From Score to Diagnosis: Search-Independent Post-Diagnosis for Symbolic Regression

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.