The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Capabilities of a four-layered feedforward neural network: four layers versus three
Abstract
Neural-network theorems state that only when there are infinitely many hidden units is a four-layered feedforward neural network equivalent to a three-layered feedforward neural network. In actual applications, however, the use of infinitely many hidden units is impractical. Therefore, studies should focus on the capabilities of a neural network with a finite number of hidden units, In this paper, a proof is given showing that a three-layered feedforward network with N-1 hidden units can give any N input-target relations exactly. Based on results of the proof, a four-layered network is constructed and is found to give any N input-target relations with a negligibly small error using only (N/2)+3 hidden units. This shows that a four-layered feedforward network is superior to a three-layered feedforward network in terms of the number of parameters needed for the training data.
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Cites
Multilayer feedforward networks are universal approximators
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Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,081
On the approximate realization of continuous mappings by neural networks
Funahashi, K.-I. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90003-8 · Cited by 4,206
Backpropagation neural nets with one and two hidden layers
de Villiers, J., & Barnard, E. (1993) · IEEE Transactions on Neural Networks · doi:10.1109/72.182704 · Cited by 344
Bounds on the number of hidden neurons in multilayer perceptrons
Huang, S.-C., & Huang, Y.-F. (1991) · IEEE Transactions on Neural Networks · doi:10.1109/72.80290 · Cited by 328
A simple method to derive bounds on the size and to train multilayer neural networks
Sartori, M. A., & Antsaklis, P. J. (1991) · IEEE Transactions on Neural Networks · doi:10.1109/72.88168 · Cited by 182
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Maier, H. R., & Dandy, G. C. (2000) · Environmental Modelling & Software · doi:10.1016/s1364-8152(99)00007-9 · Cited by 2,377
Review of surrogate modeling in water resources
Razavi, S., Tolson, B. A., & Burn, D. H. (2012) · Water Resources Research · doi:10.1029/2011wr011527 · Cited by 983
Learning capability and storage capacity of two-hidden-layer feedforward networks
Huang, G.-B. (2003) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2003.809401 · Cited by 810
Advanced Spectral Classifiers for Hyperspectral Images: A review
Ghamisi, P., Plaza, J., Chen, Y., Li, J., & Plaza, A. J. (2017) · IEEE Geoscience and Remote Sensing Magazine · doi:10.1109/mgrs.2016.2616418 · Cited by 675
Metadata
- Authors
- Tamura, S., & Tateishi, M.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1997-03
- Volume
- 8
- Issue
- 2
- Pages
- 251-255
- ISSN
- 1045-9227 (ISSN-L)
- 1941-0093
- OpenAlex
- W2104714048
- Cited by
- 422
- References
- 7
- FWCI
- 4.28
- Type
- journal article
- Language
- en
- Open access
- closed
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