rKAN：有理Kolmogorov-Arnold网络
rKAN: Rational Kolmogorov-Arnold Networks
AI总结：
针对KAN原有B样条基函数实现复杂的问题，研究提出以有理函数为新型基函数的rKAN，基于Pade逼近和有理雅可比函数构建可训练基函数，在多类任务中验证了其函数逼近的实用性与有效性。
摘要：
Kolmogorov-Arnold网络（KAN）的发展标志着深度学习领域相较于传统多层感知机的重大转变。最初，KAN采用B样条曲线作为主要基函数，但其固有复杂度带来了实现难题。因此，研究人员探索了小波、多项式、分数阶函数等替代基函数。本研究探索将有理函数作为KAN的新型基函数，提出基于Pade逼近和有理雅可比函数的两种可训练基函数方案，构建了有理KAN（rKAN）。随后我们在多项深度学习与物理信息任务中评估rKAN的性能，验证其在函数逼近方面的实用性与有效性。
英文摘要：
The development of Kolmogorov-Arnold networks (KANs) marks a significant shift from traditional multi-layer perceptrons in deep learning. Initially, KANs employed B-spline curves as their primary basis function, but their inherent complexity posed implementation challenges. Consequently, researchers have explored alternative basis functions such as Wavelets, Polynomials, and Fractional functions. In this research, we explore the use of rational functions as a novel basis function for KANs. We propose two different approaches based on Pade approximation and rational Jacobi functions as trainable basis functions, establishing the rational KAN (rKAN). We then evaluate rKAN's performance in various deep learning and physics-informed tasks to demonstrate its practicality and effectiveness in function approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
