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

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