mlsanityData to 14 Oct 2026

KAN: Kolmogorov-Arnold Networks

arXiv 2404.19756 ↗First posted 30 Apr 2024cs.LG cond-mat.dis-nn cs.AIcited by 649

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Abstract (arXiv)

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Key facts. Cited by 649 papers in the map (data through 14 Oct 2026). Builds on 59 of its 151 references that are in the map. First posted on arXiv 30 Apr 2024.

Builds on

59 of 151 references.

References · 59

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 185; 2025: 244; 2026: 220.

649 papers.

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  1. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 179
  2. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 128
  3. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  4. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  5. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  6. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  7. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  8. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 71
  9. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 70
  10. 2024A Survey on Kolmogorov-Arnold Networkcited by 68
  11. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 64
  12. 2024Kolmogorov-Arnold Transformercited by 56
38 more
  1. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 52
  2. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 49
  3. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 47
  4. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 46
  5. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  6. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  7. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 37
  8. 2024On the expressiveness and spectral bias of KANscited by 37
  9. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 35
  10. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 35
  11. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  12. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 34
  13. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 34
  14. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 32
  15. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  16. 2025Exploring the Evolution of Physics Cognition in Video Generation: A Surveycited by 31
  17. 2025TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecastingcited by 30
  18. 2024RoPINN: Region Optimized Physics-Informed Neural Networkscited by 26
  19. 2024Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advancescited by 26
  20. 2024A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Datacited by 25
  21. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  22. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 24
  23. 2025From Zero to Detail: Deconstructing Ultra-High-Definition Image Restoration from Progressive Spectral Perspectivecited by 23
  24. 2025AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mappingcited by 23
  25. 2024Smooth Kolmogorov Arnold networks enabling structural knowledge representationcited by 22
  26. 2024Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementationcited by 22
  27. 2024CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysiscited by 22
  28. 2024How to Learn More? Exploring Kolmogorov-Arnold Networks for Hyperspectral Image Classificationcited by 20
  29. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 19
  30. 2024DaWin: Training-free Dynamic Weight Interpolation for Robust Adaptationcited by 19
  31. 2025A Comprehensive Survey on Self-Interpretable Neural Networkscited by 18
  32. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 18
  33. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  34. 2024Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysiscited by 16
  35. 2024On Efficient Variants of Segment Anything Model: A Surveycited by 16
  36. 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
  37. 2024PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Setscited by 15
  38. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14

50 most cited of 649 All 649 (JSON)