Daily Papers

Humans rapidly learn abstract knowledge when encountering novel environments and flexibly deploy this knowledge to guide efficient and intelligent action. Can modern AI systems learn and plan in a similar way? We study this question using a dataset of complex human gameplay with concurrent fMRI recordings, in which participants learn novel video games that require rule discovery, hypothesis revision, and multi-step planning. We jointly evaluate models by their ability to play the games, match human learning behavior, and predict brain activity during the same task, comparing a suite of frontier Large Reasoning Models (LRMs) against model-free and model-based deep reinforcement learning agents and a Bayesian theory-based agent. We find that frontier LRMs most closely match human behavioral patterns during game discovery and predict brain activity an order of magnitude better than both reinforcement learning alternatives across cortical and subcortical regions, with effects robust to permutation controls. Through targeted manipulations, we further show that brain alignment reflects the model's in-context representation of the game state rather than its downstream planning or reasoning. Our results establish LRMs as compelling computational accounts of human learning and decision making in complex, naturalistic environments. Project page with interactive replays: https://botcs.github.io/reason-to-play/

Existing LLM reasoning methods have shown impressive capabilities across various tasks, such as solving math and coding problems. However, applying these methods to scenarios without ground-truth answers or rule-based verification methods - such as tracking the mental states of an agent - remains challenging. Inspired by the sequential Monte Carlo algorithm, we introduce thought-tracing, an inference-time reasoning algorithm designed to trace the mental states of specific agents by generating hypotheses and weighting them based on observations without relying on ground-truth solutions to questions in datasets. Our algorithm is modeled after the Bayesian theory-of-mind framework, using LLMs to approximate probabilistic inference over agents' evolving mental states based on their perceptions and actions. We evaluate thought-tracing on diverse theory-of-mind benchmarks, demonstrating significant performance improvements compared to baseline LLMs. Our experiments also reveal interesting behaviors of the recent reasoning models - e.g., o3 and R1 - on theory-of-mind, highlighting the difference of social reasoning compared to other domains.

Theory of Mind (ToM), the ability to understand people's mental variables based on their behavior, is key to developing socially intelligent agents. Current approaches to Theory of Mind reasoning either rely on prompting Large Language Models (LLMs), which are prone to systematic errors, or use rigid, handcrafted Bayesian Theory of Mind (BToM) models, which are more robust but cannot generalize across different domains. In this work, we introduce AutoToM, an automated Bayesian Theory of Mind method for achieving open-ended machine Theory of Mind. AutoToM can operate in any domain, infer any mental variable, and conduct robust Theory of Mind reasoning of any order. Given a Theory of Mind inference problem, AutoToM first proposes an initial BToM model. It then conducts automated Bayesian inverse planning based on the proposed model, leveraging an LLM as the backend. Based on the uncertainty of the inference, it iteratively refines the model, by introducing additional mental variables and/or incorporating more timesteps in the context. Empirical evaluations across multiple Theory of Mind benchmarks demonstrate that AutoToM consistently achieves state-of-the-art performance, offering a scalable, robust, and interpretable approach to machine Theory of Mind.

LLM agents increasingly rely on external inference conditions: prompts, tools, memory, SOPs, skills, and harness feedback. These assets can improve task execution without changing model weights, but they are often revised by heuristic reflection or by reusing observed successes and failures as if counts alone were reliable belief. We introduce Bayesian-Agent, a native and cross-harness framework that treats reusable skills and SOPs as hypotheses about whether a frozen model will succeed under a particular prompt, context, and harness environment. Bayesian-Agent records verified trajectory evidence, maintains a feature-conditioned categorical posterior over each skill, and maps posterior state into inspectable actions such as patch, split, compress, retire, and explore. Model-facing prompts receive executable guardrails and failure-mode patches, while posterior summaries remain available for audit. With deepseek-v4-flash, incremental repair improves SOP-Bench from 80\% to 95\%, Lifelong AgentBench from 90\% to 100\%, and RealFin-Bench from 45\% to 65\%. We further evaluate Bayesian-Agent's native backend and optional GenericAgent, mini-swe-agent, and Claude Code backends. The results include positive, negative, saturated, and case-study settings, suggesting that agent skill evolution is best viewed as posterior-guided harness optimization rather than uncalibrated prompt accumulation. The source code is available at https://github.com/DataArcTech/Bayesian-Agent.

As autonomous agents powered by foundation models are increasingly integrated into social and economic systems, understanding the principles governing their collective behavior is essential for ensuring safety and cooperation. Classical game theory, the dominant framework for modeling rational interaction, is built upon the assumption of `decoupled agency,' where agents treat their own decision-making as independent of the environment and other actors. Modern AI agents, however, jointly predict their own future actions alongside external observations. Here, we report a striking finding: when interacting in stylized social dilemmas, foundation model agents engaging in optimal planning consistently converge to stable cooperation, directly contradicting classical game-theoretic predictions of mutual defection. To understand this phenomenon, we introduce the `embedded Bayesian agent,' a theoretical model for foundation model agents. By shifting from decoupled to embedded agency, these agents model themselves as part of the universe they inhabit, maintaining epistemic uncertainty about their own decision-making algorithms. We show that by inferring whether others are behaviorally similar, an embedded agent treats its own deliberation during planning as evidence: a decision to cooperate predicts a similar decision by a similar partner. We formalize this mechanism of similarity inference through the `embedded equilibrium,' a novel solution concept replacing the Nash equilibrium to provide a foundational game theory for the social behavior of modern AI agents.

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning might serve as a general technique for numerically approximating Bayes-optimal agents - that is, even for task distributions for which we currently don't possess tractable models.

Is there a canonical way to think of agency beyond reward maximisation? In this paper, we show that any type of behaviour complying with physically sound assumptions about how macroscopic biological agents interact with the world canonically integrates exploration and exploitation in the sense of minimising risk and ambiguity about states of the world. This description, known as active inference, refines the free energy principle, a popular descriptive framework for action and perception originating in neuroscience. Active inference provides a normative Bayesian framework to simulate and model agency that is widely used in behavioural neuroscience, reinforcement learning (RL) and robotics. The usefulness of active inference for RL is three-fold. a) Active inference provides a principled solution to the exploration-exploitation dilemma that usefully simulates biological agency. b) It provides an explainable recipe to simulate behaviour, whence behaviour follows as an explainable mixture of exploration and exploitation under a generative world model, and all differences in behaviour are explicit in differences in world model. c) This framework is universal in the sense that it is theoretically possible to rewrite any RL algorithm conforming to the descriptive assumptions of active inference as an active inference algorithm. Thus, active inference can be used as a tool to uncover and compare the commitments and assumptions of more specific models of agency.

Autonomous scientific discovery systems increasingly use large language models (LLMs) to propose new hypotheses, but many such systems condition primarily on experimental memory: archives of high-scoring candidates or heuristic summaries of recent trials. We argue that discovery agents should instead maintain explicit, uncertainty-aware beliefs about hypothesis quality. We introduce BayesEvolve, a belief-guided discovery framework that converts experimental evidence into a predictive belief state and uses this belief to guide future experimentation. As a controlled testbed for belief-guided discovery, we evaluate BayesEvolve on shifted BBOB-style black-box optimization tasks, leaving program and laboratory discovery domains to future work. BayesEvolve improves sample efficiency over memory- and archive-guided LLM baselines under a fixed evaluation budget. We further show that the belief state is predictive on held-out candidate pools, that controlled decision-rule ablations favor belief-guided selection with an annealed uncertainty bonus, and that BayesEvolve exhibits productive late-stage concentration rather than unfocused exploration.

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

In social sciences, researchers often face challenges when conducting large-scale experiments, particularly due to the simulations' complexity and the lack of technical expertise required to develop such frameworks. Agent-Based Modeling (ABM) is a computational approach that simulates agents' actions and interactions to evaluate how their behaviors influence the outcomes. However, the traditional implementation of ABM can be demanding and complex. Generative Agent-Based Modeling (GABM) offers a solution by enabling scholars to create simulations where AI-driven agents can generate complex behaviors based on underlying rules and interactions. This paper introduces a framework for designing reliable experiments using GABM, making sophisticated simulation techniques more accessible to researchers across various fields. We provide a step-by-step guide for selecting appropriate tools, designing the model, establishing experimentation protocols, and validating results.

LLM agents operate in two distinct regimes: open-weight agents amenable to reinforcement learning (RL) and black-box agents whose behaviour must be controlled purely at test time. Although black-box agents are often backed by state-of-the-art proprietary LLMs, API-only access precludes parameter-level optimization, rendering most RL methods inapplicable. To address this limitation, we turn to a known equivalence between RL and Bayesian inference. We propose Agentic Monte Carlo (AMC) to directly sample from the optimal policy of a black-box agent rather than training it through RL. The optimal policy is a posterior over trajectories whose prior we define as the fixed black-box LLM agent. We employ Sequential Monte Carlo to sample from this posterior by learning a value function to steer the agent while leaving the underlying black-box model unchanged. We validate AMC on three diverse environments from the AgentGym benchmark, demonstrating significant improvements over prompting baselines and even outperforming Group Relative Policy Optimization (GRPO) as we scale the test-time compute of our method. AMC demonstrates the feasibility of performing principled RL-style optimization of black-box LLM agents. Code is available at https://github.com/layer6ai-labs/Agentic-Monte-Carlo

Bayesian inference provides principled uncertainty quantification but is often limited by challenges of prior elicitation, likelihood misspecification, and computational burden. The martingale posterior (MGP, Fong et al., 2023) offers an alternative, replacing prior-likelihood elicitation with a predictive rule - namely, a sequence of one-step-ahead predictive distributions - for forward data generation. The utility of MGPs depends on the choice of predictive rule, yet the literature has offered few compelling examples. Foundation transformers are well-suited here, as their autoregressive generation mirrors this forward simulation and their general-purpose design enables rich predictive modeling. We introduce TabMGP, an MGP built on TabPFN, a transformer foundation model that is currently state-of-the-art for tabular data. TabMGP produces credible sets with near-nominal coverage and often outperforms both existing MGP constructions and standard Bayes.

The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

Understanding the world and explaining it with scientific theories is a central aspiration of artificial intelligence research. Proposing theories, designing experiments to test them, and then revising them based on data are fundamental to scientific discovery. Despite the significant promise of LLM-based scientific agents, no benchmarks systematically test LLM's ability to propose scientific models, collect experimental data, and revise them in light of new data. We introduce BoxingGym, a benchmark with 10 environments for systematically evaluating both experimental design (e.g. collecting data to test a scientific theory) and model discovery (e.g. proposing and revising scientific theories). To enable tractable and quantitative evaluation, we implement each environment as a generative probabilistic model with which a scientific agent can run interactive experiments. These probabilistic models are drawn from various real-world scientific domains ranging from psychology to ecology. To quantitatively evaluate a scientific agent's ability to collect informative experimental data, we compute the expected information gain (EIG), an information-theoretic quantity which measures how much an experiment reduces uncertainty about the parameters of a generative model. A good scientific theory is a concise and predictive explanation. Therefore, to quantitatively evaluate model discovery, we ask a scientific agent to explain their model and then assess whether this explanation enables another scientific agent to make reliable predictions about this environment. In addition to this explanation-based evaluation, we compute standard model evaluation metrics such as prediction errors. We find that current LLMs, such as GPT-4o, struggle with both experimental design and model discovery. We find that augmenting the LLM-based agent with an explicit statistical model does not reliably improve these results.

We introduce and study the problem of detecting whether an agent is updating their prior beliefs given new evidence in an optimal way that is Bayesian, or whether they are biased towards their own prior. In our model, biased agents form posterior beliefs that are a convex combination of their prior and the Bayesian posterior, where the more biased an agent is, the closer their posterior is to the prior. Since we often cannot observe the agent's beliefs directly, we take an approach inspired by information design. Specifically, we measure an agent's bias by designing a signaling scheme and observing the actions they take in response to different signals, assuming that they are maximizing their own expected utility; our goal is to detect bias with a minimum number of signals. Our main results include a characterization of scenarios where a single signal suffices and a computationally efficient algorithm to compute optimal signaling schemes.

Deception is prevalent in human social settings. However, studies into the effect of deception on reinforcement learning algorithms have been limited to simplistic settings, restricting their applicability to complex real-world problems. This paper addresses this by introducing a new mixed competitive-cooperative multi-agent reinforcement learning (MARL) environment inspired by popular role-based deception games such as Werewolf, Avalon, and Among Us. The environment's unique challenge lies in the necessity to cooperate with other agents despite not knowing if they are friend or foe. Furthermore, we introduce a model of deception, which we call Bayesian belief manipulation (BBM) and demonstrate its effectiveness at deceiving other agents in this environment while also increasing the deceiving agent's performance.

As large language models evolve into tool-augmented agents, a central question remains unresolved: when is external tool use actually justified? Existing agent frameworks typically treat tools as ordinary actions and optimize for task success or reward, offering little principled distinction between epistemically necessary interaction and unnecessary delegation. This position paper argues that agents should invoke external tools only when epistemically necessary. Here, epistemic necessity means that a task cannot be completed reliably via the agent's internal reasoning over its current context, without any external interaction. We introduce the Theory of Agent (ToA), a framework that treats agents as making sequential decisions about whether remaining uncertainty should be resolved internally or delegated externally. From this perspective, common agent failure modes (e.g., overthinking and overacting) arise from miscalibrated decisions under uncertainty rather than deficiencies in reasoning or tool execution alone. We further discuss implications for training, evaluation, and agent design, highlighting that unnecessary delegation not only causes inefficiency but can impede the development of internal reasoning capability. Our position provides a normative criterion for tool use that complements existing decision-theoretic models and is essential for building agents that are not only correct, but increasingly intelligent.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the importance of proper interpretation as it pertains to inference about latent variables. We consider a recently-proposed method "distributional evidence" as well as revisit two older methods: Jeffrey's rule and virtual evidence. We devise guidelines on how to account for uncertain evidence and we provide new insights, particularly regarding consistency. To showcase the impact of different interpretations of the same uncertain evidence, we carry out experiments in which one interpretation is defined as "correct." We then compare inference results from each different interpretation illustrating the importance of careful consideration of uncertain evidence.

High-fidelity social simulation is pivotal for addressing complex Web societal challenges, yet it demands agents capable of authentically replicating the dynamic spectrum of human interaction. Current LLM-based multi-agent frameworks, however, predominantly adhere to static interaction topologies, failing to capture the fluid oscillation between cooperative knowledge synthesis and competitive critical reasoning seen in real-world scenarios. This rigidity often leads to unrealistic ``groupthink'' or unproductive deadlocks, undermining the credibility of simulations for decision support. To bridge this gap, we propose BEACOF, a belief-driven adaptive collaboration framework inspired by Perfect Bayesian Equilibrium (PBE). By modeling social interaction as a dynamic game of incomplete information, BEACOF rigorously addresses the circular dependency between collaboration type selection and capability estimation. Agents iteratively refine probabilistic beliefs about peer capabilities and autonomously modulate their collaboration strategy, thereby ensuring sequentially rational decisions under uncertainty. Validated across adversarial (judicial), open-ended (social) and mixed (medical) scenarios, BEACOF prevents coordination failures and fosters robust convergence toward high-quality solutions, demonstrating superior potential for reliable social simulation. Source codes and datasets are publicly released at: https://github.com/WUT-IDEA/BEACOF.

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.

Popular offline reinforcement learning (RL) methods rely on conservatism, either by penalizing out-of-dataset actions or by restricting rollout horizons. In this work, we question the universality of this principle and instead revisit a complementary one: a Bayesian perspective. Rather than enforcing conservatism, the Bayesian approach tackles epistemic uncertainty in offline data by modeling a posterior distribution over plausible world models and training a history-dependent agent to maximize expected rewards, enabling test-time generalization. We first illustrate, in a bandit setting, that Bayesianism excels on low-quality datasets where conservatism fails. We then scale this principle to realistic tasks and show that long-horizon planning is critical for reducing value overestimation once conservatism is removed. To make this feasible, we introduce key design choices for performing and learning from long-horizon rollouts while controlling compounding errors. These yield our algorithm, NEUBAY, grounded in the neutral Bayesian principle. On D4RL and NeoRL benchmarks, NEUBAY generally matches or surpasses leading conservative algorithms, achieving new state-of-the-art on 7 datasets. Notably, it succeeds with rollout horizons of several hundred steps, contrary to dominant practice. Finally, we characterize datasets by quality and coverage, showing when NEUBAY is preferable to conservative methods. Together, we argue NEUBAY lays the foundation for a new practical direction in offline and model-based RL.

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains. To do so, we present basic algorithmic templates for building near-optimal predictors and reinforcement learners which behave as if they had a probabilistic model that allowed them to efficiently exploit task structure. Furthermore, we recast memory-based meta-learning within a Bayesian framework, showing that the meta-learned strategies are near-optimal because they amortize Bayes-filtered data, where the adaptation is implemented in the memory dynamics as a state-machine of sufficient statistics. Essentially, memory-based meta-learning translates the hard problem of probabilistic sequential inference into a regression problem.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

Agent-based modeling (ABM) seeks to understand the behavior of complex systems by simulating a collection of agents that act and interact within an environment. Their practical utility requires capturing realistic environment dynamics and adaptive agent behavior while efficiently simulating million-size populations. Recent advancements in large language models (LLMs) present an opportunity to enhance ABMs by using LLMs as agents with further potential to capture adaptive behavior. However, the computational infeasibility of using LLMs for large populations has hindered their widespread adoption. In this paper, we introduce AgentTorch -- a framework that scales ABMs to millions of agents while capturing high-resolution agent behavior using LLMs. We benchmark the utility of LLMs as ABM agents, exploring the trade-off between simulation scale and individual agency. Using the COVID-19 pandemic as a case study, we demonstrate how AgentTorch can simulate 8.4 million agents representing New York City, capturing the impact of isolation and employment behavior on health and economic outcomes. We compare the performance of different agent architectures based on heuristic and LLM agents in predicting disease waves and unemployment rates. Furthermore, we showcase AgentTorch's capabilities for retrospective, counterfactual, and prospective analyses, highlighting how adaptive agent behavior can help overcome the limitations of historical data in policy design. AgentTorch is an open-source project actively being used for policy-making and scientific discovery around the world. The framework is available here: github.com/AgentTorch/AgentTorch.

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifies the learning of both network structure and weights. Empirically, our method exhibits competitive predictive performance while preserving the benefits of Bayesian principles across challenging scenarios. We also provide convincing experimental justification for our modeling choice.

Bayesian predictive inference provides a principled framework for uncertainty quantification, data efficiency, and robust generalization. However, exact inference is often intractable, and scalable approximations may remain computationally expensive or require restrictive modeling assumptions that degrade predictive performance. Prior-Data Fitted and in-context models have recently emerged as an amortized alternative by learning to map datasets directly to predictive distributions, but existing approaches are tightly coupled to the support of the training prior and lack explicit mechanisms for adapting to new priors at test time, resulting in limited robustness under distribution shift. We introduce a multi-task in-context learning framework for amortized hierarchical Bayesian predictive inference that explicitly represents prior information as a prefix of in-context datasets. A transformer trained on sequences of prior and target tasks learns to adapt its predictions across families of priors. On a suite of evaluations with increasing difficulty, including out-of-meta-distribution priors and priors with high-dimensional latent structures, our method matches oracle Bayesian predictors while being orders of magnitude faster. We further demonstrate its practical relevance on a real-world spatiotemporal temperature prediction benchmark. Code is available at https://github.com/martianmartina/multi-task-bayesian-icl/.

Large language model (LLM)-based multi-agent systems enable expressive agent reasoning but are expensive to scale and poorly calibrated for timestep-aligned state-transition simulation, while classical agent-based models (ABMs) offer interpretability but struggle to integrate rich individual-level signals and non-stationary behaviors. We propose PhysicsAgentABM, which shifts inference to behaviorally coherent agent clusters: state-specialized symbolic agents encode mechanistic transition priors, a multimodal neural transition model captures temporal and interaction dynamics, and uncertainty-aware epistemic fusion yields calibrated cluster-level transition distributions. Individual agents then stochastically realize transitions under local constraints, decoupling population inference from entity-level variability. We further introduce ANCHOR, an LLM agent-driven clustering strategy based on cross-contextual behavioral responses and a novel contrastive loss, reducing LLM calls by up to 6-8 times. Experiments across public health, finance, and social sciences show consistent gains in event-time accuracy and calibration over mechanistic, neural, and LLM baselines. By re-architecting generative ABM around population-level inference with uncertainty-aware neuro-symbolic fusion, PhysicsAgentABM establishes a new paradigm for scalable and calibrated simulation with LLMs.

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However, existing methods are often computationally expensive, or demand costly retraining when priors change, limiting their utility, particularly in sequential inference problems such as real-time sensor fusion. To address these challenges, we introduce the Distribution Transformer -- a novel architecture that can learn arbitrary distribution-to-distribution mappings. Our method can be trained to map a prior to the corresponding posterior, conditioned on some dataset -- thus performing approximate Bayesian inference. Our novel architecture represents a prior distribution as a (universally-approximating) Gaussian Mixture Model (GMM), and transforms it into a GMM representation of the posterior. The components of the GMM attend to each other via self-attention, and to the datapoints via cross-attention. We demonstrate that Distribution Transformers both maintain flexibility to vary the prior, and significantly reduces computation times-from minutes to milliseconds-while achieving log-likelihood performance on par with or superior to existing approximate inference methods across tasks such as sequential inference, quantum system parameter inference, and Gaussian Process predictive posterior inference with hyperpriors.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.

When humans cooperate, they frequently coordinate their activity through both verbal communication and non-verbal actions, using this information to infer a shared goal and plan. How can we model this inferential ability? In this paper, we introduce a model of a cooperative team where one agent, the principal, may communicate natural language instructions about their shared plan to another agent, the assistant, using GPT-3 as a likelihood function for instruction utterances. We then show how a third person observer can infer the team's goal via multi-modal Bayesian inverse planning from actions and instructions, computing the posterior distribution over goals under the assumption that agents will act and communicate rationally to achieve them. We evaluate this approach by comparing it with human goal inferences in a multi-agent gridworld, finding that our model's inferences closely correlate with human judgments (R = 0.96). When compared to inference from actions alone, we also find that instructions lead to more rapid and less uncertain goal inference, highlighting the importance of verbal communication for cooperative agents.

Executing actions in a correlated manner is a common strategy for human coordination that often leads to better cooperation, which is also potentially beneficial for cooperative multi-agent reinforcement learning (MARL). However, the recent success of MARL relies heavily on the convenient paradigm of purely decentralized execution, where there is no action correlation among agents for scalability considerations. In this work, we introduce a Bayesian network to inaugurate correlations between agents' action selections in their joint policy. Theoretically, we establish a theoretical justification for why action dependencies are beneficial by deriving the multi-agent policy gradient formula under such a Bayesian network joint policy and proving its global convergence to Nash equilibria under tabular softmax policy parameterization in cooperative Markov games. Further, by equipping existing MARL algorithms with a recent method of differentiable directed acyclic graphs (DAGs), we develop practical algorithms to learn the context-aware Bayesian network policies in scenarios with partial observability and various difficulty. We also dynamically decrease the sparsity of the learned DAG throughout the training process, which leads to weakly or even purely independent policies for decentralized execution. Empirical results on a range of MARL benchmarks show the benefits of our approach.

We study a class of emergent misalignment in multi-agent systems (MAS), with a focus on automated workflows, which we refer to agentic misalignment. Although these systems can solve complex tasks, they often fail because agents act according to implicit proxy utilities that do not align with the intended human goals. We formally define these behaviors and analyze them within a Bayesian framework, showing that generic utilities naturally lead to posterior collapse of agents in automated workflows. To address this issue, we propose Agentic Evidence Attribution (AEA), a novel alignment paradigm that improves agent posteriors using context-specific evidence. AEA reasons over agent actions and provides structured evidence to correct misaligned behavior during collaboration. To better understand the role of evidence, we study two instantiations of AEA: self-reflection (internal evidence from the model) and weak-to-strong generalization (external evidence on the agentic trajectory). We show that a small evidence model effectively aligns the MAS by providing orthogonal failure attribution. Our results clarify the sources of agentic misalignment in automated workflows and show that evidence-based alignment can effectively improve agent collaboration and leads to reliable multi-agent systems built on automated workflows.

Generative Agent-Based Modeling (GABM) is an emerging simulation paradigm that combines the reasoning abilities of Large Language Models with traditional Agent-Based Modeling to replicate complex social behaviors, including interactions on social media. While prior work has focused on localized phenomena such as opinion formation and information spread, its potential to capture global network dynamics remains underexplored. This paper addresses this gap by analyzing GABM-based social media simulations through the lens of the Friendship Paradox (FP), a counterintuitive phenomenon where individuals, on average, have fewer friends than their friends. We propose a GABM framework for social media simulations, featuring generative agents that emulate real users with distinct personalities and interests. Using Twitter datasets on the US 2020 Election and the QAnon conspiracy, we show that the FP emerges naturally in GABM simulations. Consistent with real-world observations, the simulations unveil a hierarchical structure, where agents preferentially connect with others displaying higher activity or influence. Additionally, we find that infrequent connections primarily drive the FP, reflecting patterns in real networks. These findings validate GABM as a robust tool for modeling global social media phenomena and highlight its potential for advancing social science by enabling nuanced analysis of user behavior.

Multi-agent reinforcement learning (MARL) methods struggle with the non-stationarity of multi-agent systems and fail to adaptively learn online when tested with novel agents. Here, we leverage large language models (LLMs) to create an autonomous agent that can handle these challenges. Our agent, Hypothetical Minds, consists of a cognitively-inspired architecture, featuring modular components for perception, memory, and hierarchical planning over two levels of abstraction. We introduce the Theory of Mind module that scaffolds the high-level planning process by generating hypotheses about other agents' strategies in natural language. It then evaluates and iteratively refines these hypotheses by reinforcing hypotheses that make correct predictions about the other agents' behavior. Hypothetical Minds significantly improves performance over previous LLM-agent and RL baselines on a range of competitive, mixed motive, and collaborative domains in the Melting Pot benchmark, including both dyadic and population-based environments. Additionally, comparisons against LLM-agent baselines and ablations reveal the importance of hypothesis evaluation and refinement for succeeding on complex scenarios.

In meta reinforcement learning (meta RL), an agent learns from a set of training tasks how to quickly solve a new task, drawn from the same task distribution. The optimal meta RL policy, a.k.a. the Bayes-optimal behavior, is well defined, and guarantees optimal reward in expectation, taken with respect to the task distribution. The question we explore in this work is how many training tasks are required to guarantee approximately optimal behavior with high probability. Recent work provided the first such PAC analysis for a model-free setting, where a history-dependent policy was learned from the training tasks. In this work, we propose a different approach: directly learn the task distribution, using density estimation techniques, and then train a policy on the learned task distribution. We show that our approach leads to bounds that depend on the dimension of the task distribution. In particular, in settings where the task distribution lies in a low-dimensional manifold, we extend our analysis to use dimensionality reduction techniques and account for such structure, obtaining significantly better bounds than previous work, which strictly depend on the number of states and actions. The key of our approach is the regularization implied by the kernel density estimation method. We further demonstrate that this regularization is useful in practice, when `plugged in' the state-of-the-art VariBAD meta RL algorithm.

Useful social science theories predict behavior across settings. However, applying a theory to make predictions in new settings is challenging: rarely can it be done without ad hoc modifications to account for setting-specific factors. We argue that AI agents put in simulations of those novel settings offer an alternative for applying theory, requiring minimal or no modifications. We present an approach for building such "general" agents that use theory-grounded natural language instructions, existing empirical data, and knowledge acquired by the underlying AI during training. To demonstrate the approach in settings where no data from that data-generating process exists--as is often the case in applied prediction problems--we design a heterogeneous population of 883,320 novel games. AI agents are constructed using human data from a small set of conceptually related but structurally distinct "seed" games. In preregistered experiments, on average, agents predict initial human play in a random sample of 1,500 games from the population better than (i) a cognitive hierarchy model, (ii) game-theoretic equilibria, and (iii) out-of-the-box agents. For a small set of separate novel games, these simulations predict responses from a new sample of human subjects better even than the most plausibly relevant published human data.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Most economic theories typically assume that financial market participants are fully rational individuals and use mathematical models to simulate human behavior in financial markets. However, human behavior is often not entirely rational and is challenging to predict accurately with mathematical models. In this paper, we propose Agent-based Simulated Financial Market (ASFM), which first constructs a simulated stock market with a real order matching system. Then, we propose a large language model based agent as the stock trader, which contains the profile, observation, and tool-learning based action module. The trading agent can comprehensively understand current market dynamics and financial policy information, and make decisions that align with their trading strategy. In the experiments, we first verify that the reactions of our ASFM are consistent with the real stock market in two controllable scenarios. In addition, we also conduct experiments in two popular economics research directions, and we find that conclusions drawn in our \model align with the preliminary findings in economics research. Based on these observations, we believe our proposed ASFM provides a new paradigm for economic research.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

While Large Language Models (LLMs) show remarkable capabilities, their unreliability remains a critical barrier to deployment in high-stakes domains. This survey charts a functional evolution in addressing this challenge: the evolution of uncertainty from a passive diagnostic metric to an active control signal guiding real-time model behavior. We demonstrate how uncertainty is leveraged as an active control signal across three frontiers: in advanced reasoning to optimize computation and trigger self-correction; in autonomous agents to govern metacognitive decisions about tool use and information seeking; and in reinforcement learning to mitigate reward hacking and enable self-improvement via intrinsic rewards. By grounding these advancements in emerging theoretical frameworks like Bayesian methods and Conformal Prediction, we provide a unified perspective on this transformative trend. This survey provides a comprehensive overview, critical analysis, and practical design patterns, arguing that mastering the new trend of uncertainty is essential for building the next generation of scalable, reliable, and trustworthy AI.

Organizations across finance, healthcare, transportation, content moderation, and critical infrastructure are rapidly deploying highly automated AI systems, yet they lack principled methods to quantify how increasing automation amplifies harm when failures occur. We propose a parsimonious Bayesian risk decomposition expressing expected loss as the product of three terms: the probability of system failure, the conditional probability that a failure propagates into harm given the automation level, and the expected severity of harm. This framework isolates a critical quantity -- the conditional probability that failures propagate into harm -- which captures execution and oversight risk rather than model accuracy alone. We develop complete theoretical foundations: formal proofs of the decomposition, a harm propagation equivalence theorem linking the harm propagation probability to observable execution controls, risk elasticity measures, efficient frontier analysis for automation policy, and optimal resource allocation principles with second-order conditions. We motivate the framework with an illustrative case study of the 2012 Knight Capital incident ($440M loss) as one instantiation of a broadly applicable failure pattern, and characterize the research design required to empirically validate the framework at scale across deployment domains. This work provides the theoretical foundations for a new class of deployment-focused risk governance tools for agentic and automated AI systems.

The surprisingly likely criterion in the seminal work of Prelec (the Bayesian Truth Serum) guarantees truthfulness in a game-theoretic multi-agent setting, by rewarding rational agents to maximise the expected information gain with their answers w.r.t. their probabilistic beliefs. We investigate the relevance of a similar criterion for responses of LLMs. We hypothesize that if the surprisingly likely criterion works in LLMs, under certain conditions, the responses that maximize the reward under this criterion should be more accurate than the responses that only maximize the posterior probability. Using benchmarks including the TruthfulQA benchmark and using openly available LLMs: GPT-2 and LLaMA-2, we show that the method indeed improves the accuracy significantly (for example, upto 24 percentage points aggregate improvement on TruthfulQA and upto 70 percentage points improvement on individual categories of questions).

Strategic dialogue requires agents to execute distinct dialogue acts, for which belief estimation is essential. While prior work often estimates beliefs accurately, it lacks a principled mechanism to use those beliefs during generation. We bridge this gap by first formalizing two core acts Adversarial and Alignment, and by operationalizing them via probabilistic constraints on what an agent may generate. We instantiate this idea in BEDA, a framework that consists of the world set, the belief estimator for belief estimation, and the conditional generator that selects acts and realizes utterances consistent with the inferred beliefs. Across three settings, Conditional Keeper Burglar (CKBG, adversarial), Mutual Friends (MF, cooperative), and CaSiNo (negotiation), BEDA consistently outperforms strong baselines: on CKBG it improves success rate by at least 5.0 points across backbones and by 20.6 points with GPT-4.1-nano; on Mutual Friends it achieves an average improvement of 9.3 points; and on CaSiNo it achieves the optimal deal relative to all baselines. These results indicate that casting belief estimation as constraints provides a simple, general mechanism for reliable strategic dialogue.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

Goal-driven persuasive dialogue, exemplified by applications like telemarketing, requires sophisticated multi-turn planning and strict factual faithfulness, which remains a significant challenge for even state-of-the-art Large Language Models (LLMs). A lack of task-specific data often limits previous works, and direct LLM application suffers from strategic brittleness and factual hallucination. In this paper, we first construct and release TeleSalesCorpus, the first real-world-grounded dialogue dataset for this domain. We then propose AI-Salesman, a novel framework featuring a dual-stage architecture. For the training stage, we design a Bayesian-supervised reinforcement learning algorithm that learns robust sales strategies from noisy dialogues. For the inference stage, we introduce the Dynamic Outline-Guided Agent (DOGA), which leverages a pre-built script library to provide dynamic, turn-by-turn strategic guidance. Moreover, we design a comprehensive evaluation framework that combines fine-grained metrics for key sales skills with the LLM-as-a-Judge paradigm. Experimental results demonstrate that our proposed AI-Salesman significantly outperforms baseline models in both automatic metrics and comprehensive human evaluations, showcasing its effectiveness in complex persuasive scenarios.

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent-variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman--Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. We show on various synthetic and real-world datasets that our proposed training scheme outperforms the state of the art in terms of predictive performance.

While Large Language Models (LLMs) have demonstrated impressive accomplishments in both reasoning and planning, their abilities in multi-agent collaborations remains largely unexplored. This study evaluates LLM-based agents in a multi-agent cooperative text game with Theory of Mind (ToM) inference tasks, comparing their performance with Multi-Agent Reinforcement Learning (MARL) and planning-based baselines. We observed evidence of emergent collaborative behaviors and high-order Theory of Mind capabilities among LLM-based agents. Our results reveal limitations in LLM-based agents' planning optimization due to systematic failures in managing long-horizon contexts and hallucination about the task state. We explore the use of explicit belief state representations to mitigate these issues, finding that it enhances task performance and the accuracy of ToM inferences for LLM-based agents.

Traditional scientific discovery relies on an iterative hypothesise-experiment-refine cycle that has driven progress for centuries, but its intuitive, ad-hoc implementation often wastes resources, yields inefficient designs, and misses critical insights. This tutorial presents Bayesian Optimisation (BO), a principled probability-driven framework that formalises and automates this core scientific cycle. BO uses surrogate models (e.g., Gaussian processes) to model empirical observations as evolving hypotheses, and acquisition functions to guide experiment selection, balancing exploitation of known knowledge and exploration of uncharted domains to eliminate guesswork and manual trial-and-error. We first frame scientific discovery as an optimisation problem, then unpack BO's core components, end-to-end workflows, and real-world efficacy via case studies in catalysis, materials science, organic synthesis, and molecule discovery. We also cover critical technical extensions for scientific applications, including batched experimentation, heteroscedasticity, contextual optimisation, and human-in-the-loop integration. Tailored for a broad audience, this tutorial bridges AI advances in BO with practical natural science applications, offering tiered content to empower cross-disciplinary researchers to design more efficient experiments and accelerate principled scientific discovery.

AI agents built on large language models (LLMs) hold enormous promise, but current practice focuses on a one-task-one-agent approach, which not only falls short of scalability and generality, but also suffers from the fundamental limitations of autoregressive LLMs. On the other hand, humans are general agents who reason by mentally simulating the outcomes of their actions and plans. Moving towards a more general and powerful AI agent, we introduce SimuRA, a goal-oriented architecture for generalized agentic reasoning. Based on a principled formulation of optimal agent in any environment, \modelname overcomes the limitations of autoregressive reasoning by introducing a world model for planning via simulation. The generalized world model is implemented using LLM, which can flexibly plan in a wide range of environments using the concept-rich latent space of natural language. Experiments on difficult web browsing tasks show that \modelname improves the success of flight search from 0\% to 32.2\%. World-model-based planning, in particular, shows consistent advantage of up to 124\% over autoregressive planning, demonstrating the advantage of world model simulation as a reasoning paradigm. We are excited about the possibility for training a single, general agent model based on LLMs that can act superintelligently in all environments. To start, we make SimuRA, a web-browsing agent built on \modelname with pretrained LLMs, available as a research demo for public testing.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

Scientific agents must learn not only how to reason, but also what to believe. However, existing LLM agents typically express scientific hypotheses in free-form text, leaving their beliefs implicit and difficult to test or revise. We introduce EvoSCM, which equips scientific agents with explicit structural causal models that evolve as new experimental evidence is collected. EvoSCM maintains a population of competing SCM hypotheses, each encoding a candidate causal explanation of the environment, and evolves them through a closed discovery loop. In each round, the agent abduces latent mechanisms from accumulated evidence, designs discriminative interventions, and commits to falsifiable predictions that it tests through experimentation. Discrepancies between prediction and observation are inductively distilled into correction rules that revise the causal structures and mechanisms of each hypothesis, and the agent then deductively validates the revised population against accumulated evidence and structural consistency to guide the next round. We evaluate EvoSCM on DiscoverPhysics, a benchmark requiring agents to uncover the hidden dynamics of noncanonical physical worlds through experimentation. EvoSCM consistently improves scientific discovery over baselines, yielding more accurate explanations and predictions while making more effective use of experimental interactions.

Before taking actions in an environment with more than one intelligent agent, an autonomous agent may benefit from reasoning about the other agents and utilizing a notion of a guarantee or confidence about the behavior of the system. In this article, we propose a novel multi-agent reinforcement learning (MARL) algorithm CAMMARL, which involves modeling the actions of other agents in different situations in the form of confident sets, i.e., sets containing their true actions with a high probability. We then use these estimates to inform an agent's decision-making. For estimating such sets, we use the concept of conformal predictions, by means of which, we not only obtain an estimate of the most probable outcome but get to quantify the operable uncertainty as well. For instance, we can predict a set that provably covers the true predictions with high probabilities (e.g., 95%). Through several experiments in two fully cooperative multi-agent tasks, we show that CAMMARL elevates the capabilities of an autonomous agent in MARL by modeling conformal prediction sets over the behavior of other agents in the environment and utilizing such estimates to enhance its policy learning.

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists ubiquitously in social media, finance and health informatics but is rarely investigated by the conventional research in reinforcement learning. To this end, we present a novel framework of the model-based reinforcement learning where the agent's actions and observations are asynchronous stochastic discrete events occurring in continuous-time. We model the dynamics of the environment by Hawkes process with external intervention control term and develop an algorithm to embed such process in the Bellman equation which guides the direction of the value gradient. We demonstrate the superiority of our method in both synthetic simulator and real-world problem.

We present an online method for embodied agents to learn and accomplish diverse user goals. While offline methods like RLHF can represent various goals but require large datasets, our approach achieves similar flexibility with online efficiency. We extract natural language goal representations from conversations with Large Language Models (LLMs). We prompt an LLM to role play as a human with different goals and use the corresponding likelihoods to run Bayesian inference over potential goals. As a result, our method can represent uncertainty over complex goals based on unrestricted dialog. We evaluate our method in grocery shopping and home robot assistance domains using a text-based interface and AI2Thor simulation respectively. Results show our method outperforms ablation baselines that lack either explicit goal representation or probabilistic inference.

Large language models (LLMs) are increasingly deployed on long-horizon tasks in partially observable environments, where they must act while inferring and tracking a complex environment state over many steps. This leads to two challenges: partial observability requires maintaining uncertainty over unobserved world attributes, and long interaction history causes context to grow without bound, diluting task-relevant information. A principled solution to both challenges is a belief state: a posterior distribution over environment states given past observations and actions, which compactly encodes history for decision making regardless of episode length. In LLM agents, however, the open-ended nature of text makes it unclear how to represent such a distribution. Therefore, we introduce Agent-BRACE: Agent Belief state Representation via Abstraction and Confidence Estimation, a method that decouples an LLM agent into a belief state model and a policy model, jointly optimized via reinforcement learning. The belief state model produces a structured approximation of the belief distribution: a set of atomic natural language claims about the environment, each annotated with an ordinal verbalized certainty label ranging from certain to unknown. The policy model conditions on this compact, structured approximate belief rather than the full history, learning to select actions under explicit uncertainty. Across long-horizon, partially observable embodied language environments, Agent-BRACE achieves an average absolute improvement of +14.5% (Qwen2.5-3B-Instruct) and +5.3% (Qwen3-4B-Instruct), outperforming strong RL baselines while maintaining a near-constant context window independent of episode length. Further analysis shows that the learned belief becomes increasingly calibrated over the course of an episode as evidence accumulates.

We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than explicitly simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models agents' computational constraints explicitly, via a latent variable (inferred jointly with a model of agents' goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks -- inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games -- we show that L-IBMs match or outperform Boltzmann models of decision-making under uncertainty. Inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty.

Large Language Models (LLMs) trained with reinforcement learning and verifiable rewards have achieved strong results on complex reasoning tasks. Recent work extends this paradigm to a multi-agent setting, where a meta-thinking agent proposes plans and monitors progress while a reasoning agent executes subtasks through sequential conversational turns. Despite promising performance, we identify a critical limitation: lazy agent behavior, in which one agent dominates while the other contributes little, undermining collaboration and collapsing the setup to an ineffective single agent. In this paper, we first provide a theoretical analysis showing why lazy behavior naturally arises in multi-agent reasoning. We then introduce a stable and efficient method for measuring causal influence, helping mitigate this issue. Finally, as collaboration intensifies, the reasoning agent risks getting lost in multi-turn interactions and trapped by previous noisy responses. To counter this, we propose a verifiable reward mechanism that encourages deliberation by allowing the reasoning agent to discard noisy outputs, consolidate instructions, and restart its reasoning process when necessary. Extensive experiments demonstrate that our framework alleviates lazy agent behavior and unlocks the full potential of multi-agent framework for complex reasoning tasks.

Predictive models often need to work with incomplete information in real-world tasks. Consequently, they must provide reliable probability or confidence estimation, especially in large-scale decision-making and planning tasks. Current large language models (LLMs) are insufficient for accurate estimations, but they can generate relevant factors that may affect the probabilities, produce coarse-grained probabilities when the information is more complete, and help determine which factors are relevant to specific downstream contexts. In this paper, we make use of these capabilities of LLMs to provide a significantly more accurate probabilistic estimation. We propose BIRD, a novel probabilistic inference framework that aligns a Bayesian network with LLM abductions and then estimates more accurate probabilities in a deduction step. We show BIRD provides reliable probability estimations that are 30% better than those provided directly by LLM baselines. These estimates further contribute to better and more trustworthy decision making.

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can diverge under interventions, so observational adequacy alone cannot guarantee interventional competence. We begin by laying foundations, definitions of knowledge, learning, intelligence, counterfactual competence and AGI, and then analyze the limits of observational learning that motivate an error centric shift. We recast the problem as three questions about how explicit and implicit errors evolve under an agent's actions, which errors are unreachable within a fixed hypothesis space, and how conjecture and criticism expand that space. From these questions we propose Causal Mechanics, a mechanisms first program in which hypothesis space change is a first class operation and probabilistic structure is used when useful rather than presumed. We advance structural principles that make error discovery and correction tractable, including a differential Locality and Autonomy Principle for modular interventions, a gauge invariant form of Independent Causal Mechanisms for separability, and the Compositional Autonomy Principle for analogy preservation, together with actionable diagnostics. The aim is a scaffold for systems that can convert unreachable errors into reachable ones and correct them.

Active inference is a unifying theory for perception and action resting upon the idea that the brain maintains an internal model of the world by minimizing free energy. From a behavioral perspective, active inference agents can be seen as self-evidencing beings that act to fulfill their optimistic predictions, namely preferred outcomes or goals. In contrast, reinforcement learning requires human-designed rewards to accomplish any desired outcome. Although active inference could provide a more natural self-supervised objective for control, its applicability has been limited because of the shortcomings in scaling the approach to complex environments. In this work, we propose a contrastive objective for active inference that strongly reduces the computational burden in learning the agent's generative model and planning future actions. Our method performs notably better than likelihood-based active inference in image-based tasks, while also being computationally cheaper and easier to train. We compare to reinforcement learning agents that have access to human-designed reward functions, showing that our approach closely matches their performance. Finally, we also show that contrastive methods perform significantly better in the case of distractors in the environment and that our method is able to generalize goals to variations in the background. Website and code: https://contrastive-aif.github.io/

The optimization of expensive-to-evaluate black-box functions is prevalent in various scientific disciplines. Bayesian optimization is an automatic, general and sample-efficient method to solve these problems with minimal knowledge of the underlying function dynamics. However, the ability of Bayesian optimization to incorporate prior knowledge or beliefs about the function at hand in order to accelerate the optimization is limited, which reduces its appeal for knowledgeable practitioners with tight budgets. To allow domain experts to customize the optimization routine, we propose ColaBO, the first Bayesian-principled framework for incorporating prior beliefs beyond the typical kernel structure, such as the likely location of the optimizer or the optimal value. The generality of ColaBO makes it applicable across different Monte Carlo acquisition functions and types of user beliefs. We empirically demonstrate ColaBO's ability to substantially accelerate optimization when the prior information is accurate, and to retain approximately default performance when it is misleading.

Pass@k is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained. We present a principled Bayesian evaluation framework that replaces Pass@k and average accuracy over N trials (avg@N) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences. Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate. Theoretically, under a uniform prior, the Bayesian posterior mean is order-equivalent to average accuracy (Pass@1), explaining its empirical robustness while adding principled uncertainty. Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT'25, and BrUMO'25, the posterior-based procedure achieves faster convergence and greater rank stability than Pass@k and recent variants, enabling reliable comparisons at far smaller sample counts. The framework clarifies when observed gaps are statistically meaningful (non-overlapping credible intervals) versus noise, and it naturally extends to graded, rubric-based evaluations. Together, these results recommend replacing Pass@k for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit. Source code is available at https://github.com/mohsenhariri/scorio

When one agent interacts with a multi-agent environment, it is challenging to deal with various opponents unseen before. Modeling the behaviors, goals, or beliefs of opponents could help the agent adjust its policy to adapt to different opponents. In addition, it is also important to consider opponents who are learning simultaneously or capable of reasoning. However, existing work usually tackles only one of the aforementioned types of opponents. In this paper, we propose model-based opponent modeling (MBOM), which employs the environment model to adapt to all kinds of opponents. MBOM simulates the recursive reasoning process in the environment model and imagines a set of improving opponent policies. To effectively and accurately represent the opponent policy, MBOM further mixes the imagined opponent policies according to the similarity with the real behaviors of opponents. Empirically, we show that MBOM achieves more effective adaptation than existing methods in a variety of tasks, respectively with different types of opponents, i.e., fixed policy, na\"ive learner, and reasoning learner.

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal set of weights but also the ability to quantify uncertainty in decision making using the posterior distribution. Markov chain Monte Carlo (MCMC) techniques are typically used to obtain sample-based estimates of the posterior distribution. However, these techniques face challenges in convergence and scalability, particularly in settings with large datasets and network architectures. This paper address these challenges in two ways. First, parallel tempering is used used to explore multiple modes of the posterior distribution and implemented in multi-core computing architecture. Second, we make within-chain sampling schemes more efficient by using Langevin gradient information in forming Metropolis-Hastings proposal distributions. We demonstrate the techniques using time series prediction and pattern classification applications. The results show that the method not only improves the computational time, but provides better prediction or decision making capabilities when compared to related methods.

Algorithms increasingly serve as information mediators--from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g. an LLM) controls the information structure of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (altruistic planner) or to induce a specific action the planner prefers (biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. We prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. Notably, in some regimes the biased planner intentionally obfuscates the agents' signals. Even under stringent transparency constraints--information parity with individuals, no lying or cherry-picking, and full observability--we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning consistent with the cognitive patterns of both humans and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators.

The rapid progress of foundation models has led to the prosperity of autonomous agents, which leverage the universal capabilities of foundation models to conduct reasoning, decision-making, and environmental interaction. However, the efficacy of agents remains limited when operating in intricate, realistic environments. In this work, we introduce the principles of Unified Alignment for Agents (UA^2), which advocate for the simultaneous alignment of agents with human intentions, environmental dynamics, and self-constraints such as the limitation of monetary budgets. From the perspective of UA^2, we review the current agent research and highlight the neglected factors in existing agent benchmarks and method candidates. We also conduct proof-of-concept studies by introducing realistic features to WebShop, including user profiles to demonstrate intentions, personalized reranking for complex environmental dynamics, and runtime cost statistics to reflect self-constraints. We then follow the principles of UA^2 to propose an initial design of our agent, and benchmark its performance with several candidate baselines in the retrofitted WebShop. The extensive experimental results further prove the importance of the principles of UA^2. Our research sheds light on the next steps of autonomous agent research with improved general problem-solving abilities.

The rapid development of mobile GUI agents has stimulated growing research interest in long-horizon task automation. However, building agents for these tasks faces a critical bottleneck: the reliance on ever-expanding interaction history incurs substantial context overhead. Existing context management and compression techniques often fail to preserve vital semantic information, leading to degraded task performance. We propose AgentProg, a program-guided approach for agent context management that reframes the interaction history as a program with variables and control flow. By organizing information according to the structure of program, this structure provides a principled mechanism to determine which information should be retained and which can be discarded. We further integrate a global belief state mechanism inspired by Belief MDP framework to handle partial observability and adapt to unexpected environmental changes. Experiments on AndroidWorld and our extended long-horizon task suite demonstrate that AgentProg has achieved the state-of-the-art success rates on these benchmarks. More importantly, it maintains robust performance on long-horizon tasks while baseline methods experience catastrophic degradation. Our system is open-sourced at https://github.com/MobileLLM/AgentProg.

Addressing the discrepancies between predictions and actual outcomes often aids individuals in expanding their thought processes and engaging in reflection, thereby facilitating reasoning in the correct direction. In this paper, we introduce PreAct, an agent framework that integrates prediction with reasoning and action. Leveraging the information provided by predictions, a large language model (LLM) based agent can offer more diversified and strategically oriented reasoning, which in turn leads to more effective actions that help the agent complete complex tasks. Our experiments demonstrate that PreAct outperforms the ReAct approach in accomplishing complex tasks and that PreAct can be co-enhanced when combined with Reflexion methods. We prompt the model with different numbers of historical predictions and find that historical predictions have a sustained positive effect on LLM planning. The differences in single-step reasoning between PreAct and ReAct show that PreAct indeed offers advantages in terms of diversity and strategic directivity over ReAct.

Theory of mind (ToM; Premack & Woodruff, 1978) broadly refers to humans' ability to represent the mental states of others, including their desires, beliefs, and intentions. We propose to train a machine to build such models too. We design a Theory of Mind neural network -- a ToMnet -- which uses meta-learning to build models of the agents it encounters, from observations of their behaviour alone. Through this process, it acquires a strong prior model for agents' behaviour, as well as the ability to bootstrap to richer predictions about agents' characteristics and mental states using only a small number of behavioural observations. We apply the ToMnet to agents behaving in simple gridworld environments, showing that it learns to model random, algorithmic, and deep reinforcement learning agents from varied populations, and that it passes classic ToM tasks such as the "Sally-Anne" test (Wimmer & Perner, 1983; Baron-Cohen et al., 1985) of recognising that others can hold false beliefs about the world. We argue that this system -- which autonomously learns how to model other agents in its world -- is an important step forward for developing multi-agent AI systems, for building intermediating technology for machine-human interaction, and for advancing the progress on interpretable AI.

The acute phase of the Covid-19 pandemic has made apparent the need for decision support based upon accurate epidemic modeling. This process is substantially hampered by under-reporting of cases and related data incompleteness issues. In this article we adopt the Bayesian paradigm and synthesize publicly available data via a discrete-time stochastic epidemic modeling framework. The models allow for estimating the total number of infections while accounting for the endemic phase of the pandemic. We assess the prediction of the infection rate utilizing mobility information, notably the principal components of the mobility data. We evaluate variational Bayes in this context and find that Hamiltonian Monte Carlo offers a robust inference alternative for such models. We elaborate upon vector analysis of the epidemic dynamics, thus enriching the traditional tools used for decision making. In particular, we show how certain 2-dimensional plots on the phase plane may yield intuitive information regarding the speed and the type of transmission dynamics. We investigate the potential of a two-stage analysis as a consequence of cutting feedback, for inference on certain functionals of the model parameters. Finally, we show that a point mass on critical parameters is overly restrictive and investigate informative priors as a suitable alternative.

Large language model (LLM)-based systems are increasingly deployed to conduct scientific research autonomously, yet whether their reasoning adheres to the epistemic norms that make scientific inquiry self-correcting is poorly understood. Here, we evaluate LLM-based scientific agents across eight domains, spanning workflow execution to hypothesis-driven inquiry, through more than 25,000 agent runs and two complementary lenses: (i) a systematic performance analysis that decomposes the contributions of the base model and the agent scaffold, and (ii) a behavioral analysis of the epistemological structure of agent reasoning. We observe that the base model is the primary determinant of both performance and behavior, accounting for 41.4% of explained variance versus 1.5% for the scaffold. Across all configurations, evidence is ignored in 68% of traces, refutation-driven belief revision occurs in 26%, and convergent multi-test evidence is rare. The same reasoning pattern appears whether the agent executes a computational workflow or conducts hypothesis-driven inquiry. They persist even when agents receive near-complete successful reasoning trajectories as context, and the resulting unreliability compounds across repeated trials in epistemically demanding domains. Thus, current LLM-based agents execute scientific workflows but do not exhibit the epistemic patterns that characterize scientific reasoning. Outcome-based evaluation cannot detect these failures, and scaffold engineering alone cannot repair them. Until reasoning itself becomes a training target, the scientific knowledge produced by such agents cannot be justified by the process that generated it.

Multi-agent systems have emerged as a powerful paradigm for automating scientific discovery. To differentiate agent behavior in the multi-agent system, current frameworks typically assign generic role-based personas such as ''reviewer'' or ''writer'' or rely on coarse grained keyword-based personas. While functional, this approach oversimplifies how human scientists operate, whose contributions are shaped by their unique research trajectories. In response, we propose INDIBATOR, a framework for molecular discovery that grounds agents in individualized scientist profiles constructed from two modalities: publication history for literature-derived knowledge and molecular history for structural priors. These agents engage in multi-turn debate through proposal, critique, and voting phases. Our evaluation demonstrates that these fine-grained individuality-grounded agents consistently outperform systems relying on coarse-grained personas, achieving competitive or state-of-the-art performance. These results validate that capturing the ``scientific DNA'' of individual agents is essential for high-quality discovery.

Data-driven social science research is inherently slow, relying on iterative cycles of observation, hypothesis generation, and experimental validation. While recent data-driven methods promise to accelerate parts of this process, they largely fail to support end-to-end scientific discovery. To address this gap, we introduce EXPERIGEN, an agentic framework that operationalizes end-to-end discovery through a Bayesian optimization inspired two-phase search, in which a Generator proposes candidate hypotheses and an Experimenter evaluates them empirically. Across multiple domains, EXPERIGEN consistently discovers 2-4x more statistically significant hypotheses that are 7-17 percent more predictive than prior approaches, and naturally extends to complex data regimes including multimodal and relational datasets. Beyond statistical performance, hypotheses must be novel, empirically grounded, and actionable to drive real scientific progress. To evaluate these qualities, we conduct an expert review of machine-generated hypotheses, collecting feedback from senior faculty. Among 25 reviewed hypotheses, 88 percent were rated moderately or strongly novel, 70 percent were deemed impactful and worth pursuing, and most demonstrated rigor comparable to senior graduate-level research. Finally, recognizing that ultimate validation requires real-world evidence, we conduct the first A/B test of LLM-generated hypotheses, observing statistically significant results with p less than 1e-6 and a large effect size of 344 percent.

Predicting the answer to interventional ``what if'' questions --- the outcome of an action never taken --- requires a mechanistic, causal model, not a curve fit; and learning such a model requires experiments, because passive data leaves its mechanisms unidentified. Experiments are expensive, so the central problem is data efficiency. We present the Model Discovery Agent (MDA), which couples a large language model (LLM), used as a proposer of candidate structures, with standard Bayesian machinery --- sequential Monte Carlo (SMC) for parameter and structure posteriors, simulation-based inference (SBI) for intractable likelihoods, and value-of-information (VoI) for experiment design --- to discover latent mechanistic world models from few interventions. MDA operates in the M-open setting: when the truth lies outside the current hypothesis class, a predictive check flags the inadequacy and the proposer expands the hypothesis space with a new model whose parameters are then identified by designed experiments. We show that discovery and design reinforce: the design step identifies the mechanism the discovery step proposes, and the identified mechanism improves predictions, enabling further discoveries from the remaining unexplained residuals. On three different benchmarks --- covering physics (\DPbench, wiemann2026discoverphysics), chemistry (\CHEMbench, kabra2026autoscilab) and biology (\HHbench, a new partially observed single-neuron electrophysiology benchmark we create) --- we show that MDA sets a new SOTA in terms of data-efficient model learning and reliable interventional prediction ability.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a generative model of the world and plan actions in the future that will maintain the agent in an homeostatic state that satisfies its preferences. This framework lends itself to being realized in silico, as it comprehends important aspects that make it computationally affordable, such as variational inference and amortized planning. In this work, we investigate the tool of deep learning to design and realize artificial agents based on active inference, presenting a deep-learning oriented presentation of the free energy principle, surveying works that are relevant in both machine learning and active inference areas, and discussing the design choices that are involved in the implementation process. This manuscript probes newer perspectives for the active inference framework, grounding its theoretical aspects into more pragmatic affairs, offering a practical guide to active inference newcomers and a starting point for deep learning practitioners that would like to investigate implementations of the free energy principle.

Reinforcement finetuning (RFT) is a key technique for aligning Large Language Models (LLMs) with human preferences and enhancing reasoning, yet its effectiveness is highly sensitive to which tasks are explored during training. Uniform task sampling is inefficient, wasting computation on tasks that are either trivial or unsolvable, while existing task selection methods often suffer from high rollout costs, poor adaptivity, or incomplete evidence. We introduce BOTS, a unified framework for Bayesian Online Task Selection in LLM reinforcement finetuning. Grounded in Bayesian inference, BOTS adaptively maintains posterior estimates of task difficulty as the model evolves. It jointly incorporates explicit evidence from direct evaluations of selected tasks and implicit evidence inferred from these evaluations for unselected tasks, with Thompson sampling ensuring a principled balance between exploration and exploitation for task selection. To make implicit evidence practical, we instantiate it with an ultra-light interpolation-based plug-in that estimates difficulties of tasks without extra rollouts, adding negligible overhead. Empirically, across diverse domains and LLM scales, BOTS consistently improves data efficiency and performance over baselines and ablations, providing a practical and extensible solution for dynamic task selection in RFT. Code is available at https://github.com/agentscope-ai/Trinity-RFT/tree/main/examples/bots.

These lecture notes give a statistical perspective on the foundations of reinforcement learning and interactive decision making. We present a unifying framework for addressing the exploration-exploitation dilemma using frequentist and Bayesian approaches, with connections and parallels between supervised learning/estimation and decision making as an overarching theme. Special attention is paid to function approximation and flexible model classes such as neural networks. Topics covered include multi-armed and contextual bandits, structured bandits, and reinforcement learning with high-dimensional feedback.

Recent advances in the intrinsic reasoning capabilities of large language models (LLMs) have given rise to LLM-based agent systems that exhibit near-human performance on a variety of automated tasks. However, although these systems share similarities in terms of their use of LLMs, different reasoning frameworks of the agent system steer and organize the reasoning process in different ways. In this survey, we propose a systematic taxonomy that decomposes agentic reasoning frameworks and analyze how these frameworks dominate framework-level reasoning by comparing their applications across different scenarios. Specifically, we propose an unified formal language to further classify agentic reasoning systems into single-agent methods, tool-based methods, and multi-agent methods. After that, we provide a comprehensive review of their key application scenarios in scientific discovery, healthcare, software engineering, social simulation, and economics. We also analyze the characteristic features of each framework and summarize different evaluation strategies. Our survey aims to provide the research community with a panoramic view to facilitate understanding of the strengths, suitable scenarios, and evaluation practices of different agentic reasoning frameworks.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

This comprehensive report distinguishes prior works by the cognitive functions they innovate. Many works claim an almost "human-like" cognitive capability in their world models. To evaluate these claims requires a proper grounding in first principles in Cognitive Architecture Theory (CAT). We present a conceptual unified framework for world models that fully incorporates all the cognitive functions associated with CAT (i.e. memory, perception, language, reasoning, imagining, motivation, and meta-cognition) and identify gaps in the research as a guide for future states of the art. In particular, we find that motivation (especially intrinsic motivation) and meta-cognition remain drastically under-researched, and we propose concrete directions informed by active inference and global workspace theory to address them. We further introduce Epistemic World Models, a new category encompassing agent frameworks for scientific discovery that operate over structured knowledge. Our taxonomy, applied across video, embodied, and epistemic world models, suggests research directions where prior taxonomies have not.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

With recent advancements in natural language processing, Large Language Models (LLMs) have emerged as powerful tools for various real-world applications. Despite their prowess, the intrinsic generative abilities of LLMs may prove insufficient for handling complex tasks which necessitate a combination of task planning and the usage of external tools. In this paper, we first propose a structured framework tailored for LLM-based AI Agents and discuss the crucial capabilities necessary for tackling intricate problems. Within this framework, we design two distinct types of agents (i.e., one-step agent and sequential agent) to execute the inference process. Subsequently, we instantiate the framework using various LLMs and evaluate their Task Planning and Tool Usage (TPTU) abilities on typical tasks. By highlighting key findings and challenges, our goal is to provide a helpful resource for researchers and practitioners to leverage the power of LLMs in their AI applications. Our study emphasizes the substantial potential of these models, while also identifying areas that need more investigation and improvement.

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

Are world models a necessary ingredient for flexible, goal-directed behaviour, or is model-free learning sufficient? We provide a formal answer to this question, showing that any agent capable of generalizing to multi-step goal-directed tasks must have learned a predictive model of its environment. We show that this model can be extracted from the agent's policy, and that increasing the agents performance or the complexity of the goals it can achieve requires learning increasingly accurate world models. This has a number of consequences: from developing safe and general agents, to bounding agent capabilities in complex environments, and providing new algorithms for eliciting world models from agents.

Understanding agent behavior requires methods that scale to thousands of trajectories and surface new patterns in long, often unfamiliar tasks where pre-built classifiers fall short. We propose to bring grounded theory into agent trajectory analysis: a six-decade-old qualitative method from the social sciences, with a principled saturation criterion and an auditable trail from data to theory. We propose AutoTraceGT (Automated Trace analysis through Grounded Theory), the first multi-agent pipeline that automates grounded theory on agent trajectories. It iteratively performs open, axial, and theoretical coding until saturation, producing a behavioral taxonomy tailored to each task. Across six trajectory corpora, AutoTraceGT produces codebooks that recover 73-91 percent of the failure modes in human-annotated taxonomies and surface additional patterns that those taxonomies miss. The emergent theoretical narrative aligns with prior expert accounts. Used as a deductive feature space, the codebook outperforms zero-shot and few-shot LLM baselines on downstream failure prediction. These results suggest Grounded Theory offers a scalable analytic tool for ML researchers and agent developers studying what agents actually do.

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms can produce computationally unfaithful posterior approximations. Our results show that all benchmarked algorithms -- (Sequential) Neural Posterior Estimation, (Sequential) Neural Ratio Estimation, Sequential Neural Likelihood and variants of Approximate Bayesian Computation -- can yield overconfident posterior approximations, which makes them unreliable for scientific use cases and falsificationist inquiry. Failing to address this issue may reduce the range of applicability of simulation-based inference. For this reason, we argue that research efforts should be made towards theoretical and methodological developments of conservative approximate inference algorithms and present research directions towards this objective. In this regard, we show empirical evidence that ensembling posterior surrogates provides more reliable approximations and mitigates the issue.

Modern AI agents increasingly combine conversational interaction with autonomous task execution, such as coding and web research, raising a natural question: what happens when an agent engaged in long-horizon tasks is subjected to user persuasion? We study how belief-level intervention can influence downstream task behavior, a phenomenon we name persuasion propagation. We introduce a behavior-centered evaluation framework that distinguishes between persuasion applied during or prior to task execution. Across web research and coding tasks, we find that on-the-fly persuasion induces weak and inconsistent behavioral effects. In contrast, when the belief state is explicitly specified at task time, belief-prefilled agents conduct on average 26.9\% fewer searches and visit 16.9\% fewer unique sources than neutral-prefilled agents. These results suggest that persuasion, even in prior interaction, can affect the agent's behavior, motivating behavior-level evaluation in agentic systems.

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight question budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one calls the class of prior distributions the `conjugate priors' of the model. This paper gives (1) an abstract formulation of this notion of conjugate prior, using channels, in a graphical language, (2) a simple abstract proof that such conjugate priors yield Bayesian inversions, and (3) a logical description of conjugate priors that highlights the required closure of the priors under updating. The theory is illustrated with several standard examples, also covering multiple updating.

Scientific research based on multimodal clinical data (including medical imaging) requires coordinating clinical, radiological, programming, and biostatistical expertise, a fragmented process that bottlenecks discovery. We present VERITAS (Verifiable Epistemic Reasoning for Image-Derived Hypothesis Testing via Agentic Systems), a clinical co-scientist: a multi-agent system that autonomously tests natural-language hypotheses and produces a fully auditable evidence trail, tracing every conclusion through executable outputs from analysis plan to segmentation masks to statistical code to final verdict. Unlike prior AI-scientist systems, which mainly operate on tabular or text data, VERITAS grounds autonomous discovery directly in medical images. It decomposes the workflow into four phases handled by role-specialized agents, and introduces an epistemic evidence label framework that mechanically classifies outcomes as Supported, Refuted, Underpowered, or Invalid by jointly evaluating significance, effect direction, and study power. This distinction is critical in medical imaging, where non-significant results often reflect insufficient sample size rather than absent effects. We construct a tiered benchmark of 64 hypotheses spanning six complexity levels across cardiac and brain glioma MRI datasets. VERITAS reaches 81.4% verdict accuracy with frontier models and 71.2% with locally-hosted open-weight models (8-30B), outperforming all single-model baselines in both classes. It also produces the highest rate of independently verifiable statistical outputs (86.6%), so even its failures remain diagnosable through artifact inspection. Structured multi-agent decomposition thus substitutes for model scale while preserving the verifiability that scientific discovery demands. We release code, hypothesis bank, and evaluation pipeline at https://github.com/LucZot/veritas.

In recent years, Model-based Multi-Agent Reinforcement Learning (MARL) has demonstrated significant advantages over model-free methods in terms of sample efficiency by using independent environment dynamics world models for data sample augmentation. However, without considering the limited sample size, these methods still lag behind model-free methods in terms of final convergence performance and stability. This is primarily due to the world model's insufficient and unstable representation of global states in partially observable environments. This limitation hampers the ability to ensure global consistency in the data samples and results in a time-varying and unstable distribution mismatch between the pseudo data samples generated by the world model and the real samples. This issue becomes particularly pronounced in more complex multi-agent environments. To address this challenge, we propose a model-based MARL method called GAWM, which enhances the centralized world model's ability to achieve globally unified and accurate representation of state information while adhering to the CTDE paradigm. GAWM uniquely leverages an additional Transformer architecture to fuse local observation information from different agents, thereby improving its ability to extract and represent global state information. This enhancement not only improves sample efficiency but also enhances training stability, leading to superior convergence performance, particularly in complex and challenging multi-agent environments. This advancement enables model-based methods to be effectively applied to more complex multi-agent environments. Experimental results demonstrate that GAWM outperforms various model-free and model-based approaches, achieving exceptional performance in the challenging domains of SMAC.

We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales. This decomposition provides a description of small things; e.g., quantum mechanics - via the Schrodinger equation, ensembles of small things - via statistical mechanics and related fluctuation theorems, through to big things - via classical mechanics. These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every thing, its main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states. The ensuing Bayesian mechanics is compatible with quantum, statistical and classical mechanics and may offer a formal description of lifelike particles.

Recent attempts to combine large language models (LLMs) with causal discovery ask models to infer pairwise directions, propose graph structures, or inject language-model outputs as priors and constraints. These approaches promise faster analysis, but they also obscure whether a causal evidence is supported by data and assumptions or by textual associations, prompt artifacts and hallucinated mechanisms. We argue for a different role for agents in causal discovery. Agents should inspect data, retrieve context, explain method assumptions and clarify graph outputs, but they should not supply edges, orientations, priors, constraints or causal conclusions. We propose the principle that agents assist the workflow, while causal claims remain grounded in data, explicit assumptions, formal algorithms, diagnostics and user or domain-expert decisions. We instantiate this principle in causal-learn+, an online platform that coordinates data analysis, preprocessing, method recommendation, expert-knowledge incorporation, formal discovery and interpretation around the algorithmic ecosystem of causal-learn. A case study on Big Five personality data illustrates agent-assisted pipeline of causal discovery without turning language-model unreliability into causal evidence. The platform is available at causallearn.com.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

Large language model (LLM) agents have demonstrated strong capabilities across diverse domains. However, designing high-performing agentic systems remains challenging. Existing agent search methods suffer from three major limitations: (1) an emphasis on optimizing agentic workflows while under-utilizing proven human-designed components such as memory, planning, and tool use; (2) high evaluation costs, as each newly generated agent must be fully evaluated on benchmarks; and (3) inefficient search in large search space. In this work, we introduce a comprehensive framework to address these challenges. First, We propose a hierarchical search space that jointly models agentic workflow and composable functional components, enabling richer agentic system designs. Building on this structured design space, we introduce a predictive value model that estimates agent performance given agentic system and task description, allowing for efficient, low-cost evaluation during the search process. Finally, we present a hierarchical Monte Carlo Tree Search (MCTS) strategy informed by uncertainty to guide the search. Experiments on seven benchmarks, covering embodied, math, web, tool, and game, show that our method achieves an average performance gain of 8.34\% over state-of-the-art baselines and exhibits faster search progress with steeper improvement trajectories. Code repo is available at https://github.com/Ericccc02/AgentSwift.

Reasoning is a fundamental cognitive process underlying inference, problem-solving, and decision-making. While large language models (LLMs) demonstrate strong reasoning capabilities in closed-world settings, they struggle in open-ended and dynamic environments. Agentic reasoning marks a paradigm shift by reframing LLMs as autonomous agents that plan, act, and learn through continual interaction. In this survey, we organize agentic reasoning along three complementary dimensions. First, we characterize environmental dynamics through three layers: foundational agentic reasoning, which establishes core single-agent capabilities including planning, tool use, and search in stable environments; self-evolving agentic reasoning, which studies how agents refine these capabilities through feedback, memory, and adaptation; and collective multi-agent reasoning, which extends intelligence to collaborative settings involving coordination, knowledge sharing, and shared goals. Across these layers, we distinguish in-context reasoning, which scales test-time interaction through structured orchestration, from post-training reasoning, which optimizes behaviors via reinforcement learning and supervised fine-tuning. We further review representative agentic reasoning frameworks across real-world applications and benchmarks, including science, robotics, healthcare, autonomous research, and mathematics. This survey synthesizes agentic reasoning methods into a unified roadmap bridging thought and action, and outlines open challenges and future directions, including personalization, long-horizon interaction, world modeling, scalable multi-agent training, and governance for real-world deployment.

We present the Bayesian Linguistic Forecaster (BLF), an agentic system for binary forecasting that achieves state-of-the-art performance on the ForecastBench benchmark. The system is built on three ideas. (1) Linguistic belief state: a semi-structured representation combining numerical probability estimates with natural-language evidence summaries, updated by the LLM at each step of an iterative tool-use loop. This contrasts with the common approach of appending all retrieved evidence to an ever-growing, unstructured context. (2) Hierarchical multi-trial aggregation: running K independent trials and combining them using logit-space averaging shrinkage with a data-dependent prior. (3) Hierarchical calibration: Platt scaling with a hierarchical prior, which avoids over-shrinking extreme predictions for sources with skewed base rates. On 400 questions from the ForecastBench leaderboard, BLF outperforms all the top public methods, including Cassi, GPT-5, Grok~4.20, and Foresight-32B. Careful ablation studies, using mixed effects analysis to control for question variability (which accounts for 62\% of the variance in performance), reveals that all 3 components contribute to the overall gains, but some components matter more than others, depending on the base LLM, and the setting (e.g.\ with or without a crowd prior). All our experiments are based on a robust back-testing framework which we develop, which has a leakage rate below 1.5\%, and may be of independent interest.

Large language models (LLMs) have demonstrated strong reasoning, planning, and communication abilities, enabling them to operate as autonomous agents in open environments. While single-agent systems remain limited in adaptability and coordination, recent progress has shifted attention toward multi-agent systems (MAS) composed of interacting LLMs that pursue cooperative, competitive, or mixed objectives. This emerging paradigm provides a powerful testbed for studying social dynamics and strategic behaviors among intelligent agents. However, current research remains fragmented and lacks a unifying theoretical foundation. To address this gap, we present a comprehensive survey of LLM-based multi-agent systems through a game-theoretic lens. By organizing existing studies around the four key elements of game theory: players, strategies, payoffs, and information, we establish a systematic framework for understanding, comparing, and guiding future research on the design and analysis of LLM-based MAS.

Explanations for AI models in high-stakes domains like medicine often lack verifiability, which can hinder trust. To address this, we propose an interactive agent that produces explanations through an auditable sequence of actions. The agent learns a policy to strategically seek external visual evidence to support its diagnostic reasoning. This policy is optimized using reinforcement learning, resulting in a model that is both efficient and generalizable. Our experiments show that this action-based reasoning process significantly improves calibrated accuracy, reducing the Brier score by 18\% compared to a non-interactive baseline. To validate the faithfulness of the agent's explanations, we introduce a causal intervention method. By masking the visual evidence the agent chooses to use, we observe a measurable degradation in its performance (DeltaBrier=+0.029), confirming that the evidence is integral to its decision-making process. Our work provides a practical framework for building AI systems with verifiable and faithful reasoning capabilities.

Reinforcement learning (RL) is frequently employed in fine-tuning large language models (LMs), such as GPT-3, to penalize them for undesirable features of generated sequences, such as offensiveness, social bias, harmfulness or falsehood. The RL formulation involves treating the LM as a policy and updating it to maximise the expected value of a reward function which captures human preferences, such as non-offensiveness. In this paper, we analyze challenges associated with treating a language model as an RL policy and show how avoiding those challenges requires moving beyond the RL paradigm. We start by observing that the standard RL approach is flawed as an objective for fine-tuning LMs because it leads to distribution collapse: turning the LM into a degenerate distribution. Then, we analyze KL-regularised RL, a widely used recipe for fine-tuning LMs, which additionally constrains the fine-tuned LM to stay close to its original distribution in terms of Kullback-Leibler (KL) divergence. We show that KL-regularised RL is equivalent to variational inference: approximating a Bayesian posterior which specifies how to update a prior LM to conform with evidence provided by the reward function. We argue that this Bayesian inference view of KL-regularised RL is more insightful than the typically employed RL perspective. The Bayesian inference view explains how KL-regularised RL avoids the distribution collapse problem and offers a first-principles derivation for its objective. While this objective happens to be equivalent to RL (with a particular choice of parametric reward), there exist other objectives for fine-tuning LMs which are no longer equivalent to RL. That observation leads to a more general point: RL is not an adequate formal framework for problems such as fine-tuning language models. These problems are best viewed as Bayesian inference: approximating a pre-defined target distribution.

Uncertainty quantification (UQ) for large language models (LLMs) is a key building block for safety guardrails of daily LLM applications. Yet, even as LLM agents are increasingly deployed in highly complex tasks, most UQ research still centers on single-turn question-answering. We argue that UQ research must shift to realistic settings with interactive agents, and that a new principled framework for agent UQ is needed. This paper presents the first general formulation of agent UQ that subsumes broad classes of existing UQ setups. Under this formulation, we show that prior works implicitly treat LLM UQ as an uncertainty accumulation process, a viewpoint that breaks down for interactive agents in an open world. In contrast, we propose a novel perspective, a conditional uncertainty reduction process, that explicitly models reducible uncertainty over an agent's trajectory by highlighting "interactivity" of actions. From this perspective, we outline a conceptual framework to provide actionable guidance for designing UQ in LLM agent setups. Finally, we conclude with practical implications of the agent UQ in frontier LLM development and domain-specific applications, as well as open remaining problems.

The study of social emergence has long been a central focus in social science. Traditional modeling approaches, such as rule-based Agent-Based Models (ABMs), struggle to capture the diversity and complexity of human behavior, particularly the irrational factors emphasized in behavioral economics. Recently, large language model (LLM) agents have gained traction as simulation tools for modeling human behavior in social science and role-playing applications. Studies suggest that LLMs can account for cognitive biases, emotional fluctuations, and other non-rational influences, enabling more realistic simulations of socio-economic dynamics. In this work, we introduce TwinMarket, a novel multi-agent framework that leverages LLMs to simulate socio-economic systems. Specifically, we examine how individual behaviors, through interactions and feedback mechanisms, give rise to collective dynamics and emergent phenomena. Through experiments in a simulated stock market environment, we demonstrate how individual actions can trigger group behaviors, leading to emergent outcomes such as financial bubbles and recessions. Our approach provides valuable insights into the complex interplay between individual decision-making and collective socio-economic patterns.

Social reasoning - inferring unobservable beliefs and intentions from partial observations of other agents - remains a challenging task for large language models (LLMs). We evaluate the limits of current reasoning language models in the social deduction game Avalon and find that while the largest models demonstrate strong performance, they require extensive test-time inference and degrade sharply when distilled to smaller, real-time-capable variants. To address this, we introduce a hybrid reasoning framework that externalizes belief inference to a structured probabilistic model, while using an LLM for language understanding and interaction. Our approach achieves competitive performance with much larger models in Agent-Agent play and, notably, is the first language agent to defeat human players in a controlled study - achieving a 67% win rate and receiving higher qualitative ratings than both reasoning baselines and human teammates. We release code, models, and a dataset to support future work on social reasoning in LLM agents, which can be found at https://camp-lab-purdue.github.io/bayesian-social-deduction/

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

Large Language Model (LLM)-based agents are widely used in real-world applications such as customer service, web navigation, and software engineering. As these systems become more autonomous and are deployed at scale, understanding why an agent takes a particular action becomes increasingly important for accountability and governance. However, existing research predominantly focuses on failure attribution to localize explicit errors in unsuccessful trajectories, which is insufficient for explaining the reason behind agent behaviors. To bridge this gap, we propose a novel framework for general agentic attribution, designed to identify the internal factors driving agent actions regardless of the task outcome. Our framework operates hierarchically to manage the complexity of agent interactions. Specifically, at the component level, we employ temporal likelihood dynamics to identify critical interaction steps; then at the sentence level, we refine this localization using perturbation-based analysis to isolate the specific textual evidence. We validate our framework across a diverse suite of agentic scenarios, including standard tool use and subtle reliability risks like memory-induced bias. Experimental results demonstrate that the proposed framework reliably pinpoints pivotal historical events and sentences behind the agent behavior, offering a critical step toward safer and more accountable agentic systems. Codes are available at https://github.com/AI45Lab/AgentDoG.

We propose a general-purpose approach for improving the ability of Large Language Models (LLMs) to intelligently and adaptively gather information from a user or other external source using the framework of sequential Bayesian experimental design (BED). This enables LLMs to act as effective multi-turn conversational agents and interactively interface with external environments. Our approach, which we call BED-LLM (Bayesian Experimental Design with Large Language Models), is based on iteratively choosing questions or queries that maximize the expected information gain (EIG) about the task of interest given the responses gathered previously. We show how this EIG can be formulated in a principled way using a probabilistic model derived from the LLM's belief distribution and provide detailed insights into key decisions in its construction. Further key to the success of BED-LLM are a number of specific innovations, such as a carefully designed estimator for the EIG, not solely relying on in-context updates for conditioning on previous responses, and a targeted strategy for proposing candidate queries. We find that BED-LLM achieves substantial gains in performance across a wide range of tests based on the 20-questions game and using the LLM to actively infer user preferences, compared to direct prompting of the LLM and other adaptive design strategies.

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have exhibited strong reasoning capabilities and emergent reflective behaviors, such as backtracking and error correction. However, conventional Markovian RL confines exploration to the training phase to learn an optimal deterministic policy and depends on the history contexts only through the current state. Therefore, it remains unclear whether reflective reasoning will emerge during Markovian RL training, or why they are beneficial at test time. To remedy this, we recast reflective exploration within the Bayes-Adaptive RL framework, which explicitly optimizes the expected return under a posterior distribution over Markov decision processes. This Bayesian formulation inherently incentivizes both reward-maximizing exploitation and information-gathering exploration via belief updates. Our resulting algorithm, BARL, instructs the LLM to stitch and switch strategies based on the observed outcomes, offering principled guidance on when and how the model should reflectively explore. Empirical results on both synthetic and mathematical reasoning tasks demonstrate that BARL outperforms standard Markovian RL approaches at test time, achieving superior token efficiency with improved exploration effectiveness. Our code is available at https://github.com/shenao-zhang/BARL.

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.

In this paper, we explore the ability to model and infer personality types of opponents, predict their responses, and use this information to adapt a dialog agent's high-level strategy in negotiation tasks. Inspired by the idea of incorporating a theory of mind (ToM) into machines, we introduce a probabilistic formulation to encapsulate the opponent's personality type during both learning and inference. We test our approach on the CraigslistBargain dataset and show that our method using ToM inference achieves a 20% higher dialog agreement rate compared to baselines on a mixed population of opponents. We also find that our model displays diverse negotiation behavior with different types of opponents.

The autoregressive world model exhibits robust generalization capabilities in vectorized scene understanding but encounters difficulties in deriving actions due to insufficient uncertainty modeling and self-delusion. In this paper, we explore the feasibility of deriving decisions from an autoregressive world model by addressing these challenges through the formulation of multiple probabilistic hypotheses. We propose LatentDriver, a framework models the environment's next states and the ego vehicle's possible actions as a mixture distribution, from which a deterministic control signal is then derived. By incorporating mixture modeling, the stochastic nature of decisionmaking is captured. Additionally, the self-delusion problem is mitigated by providing intermediate actions sampled from a distribution to the world model. Experimental results on the recently released close-loop benchmark Waymax demonstrate that LatentDriver surpasses state-of-the-art reinforcement learning and imitation learning methods, achieving expert-level performance. The code and models will be made available at https://github.com/Sephirex-X/LatentDriver.

Can AI effectively perform complex econometric analysis traditionally requiring human expertise? This paper evaluates an agentic AI's capability to master econometrics, focusing on empirical analysis performance. We develop an ``Econometrics AI Agent'' built on the open-source MetaGPT framework. This agent exhibits outstanding performance in: (1) planning econometric tasks strategically, (2) generating and executing code, (3) employing error-based reflection for improved robustness, and (4) allowing iterative refinement through multi-round conversations. We construct two datasets from academic coursework materials and published research papers to evaluate performance against real-world challenges. Comparative testing shows our domain-specialized agent significantly outperforms both benchmark large language models (LLMs) and general-purpose AI agents. This work establishes a testbed for exploring AI's impact on social science research and enables cost-effective integration of domain expertise, making advanced econometric methods accessible to users with minimal coding expertise. Furthermore, our agent enhances research reproducibility and offers promising pedagogical applications for econometrics teaching.

Multi-agent settings in the real world often involve tasks with varying types and quantities of agents and non-agent entities; however, common patterns of behavior often emerge among these agents/entities. Our method aims to leverage these commonalities by asking the question: ``What is the expected utility of each agent when only considering a randomly selected sub-group of its observed entities?'' By posing this counterfactual question, we can recognize state-action trajectories within sub-groups of entities that we may have encountered in another task and use what we learned in that task to inform our prediction in the current one. We then reconstruct a prediction of the full returns as a combination of factors considering these disjoint groups of entities and train this ``randomly factorized" value function as an auxiliary objective for value-based multi-agent reinforcement learning. By doing so, our model can recognize and leverage similarities across tasks to improve learning efficiency in a multi-task setting. Our approach, Randomized Entity-wise Factorization for Imagined Learning (REFIL), outperforms all strong baselines by a significant margin in challenging multi-task StarCraft micromanagement settings.