fKAN: Fractional Kolmogorov–Arnold Networks with trainable Jacobi basis functions

Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance interpretability and precision of these systems. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN), a novel neural network architecture that incorporates the distinctive attributes of KANs with a trainable adaptive fractional-orthogonal Jacobi function as its basis function. By leveraging the unique mathematical properties of fractional Jacobi functions, including simple derivative formulas, non-polynomial behavior, and activity for both positive and negative input values, this approach ensures efficient learning and enhanced accuracy. The proposed architecture…