Approximation capabilities of multilayer feedforward networks
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For ordinal deep learning models such as FFNs and CNNs, deep architecture benefits from universal approximation power and expressive capacity.
“For ordinal deep learning models, such as FFNs and CNNs, deep architecture immediately benefits from the universal approximation power and expressive capacity (Cybenko, 1989; Hornik, 1991; Telgarsky, 2016; Lu et al., 2017; Petersen & Voigtlaender, 2020; Zhou, 2020).”
From Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practice (2022) · cites this paper as Hornik, 1991
General-purpose neural networks are universal approximators, allowing functional relationships to be learned.
“Instead, general-purpose neural networks are universal approximators, allowing functional relationships to be learned 62,63 .”
From Machine culture (2023) · cites this paper as [62]
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 [196]
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 [196]
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Multilayer feedforward networks are universal approximators
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“…models, such as FFNs and CNNs, deep architecture immediately benefits from the universal approximation power and expressive capacity (Cybenko, 1989; Hornik, 1991; Telgarsky, 2016; Lu et al., 2017; Petersen & Voigtlaender, 2020; Zhou, 2020 (Vaswani et al., 2017; Brown et al., 2020), while vision…”
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“Turing completeness can be achieved using radically different substrates [72–75], whether simple [46, 76] or complex, feedfor-ward [77] or recurrent [78, 79].”
- Authors
- Hornik, K.
- Affiliations
- TU Wien (AT)
- Corresponding author
- Hornik, Kurt
- ORCID
- Hornik, Kurt
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 1991
- Volume
- 4
- Issue
- 2
- Pages
- 251-257
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W1988115241
- Cited by
- 6,091
- References
- 13
- Citations by year
- 2026: 290 · 2025: 426 · 2024: 399 · 2023: 455 · 2022: 485 · 2021: 716 · 2020: 586 · 2019: 523 · 2018: 346 · 2017: 243 · 2016: 157 · 2015: 112 · 2014: 104 · 2013: 95 · 2012: 103
- FWCI
- 35.95
- 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
- multilayer perceptron, universal approximation, single hidden layer, Lp approximation, uniform approximation, continuous functions, derivative approximation, hidden units
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