mlsanityData to 7 Oct 2026

FC-KAN: Function Combinations in Kolmogorov-Arnold Networks

arXiv 2409.01763 ↗First posted 3 Sep 2024cs.LG cs.CLcited by 18

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Abstract (arXiv)

In this paper, we introduce FC-KAN, a Kolmogorov-Arnold Network (KAN) that leverages combinations of popular mathematical functions such as B-splines, wavelets, and radial basis functions on low-dimensional data through element-wise operations. We explore several methods for combining the outputs of these functions, including sum, element-wise product, the addition of sum and element-wise product, representations of quadratic and cubic functions, concatenation, linear transformation of the concatenated output, and others. In our experiments, we compare FC-KAN with a multi-layer perceptron network (MLP) and other existing KANs, such as BSRBF-KAN, EfficientKAN, FastKAN, and FasterKAN, on the MNIST and Fashion-MNIST datasets. Two variants of FC-KAN, which use a combination of outputs from B-splines and Derivative of Gaussians (DoG) and from B-splines and linear transformations in the form of a quadratic function, outperformed overall other models on the average of 5 independent training runs. We expect that FC-KAN can leverage function combinations to design future KANs. Our repository is publicly available at: https://github.com/hoangthangta/FC_KAN.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 35 of its 78 references that are in the map. First posted on arXiv 3 Sep 2024.

Builds on

35 of 78 references.

References · 35

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  3. 2017Tensor Fusion Network for Multimodal Sentiment Analysiscited by 429
  4. 2018Efficient Low-rank Multimodal Fusion with Modality-Specific Factorscited by 268
  5. 2016Multimodal Compact Bilinear Pooling for Visual Question Answering and Visual Groundingcited by 243
  6. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 176
  7. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 125
  8. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  9. 2017Multi-modal Factorized Bilinear Pooling with Co-Attention Learning for Visual Question Answeringcited by 117
  10. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  11. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  12. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
23 more
  1. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  2. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
  3. 2024KAN or MLP: A Fairer Comparisoncited by 71
  4. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  5. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 69
  6. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 50
  7. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 43
  8. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 39
  9. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
  10. 2022ExSpliNet: An interpretable and expressive spline-based neural networkcited by 33
  11. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  12. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 33
  13. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 32
  14. 2018Universal Approximation with Quadratic Deep Networkscited by 29
  15. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  16. 2020Accelerating Sparse Matrix-Matrix Multiplication with GPU Tensor Corescited by 9
  17. 2024Activation Space Selectable Kolmogorov-Arnold Networkscited by 9
  18. 2024Addressing common misinterpretations of KART and UAT in neural network literaturecited by 9
  19. 2024A First Look at Kolmogorov-Arnold Networks in Surrogate-assisted Evolutionary Algorithmscited by 7
  20. 2024Sparks of Quantum Advantage and Rapid Retraining in Machine Learningcited by 5
  21. 2024Rethinking the Function of Neurons in KANscited by 5
  22. 2022TreeDRNet:A Robust Deep Model for Long Term Time Series Forecastingcited by 4
  23. 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: 3; 2025: 10; 2026: 5.

18 papers.

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  1. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  2. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 16
  3. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  4. 2025Medical Image Classification with KAN-Integrated Transformers and Dilated Neighborhood Attentioncited by 5
  5. 2025ChemKANs for Combustion Chemistry Modeling and Accelerationcited by 4
  6. 2025AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learningcited by 3
  7. 2025TabKAN: Advancing Tabular Data Analysis using Kolmogorov-Arnold Networkcited by 3
  8. 2025Kolmogorov GAM Networks are all you need!cited by 1
  9. 2026Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networkscited by 1
  10. 2026SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functionscited by 1
  11. 2024On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networkscited by 0
  12. 2025HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagationcited by 0
6 more
  1. 2025Label-Noise Resistant Learning via Optimal Brain Damage Maskingcited by 0
  2. 2025Combinations of Fast Activation and Trigonometric Functions in Kolmogorov-Arnold Networkscited by 0
  3. 2025Projective Kolmogorov Arnold Neural Networks (P-KANs): Entropy-Driven Functional Space Discovery for Interpretable Machine Learningcited by 0
  4. 2026In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networkscited by 0
  5. 2026YOLO with Kolmogorov-Arnold networks and vision-language foundation models for interpretable object detection with trustworthy multimodal AI in computer vision perceptioncited by 0
  6. 2026Sample-Efficiency of Kolmogorov-Arnold Networkscited by 0