Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. This framework calibrates prediction intervals by constructing nonconformity scores on a calibration set, thereby yielding distribution-free uncertainty estimates with rigorous finite-sample coverage guarantees for PINNs. To handle spatial het-eroskedasticity, we further introduce local conformal quantile estimation, enabling spatially adaptive uncertainty bands while preserving theoretical guarantee. Through systematic evaluations on typical PDEs (damped harmonic oscillator, Poisson, Allen-Cahn, and Helmholtz equations) and comprehensive testing across multiple uncertainty metrics, our results demonstrate that the proposed framework achieves reliable calibration and locally adaptive uncertainty intervals, consistently outperforming heuristic UQ approaches. By bridging PINNs with distribution-free UQ, this work introduces a general framework that not only enhances calibration and reliability, but also opens new avenues for uncertainty-aware modeling of complex PDE systems.1. Introduction Physics-Informed Neural Networks (PINNs) have emerged as a versatile framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training [1, 2]. Numerous variants have been developed to enhance accuracy, efficiency, and applicability [3, 4, 5, 6, 7, 8], enabling PINNs to address complex geometries [9, 10], high-dimensional and multiscale problems [11, 12, 13], and inverse formulations [14, 15] within a unified mesh-free paradigm. Applications span fluid mechanics [16, 17], heat transfer [18, 19], and materials science [20, 21]; see [16, 22, 23, 24, 25] for comprehensive reviews.

Trajectory prediction is central to the safe and seamless operation of autonomous vehicles (AVs). In deployment, however, prediction models inevitably face distribution shifts between training data and real-world conditions, where rare or underrepresented traffic scenarios induce out-of-distribution (OOD) cases. While most prior OOD detection research in AVs has concentrated on computer vision tasks such as object detection and segmentation, trajectory-level OOD detection remains largely underexplored. A recent study formulated this problem as a quickest change detection (QCD) task, providing formal guarantees on the trade-off between detection delay and false alarms [1]. Building on this foundation, we propose a new framework that introduces adaptive mechanisms to achieve robust detection in complex driving environments. Empirical analysis across multiple real-world datasets reveals that prediction errors -- even on in-distribution samples -- exhibit mode-dependent distributions that evolve over time with dataset-specific dynamics. By explicitly modeling these error modes, our method achieves substantial improvements in both detection delay and false alarm rates. Comprehensive experiments on established trajectory prediction benchmarks show that our framework significantly outperforms prior UQ- and vision-based OOD approaches in both accuracy and computational efficiency, offering a practical path toward reliable, driving-aware autonomy.

Autonomous Underwater Vehicles (AUVs) have shown great potential for cooperative detection and reconnaissance. However, collaborative AUV communications introduce risks of exposure. In adversarial environments, achieving efficient collaboration while ensuring covert operations becomes a key challenge for underwater cooperative missions. In this paper, we propose a novel dual time-scale Hierarchical Multi-Agent Proximal Policy Optimization (H-MAPPO) framework. The high-level component determines the individuals participating in the task based on a central AUV, while the low-level component reduces exposure probabilities through power and trajectory control by the participating AUVs. Simulation results show that the proposed framework achieves rapid convergence, outperforms benchmark algorithms in terms of performance, and maximizes long-term cooperative efficiency while ensuring covert operations.

Recent advances in spatial omics technologies have revolutionized our ability to study biological systems with unprecedented resolution. By preserving the spatial context of molecular measurements, these methods enable comprehensive mapping of cellular het erogeneity, tissue architecture, and dynamic biological processes in developmental biology, neuroscience, oncology, and evolutionary studies . This review highlights a systematic overview of the continuous advancements in both technology and computational a lgorithms that are paving the way for a deeper, more systematic comprehension of the structure and mechanisms of mammalian tissues and organs by using spatial multi - omics . Our viewpoint demonstrates how advanced machine learning algorithms and multi - omics integrative modeling can decode complex biological processes, including the spatial organization and topological relationships of cells during organ development, as well as key molecular signatures and regulatory networks underlying tumorigenesis and metas tasis . Finally, we outline future directions for technological innovation and modeling insights of spatial omics in precision medicine.

Discrete Bayesian networks (DBNs) provide a broadly useful framework for modeling dependence structures in multivariate categorical data. There is a vast literature on methods for inferring conditional probabilities and graphical structure in DBNs, but data sparsity and parametric assumptions are major practical issues. In this article, we detail a comprehensive Bayesian framework for learning DBNs. First, we propose a hierarchical prior for the conditional probabilities that enables complicated interactions between parent variables and stability in sparse regimes. We give a novel Markov chain Monte Carlo (MCMC) algorithm utilizing parallel Langevin proposals to generate exact posterior samples, avoiding the pitfalls of variational approximations. Moreover, we verify that the full conditional distribution of the concentration parameters is log-concave under mild conditions, facilitating efficient sampling. We then propose two methods for learning network structures, including parent sets, Markov blankets, and DAGs, from categorical data. The first cycles through individual edges each MCMC iteration, whereas the second updates the entire structure as a single step. We evaluate the accuracy, power, and MCMC performance of our methods on several simulation studies. Finally, we apply our methodology to uncover prognostic network structure from primary breast cancer samples.

Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical applications where prediction confidence is essential. Parametric matrix models have emerged as powerful tools for scientific machine learning, achieving exceptional performance by learning governing equations. However, their deterministic nature limits deployment in uncertainty quantification applications. We introduce Bayesian parametric matrix models (B-PMMs), a principled framework that extends PMMs to provide uncertainty estimates while preserving their spectral structure and computational efficiency. B-PMM addresses the fundamental challenge of quantifying uncertainty in matrix eigenvalue problems where standard Bayesian methods fail due to the geometric constraints of spectral decomposition. The theoretical contributions include: (i) adaptive spectral decomposition with regularized matrix perturbation bounds that characterize eigenvalue uncertainty propagation, (ii) structured variational inference algorithms using manifold-aware matrix-variate Gaussian posteriors that respect Hermitian constraints, and (iii) finite-sample calibration guarantees with explicit dependence on spectral gaps and problem conditioning. Experimental validation across matrix dimensions from 5x5 to 500x500 with perfect convergence rates demonstrates that B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling. The framework exhibits graceful degradation under spectral ill-conditioning and provides reliable uncertainty estimates even in near-degenerate regimes. The proposed framework supports robust spectral learning in uncertainty-critical domains and lays the groundwork for broader Bayesian spectral machine learning.

We investigate individual fairness in generative probabilistic classifiers by analysing the robustness of posterior inferences to perturbations in private features. Building on established results in robustness analysis, we hypothesise a correlation between robustness and predictive accuracy, specifically, instances exhibiting greater robustness are more likely to be classified accurately. We empirically assess this hypothesis using a benchmark of fourteen datasets with fairness concerns, employing Bayesian networks as the underlying generative models. To address the computational complexity associated with robustness analysis over multiple private features with Bayesian networks, we reformulate the problem as a most probable explanation task in an auxiliary Markov random field. Our experiments confirm the hypothesis about the correlation, suggesting novel directions to mitigate the traditional trade-off between fairness and accuracy.

This work introduces xOffense, an AI-driven, multi-agent penetration testing framework that shifts the process from labor-intensive, expert-driven manual efforts to fully automated, machine-executable workflows capable of scaling seamlessly with computational infrastructure. At its core, xOffense leverages a fine-tuned, mid-scale open-source LLM (Qwen3-32B) to drive reasoning and decision-making in penetration testing. The framework assigns specialized agents to reconnaissance, vulnerability scanning, and exploitation, with an orchestration layer ensuring seamless coordination across phases. Fine-tuning on Chain-of-Thought penetration testing data further enables the model to generate precise tool commands and perform consistent multi-step reasoning. We evaluate xOffense on two rigorous benchmarks: AutoPenBench and AI-Pentest-Benchmark. The results demonstrate that xOffense consistently outperforms contemporary methods, achieving a sub-task completion rate of 79.17%, decisively surpassing leading systems such as VulnBot and PentestGPT. These findings highlight the potential of domain-adapted mid-scale LLMs, when embedded within structured multi-agent orchestration, to deliver superior, cost-efficient, and reproducible solutions for autonomous penetration testing.

Estimating the difficulty of input questions as perceived by large language models (LLMs) is essential for accurate performance evaluation and adaptive inference. Existing methods typically rely on repeated response sampling, auxiliary models, or fine-tuning the target model itself, which may incur substantial computational costs or compromise generality. In this paper, we propose a novel approach for difficulty estimation that leverages only the hidden representations produced by the target LLM. We model the token-level generation process as a Markov chain and define a value function to estimate the expected output quality given any hidden state. This allows for efficient and accurate difficulty estimation based solely on the initial hidden state, without generating any output tokens. Extensive experiments across both textual and multimodal tasks demonstrate that our method consistently outperforms existing baselines in difficulty estimation. Moreover, we apply our difficulty estimates to guide adaptive reasoning strategies, including Self-Consistency, Best-of-N, and Self-Refine, achieving higher inference efficiency with fewer generated tokens.

Abstract-- Reinforcement learning has produced remarkable advances in humanoid locomotion, yet a fundamental dilemma persists for real-world deployment: policies must choose between the robustness of reactive proprioceptive control or the proactivity of complex, fragile perception-driven systems. Our core contribution is a contrastive learning framework that compels the actor's latent state to encode privileged environmental information from simulation. Crucially, this "distilled awareness" empowers an adaptive gait clock, allowing the policy to proactively adjust its rhythm based on an inferred understanding of the terrain. This synergy resolves the classic trade-off between rigid, clocked gaits and unstable clock-free policies. I. INTRODUCTION Achieving stable and adaptive locomotion in unstructured environments is a grand challenge for humanoid robotics. While Deep Reinforcement Learning (DRL) has become a cornerstone for synthesizing such behaviors, a fundamental information gap complicates real-world deployment.