Article
Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
Author/s | González Díaz, Rocío
Gutiérrez Naranjo, Miguel Ángel Paluzo Hidalgo, Eduardo |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Publication Date | 2019 |
Deposit Date | 2020-06-17 |
Published in |
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Abstract | It is well known that Artificial Neural Networks are universal approximators. The classical result
proves that, given a continuous function on a compact set on an n-dimensional space, then there exists
a one-hidden-layer ... It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does not provide a method for finding it. In this paper, a constructive approach to the proof of this property is given for the case of two-hidden-layer feedforward networks. This approach is based on an approximation of continuous functions by simplicial maps. Once a triangulation of the space is given, a concrete architecture and set of weights can be obtained. The quality of the approximation depends on the refinement of the covering of the space by simplicial complexes. |
Citation | González Díaz, R., Gutiérrez Naranjo, M.Á. y Paluzo Hidalgo, E. (2019). Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach. ArXiv.org, arXiv:1907.11457 |
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