Artificial Neural Nets and Genetic Algorithms pp 495-499 | Cite as

# Upper Bounds on the Approximation Rates of Real-valued Boolean Functions by Neural Networks

Conference paper

## Abstract

Real-valued functions with multiple boolean variables are represented by one-hidden-layer Heaviside perceptron networks with an exponential number of hidden units. We derive upper bounds on approximation error using a given number *n* of hidden units. The bounds on error axe of the form \(\frac{c}{\sqrt{n}}\) where c depends on certain norms of the function being approximated and *n* is the number of hidden units. We show examples of functions for which these norms grow polynomially and exponentially with increasing input dimension.

## Keywords

Neural Network Orthonormal Basis Hide Unit Real Vector Space Fourier Basis
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© Springer-Verlag Wien 1998