arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

At least 37 records · Page 2Linked to original sources

arXiv2026

An Asymptotic-Preserving Dynamical Low-Rank Semi-Lagrangian Method for Multiscale Linear Kinetic Transport Equations

In this paper, we develop an asymptotic-preserving (AP) dynamical low-rank semi-Lagrangian method for multiscale linear kinetic transport equations. The method combines the large-time-step capability of semi-Lagrangian discretizations with the storage and cost reduction provided by low-rank representations. The proposed scheme couples an approximate macroscopic density update with the basis update Galerkin integrator for the kinetic distribution. To retain the reduced complexity in the semi-Lagrangian flux evaluation, the flux derivative is computed through a sampled angular quadrature strategy. We establish an unconditional stability analysis of the full-quadrature low-rank scheme in the constant-coefficient case. The error induced by angular sampling in the flux derivative is quantified. The resulting scheme is shown to be AP in the diffusive limit. Numerical experiments, including high-dimensional test cases, demonstrate that the proposed method is AP, stable under large time steps, and computationally efficient across kinetic and diffusive regimes.

math.NA↗

arXiv2026

Weighted Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Methods for Conservation Laws

In this paper, we propose a weighted inverse Lax-Wendroff (WILW) boundary treatment for the discontinuous Galerkin (DG) method on unfitted meshes to efficiently solve hyperbolic conservation laws in complex geometries. The proposed method employs the standard DG scheme for interior cells and reconstructs high-order approximation polynomials via the ILW principle for cut cells near boundaries to impose numerical boundary conditions, effectively eliminating the time-step restriction typically caused by small cut cells. In particular, to address the sensitivity of numerical errors to the geometric size of cut cells in the basic ILW scheme, we raise the reconstruction order at the boundary, ensuring that accuracy becomes independent of the cut-cell size. Furthermore, it incorporates a weighted least-squares reconstruction to reduce the need for complex high-order boundary derivatives during construction. As a result, the method maintains high-order accuracy while significantly improving computational efficiency for multi-dimensional problems. Finally, the stability of the proposed method is theoretically validated through linear stability analysis, and the effectiveness and robustness of the proposed scheme are numerically verified through a series of one-dimensional and two-dimensional numerical experiments for scalar and system equations.

math.NA↗

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

Break the Block: Dynamic-size Reasoning Blocks for Diffusion Large Language Models via Monotonic Entropy Descent with Reinforcement Learning

Recent diffusion large language models (dLLMs) have demonstrated both effectiveness and efficiency in reasoning via a block-based semi-autoregressive generation paradigm. Despite their progress, the fixed-size block generations remain a critical bottleneck for effective and coherent reasoning. 1. From a global perspective, different reasoning tasks would correspond to different optimal decoding block sizes, which makes a ``one-size-fits-all'' assumption ineffective. 2. Even within a single reasoning task, the rigid block partitioning would break the logical flow and reduce reasoning coherence. Through empirical observations, we reveal that for block-wise entropy, incorrect reasoning exhibits a fluctuating and unsteady trend between blocks, whereas the correctly generated tasks follow a consistent descending trend. Therefore, this paper proposes b1, a novel post-training framework for dLLMs that learns dynamic-size reasoning blocks via a Monotonic Entropy Descent objective with reinforcement learning to enhance reasoning coherence.b1 integrates seamlessly as a plug-and-play module with existing dLLM's post-training algorithms. Extensive experiments across various reasoning benchmarks showcase b1's consistent improvement over existing fixed-size block baselines. Our code has been released at https://github.com/YanJiangJerry/Block-R1.

cs.LG↗

arXiv2026

GFMate: Empowering Graph Foundation Models with Test-time Prompt Tuning

Graph prompt tuning has shown great potential in graph learning by introducing trainable prompts to enhance the model performance in conventional single-domain scenarios. Recent research has extended graph prompts to improve Graph Foundation Models (GFMs) by few-shot tuning auxiliary prompts. Despite their progress, most existing methods embed source-domain information into prompts, which serve either as input to GFMs or encoded during model pre-training. Such prompt entanglement with specific source domains and GFM pre-training strategy restricts their generalisability to other domains and different GFMs. Furthermore, existing GFM prompts merely rely on few-shot tuning for adaptation, neglecting the rich information in unlabelled target domain test data. Motivated by these insights, this paper aims to empower GFMs with pre-training-agnostic test-time graph prompt tuning, named GFMate. GFMate introduces centroid and layer prompts applied after pre-training on target domains, avoiding entanglement with specific source domains and model pre-training. In addition, a test-time complementary learning objective is devised to exploit both labelled and unlabelled target domain data for effective test-time prompt tuning. Extensive experiments on 12 benchmark datasets demonstrate the superior performance and efficiency of GFMate, achieving improvements of up to 30.63%. Code is available at https://github.com/YanJiangJerry/GFMate.

cs.LG↗

arXiv2026

Determining evolutionary equations from a single passive boundary observation

We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown medium without active inputs. The goal is the simultaneous recovery of coupled unknowns (sources and coefficients) from severely limited data. Unlike active methods with rich, structured inputs, passive observation poses two core challenges: minimal information and intrinsic coupling of multiple unknowns. Consequently, such problems remain largely open and unsystematically studied. We develop a unified framework based on integral identities, harmonic and microlocal analysis, and low-/high-frequency asymptotics. This approach yields the first systematic resolution for second-order hyperbolic, parabolic, and Schrödinger equations under a single coherent method. The key condition requires the measurement dataset's cardinality to exceed the unknowns' by at least one dimension, providing room to decouple unknowns and linearize the nonlinear inverse problem. Our unique identifiability results subsume all existing literature and cover more general configurations of practical interest. This framework complements classical theories and opens a promising new direction for future development.

math.AP↗

arXiv2026

False Reality: Uncovering Sensor-induced Human-VR Interaction Vulnerability

Virtual Reality (VR) techniques, serving as the bridge between the real and virtual worlds, have boomed and are widely used in manufacturing, remote healthcare, gaming, etc. Specifically, VR systems offer users immersive experiences that include both perceptions and actions. Various studies have demonstrated that attackers can manipulate VR software to influence users' interactions, including perception and actions. However, such attacks typically require strong access and specialized expertise. In this paper, we are the first to present a systematic analysis of physical attacks against VR systems and introduce False Reality, a new attack threat to VR devices without requiring access to or modification of their software. False Reality disturbs VR system services by tampering with sensor measurements, and further spoofing users' perception even inducing harmful actions, e.g., inducing dizziness or causing users to crash into obstacles, by exploiting perceptual and psychological effects. We formalize these threats through an attack pathway framework and validate three representative pathways via physical experiments and user studies on five commercial VR devices. Finally, we further propose a defense prototype to mitigate such threats. Our findings shall provide valuable insights for enhancing the security and resilience of future VR systems.

cs.CR↗

arXiv2026

RAG-Match: Retrieval-Augmented Knowledge Injection and Hierarchical Reasoning for Calibrated Semantic Relevance

Semantic relevance judgment for search is particularly challenging in knowledge-intensive scenarios, where accurate ranking requires not only semantic matching but also background grounding, multi-step reasoning, and well-calibrated decision boundaries. Existing relevance models mainly rely on direct label supervision or shallow semantic similarity, which limits their ability to handle implicit intent, factual equivalence, and fine-grained relevance distinctions. To address this issue, we propose \textsc{RAG-Match}, a three-stage framework that integrates knowledge-augmented pretraining, hierarchical reasoning alignment, and preference-based decision calibration for relevance modeling. The key idea is to first strengthen query-centered semantic grounding, then align the model with structured relevance reasoning, and finally correct decision-level inconsistencies in difficult boundary cases. Experimental results on a real-world search relevance benchmark show that \textsc{RAG-Match} consistently outperforms strong LLM-based baselines across multiple ranking metrics, demonstrating the effectiveness of combining knowledge injection, reasoning supervision, and preference optimization for fine-grained relevance judgment.

cs.IR↗

arXiv2026

NaviAgent: Graph-Driven Bilevel Planning for Scalable Tool Orchestration

Large Language Models (LLMs) increasingly act as function-call agents that invoke external tools to tackle tasks beyond their static knowledge. However, they typically invoke tools one at a time without a global view of task structure. As tools often depend on one another, this leads to error accumulation and poor scalability, particularly when scaling to hundreds or thousands of tools. To address these limitations, we propose NaviAgent, an explicit bilevel architecture that decouples task planning from tool execution through graph-based modeling of tool relations. At the planning level, the LLM-based agent decides whether to respond directly, clarify intent, or retrieve and execute a toolchain independent of inter-tool complexity. At the execution level, a Tool World Navigation Model (TWNM) encodes structural and behavioral relations among tools, steering the agent to compose scalable and robust invocation sequences. Incorporating feedback from real tool interactions, NaviAgent achieves closed-loop alignment between planning and execution, enabling adaptive navigation in large-scale tool ecosystems. Evaluations on API-Bank and ToolBench show consistent improvements in task success rate (TSR), with TWNM yielding an average gain of 13.1 points on complex tasks. Further tests on 50 real APIs across 7 domains show consistent gains of 4.3--12.0 points, with fewer steps and latency, demonstrating robust generalization under real-world dynamics.

cs.AI↗

arXiv2026

A Comparative Evaluation of Structural Topic Models and BERTopic for Short, Open-Ended Survey Responses

Topic modeling in applied psychology increasingly spans two methodological traditions: probabilistic bag-of-words models and newer embedding-based approaches. Yet many evaluations of these methods rely on longer and cleaner benchmark corpora, leaving less guidance for short, open-ended survey responses. This paper compares Structural Topic Models (STM), a probabilistic topic model, and BERTopic, an embedding-based model, for analyzing open-ended survey responses. We evaluated three STM conditions and five BERTopic conditions, varying typographical correction, stemming, embedding choice, and contextual augmentation, a strategy we introduced to provide additional semantic context for very short responses. Results indicate that BERTopic consistently produced higher topic coherence than STM, with contextual augmentation yielding the strongest performance gains. In contrast, higher-dimensional embeddings alone did not improve coherence and were associated with greater data loss. Qualitative evaluation showed that BERTopic generated more interpretable and stable topics, while STM topics were often broader and more mixed. However, STM provides stronger support for inferential covariate analysis, whereas BERTopic covariate comparisons are primarily descriptive. These findings suggest that STM and BERTopic offer complementary strengths. We conclude with practical guidance for selecting and combining topic modeling approaches in applied social science research.

cs.CL↗

arXiv2026

Block-R1: Rethinking the Role of Block Size in Multi-domain Reinforcement Learning for Diffusion Large Language Models

Recently, reinforcement learning (RL) has been widely applied during post-training for diffusion large language models (dLLMs) to enhance reasoning with block-wise semi-autoregressive generation. Block size has therefore become a vital factor in dLLMs, since it determines the parallel decoding granularity and affects the rollout trajectories during RL optimisation, e.g., GRPO. Instead of investigating the effect of block size during inference on individual domains, this paper studies block size from a domain conflict perspective for dLLM RL post-training in multi-domain scenarios. The main contributions are: (1) a formulation of domain block size conflict in multi-domain RL for dLLMs, which will largely affect the post-training effectiveness for rollout-based RL methods; (2) a novel dataset, Block-R1-41K is constructed with a best-improved training block size for each sample, which also induces a Block Size Conflict Score to quantitatively measure the domain conflict; (3) a new benchmark, Block-R1, for flexible RL post-training for dLLMs in both single and cross domain; and (4) a simple yet powerful cross-domain post-training method with sample-level best-improved training block sizes. Extensive experiments on 13 distinct datasets, 7 latest RL algorithms and diverse dLLM backbones are comprehensively covered in Block-R1. The benchmark is open-sourced at https://github.com/YanJiangJerry/Block-R1 with the dataset released at https://huggingface.co/datasets/YanJiangJerry/Block-R1-41K.

cs.LG↗

arXiv2026

Hierarchical Attacks for Multi-Modal Multi-Agent Reasoning

Multi-modal multi-agent systems (MM-MAS) have gained increasing attention for their capacity to enable complex reasoning and coordination across diverse modalities. As these systems continue to expand in scale and functionality, investigating their potential vulnerabilities has become increasingly important. However, existing studies on adversarial attacks in multi-agent systems primarily focus on isolated agents or unimodal settings, leaving the vulnerabilities of MM-MAS largely underexplored. To bridge this gap, we introduce HAM$^{3}$, a Hierarchical Attack framework for multi-modal multi-agent systems that decomposes attacks into three interconnected layers. Specifically, at the perception layer, HAM$^{3}$ mounts attacks by perturbing visual inputs, textual inputs, and their fused visual-textual representations. At the communication layer, it performs communication-level attacks that corrupt message content and interaction topology, such as manipulating shared context or communication links to distort collective information flow. At the reasoning layer, it conducts reasoning-level attacks that interfere with each agent's cognitive pipeline, biasing reasoning trajectories and ultimately compromising final decisions. We evaluate HAM$^{3}$ on the GQA benchmark through multi-agent systems built on distinct reasoning paradigms including ReAct, Plan-and-Solve, and Reflexion. Experiments demonstrate that our framework achieves an Attack Success Rate of up to 78.3%, with reasoning-layer attacks being the most effective. More than half of the successful attacks lead multiple agents to produce consistent errors. These findings offer valuable insights for building more robust and interpretable multi-agent intelligence.

cs.AI↗

arXiv2026

TaFall: Balance-Informed Fall Detection via Passive Thermal Sensing

Falls are a major cause of injury and mortality among older adults, yet most incidents occur in private indoor environments where monitoring must balance effectiveness with privacy. Existing privacy-preserving fall detection approaches, particularly those based on radio frequency sensing, often rely on coarse motion cues, which limits reliability in real-world deployments. We introduce TaFall, a balance-informed fall detection system based on low-cost, privacy-preserving thermal array sensing. The key insight is that TaFall models a fall as a process of balance degradation and detects falls by estimating pose-driven biomechanical balance dynamics. To enable this capability from low-resolution thermal array maps, we propose (i) an appearance-motion fusion model for robust pose reconstruction, (ii) physically grounded balance-aware learning, and (iii) pose-bridged pretraining to improve robustness. TaFall achieves a detection rate of 98.26% with a false alarm rate of 0.65% on our dataset with over 3,000 fall instances from 35 participants across diverse indoor environments. In 27 day deployments across four homes, TaFall attains an ultra-low false alarm rate of 0.00126% and a pilot bathroom study confirms robustness under moisture and thermal interference. Together, these results establish TaFall as a reliable and privacy-preserving approach to fall detection in everyday living environments.

cs.CV↗

arXiv2026

A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws

This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell averages of classical DG solutions with forward Euler time stepping satisfy an ``entropy-stable-like'' property. Building on this result, fully-discrete entropy stability is rigorously enforced through a simple Zhang--Shu-type scaling limiter [45] applied as a post-processing step, without modifying the underlying spatial discretization. Furthermore, the proposed methodology can simultaneously enforce multiple cell entropy inequalities, a capability unavailable in existing ES DG schemes. High-order accuracy in time is achieved by using strong-stability-preserving (SSP) multistep methods. Theoretically, we prove that the proposed scheme indeed maintains high-order accuracy and establish a Lax--Wendroff-type theorem guaranteeing that the limit of the numerical solutions, if it exists, satisfies the desired entropy inequality. Extensive numerical tests for scalar equations and systems, including the nonconvex Buckley--Leverett problem and extreme examples of Euler equations, demonstrate optimal accuracy, enforcement of multiple entropy conditions, and strong robustness.

math.NA↗

arXiv2026

Spectral properties of surface-localized transmission eigenmodes and applications to inverse scattering problems

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of eigenfunctions and their spectral properties. Though primarily explored within a radially symmetric framework, this study provides rigorous theoretical insights, advances new perspectives in this emerging field, and offers meaningful implications for inverse scattering theory.

math.AP↗

arXiv2026

Learning-Augmented Primal-Dual Control Design for Secondary Frequency Regulation

Frequency stability is fundamental to the secure operation of power systems. With growing uncertainty and volatility introduced by renewable generation, secondary frequency regulation must now deliver enhanced performance not only in the steady state but also during transients. This paper presents a systematic framework to embed learning in the design of a primal-dual controller that provides provable (potentially exponential) stability and steady-state optimality, while simultaneously improving key transient metrics, including frequency nadir and control effort, in a data-driven manner. In particular, we employ the primal-dual dynamics of an optimization problem that encodes steady-state objectives to realize secondary frequency control with asymptotic stability guarantee. To augment transient performance of the controller via learning, a change of variables on control inputs, which will be deployed by neural networks, is proposed such that under mild conditions, stability and steady-state optimality are preserved. It further allows us to define a learning goal that accounts for the exponential convergence rate, frequency nadir and accumulated control effort, and use sample trajectories to enhance these metrics. Simulation results validate the theories and demonstrate superior transient performance of the learning-augmented primal-dual controller.

eess.SY↗

arXiv2026

Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states

We develop an entropy-stable nodal discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced with respect to general equilibrium solutions, including both hydrostatic and moving equilibria. The core of our approach lies in a novel treatment of the gravitational source term, combining entropy-conservative numerical fluxes with a linear entropy correction. In addition, the proposed formulation is carefully designed to ensure compatibility with a positivity-preserving limiter. We provide a rigorous theoretical analysis to establish the accuracy and structure-preserving properties of the proposed scheme. Extensive numerical experiments confirm the robustness and efficiency of the scheme.

math.NA↗

arXiv2026

Temporal-Stability-Enhanced and Energy-Stable Dynamical Low-Rank Approximation for Multiscale Linear Kinetic Transport Equations

In this paper, we develop an asymptotic-preserving dynamical low-rank method for the multiscale linear kinetic transport equation. The proposed scheme is unconditionally stable in the diffusive regime while preserving the correct asymptotic behavior, and can achieve significant reductions in computational cost through a low-rank representation and large time step stability. A low-rank formulation consistent with the discrete energy is introduced under the discrete ordinates discretization, and energy stability of the resulting scheme is established. Numerical experiments confirm the energy stability and demonstrate that the method is efficient while maintaining accuracy across different regimes and capturing the correct asymptotic limits.

math.NA↗