CVKAN: Complex-Valued Kolmogorov-Arnold Networks
This work addresses the need for interpretable complex-valued neural networks in domains like physics and knot theory, though it appears incremental as it adapts existing KANs to complex values.
The authors tackled the problem of combining interpretable Kolmogorov-Arnold Networks (KANs) with complex-valued neural networks (CVNNs) by proposing CVKAN, which transfers KAN mechanisms to the complex domain. The result shows CVKAN is more stable, performs on par or better than real-valued KANs with fewer parameters and shallower architecture, enhancing explainability.
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.