Papers › Guidelines for the Regularization of Gammas in Batch Normalization for Deep Residual Networks

Guidelines for the Regularization of Gammas in Batch Normalization for Deep Residual Networks

15 May 2022arXiv:2205.07260archive 2025-07-28

Bum Jun Kim, Hyeyeon Choi, Hyeonah Jang, Dong Gu Lee, Wonseok Jeong, Sang Woo Kim

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.

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Tasks

L2 Regularization Machine Translation Text Classification

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Results from the paper archive 2025-07-28

Task	Dataset	Model	Metric	Value	Rank at snapshot	Leaderboard	Report
Machine Translation	IWSLT2014 German-English	Transformer	BLEU score	35.1385	#25 of 34	Archive leaderboard	report
Text Classification	GLUE SST2	BERT	Accuracy	92.0872	#2 of 2	Archive leaderboard	report

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Methods

1x1 Convolution Absolute Position Encodings Batch Normalization Bottleneck Residual Block Kaiming Initialization Layer Normalization ReLU Residual Block Residual Connection Transformer

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