# rKAN: Rational Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2406.14495 · HTML: https://mlsanity.com/paper/2406.14495/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 55 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 30 of 30)

- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Rational neural networks](https://mlsanity.com/paper/2004.01902/) (2020)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Neural networks and rational functions](https://mlsanity.com/paper/1706.03301/) (2017)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classification](https://mlsanity.com/paper/2406.07869/) (2024)
- [Suitability of KANs for Computer Vision: A preliminary investigation](https://mlsanity.com/paper/2406.09087/) (2024)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [Smooth Kolmogorov Arnold networks enabling structural knowledge representation](https://mlsanity.com/paper/2405.11318/) (2024)
- [iKAN: Global Incremental Learning with KAN for Human Activity Recognition Across Heterogeneous Datasets](https://mlsanity.com/paper/2406.01646/) (2024)
- [Endowing Interpretability for Neural Cognitive Diagnosis by Efficient Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.14399/) (2024)
- [Initial Investigation of Kolmogorov-Arnold Networks (KANs) as Feature Extractors for IMU Based Human Activity Recognition](https://mlsanity.com/paper/2406.11914/) (2024)
- [Leveraging KANs For Enhanced Deep Koopman Operator Discovery](https://mlsanity.com/paper/2406.02875/) (2024)
- [deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equations](https://mlsanity.com/paper/2309.07684/) (2023)
- [A structured proof of Kolmogorov's Superposition Theorem](https://mlsanity.com/paper/2105.00408/) (2021)
- [Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks](https://mlsanity.com/paper/2308.03337/) (2023)

## Built on by (most cited first, 30 of 35)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions](https://mlsanity.com/paper/2407.04149/) (2024)
- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and faster](https://mlsanity.com/paper/2409.14248/) (2024)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [KANO: Kolmogorov-Arnold Neural Operator](https://mlsanity.com/paper/2509.16825/) (2025)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [Fast and Accurate Gigapixel Pathological Image Classification with Hierarchical Distillation Multi-Instance Learning](https://mlsanity.com/paper/2502.21130/) (2025)
- [On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators](https://mlsanity.com/paper/2509.19830/) (2025)
- [KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems](https://mlsanity.com/paper/2409.06649/) (2024)
- [KAN v.s. MLP for Offline Reinforcement Learning](https://mlsanity.com/paper/2409.09653/) (2024)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [TabKAN: Advancing Tabular Data Analysis using Kolmogorov-Arnold Network](https://mlsanity.com/paper/2504.06559/) (2025)
- [Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practice](https://mlsanity.com/paper/2408.10263/) (2024)
- [MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Network](https://mlsanity.com/paper/2510.19105/) (2025)
- [Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities](https://mlsanity.com/paper/2410.04096/) (2024)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2410.08041/) (2024)
- [HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation](https://mlsanity.com/paper/2501.18199/) (2025)
- [Polynomial, trigonometric, and tropical activations](https://mlsanity.com/paper/2502.01247/) (2025)
- [KARMA: Efficient Structural Defect Segmentation via Kolmogorov-Arnold Representation Learning](https://mlsanity.com/paper/2508.08186/) (2025)
- [Algorithms and data structures for automatic precision estimation of neural networks](https://mlsanity.com/paper/2509.24607/) (2025)
- [KAN We Flow? Advancing Robotic Manipulation with 3D Flow Matching via KAN & RWKV](https://mlsanity.com/paper/2602.01115/) (2026)
- [Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions](https://mlsanity.com/paper/2602.06737/) (2026)
- [In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2603.15250/) (2026)
- [Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches](https://mlsanity.com/paper/2604.16842/) (2026)
- [KANEx: Translating Kolmogorov-Arnold Networks' Interpretability to Medical Explainability](https://mlsanity.com/paper/2607.24730/) (2026)

## Abstract (arXiv)

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.