HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation

Abstract: This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on backpropagation, HKAN adopts a randomized learning approach, where the parameters of its basis functions are fixed, and linear aggregations are optimized using least-squares regression. HKAN utilizes a hierarchical multi-stacking framework, with each layer refining the predictions from the previous one by solving a series of linear regression problems. This non-iterative training method simplifies computation and eliminates sensitivity to local minima in the loss function. Empirical results show that HKAN delivers comparable, if not superior, accuracy and stability relative to KAN across various regression tasks, while also providing insights into variable importance. The proposed approach seamlessly integrates theoretical insights with practical applications, presenting a robust and efficient alternative for neural network modeling.