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Combinations of Fast Activation and Trigonometric Functions in Kolmogorov-Arnold Networks

arXiv 2508.11876 ↗First posted 16 Aug 2025cs.LGcited by 0

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Abstract (arXiv)

For years, many neural networks have been developed based on the Kolmogorov-Arnold Representation Theorem (KART), which was created to address Hilbert's 13th problem. Recently, relying on KART, Kolmogorov-Arnold Networks (KANs) have attracted attention from the research community, stimulating the use of polynomial functions such as B-splines and RBFs. However, these functions are not fully supported by GPU devices and are still considered less popular. In this paper, we propose the use of fast computational functions, such as ReLU and trigonometric functions (e.g., ReLU, sin, cos, arctan), as basis components in Kolmogorov-Arnold Networks (KANs). By integrating these function combinations into the network structure, we aim to enhance computational efficiency. Experimental results show that these combinations maintain competitive performance while offering potential improvements in training time and generalization.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 27 of its 41 references that are in the map. First posted on arXiv 16 Aug 2025.

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References · 27

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  3. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 128
  4. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  5. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  6. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 118
  7. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  8. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  9. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  10. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 71
  11. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 70
  12. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 52
15 more
  1. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 46
  2. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  3. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 37
  4. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 35
  5. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 34
  6. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 33
  7. 2024CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysiscited by 22
  8. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 19
  9. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  10. 2024Activation Space Selectable Kolmogorov-Arnold Networkscited by 9
  11. 2024A First Look at Kolmogorov-Arnold Networks in Surrogate-assisted Evolutionary Algorithmscited by 7
  12. 2024Sparks of Quantum Advantage and Rapid Retraining in Machine Learningcited by 5
  13. 2024Rethinking the Function of Neurons in KANscited by 5
  14. 2024Effective Integration of KAN for Keyword Spottingcited by 5
  15. 2020Regularized Flexible Activation Function Combinations for Deep Neural Networkscited by 3

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