Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical methods. This paper introduces a novel two-stage Bayesian framework that synergistically integrates training, physics-based deep kernel learning (DKL) with Hamiltonian Monte Carlo (HMC) to robustly infer unknown PDE parameters and quantify their uncertainties from sparse, exact observations. The first stage leverages physics-based DKL to train a surrogate model, which jointly yields an optimized neural network feature extractor and robust initial estimates for the PDE parameters. In the second stage, with the neural network weights fixed, HMC is employed within a full Bayesian framework to efficiently sample the joint posterior distribution of the kernel hyperparameters and the PDE parameters. Numerical experiments on canonical and high-dimensional inverse PDE problems demonstrate that our framework accurately estimates parameters, provides reliable uncertainty estimates, and effectively addresses challenges of data sparsity and model complexity, offering a robust and scalable tool for diverse scientific and engineering applications.

High-quality annotated data is a cornerstone of modern Natural Language Processing (NLP). While recent methods begin to leverage diverse annotation sources-including Large Language Models (LLMs), Small Language Models (SLMs), and human experts-they often focus narrowly on the labeling step itself. A critical gap remains in the holistic process control required to manage these sources dynamically, addressing complex scheduling and quality-cost trade-offs in a unified manner. Inspired by real-world crowdsourcing companies, we introduce CrowdAgent, a multi-agent system that provides end-to-end process control by integrating task assignment, data annotation, and quality/cost management. It implements a novel methodology that rationally assigns tasks, enabling LLMs, SLMs, and human experts to advance synergistically in a collaborative annotation workflow. We demonstrate the effectiveness of CrowdAgent through extensive experiments on six diverse multimodal classification tasks. The source code and video demo are available at https://github.com/QMMMS/CrowdAgent.

Directed graphs are ubiquitous across numerous domains, where the directionality of edges encodes critical causal dependencies. However, existing GNNs and graph Transformers tailored for directed graphs face two major challenges: (1) effectively capturing long-range causal dependencies derived from directed edges; (2) balancing accuracy and training efficiency when processing large-scale graph datasets. In recent years, state space models (SSMs) have achieved substantial progress in causal sequence tasks, and their variants designed for graphs have demonstrated state-of-the-art accuracy while maintaining high efficiency across various graph learning benchmarks. However, existing graph state space models are exclusively designed for undirected graphs, which limits their performance in directed graph learning. To this end, we propose an innovative approach DirEgo2Token which sequentializes directed graphs via k-hop ego graphs. This marks the first systematic extension of state space models to the field of directed graph learning. Building upon this, we develop DirGraphSSM, a novel directed graph neural network architecture that implements state space models on directed graphs via the message-passing mechanism. Experimental results demonstrate that DirGraphSSM achieves state-of-the-art performance on three representative directed graph learning tasks while attaining competitive performance on two additional tasks with 1.5$\times $ to 2$\times $ training speed improvements compared to existing state-of-the-art models.

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.