BN-invariant Sharpness Regularizes the Training Model to Better Generalization

BN-invariant Sharpness Regularizes the Training Model to Better Generalization

Mingyang Yi, Huishuai Zhang, Wei Chen, Zhi-Ming Ma, Tie-Yan Liu

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 4164-4170. https://doi.org/10.24963/ijcai.2019/578

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.
Keywords:
Machine Learning: Learning Theory
Machine Learning: Deep Learning
Machine Learning: Explainable Machine Learning