Test-Time Scaling for Scientific Equation Discovery

• URL: http://arxiv.org/abs/2608.28660v1
• Date: Fri, 21 Aug 2026 07:46:04 GMT
• Title: Test-Time Scaling for Scientific Equation Discovery
• Abstract summary: Test-time scaling (TTS) improves language model reasoning by allocating additional test-time compute.<n>We study TTS for automated equation discovery, an open-ended setting where models search over candidate equations and rely on observed datapoints for feedback.<n>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.
• Score: 9.655883330665942
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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