# MatrixKAN: Parallelized Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2502.07176 · HTML: https://mlsanity.com/paper/2502.07176/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.00278/) (2024)
- [How to Learn More? Exploring Kolmogorov-Arnold Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2406.15719/) (2024)
- [Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Design](https://mlsanity.com/paper/2410.14951/) (2024)
- [Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability](https://mlsanity.com/paper/2501.09283/) (2025)
- [Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations](https://mlsanity.com/paper/2501.14404/) (2025)
- [Incorporating Arbitrary Matrix Group Equivariance into KANs](https://mlsanity.com/paper/2410.00435/) (2024)

## Built on by (most cited first, 7 of 7)

- [FlashKAT: Understanding and Addressing Performance Bottlenecks in the Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2505.13813/) (2025)
- [MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Network](https://mlsanity.com/paper/2510.19105/) (2025)
- [InKAN: B-Spline KANs via Truncated Power Form](https://mlsanity.com/paper/2609.01956/) (2026)
- [An Efficient and Explainable KAN Framework for Wireless Radiation Field Prediction](https://mlsanity.com/paper/2601.11656/) (2026)
- [Scalability Analysis of Distributed Kolmogorov-Arnold Network Training on High-Performance Computing Systems](https://mlsanity.com/paper/2609.07740/) (2026)
- [Rethinking Vision Architectures with Gated Linear Attention and KAN](https://mlsanity.com/paper/2609.22506/) (2026)
- [SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomials](https://mlsanity.com/paper/2610.00050/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from slow training and inference speeds relative to MLPs due in part to the recursive nature of the underlying B-spline calculations. This issue is particularly apparent with respect to KANs utilizing high-degree B-splines, as the number of required non-parallelizable recursions is proportional to B-spline degree. We solve this issue by proposing MatrixKAN, a novel optimization that parallelizes B-spline calculations with matrix representation and operations, thus significantly improving effective computation time for models utilizing high-degree B-splines. In this paper, we demonstrate the superior scaling of MatrixKAN's computation time relative to B-spline degree. Further, our experiments demonstrate speedups of approximately 40x relative to KAN, with significant additional speedup potential for larger datasets or higher spline degrees.