On the approximate realization of continuous mappings by neural networks
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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.”
From A comprehensive survey on machine learning for networking: Evolution, applications and research opportunities (2018) · cites this paper as [158]
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].”
From A comprehensive survey on machine learning for networking: Evolution, applications and research opportunities (2018) · cites this paper as [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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