<ul><li>Function approximation is crucial in various fields, but existing neural network methods struggle with locally complex or discontinuous functions due to relying on a single global model.</li><li>X-KAN is introduced as a new approach that optimizes multiple local Kolmogorov-Arnold Networks (KANs) using an evolutionary rule-based machine learning framework called XCSF.</li><li>Experimental results show that X-KAN outperforms traditional methods like XCSF, Multi-Layer Perceptron, and KAN in terms of approximation accuracy, especially for functions with complex or discontinuous structures.</li><li>By utilizing a compact set of rules, X-KAN effectively handles challenging functions by combining the high expressiveness of KAN with XCSF's adaptive partitioning capability.</li></ul>

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

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