mlsanityData to 14 Oct 2026

Addressing common misinterpretations of KART and UAT in neural network literature

arXiv 2408.16389 ↗First posted 29 Aug 2024cs.LG cs.NEcited by 9

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Abstract (arXiv)

This note addresses the Kolmogorov-Arnold Representation Theorem (KART) and the Universal Approximation Theorem (UAT), focusing on their frequent misinterpretations found in the neural network literature. Our remarks aim to support a more accurate understanding of KART and UAT among neural network specialists. In addition, we explore the minimal number of neurons required for universal approximation, showing that the same number of neurons needed for exact representation of functions in KART-based networks also suffices for standard multilayer perceptrons in the context of approximation.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 16 of its 31 references that are in the map. First posted on arXiv 29 Aug 2024.

Builds on

16 of 31 references.

References · 16

  1. 2017Approximating Continuous Functions by ReLU Nets of Minimal Widthcited by 122
  2. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  3. 2020Minimum Width for Universal Approximationcited by 94
  4. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 53
  5. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 49
  6. 2018Deep, Skinny Neural Networks are not Universal Approximatorscited by 38
  7. 2024Kolmogorov-Arnold Graph Neural Networkscited by 32
  8. 2022Achieve the Minimum Width of Neural Networks for Universal Approximationcited by 26
  9. 2021Approximation capability of two hidden layer feedforward neural networks with fixed weightscited by 24
  10. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 24
  11. 2023On the Kolmogorov neural networkscited by 19
  12. 2024Kolmogorov-Arnold Networks (KAN) for Time Series Classification and Robust Analysiscited by 16
4 more
  1. 2024Initial Investigation of Kolmogorov-Arnold Networks (KANs) as Feature Extractors for IMU Based Human Activity Recognitioncited by 13
  2. 2015A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate functioncited by 6
  3. 2024Minimum number of neurons in fully connected layers of a given neural network (the first approximation)cited by 3
  4. 2022Approximation error of single hidden layer neural networks with fixed weightscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 7.

9 papers.

  1. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 19
  2. 2026SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functionscited by 2
  3. 2025Polynomial, trigonometric, and tropical activationscited by 0
  4. 2026Universality of shallow and deep neural networks on non-Euclidean spacescited by 0
  5. 2026Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNscited by 0
  6. 2026Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued mapscited by 0
  7. 2026Kolmogorov--Arnold against bounded translationscited by 0
  8. 2026Kolmogorov--Arnold stability for discontinuous functionscited by 0
  9. 2026Evaluating the Effectiveness of SechKAN on 1D Datacited by 0