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.

提出了一种使用广义偏差测量的 Batch Normalization（BN）变换，与传统的 BN 相比，它通过使用风险理论和量化风险管理的最新概念，加速神经网络训练的收敛速度，在结合 ReLU 非线性时，可以自然选择偏差测量和统计，实验证明在保持错误率方面与传统 BN 相比有所提高，总体而言，为设计选择提供了一个更灵活的 BN 变换。