将KAN拓展到复数域，提升模型稳定性和可解释性。
CVKAN: Complex-Valued Kolmogorov-Arnold Networks
- 用复数域重构KAN的激活函数与网络结构
- 在复数函数拟合和纽结理论数据上表现更优，参数更少
- 适合需要高可解释性的复杂系统建模任务
本文提出一种复数域的Kolmogorov-Arnold网络（CVKAN），融合KAN的内在可解释性与复值神经网络（CVNN）的优势。我们展示了如何将KAN及其相关机制迁移至复数域。通过在符号复数函数拟合、物理有意义公式以及纽结理论的真实数据集上的实验，验证了CVKAN的有效性。结果表明，该模型在保持或超越实数域KAN性能的同时，参数更少、网络更浅，且更具稳定性，从而实现更强的可解释性。
原文摘要 · Abstract (English)
In this work we propose CVKAN, a complex-valued Kolmogorov-Arnold Network (KAN), to join the intrinsic interpretability of KANs and the advantages of Complex-Valued Neural Networks (CVNNs). We show how to transfer a KAN and the necessary associated mechanisms into the complex domain. To confirm that CVKAN meets expectations we conduct experiments on symbolic complex-valued function fitting and physically meaningful formulae as well as on a more realistic dataset from knot theory. Our proposed CVKAN is more stable and performs on par or better than real-valued KANs while requiring less parameters and a shallower network architecture, making it more explainable.
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