mlsanityData to 7 Oct 2026

On the Kolmogorov neural networks

arXiv 2311.00049 ↗First posted 31 Oct 2023cs.NE cs.LG math.FAcited by 19

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Abstract (arXiv)

In this paper, we show that the Kolmogorov two hidden layer neural network model with a continuous, discontinuous bounded or unbounded activation function in the second hidden layer can precisely represent continuous, discontinuous bounded and all unbounded multivariate functions, respectively.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 4 of its 36 references that are in the map. First posted on arXiv 31 Oct 2023.

Builds on

4 of 36 references.

References · 4

  1. 2020The Kolmogorov-Arnold representation theorem revisitedcited by 89
  2. 2020Neural Network Approximation: Three Hidden Layers Are Enoughcited by 63
  3. 2019Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theoremcited by 49
  4. 2021Approximation capability of two hidden layer feedforward neural networks with fixed weightscited by 24

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 7; 2026: 3.

19 papers.

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  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  2. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 39
  3. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 16
  4. 2025LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behaviorcited by 12
  5. 2024Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networkscited by 11
  6. 2024Addressing common misinterpretations of KART and UAT in neural network literaturecited by 9
  7. 2024Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representationcited by 3
  8. 2024Structured and Balanced Multi-Component and Multi-Layer Neural Networkscited by 3
  9. 2025Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometriescited by 3
  10. 2025Relating Piecewise Linear Kolmogorov Arnold Networks to ReLU Networkscited by 2
  11. 2025On shallow feedforward neural networks with inputs from a topological spacecited by 2
  12. 2024Generalizable autoregressive modeling of time series through functional narrativescited by 1
7 more
  1. 2024GrokFormer: Graph Fourier Kolmogorov-Arnold Transformerscited by 1
  2. 2025Kolmogorov GAM Networks are all you need!cited by 1
  3. 2024The Function-Representation Model of Computationcited by 0
  4. 2025Exploring Kolmogorov-Arnold Network Expansions in Vision Transformers for Mitigating Catastrophic Forgetting in Continual Learningcited by 0
  5. 2026Clifford Kolmogorov-Arnold Networkscited by 0
  6. 2026Universality of shallow and deep neural networks on non-Euclidean spacescited by 0
  7. 2026Kolmogorov--Arnold stability for discontinuous functionscited by 0