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Batch Normalization is a commonly used trick to improve the training of deepneural networks. These neural networks use L2 regularization, also calledweight decay, ostensibly to prevent overfitting. However, we show that L2regularization has no regularizing effect when combined with normalization.Instead, regularization has an influence on the scale of weights, and therebyon the effective learning rate. We investigate this dependence, both in theory,and experimentally. We show that popular optimization methods such as ADAM onlypartially eliminate the influence of normalization on the learning rate. Thisleads to a discussion on other ways to mitigate this issue.

L2 Regularization versus Batch and Weight Normalization