Revisit Batch Normalization: New Understanding from an Optimization View and a Refinement via Composition Optimization

Abstract: Batch Normalization (BN) has been used extensively in deep learning to achieve faster training process and better resulting models. However, whether BN works strongly depends on how the batches are constructed during training and it may not converge to a desired solution if the statistics on a batch are not close to the statistics over the whole dataset. In this paper, we try to understand BN from an optimization perspective by formulating the optimization problem which motivates BN. We show when BN works and when BN does not work by analyzing the optimization problem. We then propose a refinement of BN based on compositional optimization techniques called Full Normalization (FN) to alleviate the issues of BN when the batches are not constructed ideally. We provide convergence analysis for FN and empirically study its effectiveness to refine BN.