Authors: Kainat Riaz, Muhammad Ahmed Mohsin, Ahsan Bilal, Muhammad Umer, Ayesha Mohsin, Aqib Riaz, Ali Subhan, John M. Cioffi
Organizations: Stanford University · University of Oklahoma · National University of Sciences and Technology
Abstract
Automated scientific discovery using large language models relies on identifying genuinely novel solutions. Standard reinforcement learning penalizes high-variance mutations, which leads the policy to prioritize familiar patterns. As a result, the maximum reward plateaus even as the average reward increases. Overcoming this limitation requires a signal that distinguishes unexplored regions from intrinsically difficult problems. This necessitates measuring disagreement across independently adapted weight hypotheses rather than relying on a single network's confidence. UG-TTT addresses this challenge by maintaining a small ensemble of low-rank adapters over a frozen base model. The per-token disagreement, quantified as the mutual information between ensemble predictions and weight hypotheses, isolates epistemic uncertainty and identifies positions where insufficient coverage leads to adapter divergence rather than intrinsic problem difficulty. This measure is incorporated as an exploration bonus into the policy gradient, directing the policy toward positions where persistent adapter disagreement signals low training coverage, the same frontier where genuine discovery is possible. A nuclear norm regularizer ensures the adapters remain distinct from one another, thereby preserving the exploration signal throughout training. Across four scientific discovery benchmarks, UG-TTT increases the maximum reward on three tasks, maintains substantially higher solution diversity, and an ablation study confirms that the regularizer is essential for sustaining this behavior.
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.
Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.
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.