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The success of deep neural networks is in part due to the use ofnormalization layers. Normalization layers like Batch Normalization, LayerNormalization and Weight Normalization are ubiquitous in practice, as theyimprove generalization performance and speed up training significantly.Nonetheless, the vast majority of current deep learning theory and non-convexoptimization literature focuses on the un-normalized setting, where thefunctions under consideration do not exhibit the properties of commonlynormalized neural networks. In this paper, we bridge this gap by giving thefirst global convergence result for two-layer neural networks with ReLUactivations trained with a normalization layer, namely Weight Normalization.Our analysis shows how the introduction of normalization layers changes theoptimization landscape and can enable faster convergence as compared withun-normalized neural networks.

Optimization Theory for ReLU Neural Networks Trained with Normalization Layers