CAPABILITIES OF A 4-LAYERED FEEDFORWARD NEURAL-NETWORK - 4 LAYERS VERSUS 3

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, Ther efore, studies should focus on the capabilities of a neural network wi th a finite number of hidden units, In this paper, a proof is given sh owing that a three-layered feedforward network with N-1 hidden units c an 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 i s superior to a three-layered feedforward network in terms of the numb er of parameters needed for the training data.