The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Networks and the best approximation property
Open accessAbstract
Networks can be considered as approximation schemes. Multilayer networks of the perceptron type can approximate arbitrarily well continuous functions (Cybenko 1988, 1989; Funahashi 1989; Stinchcombe and White 1989). We prove that networks derived from regularization theory and including Radial Basis Functions (Poggio and Girosi 1989), have a similar property. From the point of view of approximation theory, however, the property of approximating continuous functions arbitrarily well is not sufficient for characterizing good approximation schemes. More critical is the property ofbest approximation. The main result of this paper is that multilayer perceptron networks, of the type used in backpropagation, do not have the best approximation property. For regularization networks (in particular Radial Basis Function networks) we prove existence and uniqueness of best approximation.
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Cites
Learning representations by back-propagating errors
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986) · Nature · doi:10.1038/323533a0 · Cited by 31,892
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
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Neural networks for nonlinear internal model control
Hunt, K. J., & Sbarbaro, D. (1991) · IEE Proceedings D Control Theory and Applications · doi:10.1049/ip-d.1991.0059 · Cited by 367
Learning to perceive and act by trial and error
Whitehead, S. D., & Ballard, D. H. (1991) · Machine Learning · doi:10.1007/bf00058926 · Cited by 300
Metaheuristic Algorithms in Modeling and Optimization
Gandomi, A. H., Yang, X.-S., Talatahari, S., & Alavi, A. H. (2013) · Metaheuristic Applications in Structures and Infrastructures · doi:10.1016/b978-0-12-398364-0.00001-2 · Cited by 268
Metadata
- Authors
- Girosi, F., & Poggio, T.
- Venue
- Biological Cybernetics
- Published
- 1990-07
- Volume
- 63
- Issue
- 3
- Pages
- 169-176
- ISSN
- 0340-1200 (ISSN-L)
- 1432-0770
- OpenAlex
- W2007700211
- Cited by
- 888
- References
- 2
- FWCI
- 16.22
- Type
- journal article
- Language
- en
- Open access
- green
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