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Dimension-independent bounds on the degree of approximation by neural networks

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2 Author(s)
Mhaskar, H.N. ; Department of Mathematics and Computer Science, California State University, Los Angeles, 90032, USA ; Micchelli, C.A.

Let φ be a univariate 2π-periodic function. Suppose that s ≥ 1 and f is a 2π-periodic function of s real variables. We study sufficient conditions in order that a neural network having a single hidden layer consisting of n neurons, each with an activation function φ, can be constructed so as to give a mean square approximation to f within a given accuracy ∈n, independent of the number of variables. We also discuss the case in which the activation function φ is not 2π-periodic.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:38 ,  Issue: 3 )

Date of Publication:

May 1994

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