# rKAN: Rational Kolmogorov-Arnold Networks Source: [rKAN: Rational Kolmogorov-Arnold Networks]() Collection index: [llms.txt]() Data updated: 2026-01-01T12:40:34.493Z Authors: Alireza Afzal Aghaei Published: 2024-06-20T16:59:38.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Function Approximation on F2](): Function Approximation; Function F2(xi); MSE: 1.889e-7. - [Function Approximation on F3(ξ)](): Function Approximation; F3(ξ); MSE: 2.59e-7. - [Root Finding on Lane-Emden differential equation](): Root Finding; Lane-Emden differential equation; Absolute Error: 0.00000486. - [Image Classification on MNIST (test)](): Image Classification; MNIST (test); Accuracy: 99.293. ## Original sources and implementation [Original paper]() [PDF]() [Implementation]()