mlsanityData to 7 Oct 2026

rKAN: Rational Kolmogorov-Arnold Networks

arXiv 2406.14495 ↗First posted 20 Jun 2024cs.LG cs.NA cs.NEcited by 31

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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.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 30 of its 55 references that are in the map. First posted on arXiv 20 Jun 2024.

Builds on

30 of 55 references.

References · 30

  1. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,061
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  3. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 176
  4. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 125
  5. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  6. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  7. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  8. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  9. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  10. 2020Rational neural networkscited by 75
  11. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  12. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 69
18 more
  1. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  2. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 52
  3. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 46
  4. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 43
  5. 2024Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformationcited by 41
  6. 2017Neural networks and rational functionscited by 40
  7. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  8. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 33
  9. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 33
  10. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 23
  11. 2024Smooth Kolmogorov Arnold networks enabling structural knowledge representationcited by 22
  12. 2024iKAN: Global Incremental Learning with KAN for Human Activity Recognition Across Heterogeneous Datasetscited by 14
  13. 2024Endowing Interpretability for Neural Cognitive Diagnosis by Efficient Kolmogorov-Arnold Networkscited by 12
  14. 2024Initial Investigation of Kolmogorov-Arnold Networks (KANs) as Feature Extractors for IMU Based Human Activity Recognitioncited by 12
  15. 2024Leveraging KANs For Enhanced Deep Koopman Operator Discoverycited by 9
  16. 2023deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equationscited by 7
  17. 2021A structured proof of Kolmogorov's Superposition Theoremcited by 3
  18. 2023Solving Falkner-Skan type equations via Legendre and Chebyshev Neural Blockscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 14; 2025: 11; 2026: 6.

31 papers.

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  1. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  2. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  3. 2024On the expressiveness and spectral bias of KANscited by 36
  4. 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
  5. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  6. 2024Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and fastercited by 13
  7. 2024Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networkscited by 11
  8. 2024DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networkscited by 7
  9. 2025KANO: Kolmogorov-Arnold Neural Operatorcited by 6
  10. 2024Rethinking the Function of Neurons in KANscited by 5
  11. 2025Fast and Accurate Gigapixel Pathological Image Classification with Hierarchical Distillation Multi-Instance Learningcited by 5
  12. 2024KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problemscited by 3
19 more
  1. 2024KAN v.s. MLP for Offline Reinforcement Learningcited by 3
  2. 2025AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learningcited by 3
  3. 2025TabKAN: Advancing Tabular Data Analysis using Kolmogorov-Arnold Networkcited by 3
  4. 2024Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practicecited by 2
  5. 2025On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimatorscited by 2
  6. 2025MetaCluster: Enabling Deep Compression of Kolmogorov-Arnold Networkcited by 2
  7. 2024Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularitiescited by 1
  8. 2025Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networkscited by 1
  9. 2024On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networkscited by 0
  10. 2025HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagationcited by 0
  11. 2025Polynomial, trigonometric, and tropical activationscited by 0
  12. 2025KARMA: Efficient Structural Defect Segmentation via Kolmogorov-Arnold Representation Learningcited by 0
  13. 2025Algorithms and data structures for automatic precision estimation of neural networkscited by 0
  14. 2026KAN We Flow? Advancing Robotic Manipulation with 3D Flow Matching via KAN & RWKVcited by 0
  15. 2026Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functionscited by 0
  16. 2026In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networkscited by 0
  17. 2026KANEx: Translating Kolmogorov-Arnold Networks' Interpretability to Medical Explainabilitycited by 0
  18. 2026Evaluating the Effectiveness of SechKAN on 1D Datacited by 0
  19. 2026SW-KAN: Kolmogorov-Arnold Networks with Stieltjes-Wigert q-Orthogonal Polynomialscited by 0