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The author presents a statistical test of the hypothesis that a given multilayer feedforward network exactly represents some unknown mapping subject to inherent noise against the alternative that the network neglects some nonlinear structure in the mapping, leading to potentially avoidable approximation errors. The tests are based on methods that statistically determine whether or not there is some advantage to be gained by adding hidden units to the network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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White (1989) studied this question.