Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs

The article presents Structural Kolmogorov-Arnold Networks (KANs), which introduce a parameter-efficient approach by placing learnable functions in the convolution structure rather than on each edge. Three models are studied: SV-KAN, AG-KAN, and RF-KAN, with RF-KAN achieving 88.47% accuracy on CIFAR-10 using approximately 0.4M parameters, outperforming traditional convolutional methods and demonstrating the importance of content-adaptive filter shapes. This work highlights a significant reduction in parameters while maintaining high performance, making it relevant for practitioners seeking efficient architectures in deep learning.