arXiv subjects

Jiajun Wang

Publications and source records attributed to Jiajun Wang.

At least 19 recordsLinked to original sources

arXiv2026

Differentially Private Distributed Optimization via the Intrinsic Randomness of Zeroth-Order Estimators: Sampling Geometry, Convergence, and Privacy Guarantees

Distributed zeroth-order optimization has gained increasing attention in applications where exact gradients are computationally expensive or unavailable. However, the iterative exchange of local decision variables makes distributed networks vulnerable to inference attacks. While differential privacy provides a rigorous framework for privacy protection, conventional approaches generally require additional random noise, which inevitably affects optimization accuracy. In this paper, we investigate whether the randomness inherent in zeroth-order estimation can itself provide privacy protection. We develop a distributed zeroth-order gradient descent method that integrates consensus updates with a ball-uniform two-point gradient estimator. Our theoretical analysis shows that our algorithm attains standard convergence guarantees in both online and offline optimization settings. We then characterize the relevant probability distributions of the associated privacy mechanism, and establish differential privacy guarantees for both the online and offline optimization settings. These results reveal the potential of intrinsic zeroth-order randomness for privacy protection.

math.OC↗

arXiv2026

Global Stability of the Kolmogorov--Zakharov Spectrum for the Wave Kinetic Equation

We prove global nonlinear stability near the mass Kolmogorov--Zakharov spectrum $f_M(ω)=ω^{-7/6}$ for the isotropic cubic wave kinetic equation, including small time-dependent external forces. For sufficiently small initial perturbations and forcing, the solution remains uniformly close to $f_M$ for all time in a weighted norm. This norm allows $f(t,ω)\sim a_0(t)ω^{-7/6}$ as $ω\to0$ and $f(t,ω)\sim a_\infty(t)ω^{-7/6}$ as $ω\to\infty$. When the external force $ϕ$ is independent of time, the solution converges at an algebraic rate to a stationary solution in weaker weighted norms. We also give a necessary and sufficient condition on the initial perturbation for convergence in the original weighted norm. These results resolve, for small perturbations of the Kolmogorov--Zakharov spectrum, the question of convergence to a stationary solution under time-independent forcing raised by Collot, Dietert, and Germain (arXiv:2208.00947, Section 1.3). To establish this stability, the collision integral is expanded around $a_0(t)f_M$ at low frequencies and $a_\infty(t)f_M$ at high frequencies, separating it into a linear term with time-dependent coefficients and a nonlinear remainder. This decomposition yields improved control of the nonlinear remainder. The main difficulty is that $a_0(t)$ may vary in time, so the linear operator itself changes with time and its evolution cannot be represented by the semigroup of a single fixed operator. To address this difficulty, we use a parametrix construction to explicitly construct the evolution operator $U_{a_0,a_\infty}$ and establish the required uniform bounds. Moreover, our arguments provide a general framework for proving global stability that may also apply to other evolution equations.

math.AP↗

arXiv2026

Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on $\mathbb{T}^d$

We study polynomial growth of Sobolev norms for the defocusing fractional nonlinear Schrödinger equation on the standard torus $\mathbb{T}^d$, $d \ge 2$. Uniform stationary phase and a frequency-dependent subdivision of time give Strichartz estimates which yield local well-posedness and, for the cubic equation, unconditional polynomial growth when $α> d^2/(d+2)$. The local theory and growth estimates extend to every integer-power nonlinearity $|u|^{2σ}u$, with explicit thresholds and growth exponents. In the final section, we identify a further approach to improving the polynomial growth bounds. By combining our arguments with the circle method, we obtain stronger Strichartz estimates, which yield local well-posedness at lower regularity and improved polynomial growth bounds.

math.AP↗

arXiv2026

Sharp Shell-Type Bilinear Decoupling and Improved Strichartz Estimates on Tori

We establish sharp bilinear decoupling under shell-type Fourier support restrictions and show that its optimal coefficient need not be optimal for the corresponding periodic bilinear Strichartz estimate. For $N_1\geq N_2$, the sharp decoupling coefficient is $N_2^{(2d-7)/4}(1+N_2^2/N_1)^{1/4}$, up to an $N_2^\varepsilon$ loss. This yields a shell-type bilinear Strichartz estimate with the same coefficient on every fixed rectangular torus, including irrational tori. On the standard square torus, we improve this Strichartz estimate for $d\geq6$, obtaining the optimal coefficient $(N_2^{d-4}+N_2^{d-2}/N_1)^{1/2}$, up to an $N_2^\varepsilon$ loss. The proof combines localization in spatial frequency and energy, a circle-method estimate for the localized high-frequency factor, and a linear estimate on arbitrarily oriented strips. As applications, we obtain estimates for toral eigenfunctions, mixed additive energy, and separated nonlinear smoothing for the periodic Zakharov system.

math.AP↗

arXiv2026

RSI-Master: Structuring Experiments to Guide Autonomous Model Improvement

Recursive self-improvement (RSI) seeks to enable AI systems to participate in improving their own capabilities. A concrete pathway is autonomous model development, where agents iteratively explore post-training strategies to improve a base model. This setting faces two challenges: agents may exploit open-ended experimental actions through hacking, and repeated experimentation may lead to strategy lock-in, where an early direction is refined rather than reconsidered. We introduce RSI-Master, which addresses the two challenges at two levels: regularize step-wise actions, avoiding hacking behaviors, and promote well-structured exploration of research directions, avoiding strategy lock-in. RSI-Master consists of an Experiment OS, which enables regularized experimental actions and maintains persistent, traceable experimental records, and Reviewer-Guided Research Orchestration, which organizes Workers and Reviewers in a dynamically growing research DAG. Workers explore diverse research directions and Reviewers compare evidence across related experiments for subsequent explorations. On PostTrainBench with Qwen3-4B-Base, it averages 54.49 versus 46.53 for the strongest agent baseline, with a 0.0\% hacking rate. Scaling to 35B model, RSI-Master surpasses the human-developed Instruct model on LiveCodeBench-v6 (41.21 vs. 37.36) and SciCode, and reaches a nonzero score on HorizonMath, a benchmark of unsolved research problems on which most frontier models score near zero.

cs.AI↗

arXiv2026

ABSeeker: Training Long-Horizon Search Agents via Answer-Backtracked Credit Assignment

Long-horizon search agents must make multiple sequential actions (steps) to search, retrieve, verify, and integrate evidence to reach a final answer. However, existing methods for training these agents typically treat all steps within a trajectory uniformly during both supervised fine-tuning (SFT) and reinforcement learning (RL), failing to distinguish useful actions from erroneous or redundant ones. In this paper, we propose Answer-Backtracked Credit Assignment (ABC), a fine-grained credit assignment framework for training long-horizon search agents by converting sparse trajectory-level outcomes into dense step-level supervision that rewards useful actions (even in failed trajectories) while suppressing erroneous or redundant actions. Specifically, given a potentially obscure query and its corresponding ground-truth answer, ABC first performs Answer-Backtracked Clue Recovery, which traces back from the answer to recover intermediate clues required to solve the question. It then applies Clue-Anchored Step Scoring to evaluate each search step against these clues, converting sparse binary outcome supervision into dense step-level rewards. Based on these rewards, we develop ABC-SFT, which reweights the loss of each turn, and ABC-GRPO, which uses the step-level scores as rewards in GRPO. Building on this framework, we train ABSeeker based on Qwen3.5-4B with only 8.5k examples. ABSeeker achieves 37.3% on BrowseComp and 39.1% on BrowseComp-ZH. With context management, the scores further improve to 55.3% and 52.9%, respectively, significantly outperforming same-scale (4B) agents and even matching the performance of larger ones (approximately 30B). These results demonstrate the effectiveness of answer-backtracked step-level credit assignment for training long-horizon search agents.

cs.AI↗

arXiv2026

LoViF 2026 Challenge on Human-oriented Semantic Image Quality Assessment: Methods and Results

This paper reviews the LoViF 2026 Challenge on Human-oriented Semantic Image Quality Assessment. This challenge aims to raise a new direction, i.e., how to evaluate the loss of semantic information from the human perspective, intending to promote the development of some new directions, like semantic coding, processing, and semantic-oriented optimization, etc. Unlike existing datasets of quality assessment, we form a dataset of human-oriented semantic quality assessment, termed the SeIQA dataset. This dataset is divided into three parts for this competition: (i) training data: 510 pairs of degraded images and their corresponding ground truth references; (ii) validation data: 80 pairs of degraded images and their corresponding ground-truth references; (iii) testing data: 160 pairs of degraded images and their corresponding ground-truth references. The primary objective of this challenge is to establish a new and powerful benchmark for human-oriented semantic image quality assessment. There are a total of 58 teams registered in this competition, and 6 teams submitted valid solutions and fact sheets for the final testing phase. These submissions achieved state-of-the-art (SOTA) performance on the SeIQA dataset.

cs.CV↗

arXiv2026

ASTRA-Net: Anatomy-Specific Transfer and Representation Alignment for Drug-Induced Sleep Endoscopy Segmentation

Quantitative drug-induced sleep endoscopy (DISE) requires reliable airway boundaries at specific anatomical levels. Pixel-level DISE annotations are scarce, and manual contouring limits the scalability of quantitative assessment. To address this limitation, we developed ASTRA-Net for known-plane DISE segmentation with limited real annotations. Stage 1 aligned intermediate ConvNeXt-Base representations from 14,250 unlabeled virtual endoscopy frames derived from computed tomography and real DISE frames. Virtual images were used only for feature alignment. Stage 2 fine-tuned four independent UNet++ decoders on 401 real annotated frames. Structured zero-mask supervision constrained incompatible plane outputs and invalid frames. Six alignment configurations used maximum mean discrepancy, domain adversarial learning, or both objectives. On a hold-out evaluation set of 100 frames, the five-model MMD-only segmentation ensemble achieved a mean Dice of 0.8927, with a 95% image-level bootstrap interval of 0.8631 to 0.9160. The mean intersection over union was 0.8239. A classification- enabled variant of the same alignment configuration reached a restricted four-plane top-1 accuracy of 0.92 on the same hold-out frames. These results indicate that ASTRA-Net can support frame-level, plane-specific DISE boundary delineation when real annotations are limited.

cs.CV↗

arXiv2026

Local existence of strong solutions to the capillary wave kinetic equation

In this paper, we follow Pan-Wu's idea [PW26] to prove local existence of the capillary wave kinetic equation. To be more specific, we will linearize the nonlinear operator and decompose it into dissipative part and bounded part. The main difficulty comes from the fact that the collision kernel has less symmetry compared with the one in gravity water wave. To overcome it, we are required to choose and pair each term delicately.

math.AP↗

arXiv2026

HyperTool: Beyond Step-Wise Tool Calls for Tool-Augmented Agents

Tool-augmented LLM agents commonly rely on step-wise atomic tool calls, where each invocation, observation, and value transfer is exposed in the main reasoning trace. This creates an \emph{execution-granularity mismatch}: locally deterministic tool workflows are unfolded into repeated model-visible decisions, consuming context and forcing the model to manage low-level dataflow in the trace. We introduce \textbf{HyperTool}, a unified executable MCP-style tool interface that changes the model-visible unit of tool execution. A model invokes HyperTool with a code block that can call existing tools through their original schemas, manipulate returned values, and pass intermediate results locally, folding deterministic tool subroutines into a single outer call. To train models to use this interface, we synthesize HyperTool-format trajectories from cross-tool compositional tasks and verify them in real MCP environments. On MCP-Universe, HyperTool improves average accuracy from 15.69\% to 35.29\% on Qwen3-32B and from 9.93\% to 33.33\% on Qwen3-8B, and surpass GPT-OSS and Kimi-k2.5 on average accuracy, showing that our HyperTool can substantially improve multi-step tool use.

cs.CL↗

arXiv2026

Global well-posedness of cubic fractional Schrödinger equation with rough data

In this paper, we apply the I-method to establish global well-posedness for the fractional nonlinear Schrödinger equation with initial data u_0 \in H^s(R^d) for s <α/2, i.e., below the energy threshold. Moreover, for radial initial data, we combine a modiffed Morawetz estimate-recovered via Balakrishnan's formula-with the I-method to obtain improved results. In the same spirit, we employ the "upside-down" I-method to derive polynomial-in-time growth bounds for the higher-order Sobolev norm. The main difffculty stems from the fact that Strichartz estimates for the fractional Schrödinger equation has a loss of derivatives, and the problem is always L^2-supercritical, thereby requiring more delicate analysis.

math.AP↗

arXiv2026

Taming System Complexity: Demystifying Software Engineering Agents in Diagnosing Linux Kernel Faults

The Linux kernel is a critical system, serving as the foundation for numerous systems. Bugs in the Linux kernel can cause serious consequences, affecting billions of users. Fault localization (FL), which aims at identifying the buggy code elements in software, plays an essential role in software quality assurance. While recent LLM agents have achieved promising accuracy in FL on recent benchmarks like SWE-bench, it remains unclear how well these methods perform in the Linux kernel, where FL is much more challenging due to the large-scale code base, limited observability, and diverse impact factors. In this paper, we introduce LinuxFLBench, a FL benchmark constructed from real-world Linux kernel bugs. We conduct an empirical study to assess the performance of state-of-the-art LLM agents on the Linux kernel. Our initial results reveal that existing agents struggle with this task, achieving a best top-1 accuracy of only 41.6% at file level. To address this challenge, we propose LinuxFL$^+$, an enhancement framework designed to improve FL effectiveness of LLM agents for the Linux kernel. LinuxFL$^+$ substantially improves the FL accuracy of all studied agents (e.g., 7.2% - 11.2% accuracy increase) with minimal costs.

cs.AI↗

arXiv2026

LongSeeker: Elastic Context Orchestration for Long-Horizon Search Agents

Long-horizon search agents must manage a rapidly growing working context as they reason, call tools, and observe information. Naively accumulating all intermediate content can overwhelm the agent, increasing costs and the risk of errors. We propose that effective context management should be adaptive: parts of the agent's trajectory are maintained at different levels of detail depending on their current relevance to the task. To operationalize this principle, we introduce Context-ReAct, a general agentic paradigm for elastic context orchestration that integrates reasoning, context management, and tool use in a unified loop. Context-ReAct provides five atomic operations: Skip, Compress, Rollback, Snippet and Delete, which allow the agent to dynamically reshape its working context, preserving important evidence, summarizing resolved information, discarding unhelpful branches, and controlling context size. We prove that the Compress operator is expressively complete, while the other specialized operators provide efficiency and fidelity guarantees that reduce generation cost and hallucination risk. Building on this paradigm, we develop LongSeeker, a long-horizon search agent fine-tuned from Qwen3-30B-A3B on 10k synthesized trajectories. Across four representative search benchmarks, LongSeeker achieves 61.5% on BrowseComp and 62.5% on BrowseComp-ZH, substantially outperforming Tongyi DeepResearch (43.2% and 46.7%) and AgentFold (36.2% and 47.3%). These results highlight the potential of adaptive context management, showing that agents can achieve more reliable and efficient long-horizon reasoning by actively shaping their working memory.

cs.AI↗

arXiv2026

MIST-RL: Mutation-based Incremental Suite Testing via Reinforcement Learning

Large Language Models (LLMs) often fail to generate correct code on the first attempt, which requires using generated unit tests as verifiers to validate the solutions. Despite the success of recent verification methods, they remain constrained by a "scaling-by-quantity" paradigm. This brute-force approach suffers from a critical limitation: it yields diminishing returns in fault detection while causing severe test redundancy. To address this, we propose MIST-RL (Mutation-based Incremental Suite Testing via Reinforcement Learning), a framework that shifts the focus to "scaling-by-utility". We formulate test generation as a sequential decision process optimized via Group Relative Policy Optimization (GRPO). Specifically, we introduce a novel incremental mutation reward combined with dynamic penalties, which incentivizes the model to discover new faults while it suppresses functionally equivalent assertions. Experiments on HumanEval+ and MBPP+ demonstrate that MIST-RL outperforms state-of-the-art baselines. It achieves a +28.5% higher mutation score while reducing the number of test cases by 19.3%. Furthermore, we show that these compact, high-utility tests serve as superior verifiers, which improves downstream code reranking accuracy on HumanEval+ by 3.05% over the SOTA baseline with 10 candidate samples. The source code and data are provided in the supplementary material.

cs.AI↗

arXiv2026

Restriction estimates for 2D surfaces of finite type 3 and applications to dispersive equations

In this paper, we prove the restriction estimates for 2D surfaces S:= {(xi1, xi2, xi1^3 +/- xi2^3) : (xi1, xi2) in [0,1]^2} by reducing to Wang-Wu's result on the perturbed paraboloid and to the results on the perturbed hyperboloid obtained by Buschenhenke, Müller, and Vargas, as well as by Guo and Oh. The method is based on the rescaling technique developed in [LMZ21]. Besides, we will use the estimates to give a better analysis for discrete nonlinear Schrödinger equations.

math.AP↗

arXiv2026

Emerging Multidimensional Real-Space Topological Structures at Chiral Bound States in the Continuum

As widely studied topological singularities, bound states in the continuum (BICs) have revealed rich physical properties through their momentum-space topology. Here, we reveal and experimentally demonstrate that magnetically induced chiral BICs possess multidimensional topological structures extending into real space. We design and realize a gyromagnetic photonic crystal slab where magnetic field breaks the time-reversal symmetry and lifts the degeneracy of BICs, creating a pair of chiral BICs with opposite circular polarizations. Near-field scanning measurements reveal phase vortices with quantized topological charges, spatially distributed near-field chirality, and skyrmionic Stokes textures arising from magnetic control. Our work unveils a previously unexplored dimension of BIC topology and establishes gyromagnetic photonic crystals as versatile platforms for manipulating complex topological states.

physics.optics↗

arXiv2026

ImmuniFraug: A Metacognitive Intervention Anti-Fraud Approach to Enhance Undergraduate Students' Cyber Fraud Awareness

Cyber fraud now constitutes over half of criminal cases in China, with undergraduate students experiencing a disproportionate rise in victimization. Traditional anti-fraud training remains predominantly passive, yielding limited engagement and retention. This paper introduces ImmuniFraug, a Large Language Model (LLM)-based metacognitive intervention that delivers immersive, multimodal fraud simulations integrating text, voice, and visual avatars across ten prevalent fraud types. Each scenario is designed to replicate real-world persuasion tactics and psychological pressure, while post-interaction debriefs provide grounded feedback in protection motivation theory and reflective prompts to reinforce learning. In a controlled study with 846 Chinese undergraduates, ImmuniFraug was compared to official text-based materials. Linear Mixed-Effects Modeling (LMEM) reveals that the interactive intervention significantly improved fraud awareness (p = 0.026), successfully providing incremental learning value even when controlling for participants' extensive prior exposure to anti-fraud education, alongside high narrative immersion (M = 56.95/77). Thematic analysis of interviews revealed key effectiveness factors: perceived realism, adaptive deception, enforced time pressure, emotional manipulation awareness, and enhanced self-efficacy. Findings demonstrate that by shifting the focus from passive knowledge acquisition to active metacognitive engagement, LLM-based simulations offer a scalable and ecologically valid new paradigm for anti-fraud training and fostering fraud resilience.

cs.HC↗

arXiv2025

Mono4DEditor: Text-Driven 4D Scene Editing from Monocular Video via Point-Level Localization of Language-Embedded Gaussians

Editing 4D scenes reconstructed from monocular videos based on text prompts is a valuable yet challenging task with broad applications in content creation and virtual environments. The key difficulty lies in achieving semantically precise edits in localized regions of complex, dynamic scenes, while preserving the integrity of unedited content. To address this, we introduce Mono4DEditor, a novel framework for flexible and accurate text-driven 4D scene editing. Our method augments 3D Gaussians with quantized CLIP features to form a language-embedded dynamic representation, enabling efficient semantic querying of arbitrary spatial regions. We further propose a two-stage point-level localization strategy that first selects candidate Gaussians via CLIP similarity and then refines their spatial extent to improve accuracy. Finally, targeted edits are performed on localized regions using a diffusion-based video editing model, with flow and scribble guidance ensuring spatial fidelity and temporal coherence. Extensive experiments demonstrate that Mono4DEditor enables high-quality, text-driven edits across diverse scenes and object types, while preserving the appearance and geometry of unedited areas and surpassing prior approaches in both flexibility and visual fidelity.

cs.CV↗