Approximation by neural networks with sigmoidal functions |
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Authors: | Dan Sheng Yu |
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Affiliation: | 1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, P. R. China
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Abstract: | In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the approximation. To improve the approximation rate, we further introduce a type of combinations of neural networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals. |
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Keywords: | Feedforward neural networks sigmoidal functions simultaneous approximation combi-nations |
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