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BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks

arXiv 2406.11173 ↗First posted 17 Jun 2024cs.CLcited by 43

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Abstract (arXiv)

In this paper, we introduce BSRBF-KAN, a Kolmogorov Arnold Network (KAN) that combines B-splines and radial basis functions (RBFs) to fit input vectors during data training. We perform experiments with BSRBF-KAN, multi-layer perception (MLP), and other popular KANs, including EfficientKAN, FastKAN, FasterKAN, and GottliebKAN over the MNIST and Fashion-MNIST datasets. BSRBF-KAN shows stability in 5 training runs with a competitive average accuracy of 97.55% on MNIST and 89.33% on Fashion-MNIST and obtains convergence better than other networks. We expect BSRBF-KAN to open many combinations of mathematical functions to design KANs. Our repo is publicly available at: https://github.com/hoangthangta/BSRBF_KAN.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 9 of its 30 references that are in the map. First posted on arXiv 17 Jun 2024.

Builds on

9 of 30 references.

References · 9

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  3. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 125
  4. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  5. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  6. 2024Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformationcited by 41
  7. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  8. 2022TreeDRNet:A Robust Deep Model for Long Term Time Series Forecastingcited by 4
  9. 2020Regularized Flexible Activation Function Combinations for Deep Neural Networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 19; 2025: 16; 2026: 8.

43 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. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
  5. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 18
  6. 2024SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functionscited by 15
  7. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  8. 2024Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networkscited by 11
  9. 2025Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networkscited by 10
  10. 2024Activation Space Selectable Kolmogorov-Arnold Networkscited by 9
  11. 2024DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networkscited by 7
  12. 2024Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equationscited by 7
31 more
  1. 2024Rethinking the Function of Neurons in KANscited by 5
  2. 2024FourierKAN outperforms MLP on Text Classification Head Fine-tuningcited by 5
  3. 2024Exploring Kolmogorov-Arnold networks for realistic image sharpness assessmentcited by 5
  4. 2025Medical Image Classification with KAN-Integrated Transformers and Dilated Neighborhood Attentioncited by 5
  5. 2025Fast and Accurate Gigapixel Pathological Image Classification with Hierarchical Distillation Multi-Instance Learningcited by 5
  6. 2025asKAN: Active Subspace embedded Kolmogorov-Arnold Networkcited by 5
  7. 2024KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics examplecited by 4
  8. 2025Exploring Adversarial Transferability between Kolmogorov-arnold Networkscited by 4
  9. 2025Input Convex Kolmogorov Arnold Networkscited by 4
  10. 2024GNN-SKAN: Harnessing the Power of SwallowKAN to Advance Molecular Representation Learning with GNNscited by 3
  11. 2024KAN v.s. MLP for Offline Reinforcement Learningcited by 3
  12. 2025AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learningcited by 3
  13. 2025Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometriescited by 3
  14. 2025TabKAN: Advancing Tabular Data Analysis using Kolmogorov-Arnold Networkcited by 3
  15. 2025Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histogramscited by 3
  16. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 3
  17. 2024Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practicecited by 2
  18. 2024P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimizationcited by 2
  19. 2026Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learningcited by 2
  20. 2025Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessmentcited by 1
  21. 2025Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum Statescited by 1
  22. 2025Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networkscited by 1
  23. 2026TruKAN: Towards More Efficient Kolmogorov-Arnold Networks Using Truncated Power Functionscited by 1
  24. 2026Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networkscited by 1
  25. 2026SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functionscited by 1
  26. 2025Combinations of Fast Activation and Trigonometric Functions in Kolmogorov-Arnold Networkscited by 0
  27. 2025Projective Kolmogorov Arnold Neural Networks (P-KANs): Entropy-Driven Functional Space Discovery for Interpretable Machine Learningcited by 0
  28. 2026ABFR-KAN: Kolmogorov-Arnold Networks for Functional Brain Analysiscited by 0
  29. 2025Learning to Anchor Visual Odometry: KAN-Based Pose Regression for Planetary Landingcited by 0
  30. 2026Evaluating the Effectiveness of SechKAN on 1D Datacited by 0
  31. 2026Neural scaling laws and evolution of learnable activation functions of Kolmogorov-Arnold networkscited by 0