Optimization Theory for ReLU Neural Networks Trained with Normalization Layers
This work addresses a gap in deep learning theory for practitioners using normalization layers, though it is incremental as it focuses on a specific case.
The paper tackles the lack of theoretical understanding for neural networks with normalization layers by providing the first global convergence result for two-layer ReLU networks using Weight Normalization, showing that normalization changes the optimization landscape and enables faster convergence compared to un-normalized networks.
The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization performance and speed up training significantly. Nonetheless, the vast majority of current deep learning theory and non-convex optimization literature focuses on the un-normalized setting, where the functions under consideration do not exhibit the properties of commonly normalized neural networks. In this paper, we bridge this gap by giving the first global convergence result for two-layer neural networks with ReLU activations trained with a normalization layer, namely Weight Normalization. Our analysis shows how the introduction of normalization layers changes the optimization landscape and can enable faster convergence as compared with un-normalized neural networks.