mlsanityData to 7 Oct 2026

KAN versus MLP on Irregular or Noisy Functions

arXiv 2408.07906 ↗First posted 15 Aug 2024cs.LG cs.AI cs.NAcited by 7

Not on the map. Why?

Abstract (arXiv)

In this paper, we compare the performance of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions. We control the number of parameters and the size of the training samples to ensure a fair comparison. For clarity, we categorize the functions into six types: regular functions, continuous functions with local non-differentiable points, functions with jump discontinuities, functions with singularities, functions with coherent oscillations, and noisy functions. Our experimental results indicate that KAN does not always perform best. For some types of functions, MLP outperforms or performs comparably to KAN. Furthermore, increasing the size of training samples can improve performance to some extent. When noise is added to functions, the irregular features are often obscured by the noise, making it challenging for both MLP and KAN to extract these features effectively. We hope these experiments provide valuable insights for future neural network research and encourage further investigations to overcome these challenges.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 31 of its 52 references that are in the map. First posted on arXiv 15 Aug 2024.

Builds on

31 of 52 references.

References · 31

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 176
  3. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  4. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  5. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  6. 2024Convolutional Kolmogorov-Arnold Networkscited by 76
  7. 2024KAN or MLP: A Fairer Comparisoncited by 71
  8. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  9. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 69
  10. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  11. 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 58
  12. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 52
19 more
  1. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
  2. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 46
  3. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
  4. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 33
  5. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 33
  6. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 32
  7. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 31
  8. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 23
  9. 2024Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementationcited by 22
  10. 2024How to Learn More? Exploring Kolmogorov-Arnold Networks for Hyperspectral Image Classificationcited by 19
  11. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  12. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  13. 2024COEFF-KANs: A Paradigm to Address the Electrolyte Field with KANscited by 9
  14. 2024DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networkscited by 7
  15. 2024RPN: Reconciled Polynomial Network Towards Unifying PGMs, Kernel SVMs, MLP and KANcited by 4
  16. 2024Diffusion Representation for Asymmetric Kernelscited by 3
  17. 2024From Black Box to Clarity: AI-Powered Smart Grid Optimization with Kolmogorov-Arnold Networkscited by 3
  18. 2024KAN based Autoencoders for Factor Modelscited by 2
  19. 2024Image Classification using Fuzzy Pooling in Convolutional Kolmogorov-Arnold Networkscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 4.

7 papers.

  1. 2025Color Matching Using Hypernetwork-Based Kolmogorov-Arnold Networkscited by 4
  2. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  3. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 3
  4. 2026Multilevel Training for Kolmogorov Arnold Networkscited by 1
  5. 2025AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecastingcited by 0
  6. 2026Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functionscited by 0
  7. 2026Sample-Efficiency of Kolmogorov-Arnold Networkscited by 0