Norm matters: efficient and accurate normalization schemes in deep networks

TL;DR

This paper offers a new perspective on normalization in deep networks, proposing alternative schemes like L1 and L-infinity normalization that enhance stability and efficiency, especially in low-precision settings.

Contribution

It introduces novel normalization methods in L1 and L-infinity spaces, connecting normalization, weight decay, and learning rate, and improves weight normalization for large-scale tasks.

Findings

L1 and L-infinity normalization improve numerical stability

Proposed methods enable batch-norm alternatives in half-precision

Modified weight normalization enhances large-scale task performance

Abstract

Over the past few years, Batch-Normalization has been commonly used in deep networks, allowing faster training and high performance for a wide variety of applications. However, the reasons behind its merits remained unanswered, with several shortcomings that hindered its use for certain tasks. In this work, we present a novel view on the purpose and function of normalization methods and weight-decay, as tools to decouple weights' norm from the underlying optimized objective. This property highlights the connection between practices such as normalization, weight decay and learning-rate adjustments. We suggest several alternatives to the widely used $L^2$ batch-norm, using normalization in $L^1$ and $L^\infty$ spaces that can substantially improve numerical stability in low-precision implementations as well as provide computational and memory benefits. We demonstrate that such methods enable the first batch-norm alternative to work for half-precision implementations. Finally, we suggest a modification to weight-normalization, which improves its performance on large-scale tasks.