Towards Understanding Regularization in Batch Normalization

TL;DR

This paper provides a theoretical understanding of how Batch Normalization acts as an implicit regularizer, affecting convergence and generalization in neural networks through a simplified analysis and experiments.

Contribution

It decomposes BN into explicit regularizers, analyzes its learning dynamics, and explores its generalization effects using statistical mechanics.

Findings

BN acts as an implicit regularizer decomposed into PN and gamma decay

Training with BN converges at large learning rates

BN improves generalization in CNNs similar to theoretical predictions

Abstract

Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a BN layer, and a nonlinear activation function. This basic network helps us understand the impacts of BN in three aspects. First, by viewing BN as an implicit regularizer, BN can be decomposed into population normalization (PN) and gamma decay as an explicit regularization. Second, learning dynamics of BN and the regularization show that training converged with large maximum and effective learning rate. Third, generalization of BN is explored by using statistical mechanics. Experiments demonstrate that BN in convolutional neural networks share the same traits of regularization as the above analyses.