# A survey on modern trainable activation functions

arXiv: https://arxiv.org/abs/2005.00817 · HTML: https://mlsanity.com/paper/2005.00817/

## Key facts

- Cited by 89 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2020.

## Built on by (most cited first, 30 of 89)

- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
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- [GELU Activation Function in Deep Learning: A Comprehensive Mathematical Analysis and Performance](https://mlsanity.com/paper/2305.12073/) (2023)
- [A Survey on Universal Approximation Theorems](https://mlsanity.com/paper/2407.12895/) (2024)
- [HOSC: A Periodic Activation Function for Preserving Sharp Features in Implicit Neural Representations](https://mlsanity.com/paper/2401.10967/) (2024)
- [Do We Always Need the Simplicity Bias? Looking for Optimal Inductive Biases in the Wild](https://mlsanity.com/paper/2503.10065/) (2025)
- [FitAct: Error Resilient Deep Neural Networks via Fine-Grained Post-Trainable Activation Functions](https://mlsanity.com/paper/2112.13544/) (2021)
- [Development of Skip Connection in Deep Neural Networks for Computer Vision and Medical Image Analysis: A Survey](https://mlsanity.com/paper/2405.01725/) (2024)
- [Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.14026/) (2025)
- [Improved weight initialization for deep and narrow feedforward neural network](https://mlsanity.com/paper/2311.03733/) (2023)
- [Don't Fear Peculiar Activation Functions: EUAF and Beyond](https://mlsanity.com/paper/2407.09580/) (2024)
- [Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations](https://mlsanity.com/paper/2411.15111/) (2024)
- [A survey on recently proposed activation functions for Deep Learning](https://mlsanity.com/paper/2204.02921/) (2022)
- [Trainable Highly-expressive Activation Functions](https://mlsanity.com/paper/2407.07564/) (2024)
- [Recent Advances in Deep Learning Techniques for Face Recognition](https://mlsanity.com/paper/2103.10492/) (2021)
- [AutoInit: Analytic Signal-Preserving Weight Initialization for Neural Networks](https://mlsanity.com/paper/2109.08958/) (2021)
- [End-to-End and Self-Supervised Learning for ComParE 2022 Stuttering Sub-Challenge](https://mlsanity.com/paper/2207.10817/) (2022)
- [Efficient Activation Function Optimization through Surrogate Modeling](https://mlsanity.com/paper/2301.05785/) (2023)
- [A Survey of Deep Learning: From Activations to Transformers](https://mlsanity.com/paper/2302.00722/) (2023)
- [Kolmogorov-Arnold Networks in Low-Data Regimes: A Comparative Study with Multilayer Perceptrons](https://mlsanity.com/paper/2409.10463/) (2024)
- [Why KDAC? A general activation function for knowledge discovery](https://mlsanity.com/paper/2111.13858/) (2021)
- [Neural Networks with A La Carte Selection of Activation Functions](https://mlsanity.com/paper/2206.12166/) (2022)
- [Stuttering Detection Using Speaker Representations and Self-supervised Contextual Embeddings](https://mlsanity.com/paper/2306.00689/) (2023)
- [Expanded Gating Ranges Improve Activation Functions](https://mlsanity.com/paper/2405.20768/) (2024)
- [ErfReLU: Adaptive Activation Function for Deep Neural Network](https://mlsanity.com/paper/2306.01822/) (2023)
- [Adaptive Activation Functions for Predictive Modeling with Sparse Experimental Data](https://mlsanity.com/paper/2402.05401/) (2024)
- [What comes after transformers? -- A selective survey connecting ideas in deep learning](https://mlsanity.com/paper/2408.00386/) (2024)

## Abstract (arXiv)

In neural networks literature, there is a strong interest in identifying and defining activation functions which can improve neural network performance. In recent years there has been a renovated interest of the scientific community in investigating activation functions which can be trained during the learning process, usually referred to as "trainable", "learnable" or "adaptable" activation functions. They appear to lead to better network performance. Diverse and heterogeneous models of trainable activation function have been proposed in the literature. In this paper, we present a survey of these models. Starting from a discussion on the use of the term "activation function" in literature, we propose a taxonomy of trainable activation functions, highlight common and distinctive proprieties of recent and past models, and discuss main advantages and limitations of this type of approach. We show that many of the proposed approaches are equivalent to adding neuron layers which use fixed (non-trainable) activation functions and some simple local rule that constraints the corresponding weight layers.