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A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function | | Namig J. Guliyev
; Vugar E. Ismailov
; | | Date: |
31 Dec 2015 | | Abstract: | The possibility of approximating a continuous function on a compact subset of
the real line by a feedforward single hidden layer neural network with a
sigmoidal activation function has been studied in many papers. Such networks
can approximate an arbitrary continuous function provided that an unlimited
number of neurons in a hidden layer is permitted. In this paper, we consider
constructive approximation on any finite interval of $mathbb{R}$ by neural
networks with only one neuron in the hidden layer. We construct algorithmically
a smooth, sigmoidal, almost monotone activation function $sigma$ providing
approximation to an arbitrary continuous function within any degree of
accuracy. | | Source: | arXiv, 1601.0013 | | Services: | Forum | Review | PDF | Favorites | |
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