# ANAct: Adaptive Normalization for Activation Functions

arXiv: https://arxiv.org/abs/2208.13315 · HTML: https://mlsanity.com/paper/2208.13315/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 29 Aug 2022.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [Data-dependent Initializations of Convolutional Neural Networks](https://mlsanity.com/paper/1511.06856/) (2015)
- [The exploding gradient problem demystified - definition, prevalence, impact, origin, tradeoffs, and solutions](https://mlsanity.com/paper/1712.05577/) (2017)
- [Batch Normalization Is Blind to the First and Second Derivatives of the Loss](https://mlsanity.com/paper/2205.15146/) (2022)

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

- [Unit Scaling: Out-of-the-Box Low-Precision Training](https://mlsanity.com/paper/2303.11257/) (2023)

## Abstract (arXiv)

In this paper, we investigate the negative effect of activation functions on forward and backward propagation and how to counteract this effect. First, We examine how activation functions affect the forward and backward propagation of neural networks and derive a general form for gradient variance that extends the previous work in this area. We try to use mini-batch statistics to dynamically update the normalization factor to ensure the normalization property throughout the training process, rather than only accounting for the state of the neural network after weight initialization. Second, we propose ANAct, a method that normalizes activation functions to maintain consistent gradient variance across layers and demonstrate its effectiveness through experiments. We observe that the convergence rate is roughly related to the normalization property. We compare ANAct with several common activation functions on CNNs and residual networks and show that ANAct consistently improves their performance. For instance, normalized Swish achieves 1.4% higher top-1 accuracy than vanilla Swish on ResNet50 with the Tiny ImageNet dataset and more than 1.2% higher with CIFAR-100.