Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape

The article introduces Structural Kolmogorov-Arnold Networks (KANs) that place learnable functions in the convolution structure rather than on individual kernel entries, organizing the design by whether the function acts on pixel values or filter shape. It presents three realizations: SV-KAN with a shared value function, AG-KAN using a content-adaptive Gaussian gate, and RF-KAN which builds filters from oriented ridge profiles in a Morlet wavelet basis.

• RF-KAN and SV-KAN achieve 88.47% and 88.20% accuracy on CIFAR-10, respectively, with approximately 0.4M parameters.
• These models outperform plain convolutions and per-edge KANs at roughly one-fifth of the parameters.
• RF-KAN constructs filters using content-adaptive amplitudes of localized oscillatory wavelet basis functions.
• Ablation studies identify the learned shape as the critical component, with its removal causing a drop in accuracy by over forty points.

The authors consider this significant because it demonstrates that parameter-efficient alternatives to per-edge KANs can achieve superior performance by leveraging content-adaptive filter shapes rather than just learnable activations.