  Understanding how neural networks generalize on unseen data is crucial for
designing more robust and reliable models. In this paper, we study the
generalization gap of neural networks using methods from topological data
analysis. For this purpose, we compute homological persistence diagrams of
weighted graphs constructed from neuron activation correlations after a
training phase, aiming to capture patterns that are linked to the
generalization capacity of the network. We compare the usefulness of different
numerical summaries from persistence diagrams and show that a combination of
some of them can accurately predict and partially explain the generalization
gap without the need of a test set. Evaluation on two computer vision
recognition tasks (CIFAR10 and SVHN) shows competitive generalization gap
prediction when compared against state-of-the-art methods.
