BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation

2026-06-29

AI Summary

This study addresses a critical gap in the evaluation of large language models (LLMs), which has predominantly focused on single-turn responses while neglecting their capacity to rationally update beliefs across multi-turn dialogues as evidence accumulates. The authors construct a multi-round simulated environment to systematically assess, for the first time, the alignment between LLMs’ belief trajectories and Bayesian posteriors under incrementally revealed evidence. Drawing on a Bayesian inference framework, they design three progressively complex tasks—parameter estimation, outcome prediction, and joint inference involving user roles—and evaluate seven models spanning 3B to 70B parameters. Results indicate that larger model scales enhance latent state inference and evidence integration, with some belief updates approaching Bayesian rationality; however, performance remains unstable in downstream prediction tasks, revealing a notable gap between theoretically rational inference and practical application.

Abstract

Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.

Problem

• belief updating
• Bayesian reasoning
• multi-turn dialogue
• evidence accumulation
• epistemic uncertainty

Innovation

• Bayesian reasoning
• belief updating
• multi-turn dialogue
• evidence accumulation
• latent inference