Understanding Regularization in Batch Normalization

Batch Normalization (BN) makes output of hidden neuron had zero mean and unit variance, improving convergence and generalization when training neural networks. This work understands these phenomena theoretically. We analyze BN by using a building block of neural networks, which consists of a weight layer, a BN layer, and a nonlinear activation function. This simple network helps us understand the characteristics of BN, where the results are generalized to deep models in numerical studies. We explore BN in three aspects. First, by viewing BN as a stochastic process, an analytical form of regularization inherited in BN is derived. Second, the optimization dynamic with this regularization shows that BN enables training converged with large maximum and effective learning rates. Third, BN's generalization with regularization is explored by using random matrix theory and statistical mechanics. Both simulations and experiments support our analyses.