Predicting the Generalization Gap in Deep Networks with Margin Distributions

TL;DR

This paper introduces a new measure based on margin distributions across multiple layers to predict the generalization gap in deep neural networks, showing strong correlation with actual generalization performance on CIFAR datasets.

Contribution

It proposes a novel margin distribution-based measure for predicting generalization gap, incorporating multi-layer analysis and normalization techniques, applicable to various deep network architectures.

Findings

Margin distribution at multiple layers correlates strongly with generalization gap.

Normalizing margins and working in log space improves prediction accuracy.

The measure is applicable across different architectures and datasets.

Abstract

As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should be predicted from the training data and network parameters. In this paper, we propose such a measure, and conduct extensive empirical studies on how well it can predict the generalization gap. Our measure is based on the concept of margin distribution, which are the distances of training points to the decision boundary. We find that it is necessary to use margin distributions at multiple layers of a deep network. On the CIFAR-10 and the CIFAR-100 datasets, our proposed measure correlates very strongly with the generalization gap. In addition, we find the following other factors to be of importance: normalizing margin values for scale independence, using characterizations of margin distribution rather than just the margin (closest distance to decision boundary), and working in log space instead of linear space (effectively using a product of margins rather than a sum). Our measure can be easily applied to feedforward deep networks with any architecture and may point towards new training loss functions that could enable better generalization.