# FixNorm: Dissecting Weight Decay for Training Deep Neural Networks

arXiv: https://arxiv.org/abs/2103.15345 · HTML: https://mlsanity.com/paper/2103.15345/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 27 of 27)

- [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)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [NAS-Bench-101: Towards Reproducible Neural Architecture Search](https://mlsanity.com/paper/1902.09635/) (2019)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [OCNet: Object Context Network for Scene Parsing](https://mlsanity.com/paper/1809.00916/) (2018)
- [L2 Regularization versus Batch and Weight Normalization](https://mlsanity.com/paper/1706.05350/) (2017)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [Three Mechanisms of Weight Decay Regularization](https://mlsanity.com/paper/1810.12281/) (2018)
- [Norm matters: efficient and accurate normalization schemes in deep networks](https://mlsanity.com/paper/1803.01814/) (2018)
- [Towards Assessing the Impact of Bayesian Optimization's Own Hyperparameters](https://mlsanity.com/paper/1908.06674/) (2019)
- [Understanding the Disharmony between Weight Normalization Family and Weight Decay: ε-shifted L2 Regularizer](https://mlsanity.com/paper/1911.05920/) (2019)

## Built on by (most cited first, 3 of 3)

- [GPT-NeoX-20B: An Open-Source Autoregressive Language Model](https://mlsanity.com/paper/2204.06745/) (2022)
- [Rotational Equilibrium: How Weight Decay Balances Learning Across Neural Networks](https://mlsanity.com/paper/2305.17212/) (2023)
- [A Stochastic Proximal Method for Nonsmooth Regularized Finite Sum Optimization](https://mlsanity.com/paper/2206.06531/) (2022)

## Abstract (arXiv)

Weight decay is a widely used technique for training Deep Neural Networks(DNN). It greatly affects generalization performance but the underlying mechanisms are not fully understood. Recent works show that for layers followed by normalizations, weight decay mainly affects the effective learning rate. However, despite normalizations have been extensively adopted in modern DNNs, layers such as the final fully-connected layer do not satisfy this precondition. For these layers, the effects of weight decay are still unclear. In this paper, we comprehensively investigate the mechanisms of weight decay and find that except for influencing effective learning rate, weight decay has another distinct mechanism that is equally important: affecting generalization performance by controlling cross-boundary risk. These two mechanisms together give a more comprehensive explanation for the effects of weight decay. Based on this discovery, we propose a new training method called FixNorm, which discards weight decay and directly controls the two mechanisms. We also propose a simple yet effective method to tune hyperparameters of FixNorm, which can find near-optimal solutions in a few trials. On ImageNet classification task, training EfficientNet-B0 with FixNorm achieves 77.7%, which outperforms the original baseline by a clear margin. Surprisingly, when scaling MobileNetV2 to the same FLOPS and applying the same tricks with EfficientNet-B0, training with FixNorm achieves 77.4%, which is only 0.3% lower. A series of SOTA results show the importance of well-tuned training procedures, and further verify the effectiveness of our approach. We set up more well-tuned baselines using FixNorm, to facilitate fair comparisons in the community.