# SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions

arXiv: https://arxiv.org/abs/2407.04149 · HTML: https://mlsanity.com/paper/2407.04149/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (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)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [Fourier Neural Networks: A Comparative Study](https://mlsanity.com/paper/1902.03011/) (2019)
- [Guidance and Control Networks with Periodic Activation Functions](https://mlsanity.com/paper/2405.18084/) (2024)
- [Leveraging sinusoidal representation networks to predict fMRI signals from EEG](https://mlsanity.com/paper/2311.04234/) (2023)
- [Implicit Neural Representation as a Differentiable Surrogate for Photon Propagation in a Monolithic Neutrino Detector](https://mlsanity.com/paper/2211.01505/) (2022)

## Built on by (most cited first, 15 of 15)

- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony](https://mlsanity.com/paper/2506.03302/) (2025)
- [Softly Symbolifying Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2512.07875/) (2025)
- [Kolmogorov GAM Networks are all you need!](https://mlsanity.com/paper/2501.00704/) (2025)
- [Advancing Out-of-Distribution Detection via Local Neuroplasticity](https://mlsanity.com/paper/2502.15833/) (2025)
- [Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2508.00247/) (2025)
- [Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions](https://mlsanity.com/paper/2508.07559/) (2025)
- [Optimized Architectures for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2512.12448/) (2025)
- [KANFIS: A Neuro-Symbolic Framework for Interpretable and Uncertainty-Aware Learning](https://mlsanity.com/paper/2602.03034/) (2026)
- [TruKAN: Towards More Efficient Kolmogorov-Arnold Networks Using Truncated Power Functions](https://mlsanity.com/paper/2602.03879/) (2026)
- [ViKANformer: Embedding Kolmogorov Arnold Networks in Vision Transformers for Pattern-Based Learning](https://mlsanity.com/paper/2503.01124/) (2025)
- [DualFlexKAN: Dual-stage Kolmogorov-Arnold Networks with Independent Function Control](https://mlsanity.com/paper/2603.08583/) (2026)

## Abstract (arXiv)

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the computational graph followed by summation on nodes. The learnable edge activation functions in the original implementation are basis spline functions (B-Spline). Here, we present a model in which learnable grids of B-Spline activation functions are replaced by grids of re-weighted sine functions (SineKAN). We evaluate numerical performance of our model on a benchmark vision task. We show that our model can perform better than or comparable to B-Spline KAN models and an alternative KAN implementation based on periodic cosine and sine functions representing a Fourier Series. Further, we show that SineKAN has numerical accuracy that could scale comparably to dense neural networks (DNNs). Compared to the two baseline KAN models, SineKAN achieves a substantial speed increase at all hidden layer sizes, batch sizes, and depths. Current advantage of DNNs due to hardware and software optimizations are discussed along with theoretical scaling. Additionally, properties of SineKAN compared to other KAN implementations and current limitations are also discussed