# AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning

arXiv: https://arxiv.org/abs/2503.06112 · HTML: https://mlsanity.com/paper/2503.06112/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 70 references that are in the map.
- First posted on arXiv 8 Mar 2025.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.02486/) (2024)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Tasks](https://mlsanity.com/paper/2406.14916/) (2024)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)

## Built on by (most cited first, 3 of 3)

- [Concurrent training methods for Kolmogorov-Arnold networks: Disjoint datasets and FPGA implementation](https://mlsanity.com/paper/2512.18921/) (2025)
- [RecKAN: Kolmogorov-Arnold Networks with a Learnable Recursive Polynomial Basis](https://mlsanity.com/paper/2609.01729/) (2026)
- [Sample-Efficiency of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2610.10627/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis and polynomial functions, such as B-splines, ReLU-KAN utilizes a combination of ReLU functions to mimic the structure of B-splines and take advantage of ReLU's speed. However, ReLU-KAN is not built for multiple inputs, and its limitations stem from ReLU's handling of negative values, which can restrict feature extraction. To address these issues, we introduce Activation Function-Based Kolmogorov-Arnold Networks (AF-KAN), expanding ReLU-KAN with various activations and their function combinations. This novel KAN also incorporates parameter reduction methods, primarily attention mechanisms and data normalization, to enhance performance on image classification datasets. We explore different activation functions, function combinations, grid sizes, and spline orders to validate the effectiveness of AF-KAN and determine its optimal configuration. In the experiments, AF-KAN significantly outperforms MLP, ReLU-KAN, and other KANs with the same parameter count. It also remains competitive even when using fewer than 6 to 10 times the parameters while maintaining the same network structure. However, AF-KAN requires a longer training time and consumes more FLOPs. The repository for this work is available at https://github.com/hoangthangta/All-KAN.