# Stochastic Adaptive Activation Function

arXiv: https://arxiv.org/abs/2210.11672 · HTML: https://mlsanity.com/paper/2210.11672/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (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)
- [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)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [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)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [Convolutional Neural Networks as a Model of the Visual System: Past, Present, and Future](https://mlsanity.com/paper/2001.07092/) (2020)
- [From Facial Parts Responses to Face Detection: A Deep Learning Approach](https://mlsanity.com/paper/1509.06451/) (2015)
- [Discovering Parametric Activation Functions](https://mlsanity.com/paper/2006.03179/) (2020)

## Built on by (most cited first, 4 of 4)

- [Trainable Highly-expressive Activation Functions](https://mlsanity.com/paper/2407.07564/) (2024)
- [Kolmogorov-Arnold Networks in Low-Data Regimes: A Comparative Study with Multilayer Perceptrons](https://mlsanity.com/paper/2409.10463/) (2024)
- [Adaptive Activation Functions for Predictive Modeling with Sparse Experimental Data](https://mlsanity.com/paper/2402.05401/) (2024)
- [Stochastic activations](https://mlsanity.com/paper/2509.22358/) (2025)

## Abstract (arXiv)

The simulation of human neurons and neurotransmission mechanisms has been realized in deep neural networks based on the theoretical implementations of activation functions. However, recent studies have reported that the threshold potential of neurons exhibits different values according to the locations and types of individual neurons, and that the activation functions have limitations in terms of representing this variability. Therefore, this study proposes a simple yet effective activation function that facilitates different thresholds and adaptive activations according to the positions of units and the contexts of inputs. Furthermore, the proposed activation function mathematically exhibits a more generalized form of Swish activation function, and thus we denoted it as Adaptive SwisH (ASH). ASH highlights informative features that exhibit large values in the top percentiles in an input, whereas it rectifies low values. Most importantly, ASH exhibits trainable, adaptive, and context-aware properties compared to other activation functions. Furthermore, ASH represents general formula of the previously studied activation function and provides a reasonable mathematical background for the superior performance. To validate the effectiveness and robustness of ASH, we implemented ASH into many deep learning models for various tasks, including classification, detection, segmentation, and image generation. Experimental analysis demonstrates that our activation function can provide the benefits of more accurate prediction and earlier convergence in many deep learning applications.