Generalized Batch Normalization: Towards Accelerating Deep Neural Networks

TL;DR

This paper introduces a generalized version of Batch Normalization (GBN) that uses alternative deviation measures and statistics, leading to faster neural network training and potentially better accuracy, supported by a theoretical framework.

Contribution

The paper proposes a flexible GBN transformation based on risk theory, offering a new theoretical foundation and practical improvements over conventional BN.

Findings

Accelerated training convergence with GBN

Improved error rates in experiments

Theoretically justified deviation and statistic choices

Abstract

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non-linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices.