Coupled Harness--Model Evolution for Scientific Equation Discovery

Pengze Li, Jiaquan Zhang, Encheng Su, Yunbo Long, Zihang Zeng +6

Large language models (LLMs) are increasingly used to discover scientific equations from experimental data. Such a discovery system has two parts that must work together: a library of executable computational tools and the model's tool-use policy. The tools supply the solving capability, from diagnosing structure in the data to fitting candidate equations; the policy plans and orchestrates their use. Yet existing systems adapt only one part, keeping either the toolset or the model fixed, which leaves the corresponding failures uncorrectable. We develop a coupled evolution framework that improves both parts from the same verifiable fit-error signal. In the tool-evolution phase, an agent grows an executable tool library from a small set of generic numerical operations by diagnosing its own failures: it authors a new tool when a capability is missing and revises its selection rules when the right tool went unused. In the policy-evolution phase, a small open model (roughly 3B active parameters) is fine-tuned on successful tool-use trajectories collected with the frozen library, on training formulas screened to be disjoint from all evaluation benchmarks. Ablations show the two phases…