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

2025-05-20

AI Summary

Global neural networks struggle to accurately approximate locally complex or discontinuous functions due to their inherent smoothness assumptions and lack of adaptive partitioning. Method: This paper proposes KAN-XCSF, a novel evolutionary rule-based system that integrates Kolmogorov–Arnold Networks (KANs) as rule consequents within the XCSF framework, enabling data-driven, adaptive regional decomposition and localized modeling. It synergistically combines KAN’s strong nonlinear representational capacity with XCSF’s online generalization capability and introduces a bi-objective fitness evaluation strategy balancing accuracy and generalization. Results: Experiments on synthetic and real-world benchmarks demonstrate that KAN-XCSF significantly outperforms XCSF, MLPs, and standard KANs. It achieves high precision in modeling strongly local, discontinuous functions using only 7.2 ± 2.3 compact, interpretable rules—yielding superior accuracy, interpretability, and low model complexity simultaneously.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Rule Mining & Pattern Mining

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 $pm$ 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.

Problem

• Optimizing local KANs for complex discontinuous functions
• Combining KAN expressiveness with XCSF adaptive partitioning
• Improving approximation accuracy over conventional methods

Innovation

• Optimizes local KANs via evolutionary rule-based learning
• Combines KAN expressiveness with XCSF adaptive partitioning
• Uses compact rule sets for complex local functions