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.
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© 1998 Springer-Verlag Wien
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Hlaváčková, K., Kůrková, V., Savický, P. (1998). Upper Bounds on the Approximation Rates of Real-valued Boolean Functions by Neural Networks. In: Artificial Neural Nets and Genetic Algorithms. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6492-1_109
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DOI: https://doi.org/10.1007/978-3-7091-6492-1_109
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83087-1
Online ISBN: 978-3-7091-6492-1
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