Neural Collapse in the Intermediate Hidden Layers of Classification
  Neural Networks
Liam Parker Emre Onal Anton Stengel Jake Intrater
Neural Collapse (NC) gives a precise description of the representations of
classes in the final hidden layer of classification neural networks. This
description provides insights into how these networks learn features and
generalize well when trained past zero training error. However, to date, (NC)
has only been studied in the final layer of these networks. In the present
paper, we provide the first comprehensive empirical analysis of the emergence
of (NC) in the intermediate hidden layers of these classifiers. We examine a
variety of network architectures, activations, and datasets, and demonstrate
that some degree of (NC) emerges in most of the intermediate hidden layers of
the network, where the degree of collapse in any given layer is typically
positively correlated with the depth of that layer in the neural network.
Moreover, we remark that: (1) almost all of the reduction in intra-class
variance in the samples occurs in the shallower layers of the networks, (2) the
angular separation between class means increases consistently with hidden layer
depth, and (3) simple datasets require only the shallower layers of the
networks to fully learn them, whereas more difficult ones require the entire
network. Ultimately, these results provide granular insights into the
structural propagation of features through classification neural networks.