#### Beyond BatchNorm: Towards a General Understanding of Normalization in Deep Learning

##### Ekdeep Singh Lubana, Robert P. Dick, Hidenori Tanaka

Inspired by BatchNorm, there has been an explosion of normalization layers in deep learning. Recent works have identified a multitude of beneficial properties in BatchNorm to explain its success. However, given the pursuit of alternative normalization techniques, these properties need to be generalized so that any given layer's success/failure can be accurately predicted. In this work, we take a first step towards this goal by extending known properties of BatchNorm in randomly initialized deep neural networks (DNNs) to nine recently proposed normalization layers. Our primary findings follow: (i) Similar to BatchNorm, activations-based normalization layers can avoid exploding activations in ResNets; (ii) Use of GroupNorm ensures rank of activations is at least $\Omega(\sqrt{\frac{\text{width}}{\text{Group Size}}})$, thus explaining why LayerNorm witnesses slow optimization speed; (iii) Small group sizes result in large gradient norm in earlier layers, hence justifying training instability issues in Instance Normalization and illustrating a speed-stability tradeoff in GroupNorm. Overall, our analysis reveals several general mechanisms that explain the success of normalization techniques in deep learning, providing us with a compass to systematically explore the vast design space of DNN normalization layers.

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