BN-invariant sharpness regularizes the training model to better generalization

TL;DR

This paper introduces BN-Sharpness, a scale-invariant sharpness measure for neural networks with batch normalization, and uses it to regularize training, resulting in improved generalization performance.

Contribution

The paper proposes BN-Sharpness, a scale-invariant sharpness measure, and develops a regularization method based on it that enhances neural network training.

Findings

BN-Sharpness provides consistent sharpness measurement for scale-invariant networks.

Regularizing with BN-Sharpness improves training performance.

The method outperforms vanilla SGD in experiments.

Abstract

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a $\delta$ ball of parameters around minima, cannot give consistent measurement for scale invariant neural networks, e.g., networks with batch normalization layer. In this paper, we first propose a measure of sharpness, BN-Sharpness, which gives consistent value for equivalent networks under BN. It achieves the property of scale invariance by connecting the integral diameter with the scale of parameter. Then we present a computation-efficient way to calculate the BN-sharpness approximately i.e., one dimensional integral along the "sharpest" direction. Furthermore, we use the BN-sharpness to regularize the training and design an algorithm to minimize the new regularized objective. Our algorithm achieves considerably better performance than vanilla SGD over various experiment settings.