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Bounds on the number of hidden neurons in multilayer perceptrons
Abstract
Fundamental issues concerning the capability of multilayer perceptrons with one hidden layer are investigated. The studies are focused on realizations of functions which map from a finite subset of E(n) into E(d). Real-valued and binary-valued functions are considered. In particular, a least upper bound is derived for the number of hidden neurons needed to realize an arbitrary function which maps from a finite subset of E(n ) into E(d). A nontrivial lower bound is also obtained for realizations of injective functions. This result can be applied in studies of pattern recognition and database retrieval. An upper bound is given for realizing binary-valued functions that are related to pattern-classification problems.
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Citations
Cites
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Cover, T. M. (1965) · IEEE Transactions on Electronic Computers · doi:10.1109/pgec.1965.264137 · Cited by 2,044
On the capabilities of multilayer perceptrons
Baum, E. B. (1988) · Journal of Complexity · doi:10.1016/0885-064x(88)90020-9 · Cited by 379
Cited by
Maier, H. R., & Dandy, G. C. (2000) · Environmental Modelling & Software · doi:10.1016/s1364-8152(99)00007-9 · Cited by 2,377
Extreme learning machines: a survey
Huang, G.-B., Wang, D. H., & Lan, Y. (2011) · International Journal of Machine Learning and Cybernetics · doi:10.1007/s13042-011-0019-y · Cited by 1,914
Approximation theory of the MLP model in neural networks
Pinkus, A. (1999) · Acta Numerica · doi:10.1017/s0962492900002919 · Cited by 1,529
Progress in supervised neural networks
Hush, D. R., & Horne, B. G. (1993) · IEEE Signal Processing Magazine · doi:10.1109/79.180705 · Cited by 1,247
Huang, G.-B., & Babri, H. A. (1998) · IEEE Transactions on Neural Networks · doi:10.1109/72.655045 · Cited by 538
Metadata
- Authors
- Huang, S.-C., & Huang, Y.-F.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1991
- Volume
- 2
- Issue
- 1
- Pages
- 47-55
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W2166915851
- Cited by
- 328
- References
- 3
- FWCI
- 15.90
- Type
- journal article
- Language
- en
- Open access
- closed
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- Huang, S.-C., & Huang, Y.-F. (1991). Bounds on the number of hidden neurons in multilayer perceptrons. IEEE Transactions on Neural Networks. https://doi.org/10.1109/72.80290
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
