Approximations of Functions by a Multilayer Perceptron: a New Approach

We provide a radically elementary proof of the universal approximation property of the one-hidden layer perceptron based on the Taylor expansion and the Vandermonde determinant. It works for both L q and uniform approximation on compact sets. This approach naturally yields some bounds for the design...

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Bibliographic Details
Published in:Neural networks 1997-08, Vol.10 (6), p.1069-1081
Main Authors: Attali, Jean-Gabriel, Pagès, Gilles
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Bernstein multinomial polynomials
Computer science
control theory
systems
Connectionism. Neural networks
Derivatives approximation
Exact sciences and technology
Function approximation
Hidden layer design
L q-approximation
on compact sets
One-hidden layer perceptron
Uniform approximation
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Summary:We provide a radically elementary proof of the universal approximation property of the one-hidden layer perceptron based on the Taylor expansion and the Vandermonde determinant. It works for both L q and uniform approximation on compact sets. This approach naturally yields some bounds for the design of the hidden layer and convergence results (including some rates) for the derivatives. A partial answer to Hornik's conjecture on the universality of the bias is proposed. An extension to vector valued functions is also carried out. © 1997 Elsevier Science Ltd.
ISSN:0893-6080
1879-2782
DOI:10.1016/S0893-6080(97)00010-5