Postdiagnosis improves symbolic regression by guiding equation fixes
From Score to Diagnosis: Search-Independent Post-Diagnosis for Symbolic Regression
Machine Learning
Summary
Symbolic regression is a way to find equations that explain data, but the usual scores it uses don't clearly show what is wrong or how to fix the equations. The authors designed a method called PostDiag that looks at detailed features of equation behavior to figure out if and how an equation should be improved. PostDiag works independently of the main equation search process and sends useful feedback to help make corrections. Tests show that using PostDiag helps different equation-finding programs make better and faster discoveries.
What this means in practice
- •For data science teams: Improve accuracy and speed when using symbolic regression to model complex datasets by integrating PostDiag feedback for automatic formula repair.
- •For financial modelers: Use enhanced equation diagnosis to refine predictive models from financial data, reducing errors and improving interpretability.
Authors
Qian Li, Yuxiao Hu, Juncheng Liu, Yanhao Jia, Yuntian Chen
Abstract
Symbolic regression (SR) solvers employ diverse search mechanisms, yet most rely on the same low-information scalar fitness. Such scores provide little guidance on why a skeleton fails or how it should be revised. Recent methods develop new methods to address this bottleneck. Their enhanced feedback mechanisms are tightly coupled to their search processes and are difficult to reuse across diverse SR solvers. Instead, we ask whether a shared feedback mechanism can further improve diverse solvers facing the same bottleneck. To this end, we propose PostDiag, a search-independent feedback mechanism, which can be shared to different SR solvers. PostDiag introduces Patch-wise Feature Profiling (PFP) to capture local behavior through patch-wise features of level, trend, and roughness. Based on PFP, PostDiag quantifies Skeleton Expressiveness Risk by comparing the fitted candidate with the observations, and Skeleton Stability Risk by measuring variability of behavior after bootstrap refitting. The Diagnostic Risk Plane (DRP) combines two risks to determine whether a skeleton should be preserved, repaired, simplified, or rewritten, while the patch-wise discrepancies provide evidence for the intervention. An LLM editor then performs the diagnosis-guided intervention, and the validated revision is returned to the original solver through a lightweight adapter. Experiments across multiple LLM-based and GP-based SR solvers show that PostDiag consistently improves accuracy and accelerates convergence.