Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation addresses the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors from a `syntax' domain to a `semantics' codomain. Notably, moralisation and triangulation can be defined inductively on such syntax via functor pre-composition. Moreover, while moralisation is fully syntactic, triangulation relies on semantics. This leads to a discussion of the variable elimination algorithm, reinterpreted here as a functor in its own right, that splits the triangulation procedure in two: one purely syntactic, the other purely semantic. This approach introduces a functorial perspective into the theory of probabilistic graphical models, which highlights the distinctions between syntactic and semantic modifications.

Collaborative pursuit-evasion in cluttered environments presents significant challenges due to sparse rewards and constrained Fields of View (FOV). Standard Multi-Agent Reinforcement Learning (MARL) often suffers from inefficient exploration and fails to scale to large scenarios. We propose PGF-MAPPO (Path-Guided Frontier MAPPO), a hierarchical framework bridging topological planning with reactive control. To resolve local minima and sparse rewards, we integrate an A*-based potential field for dense reward shaping. Furthermore, we introduce Directional Frontier Allocation, combining Farthest Point Sampling (FPS) with geometric angle suppression to enforce spatial dispersion and accelerate coverage. The architecture employs a parameter-shared decentralized critic, maintaining O(1) model complexity suitable for robotic swarms. Experiments demonstrate that PGF-MAPPO achieves superior capture efficiency against faster evaders. Policies trained on 10x10 maps exhibit robust zero-shot generalization to unseen 20x20 environments, significantly outperforming rule-based and learning-based baselines.

Inferring the eventual goal of a mobile agent from noisy observations of its trajectory is a fundamental estimation problem. We initiate the study of such intent inference using a variant of a Rao-Blackwellized Particle Filter (RBPF), subject to the assumption that the agent's intent manifests through closed-loop behavior with a state-of-the-art provable practical stability property. Leveraging the assumed closed-form agent dynamics, the RBPF analytically marginalizes the linear-Gaussian substructure and updates particle weights only, improving sample efficiency over a standard particle filter. Two difference estimators are introduced: a Gaussian mixture model using the RBPF weights and a reduced version confining the mixture to the effective sample. We quantify how well the adversary can recover the agent's intent using information-theoretic leakage metrics and provide computable lower bounds on the Kullback-Leibler (KL) divergence between the true intent distribution and RBPF estimates via Gaussian-mixture KL bounds. We also provide a bound on the difference in performance between the two estimators, highlighting the fact that the reduced estimator performs almost as well as the complete one. Experiments illustrate fast and accurate intent recovery for compliant agents, motivating future work on designing intent-obfuscating controllers.

Energy-based models trained on evolutionary data can now generate novel protein sequences with custom functions [38]. A crucial, yet poorly understood, step in these successes is the use of an artificially low sampling "temperature" to produce functional sequences from the trained model. This adjustment is often the deciding factor between generating functional enzymes and inert polypeptides. A fundamental question arises as to what necessitates temperature tuning and what it reveals about the space of functional proteins and the limits of the models trained on finite data. Temperature tuning is a broadly used heuristic across machine learning contexts, used to improve training [16, 33, 34], generalization/generative performance [14, 45, 47, 48], and energy-landscape dynamics for memory retrieval [35]. It follows the basic intuition that one can navigate the trade-off between fidelity (producing believable, high-probability outputs at low temperature) and diversity (exploring a wide range of novel outputs at high temperature). Despite its widespread use, this practice lacks a principled, quantitative explanation and has not been systematically connected to known issues of the fitting procedure--particularly how it connects to fundamental limits in the learning process, such as biases introduced by training on finite data [5, 9, 10, 21, 22, 41].

Scalable multi-agent driving simulation requires behavior models that are both realistic and computationally efficient. We address this by optimizing the behavior model that controls individual traffic participants. To improve efficiency, we adopt an instance-centric scene representation, where each traffic participant and map element is modeled in its own local coordinate frame. This design enables efficient, viewpoint-invariant scene encoding and allows static map tokens to be reused across simulation steps. To model interactions, we employ a query-centric symmetric context encoder with relative positional encodings between local frames. We use Adversarial Inverse Reinforcement Learning to learn the behavior model and propose an adaptive reward transformation that automatically balances robustness and realism during training. Experiments demonstrate that our approach scales efficiently with the number of tokens, significantly reducing training and inference times, while outperforming several agent-centric baselines in terms of positional accuracy and robustness.

Cooperative Multi-Agent Reinforcement Learning (MARL) faces two major design bottlenecks: crafting dense reward functions and constructing curricula that avoid local optima in high-dimensional, non-stationary environments. Existing approaches rely on fixed heuristics or use Large Language Models (LLMs) directly in the control loop, which is costly and unsuitable for real-time systems. We propose MAESTRO (Multi-Agent Environment Shaping through Task and Reward Optimization), a framework that moves the LLM outside the execution loop and uses it as an offline training architect. MAESTRO introduces two generative components: (i) a semantic curriculum generator that creates diverse, performance-driven traffic scenarios, and (ii) an automated reward synthesizer that produces executable Python reward functions adapted to evolving curriculum difficulty. These components guide a standard MARL backbone (MADDPG) without increasing inference cost at deployment. We evaluate MAESTRO on large-scale traffic signal control (Hangzhou, 16 intersections) and conduct controlled ablations. Results show that combining LLM-generated curricula with LLM-generated reward shaping yields improved performance and stability. Across four seeds, the full system achieves +4.0% higher mean return (163.26 vs. 156.93) and 2.2% better risk-adjusted performance (Sharpe 1.53 vs. 0.70) over a strong curriculum baseline. These findings highlight LLMs as effective high-level designers for cooperative MARL training.

Model-learning agents should gather information to learn world models that support many downstream tasks and inferences, such as predicting unobserved states, estimating near- and far-term consequences of actions, planning action sequences, and detecting changes in dynamics. Current methods for learning and evaluating world models diverge from this goal: training and evaluation are anchored to next-frame prediction, and success is scored by reward maximization in the same environment. We propose WorldTest, a protocol to evaluate model-learning agents that separates reward-free interaction from a scored test phase in a different but related environment. WorldTest is open-ended $\unicode{x2014}$ models should support many different tasks unknown ahead of time $\unicode{x2014}$ and agnostic to model representation, allowing comparison across approaches. We instantiated WorldTest with AutumnBench, a suite of 43 interactive grid-world environments and 129 tasks across three families: masked-frame prediction, planning, and predicting changes to the causal dynamics. We compared 517 human participants and three frontier models on AutumnBench. We found that humans outperform the models, and scaling compute improves performance only in some environments but not others. WorldTest provides a novel template $\unicode{x2014}$ reward-free exploration, derived tests, and behavior-based scoring $\unicode{x2014}$ to evaluate what agents learn about environment dynamics, and AutumnBench exposes significant headroom in world-model learning.

Large language models (LLMs) have demonstrated emergent in-context learning (ICL) capabilities across a range of tasks, including zero-shot time-series forecasting. We show that text-trained foundation models can accurately extrapolate spatiotemporal dynamics from discretized partial differential equation (PDE) solutions without fine-tuning or natural language prompting. Predictive accuracy improves with longer temporal contexts but degrades at finer spatial discretizations. In multi-step rollouts, where the model recursively predicts future spatial states over multiple time steps, errors grow algebraically with the time horizon, reminiscent of global error accumulation in classical finite-difference solvers. We interpret these trends as in-context neural scaling laws, where prediction quality varies predictably with both context length and output length. To better understand how LLMs are able to internally process PDE solutions so as to accurately roll them out, we analyze token-level output distributions and uncover a consistent three-stage ICL progression: beginning with syntactic pattern imitation, transitioning through an exploratory high-entropy phase, and culminating in confident, numerically grounded predictions.

Existing benchmarks in e-commerce primarily focus on basic user intents, such as finding or purchasing products. However, real-world users often pursue more complex goals, such as applying vouchers, managing budgets, and finding multi-products seller. To bridge this gap, we propose ShoppingBench, a novel end-to-end shopping benchmark designed to encompass increasingly challenging levels of grounded intent. Specifically, we propose a scalable framework to simulate user instructions based on various intents derived from sampled real-world products. To facilitate consistent and reliable evaluations, we provide a large-scale shopping sandbox that serves as an interactive simulated environment, incorporating over 2.5 million real-world products. Experimental results demonstrate that even state-of-the-art language agents (such as GPT-4.1) achieve absolute success rates under 50% on our benchmark tasks, highlighting the significant challenges posed by our ShoppingBench. In addition, we propose a trajectory distillation strategy and leverage supervised fine-tuning, along with reinforcement learning on synthetic trajectories, to distill the capabilities of a large language agent into a smaller one. As a result, our trained agent achieves competitive performance compared to GPT-4.1.

Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size. We introduce a quantum version of the em algorithm, an information-geometric generalization of the classical Expectation-Maximization method, which circumvents gradient-based optimization on non-convex functions. Implemented on a semi-quantum restricted Boltzmann machine (sqRBM) -- a hybrid architecture with quantum effects confined to the hidden layer -- our method achieves stable learning and outperforms gradient descent on multiple benchmark datasets. These results establish a structured and scalable alternative to gradient-based training in QML, offering a pathway to mitigate barren plateaus and enhance quantum generative modeling.