# Delving into Variance Transmission and Normalization: Shift of Average Gradient Makes the Network Collapse

arXiv: https://arxiv.org/abs/2103.11590 · HTML: https://mlsanity.com/paper/2103.11590/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [Understanding Batch Normalization](https://mlsanity.com/paper/1806.02375/) (2018)
- [Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks](https://mlsanity.com/paper/1709.06079/) (2017)
- [Micro-Batch Training with Batch-Channel Normalization and Weight Standardization](https://mlsanity.com/paper/1903.10520/) (2019)
- [DSOD: Learning Deeply Supervised Object Detectors from Scratch](https://mlsanity.com/paper/1708.01241/) (2017)
- [Differentiable Learning-to-Normalize via Switchable Normalization](https://mlsanity.com/paper/1806.10779/) (2018)
- [ScratchDet: Training Single-Shot Object Detectors from Scratch](https://mlsanity.com/paper/1810.08425/) (2018)

## Built on by (most cited first, 1 of 1)

- [Efficient Visual Computing with Camera RAW Snapshots](https://mlsanity.com/paper/2212.07778/) (2022)

## Abstract (arXiv)

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.