Scientific discovery as meta-optimization: a combinatorial optimization case study

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.

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 is an inherently creative and uncertain process, requiring reasoning beyond the recall of known knowledge. While many benchmarks have been proposed to evaluate large language model (LLM) performance on deep research tasks via multi-hop retrieval, their innovative reasoning abilities essential for true scientific discovery remain largely untested. We introduce a benchmark framework for evaluating model performance in scientific discovery and reasoning, building up from a raw problem to the classical null hypothesis test. In our framework, models initially receive only the topic and research question from a recent paper, with technical details progressively revealed. At each stage of information disclosure, the model is tasked with generating hypotheses that address the research question, which is compared with the conclusions from the original paper and evaluated via automated semantic similarity of constituent atomic claims. This progressive evaluation of semantic divergence from ground-truth conclusions enables assessment of a model's innovativeness (under minimal information) to grounded reasoning capabilities (under full experimental details), both critical for using LLMs for scientific discovery purposes. Our framework provides a foundation for systematically evaluating scientific reasoning and discovery capabilities in LLMs, crucial for advancing the development of next-generation AI scientist/co-scientist systems. Specifically, here we evaluate GPT-5, GPT-5.4, Gemini 2.5 pro, and Gemini 3.1 pro preview across 45 papers spanning bioactive materials, mechanical materials, and nanomaterials. We find that GPT-5.4 and Gemini 3.1 pro outperform their previous generation counterparts as expected, and GPT-5.4 in particular maintains 0.7 F1 score alignment with ground truth conclusions even under minimal context.