Approximation properties of some two-layer feedforward neural networks
In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2007-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2706.pdf |
| Summary: | In this article, we present a multivariate two-layer feedforward neural networks that approximate continuous functions defined on \([0,1]^d\). We show that the \(L_1\) error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at \(\sqrt{d}/n\), where \(n\) is the number of function values used. |
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| ISSN: | 1232-9274 |