The approximation capabilities of two different four-layered neural networks are studied. First, anetwork with the backpropagation algorithm is analyzed, and its error surface, convergenceproperties, and network design are considered. An alternative to the backpropagation approach ispresented, namely, we construct a network that uses a one-pass algorithm. We show that theproposed network can correctly classify N different patterns with 4 sqrt(N)- 3 hidden units. We alsoshow that an arbitrarily small approximation error can be obtained for this network by adjusting theappropriate parameters.
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