Guidelines for the Regularization of Gammas in Batch Normalization for Deep Residual Networks
This work addresses an undiscussed mystery in deep learning practice, providing practical guidelines for regularization in batch normalization, but it is incremental as it builds on existing methods without introducing a new paradigm.
The paper investigates the validity of L2 regularization for gamma parameters in batch normalization, proposing four guidelines based on analyses of variance control and stable optimization to manage desirable and undesirable gammas. Experiments across tasks and architectures, such as residual networks and transformers, show performance changes consistent with these guidelines.
L2 regularization for weights in neural networks is widely used as a standard training trick. However, L2 regularization for gamma, a trainable parameter of batch normalization, remains an undiscussed mystery and is applied in different ways depending on the library and practitioner. In this paper, we study whether L2 regularization for gamma is valid. To explore this issue, we consider two approaches: 1) variance control to make the residual network behave like identity mapping and 2) stable optimization through the improvement of effective learning rate. Through two analyses, we specify the desirable and undesirable gamma to apply L2 regularization and propose four guidelines for managing them. In several experiments, we observed the increase and decrease in performance caused by applying L2 regularization to gamma of four categories, which is consistent with our four guidelines. Our proposed guidelines were validated through various tasks and architectures, including variants of residual networks and transformers.