mlsanityData to 14 Oct 2026

Incorporating Arbitrary Matrix Group Equivariance into KANs

arXiv 2410.00435 ↗First posted 1 Oct 2024cs.LGcited by 4

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Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). However, spline functions may not respect symmetry in tasks, which is crucial prior knowledge in machine learning. In this paper, we propose Equivariant Kolmogorov-Arnold Networks (EKAN), a method for incorporating arbitrary matrix group equivariance into KANs, aiming to broaden their applicability to more fields. We first construct gated spline basis functions, which form the EKAN layer together with equivariant linear weights, and then define a lift layer to align the input space of EKAN with the feature space of the dataset, thereby building the entire EKAN architecture. Compared with baseline models, EKAN achieves higher accuracy with smaller datasets or fewer parameters on symmetry-related tasks, such as particle scattering and the three-body problem, often reducing test MSE by several orders of magnitude. Even in non-symbolic formula scenarios, such as top quark tagging with three jet constituents, EKAN achieves comparable results with state-of-the-art equivariant architectures using fewer than 40% of the parameters, while KANs do not outperform MLPs as expected. Code and data are available at https://github.com/hulx2002/EKAN .

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 44 of its 61 references that are in the map. First posted on arXiv 1 Oct 2024.

Builds on

44 of 61 references.

References · 44

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  2. 2020GLU Variants Improve Transformercited by 1,804
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32 more
  1. 2020Self-supervised Equivariant Attention Mechanism for Weakly Supervised Semantic Segmentationcited by 300
  2. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 194
  3. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  4. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  5. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 179
  6. 2022Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Modelscited by 174
  7. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 126
  8. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 121
  9. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
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  11. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 92
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  15. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 70
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  17. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 53
  18. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 52
  19. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 49
  20. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 47
  21. 2023Self-supervised learning of Split Invariant Equivariant representationscited by 44
  22. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  23. 2020PDO-eConvs: Partial Differential Operator Based Equivariant Convolutionscited by 34
  24. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 34
  25. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 34
  26. 2020Dense Steerable Filter CNNs for Exploiting Rotational Symmetry in Histology Imagescited by 33
  27. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 32
  28. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  29. 2022Self-Supervised Equivariant Learning for Oriented Keypoint Detectioncited by 26
  30. 2023Structuring Representation Geometry with Rotationally Equivariant Contrastive Learningcited by 25
  31. 2021PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNscited by 19
  32. 2022PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025MatrixKAN: Parallelized Kolmogorov-Arnold Networkcited by 7
  2. 2025Variational Kolmogorov-Arnold Networkcited by 1
  3. 2025FS-KAN: Permutation Equivariant Kolmogorov-Arnold Networks via Function Sharingcited by 0
  4. 2026Clifford Kolmogorov-Arnold Networkscited by 0