Recurrent Neural Networks Are Universal Approximators
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A deep neural network can be replaced with a single-layer neural network because both can approximate any given function.
“or replacing a deep neural network with a single-layer neural network, since both types of networks can approximate any given function (Hornik et al. 1989; Schäfer and Zimmermann 2006).”
From Falsification and consciousness (2021) · cites this paper as Schäfer and Zimmermann 2006
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Recurrent Neural Networks for Time Series Forecasting: Current status and future directions
Hewamalage, H., Bergmeir, C., & Bandara, K. (2021) · International Journal of Forecasting · doi:10.1016/j.ijforecast.2020.06.008 · Cited by 1,371 · see citing works
Deep Learning in Human Activity Recognition with Wearable Sensors: A Review on Advances
Zhang, S., Li, Y., Zhang, S., Shahabi, F., Xia, S., Deng, Y., & Alshurafa, N. (2022) · Sensors · doi:10.3390/s22041476 · Cited by 625 · see citing works
“Second, deep neural networks have been shown to be universal function approximators, capable of approximating almost any function given a large enough network and sufficient observations [77, 243, 340].”
BackgroundHard criteria for empirical theories of consciousness
Doerig, A., Schurger, A., & Herzog, M. H. (2021) · Cognitive Neuroscience · doi:10.1080/17588928.2020.1772214 · Cited by 194 · see citing works
“It is a mathematical fact that both recurrent and feedforward networks (along with many other kinds of universal function approximators) can approximate any input-output function to any degree of accuracy (Hornik et al., 1989; Schäfer & Zimmermann, 2006).”
BackgroundThe unfolding argument: Why IIT and other causal structure theories cannot explain consciousness
Doerig, A., Schurger, A., Hess, K., & Herzog, M. H. (2019) · Consciousness and Cognition · doi:10.1016/j.concog.2019.04.002 · Cited by 140 · see citing works
Falsification and consciousness
Kleiner, J., & Hoel, E. (2021) · Neuroscience of Consciousness · doi:10.1093/nc/niab001 · Cited by 46 · see citing works
“…are capable of universal computation (Turing 1937; Wolfram 1984) and hence may emulate the brain’s responses, or replacing a deep neural network with a single-layer neural network, since both types of networks can approximate any given function (Hornik et al. 1989; Schäfer and Zimmermann 2006).”
BackgroundMethodInfluentialFalsification and consciousness
Kleiner, J., & Hoel, E. (2020) · arXiv · doi:10.48550/arxiv.2004.03541 · Cited by 46
First-person experience cannot rescue causal structure theories from the unfolding argument
Herzog, M. H., Schurger, A., & Doerig, A. (2022) · Consciousness and Cognition · doi:10.1016/j.concog.2021.103261 · Cited by 14 · see citing works
- Authors
- Schäfer, A. M., & Zimmermann, H. G.
- Affiliations
- Siemens (Germany) (DE)
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2006
- Pages
- 632-640
- ISSN
- 0302-9743 (ISSN-L)
- 1611-3349
- OpenAlex
- W1604264128
- Cited by
- 297
- References
- 0
- Citations by year
- 2026: 11 · 2025: 23 · 2024: 34 · 2023: 39 · 2022: 31 · 2021: 59 · 2020: 21 · 2019: 19 · 2018: 8 · 2017: 8 · 2016: 4 · 2015: 2 · 2014: 4 · 2013: 2 · 2012: 10
- FWCI
- 2.88
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Lecture notes in computer science (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and ELM
- Keywords
- recurrent neural networks, universal approximation, state-space model, open dynamical systems, feedforward neural networks, function approximation, Borel measurable functions
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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