Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
In this manuscript, we propose and analyze hierarchical Kolmogorov--Arnold neural network architectures employing radial basis functions as activation functions for approximating deterministic functions and random field models. Specifically, we develop a hierarchical radial-basis-function Kolmogorov--Arnold network (hierarchical RBF-KAN) for multidimensional deterministic function approximation and a hierarchical radial-basis-function stochastic Kolmogorov--Arnold network (hierarchical RBF-SKAN) for random field learning. From a theoretical perspective, we establish universal approximation results for both architectures. In particular, we derive quantitative approximation estimates for th...
| Authors | Mingtao Xia, Qijing Shen |
|---|---|
| Primary category | cs.LG |
| Published | 1 June 2026 |
| Last updated at source | 1 June 2026 |
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