ML Anthology

Kolmogorov's Theorem Is Relevant

Vera Kurková
NeCo 1991 pp. 617-622
doi:10.1162/NECO.1991.3.4.617 /neco/1991/kurkova1991neco-kolmogorov/

Abstract

We show that Kolmogorov's theorem on representations of continuous functions of n-variables by sums and superpositions of continuous functions of one variable is relevant in the context of neural networks. We give a version of this theorem with all of the one-variable functions approximated arbitrarily well by linear combinations of compositions of affine functions with some given sigmoidal function. We derive an upper estimate of the number of hidden units.

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Cite

Text

Kurková. "Kolmogorov's Theorem Is Relevant." Neural Computation, 1991. doi:10.1162/NECO.1991.3.4.617

Markdown

[Kurková. "Kolmogorov's Theorem Is Relevant." Neural Computation, 1991.](https://mlanthology.org/neco/1991/kurkova1991neco-kolmogorov/) doi:10.1162/NECO.1991.3.4.617

BibTeX

@article{kurkova1991neco-kolmogorov,
  title     = {{Kolmogorov's Theorem Is Relevant}},
  author    = {Kurková, Vera},
  journal   = {Neural Computation},
  year      = {1991},
  pages     = {617-622},
  doi       = {10.1162/NECO.1991.3.4.617},
  volume    = {3},
  url       = {https://mlanthology.org/neco/1991/kurkova1991neco-kolmogorov/}
}