# X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning

arXiv: https://arxiv.org/abs/2505.14273 · HTML: https://mlsanity.com/paper/2505.14273/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 13 of 13)

- [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)
- [Efficient Large-Scale Language Model Training on GPU Clusters Using Megatron-LM](https://mlsanity.com/paper/2104.04473/) (2021)
- [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)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [F-KANs: Federated Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.20100/) (2024)
- [PowerMLP: An Efficient Version of KAN](https://mlsanity.com/paper/2412.13571/) (2024)
- [Autoencoding with a Classifier System](https://mlsanity.com/paper/1910.10579/) (2019)
- [KANs for Computer Vision: An Experimental Study](https://mlsanity.com/paper/2411.18224/) (2024)
- [Integrating Symbolic Neural Networks with Building Physics: A Study and Proposal](https://mlsanity.com/paper/2411.00800/) (2024)

## Built on by (most cited first, 2 of 2)

- [KANO: Kolmogorov-Arnold Neural Operator](https://mlsanity.com/paper/2509.16825/) (2025)
- [Kolmogorov-Arnold Classifier Systems as Universal Approximators](https://mlsanity.com/paper/2609.37958/) (2026)

## Abstract (arXiv)

Function approximation is a critical task in various fields. However, existing neural network approaches struggle with locally complex or discontinuous functions due to their reliance on a single global model covering the entire problem space. We propose X-KAN, a novel method that optimizes multiple local Kolmogorov-Arnold Networks (KANs) through an evolutionary rule-based machine learning framework called XCSF. X-KAN combines KAN's high expressiveness with XCSF's adaptive partitioning capability by implementing local KAN models as rule consequents and defining local regions via rule antecedents. Our experimental results on artificial test functions and real-world datasets demonstrate that X-KAN significantly outperforms conventional methods, including XCSF, Multi-Layer Perceptron, and KAN, in terms of approximation accuracy. Notably, X-KAN effectively handles functions with locally complex or discontinuous structures that are challenging for conventional KAN, using a compact set of rules (average 7.2 ± 2.3 rules). These results validate the effectiveness of using KAN as a local model in XCSF, which evaluates the rule fitness based on both accuracy and generality. Our X-KAN implementation is available at https://github.com/YNU-NakataLab/X-KAN.