then design a novel Region-aware Handwriting Descriptor (RHD) to capture the intrinsic variability of human handwriting at the sentence level. A simple conventional classifier can then be seamlessly integrated with our designed descriptor, demonstrating strong classification performance for distinguishing handwritten and printed sentence-level text images, highlighting that the proposed descriptor is agnostic to the choice of classifier. Extensive experiments are performed on our self-constructed Multilingual High-Quality Annotated Dataset for Handwritten and Printed Text Segmentation (MAD-HPTS) and a public benchmark PHD-AS, and the experimental results demonstrate that the proposed framework outperforms current state-of-the-art methods in both accuracy and computational efficiency. On MAD-HPTS, our method sacrifices only 1.4% accuracy compared to the leading deep neural network baseline, yet achieves more than 8 times speedup in inference, making it well-suited for lightweight deployment.

cs.CV↗
arXiv2026

Isospin-breaking contribution to the model-independent axion-photon-photon coupling in $U(3)$ chiral theory

We pursue the calculation of the model-independent component of the axion-photon-photon coupling in the $U(3)$ chiral perturbation theory up to next-to-leading order, with the emphasis on the isospin breaking effect. The mixing of the $π^0$-$η$-$η'$-axion system is revised as well by working out the complete linear isospin-breaking terms. Our calculation shows that the isospin-breaking correction to the axion-photon-photon coupling amounts to more than 15%, comparing with the result in the isospin limit.

hep-ph↗
arXiv2026

Bridging Modality Disconnect in Self-Reflection via Closed-Loop Visually Grounded Verification

In the era of Vision-Language Models (VLMs), enhancing multimodal reasoning capabilities remains a critical challenge, particularly in handling ambiguous or complex visual inputs, where initial inferences often lead to hallucinations or logic errors. Existing VLMs often produce plausible yet ungrounded answers, and even when prompted to "reflect", their corrections may remain detached from the image evidence. To address this, we propose the MIRROR framework for Multimodal Iterative Reasoning via Reflection On visual Regions. By embedding visual reflection as a core mechanism, MIRROR is formulated as a closed-loop process comprising draft, critique, region-based verification, and revision, which are repeated until the output is visually grounded. To facilitate training of this model, we construct **ReflectV**, a visual reflective dataset for multi-turn supervision that explicitly contains reflection triggers, region-based verification actions, and answer revision grounded in visual evidence. Experiments on both general vision-language benchmarks and representative vision-language reasoning benchmarks show that MIRROR improves correctness and reduces visual hallucinations, demonstrating the value of training reflection as an evidence-seeking, region-aware verification process rather than a purely textual revision step.

cs.CV↗
arXiv2026

MiniMax Sparse Attention

Ultra-long-context capability is becoming indispensable for frontier LLMs: agentic workflows, repository-scale code reasoning, and persistent memory all require the model to jointly attend over hundreds of thousands to millions of tokens, yet the quadratic cost of softmax attention makes this untenable at deployment scale. We introduce MiniMax Sparse Attention (MSA), a blockwise sparse attention built upon Grouped Query Attention (GQA). A lightweight Index Branch scores key-value blocks and independently selects a Top-k subset for each GQA group, enabling group-specific sparse retrieval while maintaining efficient block-level execution; the Main Branch then performs exact block-sparse attention over only the selected blocks. Designed around a principle of simplicity and scalability, MSA is deliberately streamlined, making it straightforward to deploy efficiently across a broad range of GPUs. To translate sparsity into practical speedups, we co-design MSA with a GPU execution path that uses exp-free Top-k selection and KV-outer sparse attention to improve tensor-core utilization under block-granular access. On a 109B-parameter model with native multimodal training, MSA performs on par with GQA while reducing per-token attention compute by 28.4x at 1M context. Paired with our co-designed kernel, MSA achieves 14.2x prefill and 7.6x decoding wall-clock speedups on H800. Our inference kernel is available at: https://github.com/MiniMax-AI/MSA. A production-grade natively multimodal model powered by MSA has been publicly released at: https://huggingface.co/MiniMaxAI/MiniMax-M3.

cs.AI↗
arXiv2026

Typicality of periodic optimization over an expanding circle map

We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical $C^r$ performance function has a unique maximizing measure and the unique maximizing measure is supported on a periodic orbit, for $r=1,2,\dots,\infty,ω$.

math.DS↗
arXiv2026

Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning

Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions. For the entropy-regularized RL objective, WPG evolves each state-conditional policy by transporting it along the action gradient of the soft Q-function together with a Langevin-type diffusion. Despite its appeal for continuous-control problems, its global convergence properties remain poorly understood. Standard Langevin analyses do not directly apply, because the RL objective depends on the policy through the Bellman recursion rather than through a static convex functional, and the Langevin drift is determined by the soft Q-function, whose regularity must be controlled along the policy iterates. In this paper, we develop a global convergence theory for WPG by exploiting the Bellman structure of entropy-regularized RL. We show that the role usually played by convexity can be replaced by a Bellman-based argument: the soft Bellman residual admits a statewise KL representation with respect to a Gibbs policy; Bellman contraction relates this residual to the global optimality gap; and a Bellman resolvent identity connects value improvement to relative Fisher information. Combined with a uniform log-Sobolev inequality (LSI) for the evolving Gibbs family, these ingredients yield a distributional Polyak--Łojasiewicz condition. We further establish the regularity and uniform bounds needed to control the discretization error, thereby obtaining geometric contraction up to a discretization bias. Conceptually, our analysis shows that although entropy-regularized RL is not convex in the usual flat sense, the Bellman recursion induces a favorable Polyak--Lojasiewicz-type (PL) geometry that supports global convergence of WPG.

cs.LG↗
arXiv2026

IR-SIM: A Lightweight Skill-Native Simulator for Navigation, Learning, and Benchmarking

Simulation plays a key role in automated robotics research supported by large language models (LLMs). However, existing simulators often require custom code or complex interfaces, creating a barrier to rapid prototyping and automated algorithm development. To this end, we propose the Intelligent Robot Simulator (IR-SIM), a lightweight skill-native navigation simulator designed for rapid scenario construction, benchmarking, and robot learning. In IR-SIM, scenarios are entirely defined by YAML configuration files that specify mobile robot kinematics, geometric collision checking, LiDAR sensing, visualization, and behavior modules. This design makes robotic simulation fully describable and reproducible, allowing scenarios to be generated and modified from text prompts through the proposed IR-SIM agent skills. The resulting scenarios can be used for automated benchmarking of navigation algorithms and for automated generation of training data for learning methods. Furthermore, IR-SIM provides bridges to high fidelity simulators and real world deployment, allowing users to validate their algorithms in more realistic settings after prototyping without extra coding. The experiments showcase the convenience and versatility of IR-SIM in multiple tasks: constructing navigation scenarios from natural language, training a collision avoidance policy, benchmarking social navigation policies, and bridging to high fidelity simulators and real world deployment. The project website is available at https://github.com/hanruihua/ir-sim.

cs.RO↗
arXiv2026

C-MORAL: Controllable Multi-Objective Molecular Optimization with Reinforcement Alignment for LLMs

Large language models (LLMs) show promise for molecular optimization, but aligning them with selective and competing drug-design constraints remains challenging. We propose C-Moral, a reinforcement learning post-training framework for controllable multi-objective molecular optimization. C-Moral combines group-based relative optimization, property score alignment for heterogeneous objectives, and bottleneck-sensitive non-linear reward aggregation to improve stability across competing molecular properties. Experiments on C-MuMOInstruct and S$^2$-Bench MolOpt show that C-Moral achieves the best performance among compared methods on both benchmarks. On C-MuMOInstruct, C-Moral achieves the best Success Optimized Rate (SOR) of 48.9\% on in-domain tasks and 39.5\% on out-of-domain tasks while preserving scaffold similarity. On S$^2$-Bench MolOpt, it also achieves the strongest results across LogP, MR, and QED optimization tasks. These results suggest that C-Moral is an effective way to align molecular LLMs with continuous and constrained molecular design objectives. Our code and models are publicly available at https://github.com/Rwigie/C-MORAL.

cs.LG↗
arXiv2026

Distributed Observer Design for Discrete-Time LTI Systems via Jordan Canonical Form

This paper addresses the problem of distributed state estimation for discrete-time linear time-invariant systems. Building on the framework proposed in Gao & Yang (2025), we exploit the Jordan canonical form of the system matrix to develop two distributed estimation schemes that ensure asymptotic convergence of local estimates to the true system state. In both approaches, each node reconstructs the components of the state that are locally detectable for it via a Luenberger observer, while employing a consensus-based mechanism to estimate the components that are not directly detectable. The first scheme relies on local observers whose dimension matches that of the original state vector; however, its applicability requires the satisfaction of a large set of inequalities. The second scheme, in contrast, can be implemented under less restrictive conditions, but results in observers of increased (augmented) order. For both methods, we derive necessary and sufficient conditions - expressed in terms of the eigenvalues of the system matrix and certain submatrices of the communication network Laplacian - that guarantee the existence of a distributed observer achieving asymptotically accurate estimation. Compared to Gao & Yang (2025), the proposed approaches offer greater flexibility in the selection of coupling gains and impose less stringent solvability conditions.

eess.SY↗
arXiv2026

Distributed State Estimation of Discrete-Time LTI Systems via Jordan Canonical Representation

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a distributed estimation scheme that ensures the asymptotic convergence of the local state estimates to the true system state. The proposed approach relies on the idea that each node reconstructs the components of the system state that are detectable for it through a local Luenberger observer, while employing a consensus-based strategy to estimate the undetectable components. Necessary and sufficient conditions for the existence of a distributed observer that guarantees asymptotic estimation accuracy are derived. Compared with the previous work [2], the proposed design offers greater flexibility in the selection of the coupling gains and leads to a less restrictive set of conditions for solvability.

eess.SY↗
arXiv2026

Fine-Grained 3D Facial Reconstruction for Micro-Expressions

Recent advances in 3D facial expression reconstruction have demonstrated remarkable performance in capturing macro-expressions, yet the reconstruction of micro-expressions remains unexplored. This novel task is particularly challenging due to the subtle, transient, and low-intensity nature of micro-expressions, which complicate the extraction of stable and discriminative features essential for accurate reconstruction. In this paper, we propose a fine-grained micro-expression reconstruction method that integrates a global dynamic feature capturing stable facial motion patterns with a locally-enriched feature incorporating multiple informative cues from 2D motions, facial priors and 3D facial geometry. Specifically, we devise a plug-and-play dynamic-encoded module to extract micro-expression feature for global facial action, allowing it to leverage prior knowledge from abundant macro-expression data to mitigate the scarcity of micro-expression data. Subsequently, a dynamic-guided mesh deformation module is designed for extracting aggregated local features from dense optical flow, sparse landmark cues and facial mesh geometry, which adaptively refines fine-grained facial micro-expression without compromising global 3D geometry. Extensive experiments on micro-expression datasets demonstrate that our method consistently outperforms state-of-the-art methods in both geometric accuracy and perceptual detail.

cs.CV↗
arXiv2026

Morphology-Independent Facial Expression Imitation for Human-Face Robots

Accurate facial expression imitation on human-face robots is crucial for achieving natural human-robot interaction. Most existing methods have achieved photorealistic expression imitation through mapping 2D facial landmarks to a robot's actuator commands. Their imitation of landmark trajectories is susceptible to interference from facial morphology, which would lead to a performance drop. In this paper, we propose a morphology-independent expression imitation method that decouples expressions from facial morphology to eliminate morphological influence and produce more realistic expressions for human-face robots. Specifically, we construct an expression decoupling module to learn expression semantics by disentangling the expression representation from the morphology representation in a self-supervised manner. We devise an expression transfer module to map the representations to the robot's actuator commands through a learning objective of perceiving expression errors, producing accurate facial expressions based on the learned expression semantics. To support experimental validation, a custom-designed and highly expressive human-face robot, namely Pengrui, is developed to serve as an experimental platform for realistic expression imitation. Extensive experiments demonstrate that our method enables the human-face robot to reproduce a wide range of human-like expressions effectively. All code and implementation details of the robot will be released.

cs.RO↗