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Article Dans Une Revue Neural Computation Année : 2016

A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function

Résumé

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 ℝ by neural networks with only one neuron in the hidden layer. We construct algorithmically a smooth, sigmoidal, almost monotone activation function σ providing approximation to an arbitrary continuous function within any degree of accuracy. This algorithm is implemented in a computer program, which computes the value of σ at any reasonable point of the real axis.
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Dates et versions

hal-01256489 , version 1 (14-01-2016)

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Citer

Namig Guliyev, Vugar Ismailov. A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function. Neural Computation, 2016, 28 (7), pp.1289-1304. ⟨10.1162/NECO_a_00849⟩. ⟨hal-01256489⟩

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