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Abstract:
We calculate lower bounds on the size of sigmoidal neural
networks that approximate continuous functions. In particular, we
show that for the approximation of polynomials the network size has
to grow as
where
k
is the degree of the polynomials. This bound is valid for any input
dimension, i.e. independently of the number of variables. The
result is obtained by introducing a new method employing upper
bounds on the Vapnik-Chervonenkis dimension for proving lower
bounds on the size of networks that approximate continuous
functions.
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