  Normalization operations are essential for state-of-the-art neural networks
and enable us to train a network from scratch with a large learning rate (LR).
We attempt to explain the real effect of Batch Normalization (BN) from the
perspective of variance transmission by investigating the relationship between
BN and Weights Normalization (WN). In this work, we demonstrate that the
problem of the shift of the average gradient will amplify the variance of every
convolutional (conv) layer. We propose Parametric Weights Standardization
(PWS), a fast and robust to mini-batch size module used for conv filters, to
solve the shift of the average gradient. PWS can provide the speed-up of BN.
Besides, it has less computation and does not change the output of a conv
layer. PWS enables the network to converge fast without normalizing the
outputs. This result enhances the persuasiveness of the shift of the average
gradient and explains why BN works from the perspective of variance
transmission. The code and appendix will be made available on
https://github.com/lyxzzz/PWSConv.
