Beyond Accuracy: A Unified Random Matrix Theory Diagnostic Framework for Crash Classification Models

TL;DR

This paper introduces a spectral diagnostic framework based on Random Matrix Theory and Heavy-Tailed Self-Regularization to evaluate crash classification models, revealing overfitting and model quality beyond traditional metrics.

Contribution

The authors develop a unified spectral diagnostic method applicable across various ML models, providing structural insights and early stopping criteria for crash classification tasks.

Findings

Well-regularized models have spectral exponent $oldsymbol{eta}$ in [2, 4]

Overfit models show $oldsymbol{eta} < 2$ or spectral collapse

Spectral exponent $oldsymbol{eta}$ correlates strongly with expert assessments

Abstract

Crash classification models in transportation safety are typically evaluated using accuracy, F1, or AUC, metrics that cannot reveal whether a model is silently overfitting. We introduce a spectral diagnostic framework grounded in Random Matrix Theory (RMT) and Heavy-Tailed Self-Regularization (HTSR) that spans the ML taxonomy: weight matrices for BERT/ALBERT/Qwen2.5, out-of-fold increment matrices for XGBoost/Random Forest, empirical Hessians for Logistic Regression, induced affinity matrices for Decision Trees, and Graph Laplacians for KNN. Evaluating nine model families on two Iowa DOT crash classification tasks (173,512 and 371,062 records respectively), we find that the power-law exponent $\alpha$ provides a structural quality signal: well-regularized models consistently yield $\alpha$ within $[2, 4]$ (mean $2.87 \pm 0.34$), while overfit variants show $\alpha < 2$ or spectral collapse. We observe a strong rank correlation between $\alpha$ and expert agreement (Spearman $\rho = 0.89$, $p < 0.001$), suggesting spectral quality captures model behaviors aligned with expert reasoning. We propose an $\alpha$-based early stopping criterion and a spectral model selection protocol, and validate both against cross-validated F1 baselines. Sparse Lanczos approximations make the framework scalable to large datasets.