Successful teamwork depends on interpersonal dynamics, the ways in which individuals coordinate, influence, and adapt to one another over time. Existing measures of interpersonal dynamics, such as CRQA, correlation, Granger causality, and transfer entropy, typically capture only a single dimension: either the synchrony/coordination or the direction of influence between individuals. What is missing is a psychologically meaningful representation that unifies these dimensions and varies systematically with behavior. We propose the "context matrix" as one such representation. The context matrix, modeled within a linear dynamical system, has psychologically interpretable entries specifying how much each individual's current behavior is attributable to their own versus every other group member's past behaviors. Critically, these entries can be distilled into summary features that represent synchrony and directional influence. Evidence for the context matrix as psychologically meaningful is provided in two steps. First, we develop a sequential Bayesian model that infers context matrices from timeseries data and show that it accurately recovers them in noisy simulations. Second, applying the model to human eyetracking data, we demonstrate that summary features of the inferred context matrices capture expected task-based differences in interpersonal dynamics (or lack thereof), predict task accuracy in psychologically reasonable ways, and show some correspondence with existing measures (CRQA and Granger causality). We conclude by situating the context matrix within a broader agenda for modeling interpersonal dynamics in joint action.

We highlight a fundamental connection between information geometry and variational Bayes (VB) and discuss its consequences for machine learning. Under certain conditions, a VB solution always requires estimation or computation of natural gradients. We show several consequences of this fact by using the natural-gradient descent algorithm of Khan and Rue (2023) called the Bayesian Learning Rule (BLR). These include (i) a simplification of Bayes' rule as addition of natural gradients, (ii) a generalization of quadratic surrogates used in gradient-based methods, and (iii) a large-scale implementation of VB algorithms for large language models. Neither the connection nor its consequences are new but we further emphasize the common origins of the two fields of information geometry and Bayes with a hope to facilitate more work at the intersection of the two fields.

Abstract-- Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely on maximum likelihood estimation or maximum consensus to produce a single set of associations. However, in ambiguous scenarios, the distribution of solutions to global data association problems is often highly multimodal, and such single-solution approaches frequently fail. In this work, we introduce a data association framework that leverages approximate Bayesian inference to capture multiple solution modes to the data association problem, thereby avoiding premature commitment to a single solution under ambiguity. Our approach represents hypothetical solutions as particles that evolve according to a deterministic or randomized update rule to cover the modes of the underlying solution distribution. Furthermore, we show that our method can incorporate optimization constraints imposed by the data association formulation and directly benefit from GPU-parallelized optimization. Extensive simulated and real-world experiments with highly ambiguous data show that our method correctly estimates the distribution over transformations when registering point clouds or object maps. I. INTRODUCTION Data association is essential in many robotic applications, enabling key perception technologies such as dynamic object tracking [1]-[3] and simultaneous localization and mapping (SLAM) [4]-[6]. In these scenarios, robots must recognize when an object or feature they are currently observing is the same as something they (or another robot) may have seen from a different perspective. Without correct data association, the environment representation may be inconsistent, leading to undesirable behaviors in downstream tasks (e.g., incorrect associations in loop closure detection can lead to dramatically distorted maps [6]).

Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring approximate methods. When the system model is unknown and must be learned from data, a key question arises: can we learn a model that (i) universally approximates general nonlinear stochastic dynamics, and (ii) supports analytical belief propagation? This paper establishes the theoretical foundations for a class of models that satisfy both properties. The proposed approach combines the expressiveness of normalizing flows for density estimation with the analytical tractability of Bernstein polynomials. Empirical results show the efficacy of our learned model over state-of-the-art data-driven methods for belief propagation, especially for highly non-linear systems with non-additive, non-Gaussian noise.

We consider the problem of recovering the true causal structure among a set of variables, generated by a linear acyclic structural equation model (SEM) with the error terms being independent and having equal variances. It is well-known that the true underlying directed acyclic graph (DAG) encoding the causal structure is uniquely identifiable under this assumption. In this work, we establish that the sum of minimum expected squared errors for every variable, while predicted by the best linear combination of its parent variables, is minimised if and only if the causal structure is represented by any supergraph of the true DAG. This property is further utilised to design a Bayesian DAG selection method that recovers the true graph consistently.

The development and evaluation of social capabilities in AI agents require complex environments where competitive and cooperative behaviours naturally emerge. While game-theoretic properties can explain why certain teams or agent populations outperform others, more abstract behaviours, such as convention following, are harder to control in training and evaluation settings. The Melting Pot contest is a social AI evaluation suite designed to assess the cooperation capabilities of AI systems. In this paper, we apply a Bayesian approach known as Measurement Layouts to infer the capability profiles of multi-agent systems in the Melting Pot contest. We show that these capability profiles not only predict future performance within the Melting Pot suite but also reveal the underlying prosocial abilities of agents. Our analysis indicates that while higher prosocial capabilities sometimes correlate with better performance, this is not a universal trend-some lower-scoring agents exhibit stronger cooperation abilities. Furthermore, we find that top-performing contest submissions are more likely to achieve high scores in scenarios where prosocial capabilities are not required. These findings, together with reports that the contest winner used a hard-coded solution tailored to specific environments, suggest that at least one top-performing team may have optimised for conditions where cooperation was not necessary, potentially exploiting limitations in the evaluation framework. We provide recommendations for improving the annotation of cooperation demands and propose future research directions to account for biases introduced by different testing environments. Our results demonstrate that Measurement Layouts offer both strong predictive accuracy and actionable insights, contributing to a more transparent and generalisable approach to evaluating AI systems in complex social settings.

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.

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.