# Activation Functions: Dive into an optimal activation function

arXiv: https://arxiv.org/abs/2202.12065 · HTML: https://mlsanity.com/paper/2202.12065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 24 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [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)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [One weird trick for parallelizing convolutional neural networks](https://mlsanity.com/paper/1404.5997/) (2014)
- [Understanding and Improving Convolutional Neural Networks via Concatenated Rectified Linear Units](https://mlsanity.com/paper/1603.05201/) (2016)
- [TanhExp: A Smooth Activation Function with High Convergence Speed for Lightweight Neural Networks](https://mlsanity.com/paper/2003.09855/) (2020)

## Abstract (arXiv)

Activation functions have come up as one of the essential components of neural networks. The choice of adequate activation function can impact the accuracy of these methods. In this study, we experiment for finding an optimal activation function by defining it as a weighted sum of existing activation functions and then further optimizing these weights while training the network. The study uses three activation functions, ReLU, tanh, and sin, over three popular image datasets, MNIST, FashionMNIST, and KMNIST. We observe that the ReLU activation function can easily overlook other activation functions. Also, we see that initial layers prefer to have ReLU or LeakyReLU type of activation functions, but deeper layers tend to prefer more convergent activation functions.