Provenance-Aware Belief Updating in Human-AI Feedback Loops

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.

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

A language model may revise the same proposition after receiving genuinely relevant evidence or after receiving directional user pressure that adds no relevant fact. The observable response shift alone therefore does not reveal which source drove the change. We introduce BeliefScope, a controlled black-box framework for separating these two sources of influence around a fixed target proposition. BeliefScope crosses Evidence and Pressure with factor-specific local controls and measures response changes through probability reports, categorical judgments, and action recommendations on channel-appropriate scales. To determine when these observable contrasts support reliable attribution, we evaluate the observation design under controlled synthetic conditions. Known-truth recovery and targeted ablations establish where Evidence- and Pressure-related effects can be separated, while semi-synthetic stress tests map how that recoverability changes as the observation process becomes noisier and more heterogeneous. Across a 36-family Qwen/Llama study, with targeted 12-family checks that also include Gemma3-12B, the resulting profiles show substantial evaluation-context dependence: broad model-level differences can change under matched controls, decoding, or response interfaces, while some narrower within-model patterns remain stable. Instruction interventions further show that reduced target-aligned Pressure following can reflect either stable resistance or movement in the opposite direction. BeliefScope summarizes these measurements as a conditional belief-response profile that keeps diagnostic effects tied to the evaluation conditions under which they are observed, together with explicit validity boundaries for that diagnosis.