# LArctan-SKAN: Simple and Efficient Single-Parameterized Kolmogorov-Arnold Networks using Learnable Trigonometric Function

arXiv: https://arxiv.org/abs/2410.19360 · HTML: https://mlsanity.com/paper/2410.19360/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 6 references that are in the map.
- First posted on arXiv 25 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (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)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Design](https://mlsanity.com/paper/2410.14951/) (2024)

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

- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [KAN-MLP-Mixer: A comprehensive investigation of the usage of Kolmogorov-Arnold Networks (KANs) for improving IMU-based Human Activity Recognition](https://mlsanity.com/paper/2605.19031/) (2026)

## Abstract (arXiv)

This paper proposes a novel approach for designing Single-Parameterized Kolmogorov-Arnold Networks (SKAN) by utilizing a Single-Parameterized Function (SFunc) constructed from trigonometric functions. Three new SKAN variants are developed: LSin-SKAN, LCos-SKAN, and LArctan-SKAN. Experimental validation on the MNIST dataset demonstrates that LArctan-SKAN excels in both accuracy and computational efficiency. Specifically, LArctan-SKAN significantly improves test set accuracy over existing models, outperforming all pure KAN variants compared, including FourierKAN, LSS-SKAN, and Spl-KAN. It also surpasses mixed MLP-based models such as MLP+rKAN and MLP+fKAN in accuracy. Furthermore, LArctan-SKAN exhibits remarkable computational efficiency, with a training speed increase of 535.01% and 49.55% compared to MLP+rKAN and MLP+fKAN, respectively. These results confirm the effectiveness and potential of SKANs constructed with trigonometric functions. The experiment code is available at https://github.com/chikkkit/LArctan-SKAN .