[2603.27885] Spectral Signatures of Data Quality: Eigenvalue Tail Index as a Diagnostic for Label Noise in Neural Networks

Computer Science > Machine Learning arXiv:2603.27885 (cs) [Submitted on 29 Mar 2026] Title:Spectral Signatures of Data Quality: Eigenvalue Tail Index as a Diagnostic for Label Noise in Neural Networks Authors:Matthew Loftus View a PDF of the paper titled Spectral Signatures of Data Quality: Eigenvalue Tail Index as a Diagnostic for Label Noise in Neural Networks, by Matthew Loftus View PDF HTML (experimental) Abstract: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...