ML Anthology

Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant

Federico Girosi, Tomaso A. Poggio
NeCo 1989 pp. 465-469
doi:10.1162/NECO.1989.1.4.465 /neco/1989/girosi1989neco-representation/

Abstract

Many neural networks can be regarded as attempting to approximate a multivariate function in terms of one-input one-output units. This note considers the problem of an exact representation of nonlinear mappings in terms of simpler functions of fewer variables. We review Kolmogorov's theorem on the representation of functions of several variables in terms of functions of one variable and show that it is irrelevant in the context of networks for learning.

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Cite

Text

Girosi and Poggio. "Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant." Neural Computation, 1989. doi:10.1162/NECO.1989.1.4.465

Markdown

[Girosi and Poggio. "Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant." Neural Computation, 1989.](https://mlanthology.org/neco/1989/girosi1989neco-representation/) doi:10.1162/NECO.1989.1.4.465

BibTeX

@article{girosi1989neco-representation,
  title     = {{Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant}},
  author    = {Girosi, Federico and Poggio, Tomaso A.},
  journal   = {Neural Computation},
  year      = {1989},
  pages     = {465-469},
  doi       = {10.1162/NECO.1989.1.4.465},
  volume    = {1},
  url       = {https://mlanthology.org/neco/1989/girosi1989neco-representation/}
}