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

2026-05-17

AI Summary

Current large language model–driven equation discovery methods suffer from insufficient reliability due to spurious structural identification under unreliable fitting, discarding nearly correct yet repairable equations, and accumulating redundant memory. To address these limitations, this work proposes a self-reflective agent framework that integrates data-aware generation, hybrid fitness evaluation, a critique-and-repair mechanism, and diverse semantic memory into a closed-loop symbolic regression system. By transforming both fitness scores and candidate actions into shared feedback signals, the framework enables dynamic equation refinement and efficient reuse of previously discovered expressions. Experimental results demonstrate that the proposed approach significantly improves accuracy, out-of-distribution robustness, and structural recovery across multiple symbolic regression benchmarks and the LSR-Synth test suite. Ablation studies further confirm the contribution of each component to the overall performance gains.

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.

Problem

• equation discovery
• symbolic regression
• LLM-based discovery
• reliability
• automatic scientific discovery

Innovation

• self-reflective agent
• equation discovery
• symbolic regression
• mixed-fitting evaluation
• semantic memory