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

doi:10.1162/neco_a_00849

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arXiv · 1601.00013

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

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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. This algorithm is implemented in a computer program, which computes the value of $\sigma$ at any reasonable point of the real axis.

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BibTeX RIS

Namig J. Guliyev, Vugar E. Ismailov. 2015-12-31. A single hidden layer feedforward network with only one neuron in the hidden layer can approximate any univariate function. https://doi.org/10.1162/neco_a_00849

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