KAN/H: Kolmogorov-Arnold Network using Haar-like bases
Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based approximations, achieving high accuracy in high dimensions remains challenging. This paper proposes KAN/H, a variant of the Kolmogorov-Arnold Network (KAN) that uses a Haar-like hierarchical basis system with nonzero first-order derivatives, instead of B-splines. We also propose a learning-rate scheduling method and a method for handling unbounded real-valued inputs, leveraging properties of linear approximation with Haar-like hierarchical bases. By applying the resulting algorithm to function-approximation problems and MNIST, we confirm that our approach requires minimal problem-specific hyperparameter tuning.