# Saturated Non-Monotonic Activation Functions

arXiv: https://arxiv.org/abs/2305.07537 · HTML: https://mlsanity.com/paper/2305.07537/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 12 May 2023.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)

## Built on by (most cited first, 2 of 2)

- [A parametric activation function based on Wendland RBF](https://mlsanity.com/paper/2507.11493/) (2025)
- [Geometric Monomial (GEM): a family of rational 2N-differentiable activation functions](https://mlsanity.com/paper/2604.21677/) (2026)

## Abstract (arXiv)

Activation functions are essential to deep learning networks. Popular and versatile activation functions are mostly monotonic functions, some non-monotonic activation functions are being explored and show promising performance. But by introducing non-monotonicity, they also alter the positive input, which is proved to be unnecessary by the success of ReLU and its variants. In this paper, we double down on the non-monotonic activation functions' development and propose the Saturated Gaussian Error Linear Units by combining the characteristics of ReLU and non-monotonic activation functions. We present three new activation functions built with our proposed method: SGELU, SSiLU, and SMish, which are composed of the negative portion of GELU, SiLU, and Mish, respectively, and ReLU's positive portion. The results of image classification experiments on CIFAR-100 indicate that our proposed activation functions are highly effective and outperform state-of-the-art baselines across multiple deep learning architectures.