Williamson, Robert C. and Helmke, Uwe (1995) Existence and uniqueness results for neural network approximations. IEEE TRANSACTIONS ON NEURAL NETWORKS, 6 (1). pp. 2-13. ISSN 1045-9227, 1941-0093
Full text not available from this repository.Abstract
Some approximation theoretic questions concerning a certain class of neural networks are considered. The networks considered are single input, single output, single hidden layer, feedforward neural. networks with continuous sigmoidal activation functions, no input weights but with hidden layer thresholds and output layer weights. Specifically, questions of existence and uniqueness of best approximations on a closed interval of the real line under mean-square and uniform approximation error measures are studied. A by-product of this study is a reparametrization of the class of networks considered in terms of rational functions of a single variable. This rational reparametrization is used to apply the theory of Pade approximation to the class of networks considered. In addition, a question related to the number of local minima arising in gradient algorithms for learning is examined.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FEEDFORWARD |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Oct 2023 09:07 |
| Last Modified: | 18 Oct 2023 09:07 |
| URI: | https://pred.uni-regensburg.de/id/eprint/52833 |
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