On the Kolmogorov neural networks

Aysu Ismayilova, Vugar E. Ismailov*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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

Original languageEnglish
Article number106333
Pages (from-to)1-6
Number of pages6
JournalNeural Networks
Early online date22 Apr 2024
Publication statusE-pub ahead of print - 22 Apr 2024


  • Conjugate operator
  • Dual space
  • Indicator function
  • Kolmogorov's superposition theorem
  • Linear functional
  • Lipschitz function


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