BayesEvolve: Explicit Belief States for Autonomous Scientific Discovery

Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.

Large language models (LLMs) are on the rise for accelerating scientific discovery, most recently in advanced tasks such as generating valid scientific hypotheses. Yet in many discovery settings, the goal is not to identify a single best hypothesis since validation can be noisy and expensive, and scientists benefit from a set of high-quality alternative hypotheses that hedge against downstream uncertainty for the best solutions. Nevertheless, commonly used evolutionary search recipes tend to prioritize optimization over exploration in hypothesis generation, and the resulting selection pressure during the search process leads to diversity collapse. Motivated by these limitations, we formulate hypothesis search as a sampling problem, where the objective is to efficiently produce diverse, high-quality hypotheses under a fixed validation budget. Building on this perspective, we propose \ours, an evolutionary framework inspired by the classical parallel tempering algorithm that searches hypotheses at multiple temperature levels and enables principled information exchange across temperatures to improve exploration without disrupting convergence. Across domains including molecular discovery, equation discovery, and algorithm discovery, our approach consistently improves both hypothesis quality and diversity under the same validation budget, and produces candidates that remain robust under more expensive downstream computational validations.

Scientific discovery often involves optimising expensive-to-evaluate objectives over vast, structured, and open-ended hypothesis spaces, such as molecules, protein sequences, and computer programs. Generative models such as large language models (LLMs) provide expressive priors over such spaces, but their likelihoods and self-assessments are unreliable proxies for the objectives and calibrated epistemic uncertainty, especially for novel candidates outside the observed data distribution. We introduce the Large Discovery Model (LDM), an empirically grounded recurrent architecture that couples a generative model with a Bayesian non-parametric reward surrogate model. The generative model proposes and refines candidate designs, while the surrogate predicts their performance and quantifies uncertainty, yielding an uncertainty-aware value that guides candidate generation, refinement, and selection. The discovery memory and the surrogate model are continually updated as each new experimental observation arrives. We evaluate LDM on three scenarios spanning different design modalities and objectives, including neural-network training, antibody design, and molecular optimisation. Compared to LLM-only reflection or traditional statistical search across these domains, LDM achieves a $2.4\times$ greater reduction in validation BPB, an $18.2\%$ relative decrease in binding energy, and more than $60\%$ relative gains in molecular multi-objective performance. These results suggests that LDM could serve as a general-purpose discovery engine for effective search over open-ended hypothesis spaces.