On the Periodic Behavior of Neural Network Training with Batch Normalization and Weight Decay

Ekaterina Lobacheva, Maxim Kodryan, Nadezhda Chirkova, Andrey Malinin, Dmitry P. Vetrov

Keywords: neural network training, batch normalization, weight decay

Abstract: Training neural networks with batch normalization and weight decay has become a common practice in recent years. In this work, we show that their combined use may result in a surprising periodic behavior of optimization dynamics: the training process regularly exhibits destabilizations that, however, do not lead to complete divergence but cause a new period of training. We rigorously investigate the mechanism underlying the discovered periodic behavior from both empirical and theoretical points of view and analyze the conditions in which it occurs in practice. We also demonstrate that periodic behavior can be regarded as a generalization of two previously opposing perspectives on training with batch normalization and weight decay, namely the equilibrium presumption and the instability presumption.

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TL;DR: We study the periodic behavior of training dynamics caused by the interaction of batch normalization and weight decay.

Code: https://github.com/tipt0p/periodic_behavior_bn_wd