Predicting the generalization gap in neural networks using topological data analysis

TL;DR

This paper introduces a novel approach using topological data analysis to predict the generalization gap of neural networks, providing insights without requiring a test set and demonstrating effectiveness on standard vision datasets.

Contribution

It applies homological persistence diagrams to neural activation data to predict generalization gaps, a new method in understanding neural network generalization.

Findings

Accurately predicts generalization gap without test data

Outperforms some state-of-the-art methods on CIFAR10 and SVHN

Identifies topological features linked to model generalization

Abstract

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.