Test-Time Scaling for Scientific Equation Discovery

Abstract:Test-time scaling (TTS) improves language model reasoning by allocating additional test-time compute, but prior work mainly studies closed-ended tasks such as math and coding. We study TTS for automated equation discovery, an open-ended setting where models search over candidate equations and rely on observed datapoints for feedback. We formulate LLM-driven equation discovery as an iterative search process that unifies Best-of-N, sequential refinement, tree search, and evolution-style methods under a common compute-allocation view. To isolate allocation effects from prompt engineering and other heuristics, we compare minimal parallel controllers under fixed budgets. On LLM-SRBench equation-discovery tasks, we find that search width is the dominant allocation parameter: the best width in our sweep generally increases with the compute budget, while the population--branching split and controller choice matter less. Appropriate width selection also improves wall-clock efficiency by increasing parallelism. These results suggest that, given an informative verifier, controlling exploration and exploitation is central to scaling LLM-based equation discovery.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2608.28660 [cs.CL]

(or arXiv:2608.28660v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2608.28660 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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