Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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Feedforward neural networks with enough free parameters can approximate any continuous function on a closed and bounded subset of R^n to arbitrary accuracy.
“These theorems guarantee that, provided enough free parameters, feedforward neural networks can approximate any continuous function on a closed and bounded subset of R n to an arbitrary degree of accuracy.”
From Continuous-variable quantum neural networks (2019) · cites this paper as [56]
The Background and Results sections support arbitrary-accuracy approximation of continuous functions on compact subsets of R^n. But the paper makes this conditional on a nonpolynomial activation function and emphasizes that the theorem fails without a threshold; having enough free parameters alone is not sufficient. Page numbers are not supplied in our copy. (LLM, conf=0.87)
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Research works printed but not linked: 6
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- Authors
- Leshno, M., Lin, V. Y., Pinkus, A., & Schocken, S.
- Affiliations
- Hebrew University of Jerusalem (IL)
- Technion – Israel Institute of Technology (IL)
- New York University (US)
- Corresponding author
- Leshno, Moshe
- Venue
- Neural Networks
- Publisher
- Elsevier BV
- Published
- 1993-01
- Volume
- 6
- Issue
- 6
- Pages
- 861-867
- ISSN
- 0893-6080 (ISSN-L)
- OpenAlex
- W2043005456
- Cited by
- 2,121
- References
- 0
- Citations by year
- 2026: 98 · 2025: 129 · 2024: 148 · 2023: 177 · 2022: 191 · 2021: 239 · 2020: 213 · 2019: 115 · 2018: 82 · 2017: 45 · 2016: 44 · 2015: 43 · 2014: 39 · 2013: 33 · 2012: 27
- FWCI
- 28.06
- Type
- journal article
- Language
- en
- Open access
- green
- archive.nyu.edu
- Locations
- Neural Networks (publishedVersion)
- Faculty Digital Archive (New York University Florence) (submittedVersion)
- SSRN Electronic Journal (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
- Physical Sciences › Mathematics › Statistics and Probability › Approximation Theory and Sequence Spaces
- Keywords
- multilayer perceptron, universal approximation, approximation of continuous functions, threshold functions, approximation theorems
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