让大模型自动发现公式更可靠，通过自我反思闭环优化。
STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery
- 用自我反思机制协调生成、评估与修复，形成闭环。
- 在多个基准上提升准确率与外部泛化能力，结构恢复更好。
- 适合需要高可靠性公式发现的研究者或工业应用。
基于大模型的方程发现为从数据中恢复符号规律提供了有前景的路径，但现有系统多依赖以生成为中心的循环：提出候选式、拟合参数、评分结果并重用选定样本。此类循环可能因拟合不可靠而误判有效公式骨架，丢弃需修复的近似正确方程，并积累提供有限指导的冗余记忆。我们提出STRIDE，一种自反思智能体框架，通过协调数据感知生成、混合拟合评估、批评-执行修复以及保多样性语义记忆，提升可靠性。将拟合得分与候选行为转化为共享反馈，使方程可在闭环中被提出、评估、优化与复用。在代表性符号回归基准和LSR-Synth套件上的实验表明，STRIDE在多种大模型底座下均提升了准确性、外部泛化鲁棒性及结构恢复能力，消融实验与分析验证了核心组件的贡献。
原文摘要 · Abstract (English)
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.
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