Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
arXiv:2606.02936v1 Announce Type: new Abstract: 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 persp
The paper leverages recent advancements and renewed interest in Kolmogorov-Arnold networks (KANs) and radial basis functions, indicating ongoing fundamental research to enhance AI model capabilities.
This research contributes to the foundational understanding and development of more efficient and robust neural network architectures for complex function approximation and random field learning, crucial for various AI applications.
The introduction of hierarchical RBF-KAN and RBF-SKAN architectures provides new mathematical frameworks for improving approximation capabilities, potentially leading to more accurate and interpretable AI models.
- · AI researchers
- · Machine learning developers
- · Scientific computing sector
- · Inefficient approximation methods
Improved performance in specific machine learning tasks requiring high-fidelity function approximation and uncertainty quantification.
Potential for more robust and data-efficient AI models, especially in scientific and engineering domains where complex systems are modeled.
These architectural advancements could subtly influence the broader AI development landscape by offering alternative, potentially superior, building blocks for future systems.
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