Topological descriptors (persistent homology) and intrinsic-dimension estimates of the last-layer data manifold in real trained CNNs change measurably across layers and training, and predict generalization performance

Magai & Ayzenberg (2022) apply persistent homology and intrinsic dimension estimation to the data manifold formed by penultimate-layer activations of real trained convolutional networks on CIFAR-10 and related image datasets, tracking how topological complexity (number and persistence of homological features) and intrinsic dimension evolve across network depth and training progress. They show these topological and geometric descriptors change in a way that is predictive of generalization performance, and extend the analysis to a face-recognition system's embedding manifold under adversarial spoofing attacks, measuring the same topological descriptors as an anomaly signature. Clears scope on quantified geometric-shape measurement (persistent homology, intrinsic dimension) on real trained CNNs' natural penultimate-layer activations; purely observational, no causal steering intervention. See [[manifolds]] for the broader topological-measurement precedent this shares with `a-141-hypothesis-automated-audit-of-scgpt-and-geneformer-finds-significant-persistent-homology-in-nearly-every-layer-and-a-cca-canonical-correlation-of-0-80-between-the-two-models`.