Neural-network theorems state that only when there are infinitely many hidden units is a four-layered feedforward neural network equivalent to a three-layered feedforward neural network. In actual applications, however, the use of infinitely many hidden units is impractical. Therefore, studies should focus on the capabilities of a neural network with a finite number of hidden units, In this paper, a proof is given showing that a three-layered feedforward network with N-1 hidden units can give any N input-target relations exactly. Based on results of the proof, a four-layered network is constructed and is found to give any N input-target relations with a negligibly small error using only (N/2)+3 hidden units. This shows that a four-layered feedforward network is superior to a three-layered feedforward network in terms of the number of parameters needed for the training data.
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