# PowerMLP: An Efficient Version of KAN

arXiv: https://arxiv.org/abs/2412.13571 · HTML: https://mlsanity.com/paper/2412.13571/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Series](https://mlsanity.com/paper/2406.17890/) (2024)
- [PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units](https://mlsanity.com/paper/1909.05136/) (2019)
- [The signature and cusp geometry of hyperbolic knots](https://mlsanity.com/paper/2111.15323/) (2021)

## Built on by (most cited first, 14 of 14)

- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)
- [Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement](https://mlsanity.com/paper/2505.18131/) (2025)
- [X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning](https://mlsanity.com/paper/2505.14273/) (2025)
- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [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)
- [TruKAN: Towards More Efficient Kolmogorov-Arnold Networks Using Truncated Power Functions](https://mlsanity.com/paper/2602.03879/) (2026)
- [Multilevel Training for Kolmogorov Arnold Networks](https://mlsanity.com/paper/2603.04827/) (2026)
- [Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.03345/) (2026)
- [Multi-Modal Scene Graph with Kolmogorov-Arnold Experts for Audio-Visual Question Answering](https://mlsanity.com/paper/2511.23304/) (2025)
- [An Efficient Additive Kolmogorov-Arnold Transformer for Point-Level Maize Localization in Unmanned Aerial Vehicle Imagery](https://mlsanity.com/paper/2601.07975/) (2026)
- [A Geometric Algebra-informed NeRF Framework for Generalizable Wireless Channel Prediction](https://mlsanity.com/paper/2604.11983/) (2026)
- [KAN-CL: Per-Knot Importance Regularization for Continual Learning with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2605.12306/) (2026)

## Abstract (arXiv)

The Kolmogorov-Arnold Network (KAN) is a new network architecture known for its high accuracy in several tasks such as function fitting and PDE solving. The superior expressive capability of KAN arises from the Kolmogorov-Arnold representation theorem and learnable spline functions. However, the computation of spline functions involves multiple iterations, which renders KAN significantly slower than MLP, thereby increasing the cost associated with model training and deployment. The authors of KAN have also noted that ``the biggest bottleneck of KANs lies in its slow training. KANs are usually 10x slower than MLPs, given the same number of parameters.'' To address this issue, we propose a novel MLP-type neural network PowerMLP that employs simpler non-iterative spline function representation, offering approximately the same training time as MLP while theoretically demonstrating stronger expressive power than KAN. Furthermore, we compare the FLOPs of KAN and PowerMLP, quantifying the faster computation speed of PowerMLP. Our comprehensive experiments demonstrate that PowerMLP generally achieves higher accuracy and a training speed about 40 times faster than KAN in various tasks.