When Should Models Change Their Minds? Contextual Belief Management in Large Language Models

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.

Large language models (LLMs) trained on next-token prediction exhibit remarkable in-context learning (ICL) abilities, yet the representations that support ICL remain poorly understood. We consider such representations in a controlled setting: prompting LLMs with data emitted from hidden Markov models (HMMs) and probing for the corresponding belief state -- the posterior distribution over the HMM's hidden states given the observed token history. Across six open-source LLMs prompted with data from 40 HMMs selected for non-trivial belief structure, we find that belief states are linearly decodable from residual stream activations, with peak probe $R^2$-values from 0.83-0.99 across HMM and LLM combinations, ranging from early to late layers. To establish functional relevance, we intervene directly on the probe-identified subspace via patching and steering, resulting in downstream prediction quality on the order of the untampered model, while controls degrade performance substantially. Together, these results provide representation-level evidence that ICL in open-source LLMs approximates optimal Bayesian prediction over a context-inferred generative model. More broadly, our findings extend prior results linking input-distribution structure to activation geometry: from toy networks trained explicitly on HMM data to production-scale LLMs.

Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.