An Information Budget for Label-Noise Memorization, and What Statistical Complexity Tracks: A Study with Multilayer Perceptrons
How much label noise has a network memorized, and when? We study a multilayer perceptron and what statistical complexity adds to a description of its predictions. Standard identities decompose predictive information into signal, memorization, and heterogeneity. The memorization term vanishes in the population under the stated noise-independence condition. A Fano-type bound relates it to training accuracies, but the memorized fraction M provides no upper bound. Across 89 MNIST runs with ten pre-specified hypotheses (five supported, four unsupported, one not testable), normalized memorization information rose with M on training samples, remained near zero on held-out samples with fresh noisy labels, and was close to its Fano bound. Unlike raw M, it has a zero population null under the independence condition and chance correction largely removed this difference. When every label was replaced by an incorrect class, test accuracy fell to 0.5%, yet predictions retained information about the true class. Mean statistical complexity peaked before memorization at corruption rates up to 40%. At higher rates, its peak fell within the memorization phase, near the epoch when mean training confidence reached 0.6 and the two could not be separated. As a stopping rule, it matched established rules only at low noise and detected corrupted samples less well than simple label-free scores. An exploratory extension of 280 runs covering Fashion-MNIST, pair-flip noise, and four training variants yielded similar results under uniform noise, but not pair-flip noise, where complexity peaked within two epochs. Conclusions are limited to this architecture, two small datasets, and synthetic noise.