STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery

TL;DR

STRIDE is a self-reflective framework that enhances the reliability of automatic equation discovery using LLMs by integrating data-aware generation, evaluation, repair, and memory mechanisms in a closed-loop process.

Contribution

It introduces a novel self-reflective agent framework that improves symbolic equation discovery accuracy and robustness across different benchmarks and LLM backbones.

Findings

STRIDE outperforms existing methods on symbolic regression benchmarks.

It improves robustness to out-of-distribution data.

Core components of STRIDE significantly contribute to its performance.

Abstract

LLM-based equation discovery offers a promising route to recovering symbolic laws from data, but many systems still rely on generation-centered loops that propose candidates, fit parameters, score results, and reuse selected examples. Such loops can misjudge useful skeletons under unreliable fitting, discard near-correct equations that require repair, and accumulate redundant memories that provide limited guidance. We propose STRIDE, a self-reflective agent framework that improves reliability by coordinating data-aware generation, mixed-fitting evaluation, critic--executor repair, and diversity-preserving semantic memory. By turning fitted scores and candidate behavior into shared feedback, STRIDE enables equations to be proposed, assessed, refined, and reused within a closed-loop discovery process. Experiments on representative symbolic-regression benchmarks and LSR-Synth suites show that STRIDE improves accuracy, OOD robustness, and structural recovery across multiple LLM backbones, with ablations and analyses confirming the contribution of its core components.