L2 Regularization versus Batch and Weight Normalization
This work addresses a fundamental issue in deep learning optimization for practitioners, revealing a key limitation in common regularization practices.
The paper demonstrates that L2 regularization does not prevent overfitting when used with normalization techniques like Batch Normalization, instead affecting weight scale and effective learning rate, with experiments showing that methods like ADAM only partially address this issue.
Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization has no regularizing effect when combined with normalization. Instead, regularization has an influence on the scale of weights, and thereby on the effective learning rate. We investigate this dependence, both in theory, and experimentally. We show that popular optimization methods such as ADAM only partially eliminate the influence of normalization on the learning rate. This leads to a discussion on other ways to mitigate this issue.