HKAN: Hierarchical Kolmogorov-Arnold network without backpropagation.

This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel neural model that eliminates the need for backpropagation. While structurally related to the standard Kolmogorov-Arnold Network (KAN), HKAN employs a randomized learning framework and a hierarchical multi-stacking design, where each layer refines the approximations produced by the preceding one through a sequence of convex optimization subproblems. This non-iterative training strategy ensures high computational efficiency and numerical stability while preserving strong approximation accuracy. Experimental results on both synthetic and real-world regression tasks show that HKAN achieves accuracy comparable to or exceeding that of standard KANs and Multi-Layer Perceptrons, while reducing training time. Moreover, HKAN enhances interpretability by incorporating a built-in mechanism for assessing the importance of input variables. The proposed framework thus bridges theoretical rigor and practical utility, offering a robust, transparent, and computationally efficient alternative to gradient-based neural models.