LLMs are thought to track "belief states," i.e., running probability distributions over the latent variables that govern language (Shai et al., 2024; Sarfati et al., 2026), but so far this has only been comprehensively demonstrated on toy synthetic data and in a few isolated case studies. It has also never been empirically connected to the geometry of LLM features (the concepts interpretability finds in model activations). In this work, we plant a controllable latent variable inside natural-looking text. An LLM teacher writes ordinary text while we "subliminally" steer it along one of K = 8 unrelated sparse autoencoder directions at each token, with the active directions following a ring-shaped Markov chain. A small transformer model trained on this corpus does indeed track the Bayesian posterior belief about our planted latent variable. Moreover, it also arranges the 8 states themselves on a ring, in the exact order of the Markov chain, which is supporting evidence that a concept's geometry can be formed by the statistical dynamics of the latent variable behind it.
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.
A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7% and 5.0% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.