用进化规则学习优化局部柯尔莫哥洛夫-阿诺德网络，提升复杂函数逼近精度。
X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning
- 将KAN作为规则后件，用规则前件划分局部区域，实现自适应分段建模。
- 在人工与真实数据上平均仅需7.2条规则，显著优于传统方法。
- 适合处理局部复杂或间断函数，尤其适合需要高精度的科学计算场景。
函数逼近在多个领域至关重要，但现有神经网络方法因依赖全局模型，在处理局部复杂或不连续函数时表现不佳。本文提出X-KAN，一种通过进化规则学习框架XCSF优化多个局部柯尔莫哥洛夫-阿诺德网络（KAN）的新方法。X-KAN将局部KAN模型作为规则后件，通过规则前件定义局部区域，结合KAN的强表达能力与XCSF的自适应分区能力。实验表明，X-KAN在人工测试函数和真实数据集上的逼近精度显著优于XCSF、多层感知机及传统KAN。尤其对局部复杂或间断函数，仅需平均7.2±2.3条规则即可有效建模，验证了在XCSF中以KAN为局部模型的有效性，其规则适应度同时考量准确率与泛化性。代码已开源：https://github.com/YNU-NakataLab/X-KAN。
原文摘要 · Abstract (English)
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.
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