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

• URL: http://arxiv.org/abs/2406.07456v1
• Date: Tue, 11 Jun 2024 17:01:45 GMT
• Title: fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions
• Authors: Alireza Afzal Aghaei,
• Abstract summary: Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs) This paper presents a novel neural network architecture that incorporates a trainable adaptive fractional-orthogonal Jacobi function as its basis function. The results demonstrate that integrating fractional Jacobi functions into KANs significantly improves training speed and performance across diverse fields and applications.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. 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 is evaluated across a range of tasks in deep learning and physics-informed deep learning. Precision is tested on synthetic regression data, image classification, image denoising, and sentiment analysis. Additionally, the performance is measured on various differential equations, including ordinary, partial, and fractional delay differential equations. The results demonstrate that integrating fractional Jacobi functions into KANs significantly improves training speed and performance across diverse fields and applications.

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