Cited by 4,206Neural Networks and ApplicationsMachine Learning and ELMStochastic Gradient Optimization Techniques

On the approximate realization of continuous mappings by neural networks

Funahashi, Ken-Ichi·1989·Neural Networks

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Crossref · 10.1016/0893-6080(89)90003-8

Cites

15 of 15 references verified0 citation errors · 0 not checkable

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  • An artificial neural network model composed of more than two layers can approximate any continuous mapping.

    “An artificial neural network model composed of more than two layers is known to be able to approximate any continuous mapping (Cybenko, 1989; Funahashi, 1989; Hornik et al., 1989), which is a theoretical basis of the universal cerebellar transform (Schmahmann, 2004).”

    From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Funahashi, 1989

  • These proofs showed that SLP-NN approximators, which employed a sufficient number of neurons of continuous sigmoidal activation type, were universal approximators, capable of approximating any continuous function to any desired accuracy.

    “These proofs showed that SLP-NN approximators, which employed sufficient number of neurons of continuous sigmoidal activation type (a constraint introduced by Cybenko and relaxed by Hornik), were universal approximators, capable of approximating any continuous function to any desired accuracy.”
  • Their primary motive was to improve accuracy over traditional AR methods, supported by rigorous independent mathematical proofs published in the late eighties and early nineties by Cybenko, Hornik, and Funahashi.

    “Their primary motive was to improve accuracy over traditional AR methods.This was supported by rigorous independent mathematical proofs published in the late eighties and the early nineties by Cybenko [106], Hornik [196], and Funahashi [158].”

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Authors
Funahashi, K.-I.
Affiliations
Advanced Telecommunications Research Institute International (JP)
Corresponding author
Funahashi, Ken-Ichi
Venue
Neural Networks
Publisher
Elsevier BV
Published
1989-01
Volume
2
Issue
3
Pages
183-192
ISSN
0893-6080 (ISSN-L)
OpenAlex
W1971735090
Cited by
4,206
References
15
Citations by year
2026: 59 · 2025: 75 · 2024: 89 · 2023: 109 · 2022: 92 · 2021: 155 · 2020: 140 · 2019: 116 · 2018: 100 · 2017: 108 · 2016: 82 · 2015: 100 · 2014: 105 · 2013: 96 · 2012: 97
FWCI
74.70
Type
journal article
Language
en
Open access
closed
Locations
Neural Networks (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
  • Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
Keywords
continuous functions, multilayer neural networks, sigmoid activation function, function approximation, integral formulas, hidden layers, universal approximation

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