ATLAS-SR: A Protocol-Indexed Structural Atlas for LLM-Guided Symbolic Regression

Symbolic regression seeks interpretable mathematical expressions that capture relationships in observed data. During search, useful components can appear in candidate equations whose overall fit is poor. We present ATLAS-SR, a framework that uses large language models (LLMs) to guide the recombination of components retained from earlier candidates. The framework tests component contributions within existing equations under consistent fitting conditions. It stores components in a shared graph alongside their tested combinations and the results of these comparisons. These records help the LLM choose which components to reuse and where to try new combinations, allowing useful structures to outlive their original candidates. We evaluate ATLAS-SR on 129 LLM-SRBench tasks spanning four scientific domains with two LLM backbones. Strict out-of-distribution accuracy (\\mathrm{Acc}^{95\\%}_{0.01}) improves by 28.69–29.46 percentage points over the strongest baseline under each backbone. Symbolic accuracy, which measures recovery of the target equation structure, reaches 24.03% with either backbone, exceeding the highest baseline result of 16.28%.