Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
Researchers have introduced novel hierarchical neural network architectures, RBF-KAN and RBF-SKAN, designed for approximating complex multidimensional functions and learning random field models. These architectures leverage radial basis functions within the Kolmogorov-Arnold Network framework. Theoretical analysis demonstrates their universal approximation capabilities and potential to mitigate the curse of dimensionality for deterministic functions, while also showing approximation under the Wasserstein-2 metric for random fields. Empirical results confirm the effectiveness of these RBF-based networks in practical learning scenarios. AI
IMPACT Introduces new theoretical frameworks for function approximation and random field learning, potentially improving efficiency in high-dimensional data analysis.