Searcharxiv⌕ Search

arXiv subjects

Jun Yan

Publications and source records attributed to Jun Yan.

At least 19 recordsLinked to original sources
arXiv2026

Extremal persistence probabilities of exchangeable sign-invariant random variables

Let $(X_1,\ldots,X_n)$ be a random variable in $(\mathbb{R}\setminus\{0\})^n$ that is both exchangeable and sign-invariant. For every $k\in[n]$, let $S_k=\sum_{i=1}^kX_i$. Define the weak persistence probability as $\mathbb{P}(S_1,\ldots,S_n\geq0)$, and the strong persistence probability as $\mathbb{P}(S_1,\ldots,S_n>0)$. From previous results, the optimal lower bound for $\mathbb{P}(S_1,\ldots,S_n\geq0)$ and the optimal upper bound for $\mathbb{P}(S_1,\ldots,S_n>0)$ are known. We complete the picture by determining the optimal upper bound for $\mathbb{P}(S_1,\ldots,S_n\geq0)$ and the optimal lower bound for $\mathbb{P}(S_1,\ldots,S_n>0)$ as follows. \[\frac{1}{2^n}\binom{n-1}{\lfloor (n-1)/2\rfloor}\leq\mathbb{P}(S_1,\ldots,S_n>0)\leq\frac{1}{4^n}\binom{2n}{n}\leq\mathbb{P}(S_1,\ldots,S_n\geq0)\leq\frac{1}{2^n}\binom{n}{\lfloor n/2\rfloor}.\] In particular, this implies that the weak and strong persistence probabilities of every exchangeable and sign-invariant random variable $(X_1,\ldots,X_n)$ in $(\mathbb{R}\setminus\{0\})^n$ are of the order $n^{-1/2}$. We also obtain some related results, one in the deterministic setting, and one when the random variables are allowed to take the value 0.

math.PR↗
arXiv2026

Robust Community Detection for Noisy Networks with Covariates: Application to Functional Brain Networks

Community detection is fundamental to understanding the modular organization in functional brain networks, yet noise in neuroimaging-derived networks and auxiliary node-level covariates pose critical challenges. Existing methods typically either assume networks are noise-free or ignore covariate information. We propose a Bayesian framework for recovering a shared latent community structure from multiple noisy network realizations and auxiliary covariates. The model combines a degree-corrected stochastic block model for the latent network, a block-structured noise model linking noisy observations to latent edges, and a covariate cluster model for node-level attributes. This specification allows anatomical or functional attributes of regions of interest to contribute information when network signals are weak or sparse. We develop an efficient Markov chain Monte Carlo algorithm for posterior sampling and select the number of communities using the widely applicable information criterion, avoiding prior specification of this quantity. Simulation studies demonstrate improved community recovery relative to existing methods across varying noise levels, covariate signal strengths, and numbers of noisy networks, with larger gains when network noise is moderate to high or only a small number of noisy networks is available. Applications to functional brain networks from the Alzheimer's Disease Neuroimaging Initiative and the Human Connectome Project identify biologically interpretable structures and capture disease-related reorganization and individual-level variation.

stat.ME↗
arXiv2026

EnvHarness: Awakening Static Worlds for Agent Learning

LLM agents learn by interacting with environments, yet these environments are hand-built and static: blind to an agent's weaknesses, and quickly left behind as it improves. While recent environment generation methods attempt to address this, they require domain-specific pipelines, rely on expensive or unreliable verifiers, and still produce static environments. To alleviate the engineering burden of rebuilding environments from scratch, we propose Environment Harness (EnvHarness), a programmable layer of plug-in components that wraps a static environment to reshape its behavior without modifying the underlying logic. Operating through standard interfaces, EnvHarness applies across diverse domains while ensuring every reshaped environment retains its original verifier. To automate this process, we introduce EnvRigger, which treats the target policy as a black box, observing its execution trajectories to synthesize EnvHarness components targeting diagnosed flaws, and validating them via fresh rollouts. Across five benchmarks in four domains, EnvHarness outperforms both original environments and domain-specific environment generation pipelines, achieving up to a 9.0-point improvement on held-out instances with 9.8% fewer execution steps. Furthermore, EnvHarness provides a superior optimization signal for reinforcement learning, enabling continuous, targeted co-evolution of the policy and its environment.

cs.AI↗
arXiv2026

PRM-as-a-Judge 1.5: A Toolkit for Robot Process Assessment

Fine-grained robotic evaluation matters for understanding embodied models, going beyond binary success rates and rule-based process scores. We present PRM-as-a-Judge 1.5, a toolkit for robot process assessment that turns rollout videos into dense progress curves and derives multiple fine metrics. PRM-as-a-Judge 1.5 introduces three metrics, building on version 1.0, that characterize failure-side progress, post-drawdown recovery, and success-side execution quality, helping users understand embodied model capability. Based on the rollout videos from benchmarks, we perform a comprehensive assessment of the embodied models, providing some fine-grained metric results and key findings. We further introduce RoboPulse++ to evaluate the reliability of process reward models (PRM), providing evaluators with a more accurate testing platform. Moreover, we release a user-friendly assessment suite, including the benchmark, metric implementation, and visualization tools, to support reproducible manipulation process evaluation. We call on the community to rethink how robots are evaluated and establish transparent, procedural, and reproducible assessment as a foundation for the next generation of embodied intelligence.

cs.RO↗
arXiv2026

A Mixed-Resonance Counterexample to the Lukic Conjecture

Let $\mu$ be a probability measure on the unit circle with Verblunsky coefficients $\alpha$. Lukic conjectured that a weighted entropy condition with finitely many critical points is equivalent to a decomposition of $\alpha$ into components localized at those points. We give a counterexample for two critical points of multiplicity three, found by GPT-5.6. The construction uses two phase modes with common power-decay exponent $3/20$. The sequence admits the Lukic's decomposition conditions, but its weighted entropy for the corresponding two-point weight equals $-\infty$.

math.CA↗
arXiv2026

AMPBench-MT: A Homology-Controlled Benchmark for Antimicrobial Peptide Potency, Spectrum, and Safety Prediction

Computational AMP discovery is often evaluated through AMP/non-AMP recognition, yet follow-up decisions depend on assay-derived evidence such as target-species potency, hemolysis, toxicity, and selectivity. Existing AMP and peptide benchmarks cover binary recognition, multilabel annotation, assay regression, or broader peptide-model comparison, but they do not jointly place AMP recognition, species-conditioned potency, spectrum, safety-facing proxy endpoints, and cross-endpoint behavior within one sequence-homology-controlled protocol. To address this problem, we introduce AMPBench-MT, a provenance-preserving benchmark that standardizes canonical peptide records and organizes them into binary recognition, species-conditioned pMIC regression, and endpoint-specific potency and safety-facing readouts. Across 161 endpoint-specific model evaluations, high binary performance does not reliably indicate assay-endpoint behavior. Frozen protein-language-model embeddings form the leading pMIC error cluster, while graph and classical regressors remain close. Spectrum labels further reveal that PR-oriented metrics can be misleading under scarce observed negatives, whereas low-toxicity, HC50 hemolysis, and selectivity expose smaller but more assay-facing signals. AMPBench-MT shows that AMP evaluation should move beyond recognition leaderboards toward endpoint-aware evidence auditing. Our proposed benchmark is available at https://huggingface.co/datasets/ZihengZhou06/AMPBench-MT.

cs.LG↗
arXiv2026

Sharp small-deviation inequalities for sums of independent nonnegative random variables

Let $(X_1,\ldots,X_n)$ be independent nonnegative random variables with $\mathbb{E} X_i\le1$, and write $S=\sum_iX_i$. For $\delta>0$, we prove that \[ \mathbb{P}\left(S<\mathbb{E} S+\delta\right)\ge b_{n,\delta}, \] where $b_{n,\delta}=\delta(n/(n+\delta))^n$ for $0<\delta<1$ and $b_{n,\delta}=(1-1/(n+\delta))^n$ for $\delta\ge1$. The bound is sharp for every $n$ and $\delta\ge 1$. In particular, since $b_{n,\delta} \ge e^{-1}$ for $\delta \ge 1$, our result proves Feige's conjecture [Feige, 2004] in the affirmative for $\delta\ge 1$. The proof is found by ChatGPT 5.6 Pro. It combines the exact Dirichlet calibration theorem of Vlassis and Thomas [Vlassis and Thomas, 2026], which resolves Gaffke's conjecture in statistics, with results in convex geometry including Gr\"unbaum's centroid theorem [Gr\"unbaum, 1960] and its generalization by Letwin and Yaskin [Letwin and Yaskin, 2024].

math.PR↗
arXiv2026

Exact enumeration of lozenge tilings of a triangular region

We prove that the number of lozenge tilings of a certain triangular region $\mathcal{T}_n$ is given by the formula \[T_n=\prod_{\substack{1\leq a<b\leq 3n+2\\(a,b)\not=(n+1,2n+2)}}\left|1+\zeta^a+\zeta^b\right|^{1/3},\] where $\zeta=e^{2\pi i/(3n+3)}$. This answers a question of Ciucu and Krattenthaler, both by finding the exact formula and by explaining why $T_n$ has many prime factors. The proof reduces the lozenge tiling enumeration problem to evaluating the determinant of the bipartite adjacency matrix $M_n$ of the dual graph of $\mathcal{T}_n$, and then evaluates this determinant by diagonalising $M_n$.

math.CO↗
arXiv2026

AMRM-Pure: Semantic-Preserving Adversarial Purification

Adversarial purification is a defense technique that employs generative models to remove adversarial perturbations. Current methods often rely on powerful generators, typically diffusion models, and focus on reducing the gap between adversarial and clean samples in the feature space, while overlooking semantic correlation within a single sample. To address this issue, we explore adversarial purification from the perspective of preserving semantic relationships among image patches. We employ an Attentive Mask Reconstruction Model (AMRM), which shows superior performance. Our theoretical and experimental analysis reveals that AMRM is highly sensitive to adversarial noise, as such noise significantly distorts patch relationships. Based on this observation, we propose AMRM-Pure, a purification framework that denoises adversarial inputs by preserving patch-level semantics, and formulate this process as a tractable optimization problem with respect to the input. To further enhance robustness, we finetune AMRM-Pure with classification loss to strengthen semantic consistency. We apply our insight to two AMRM architectures, including Mask Autoencoder (MAE) and MaskDiT. Extensive experiments confirm the effectiveness of our method, establishing new state-of-the-art performance across multiple benchmarks.

cs.CR↗
arXiv2026

Orca: The World is in Your Mind

We introduce Orca, an initial instantiation of a general world foundation model. Orca learns a unified world latent space from multimodal world signals and exposes it through multimodal readout interfaces. Rather than optimizing isolated next-token, next-frame, or next-action prediction, we are centered on Next-State-Prediction modeling, offering a unified state-transition modeling route toward understanding, predicting, and acting upon the world. Orca learns through two complementary paradigms: unconscious learning captures dense natural state transitions from continuous videos, and conscious learning models sparse meaningful state transitions by language-described events and VQA supervision. For pre-training, we construct a large-scale world-learning inventory data, including 125K hours of video data and 160M event annotations. After pre-training, Orca learns a unified world latent space. To examine whether the learned latent supports downstream, we evaluate it by three representative downstream readouts: text generation, image prediction, and embodied action generation. Orca's backbone is frozen, and only the lightweight modality-specific decoders are trainable. Experiments show the scalability of the proposed paradigm and verify that stronger world latent enables stronger downstream readouts. Orca outperforms similar-sized specialized baselines. These results show that Orca, as a general world foundation model, presents a promising approach to understanding, predicting, and acting upon the world. Finally, we discuss the current limitations, aiming to provide useful insights and inspiration for the community.

cs.CV↗
arXiv2026

When Muon Optimizer Meets Adversarial Training: A Theoretical and Empirical Study

Adversarial training (AT) remains one of the most reliable empirical defenses against adversarial attacks. Its robustness critically depends on how the underlying min-max objective is optimized. In practice, Stochastic Gradient Descent (SGD) optimizer remains the default optimization choice for AT, whereas adaptive optimizers often improve standard training but may yield inferior robustness. Recently, the Muon optimizer, which orthogonalizes matrix-valued updates via an approximate polar decomposition, has achieved notable success in large-scale training at a memory cost comparable to SGD. This raises a security-relevant question: \textit{can orthogonalized optimization improve AT under strong and heterogeneous threat models?} Focusing on this problem, we conduct a comprehensive theoretical and empirical study. Theoretically, we show that Muon imposes a spectral-norm stability ceiling on matrix updates, limiting uncontrolled spectral growth in the training dynamics without explicitly shrinking the learned weights. Empirically, across five architectures and three $\ell_p$ threat models ($\ell_\infty$, $\ell_1$, $\ell_2$) and their union, Muon is competitive with SGD on CNNs and substantially outperforms AdamW on both CNNs and ViTs. These results identify optimizer geometry as a security-relevant factor in adversarial training, while clarifying the empirical regimes in which orthogonalized updates are beneficial. Overall, our findings highlight optimizer design as a security-critical component of AT.

cs.LG↗
arXiv2026

Unobserved Heterogeneity in Threshold Regression Based on the Hitting Times of a Reflected Brownian Motion for Recurrent Hypoglycemia

Analyses of recurrent hypoglycemia are critical for effective treatment management in diabetic patients. Typically, within-subject dependency in such analyses is captured through subject-level frailty. Recent research has modeled recurrent hypoglycemia using the first hitting times of a reflected Brownian motion. A close examination of this approach reveals that it does not adequately account for varying frailties among individuals, which indicate notable heterogeneity. To address this gap, we propose a finite mixture model of the first hitting time distribution of the reflected Brownian motion. This model allows for component-specific regression coefficients and frailty parameters, providing nuanced insights into how risk factors differently affect patient subgroups. We employ a Bayesian framework for inference, utilizing Markov chain Monte Carlo for estimation. Model selection is conducted using the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood. The effectiveness of these criteria is assessed through simulation studies. Application to recurrent hypoglycemia modeling revealed two subgroups with different risk profiles, as reflected in their volatilities. Bayesian model comparison criteria favor the model with component specific regression coefficients for volatilities. The subgroup with lower volatility exhibits a larger variance and, hence, a greater level of heterogeneity.

stat.ME↗
arXiv2026

Beyond Normal References: Discriminative Few-Shot Anomaly Detection

This paper considers a practical few-shot anomaly detection (FSAD) setting, termed discriminative FSAD, where a limited number of both normal and anomalous examples are available as references during inference. Existing FSAD methods rely on normal-only references through normality matching, ignoring the discriminative clues in anomalous references, while directly fitting both references can overfit to the seen anomalies. We introduce IDEAL, an intrinsic deviation learning framework that leverages both reference types to learn intrinsic deviation patterns characterizing generalizable abnormality as deviations from normality. IDEAL decomposes the learning process into two novel components: 1) a Normal Variation Eraser to suppress nuisance normal variations that may lead to noisy deviations from normality, thereby highlighting anomaly-relevant deviation representations; 2) an Intrinsic Deviation Encoder to decompose these denoised deviation representations into intrinsic deviation vectors capturing the most discriminative orthogonal deviation directions. At inference, IDEAL scores query-to-normal deviations preserved after projection onto the learned intrinsic deviation vectors, enabling generalization for both seen and unseen anomalies. Extensive experiments on eight real-world datasets show that IDEAL generalizes effectively to unseen anomalies and consistently outperforms existing state-of-the-art FSAD methods. Code and data will be available at \href{https://github.com/mala-lab/IDEAL}{https://github.com/mala-lab/IDEAL}.

cs.CV↗
arXiv2026

FedHPro: Federated Hyper-Prototype Learning via Gradient Matching

Federated Learning (FL) enables collaborative training of distributed clients while protecting privacy. To enhance generalization capability in FL, prototype-based FL is in the spotlight, since shared global prototypes offer semantic anchors for aligning client-specific local prototypes. However, existing methods update global prototypes at the prototype-level via averaging local prototypes or refining global anchors, which often leads to semantic drift across clients and subsequently yields a misaligned global signal. To alleviate this issue, we introduce hyper-prototypes, defined by a set of learnable global class-wise prototypes to preserve underlying semantic knowledge across clients. The hyper-prototypes are optimized via gradient matching to align with class-relevant characteristics distilled directly from clients' real samples, rather than prototype-level descriptors. We further propose FedHPro, a Federated Hyper-Prototype Learning framework, to leverage hyper-prototypes to promote inter-class separability via mutual-contrastive learning with client-specific margin, while encouraging intra-class uniformity through a consistency penalty. Comprehensive experiments under diverse heterogeneous scenarios confirm that 1) hyper-prototypes produce a more semantically consistent global signal, and 2) FedHPro achieves state-of-the-art performance on several benchmark datasets. Code is available at \href{https://github.com/mala-lab/FedHPro}{https://github.com/mala-lab/FedHPro}.

cs.CV↗
arXiv2026

RubricEM: Meta-RL with Rubric-guided Policy Decomposition beyond Verifiable Rewards

Training deep research agents, namely systems that plan, search, evaluate evidence, and synthesize long-form reports, pushes reinforcement learning beyond the regime of verifiable rewards. Their outputs lack ground-truth answers, their trajectories span many tool-augmented decisions, and standard post-training offers little mechanism for turning past attempts into reusable experience. In this work, we argue that rubrics should serve not merely as final-answer evaluators, but as the shared interface that structures policy execution, judge feedback, and agent memory. Based on this view, we introduce RubricEM, a rubric-guided reinforcement learning framework that combines stagewise policy decomposition with reflection-based meta-policy evolution. RubricEM first makes research trajectories stage-aware by conditioning planning, evidence gathering, review, and synthesis on self-generated rubrics. It then assigns credit with Stage-Structured GRPO, which uses stagewise rubric judgments to provide denser semantic feedback for long-horizon optimization. In parallel, RubricEM trains a shared-backbone reflection meta-policy that distills judged trajectories into reusable rubric-grounded guidance for future attempts. The resulting RubricEM-8B achieves strong performance across four long-form research benchmarks, outperforming comparable open models and approaching proprietary deep-research systems. Beyond final performance, we perform thorough analyses to understand the key ingredients of RubricEM.

cs.CL↗
arXiv2026

ShellfishNet: A Domain-Specific Benchmark for Visual Recognition of Marine Molluscs

The decline of global shellfish biodiversity poses a severe threat to coastal ecosystems. Although artificial intelligence (AI) technologies show potential for automated ecological monitoring, existing marine benthic datasets often lack adaptation to the complexities of real underwater environments (e.g., variable lighting conditions and diverse species postures), posing challenges for the robust generalization of vision models in practical ecological monitoring. To address this problem, we construct ShellfishNet, a comprehensive image benchmark dataset designed specifically for real-world ecological monitoring constraints. Comprising 8,691 images across 32 taxa, this dataset includes a curated subset annotated with descriptive captions. It is constructed through field photography and web scraping, encompassing samples from complex real-world environments. Based on this benchmark, we systematically evaluate 80 representative neural network models, including Convolutional Neural Networks (CNNs), Vision Transformers (ViTs), State Space Models (SSMs), and Self-Supervised Learning (SSL) methods. Furthermore, we evaluate the performance of fine-grained visual categorization (FGVC) models and investigate the image captioning capabilities of several mainstream multimodal large language models (MLLMs). Meanwhile, we introduce image corruption benchmark tests to simulate common underwater degradation scenarios (turbidity, severe weather) and assess the robustness of vision models, enabling trustworthy decisions on ecological protection in the wild. ShellfishNet is dedicated to providing a data foundation and a model-evaluation benchmark for the intelligent monitoring of benthic organisms.

cs.CV↗
arXiv2026

On the inhomogeneous discounted Hamilton-Jacobi equations

In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} \lambda(x)u+h(x,d_x u)=c \quad \tag{$\ast$} \end{equation} on a closed manifold $M$ with a non-identically vanishing discount factor $\lambda(x)$. There is a critical value $c_0\in[-\infty,\infty)$ such that \eqref{hjs1} admits a viscosity solution if $c>c_0$ and no solution if $c c_0$. In this case, we determine the basin of the stable solution and investigate the long time behavior of the solution semigroup associated to \eqref{hjs1}. In particular, we relate the lowest convergence rate to the integral of $\lambda$ over Mather measures, which leads to an asymptotic behavior of Mather measures when $c$ goes to infinity. Assume $c\geqslant c_0$ and the equation admits a solution, we classify ergodic Mather measures and locate their distribution in the phase space.

math.AP↗
arXiv2026

SkillOS: Learning Skill Curation for Self-Evolving Agents

LLM-based agents are increasingly deployed to handle streaming tasks, yet they often remain one-off problem solvers that fail to learn from past interactions. Reusable skills distilled from experience provide a natural substrate for self-evolution, where high-quality skill curation serves as the key bottleneck. Existing approaches either rely on manual skill curation, prescribe heuristic skill operations, or train for short-horizon skill operations. However, they still struggle to learn complex long-term curation policies from indirect and delayed feedback. To tackle this challenge, we propose SkillOS, an experience-driven RL training recipe for learning skill curation in self-evolving agents. SkillOS pairs a frozen agent executor that retrieves and applies skills with a trainable skill curator that updates an external SkillRepo from accumulated experience. To provide learning signals for curation, we design composite rewards and train on grouped task streams based on skill-relevant task dependencies, where earlier trajectories update the SkillRepo, and later related tasks evaluate these updates. Across multi-turn agentic tasks and single-turn reasoning tasks, SkillOS consistently outperforms memory-free and strong memory-based baselines in both effectiveness and efficiency, with the learned skill curator generalizing across different executor backbones and task domains. Further analyses show that the learned curator produces more targeted skill use, while the skills in SkillRepo evolve into more richly structured Markdown files that encode higher-level meta-skills over time.

cs.AI↗