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

Training Neural Networks (NNs) without overfitting is difficult; detecting that overfitting is difficult as well. We present a novel Random Matrix Theory method that detects the onset of overfitting in deep learning models without access to train or test data. For each model layer, we randomize each weight matrix element-wise, $\mathbf{W} \to \mathbf{W}^{\mathrm{rand}}$, fit the randomized empirical spectral distribution with a Marchenko-Pastur distribution, and identify large outliers that violate self-averaging. We call these outliers Correlation Traps. During the onset of overfitting, which we call the "anti-grokking" phase in long-horizon grokking, Correlation Traps form and grow in number and scale as test accuracy decreases while train accuracy remains high. Traps may be benign or may harm generalization; we provide an empirical approach to distinguish between them by passing random data through the trained model and evaluating the JS divergence of output logits. Our findings show that anti-grokking is an additional grokking phase with high train accuracy and decreasing test accuracy, structurally distinct from pre-grokking through its Correlation Traps. More broadly, we find that some foundation-scale LLMs exhibit the same Correlation Traps, indicating potentially harmful overfitting.

We investigate whether spectral properties of neural network weight matrices can predict test accuracy. Under controlled label noise variation, the tail index alpha of the eigenvalue distribution at the network's bottleneck layer predicts test accuracy with leave-one-out R^2 = 0.984 (21 noise levels, 3 seeds per level), far exceeding all baselines: the best conventional metric (Frobenius norm of the optimal layer) achieves LOO R^2 = 0.149. This relationship holds across three architectures (MLP, CNN, ResNet-18) and two datasets (MNIST, CIFAR-10). However, under hyperparameter variation at fixed data quality (180 configurations varying width, depth, learning rate, and weight decay), all spectral and conventional measures are weak predictors (R^2 < 0.25), with simple baselines (global L_2 norm, LOO R^2 = 0.219) slightly outperforming spectral measures (tail alpha, LOO R^2 = 0.167). We therefore frame the tail index as a data quality diagnostic: a powerful detector of label corruption and training set degradation, rather than a universal generalization predictor. A noise detector calibrated on synthetic noise successfully identifies real human annotation errors in CIFAR-10N (9% noise detected with 3% error). We identify the information-processing bottleneck layer as the locus of this signature and connect the observations to the BBP phase transition in spiked random matrix models. We also report a negative result: the level spacing ratio <r> is uninformative for weight matrices due to Wishart universality.

Transportation agencies increasingly predict crash-injury severity with statistical and machine-learning models, but these models do not state how often their output contains the recorded injury level or for which groups of drivers it fails, a gap that matters most for motorcyclists and unrestrained drivers. This study develops and evaluates a certification layer that gives any fitted severity model a finite-sample, distribution-free coverage guarantee within prespecified safety strata. The layer, CHOIR (Conformal Heterogeneity-aware Ordinal Inference with Risk control), combines groupwise and weighted conformal prediction with conformal risk control to return contiguous KABCO intervals, and adds a declared sensitivity analysis for medically assessed injury and bounds on fatal omission. It is evaluated on 4.04 million Texas crashes from 2017-2023, one sampled driver per crash, with seven base models from the ordered logit to a tabular foundation model, and on held-out counties and later years. Under one pooled threshold every model reaches 0.90 coverage overall but covers motorcyclists or unrestrained drivers at 0.868 or lower, and class-balanced gradient boosting covers unrestrained drivers at only 0.374. Calibration within four safety strata places all 28 model-by-stratum estimates between 0.898 and 0.907, at the cost of sets spanning 3.6 to 4.6 of five categories for these groups, and the certified ordered logit is within 0.03 categories of the narrowest model. Injury-model coverage should therefore be certified within safety groups rather than on average, calibration rather than model complexity determines validity, and a statewide threshold should not be applied to small rural counties without local calibration data.