Test-Time Scaling for Scientific Equation Discovery

A new arXiv preprint (2608.28660v1) finds that search width is the dominant test-time scaling parameter for LLM-driven scientific equation discovery, with the optimal width generally increasing with compute budget. The study, which unifies Best-of-N, sequential refinement, tree search, and evolution-style methods under a common compute-allocation view, shows that appropriate width selection also improves wall-clock efficiency by increasing parallelism on LLM-SRBench tasks.

arXiv:2608.28660v1 Announce Type: new 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.