Robust Equation Structure Learning with Adaptive Refinement

Abstract

Symbolic regression (SR) aims to automate scientific discovery, but often truncates the hypothetico–deductive cycle, focusing on hypothesis and experiment while lacking systematic analysis. We introduce RESTART, a framework that closes this loop by adding a principled analysis stage to diagnose and correct structural errors. RESTART features two core mechanisms: a short-term refinement process that uses boosting to identify unexplained signals and guide an LLM toward targeted corrections, and a long-term structure library that distills successful refinements into reusable code snippets for cumulative knowledge. On LLM-SRBench across Physics, Biology, and Materials Science, RESTART achieves lower error and higher accuracy than state-of-the-art baselines. It also generalizes robustly, recovering near-exact functional forms on out-of-distribution data, representing a significant advance toward fully automated scientific discovery.