A SIMPLE METHOD TO DERIVE BOUNDS ON THE SIZE AND TO TRAIN MULTILAYER NEURAL NETWORKS

For an arbitrary training set with p training patterns, a multilayer neural network with one hidden layer and with p - 1 hidden layer neurons can exactly implement the training set. Previous derivations proved these bounds by separating the input patterns with particular hyperplanes and using the equations describing the hyperplanes to choose the weights for the hidden layer. Here, the bounds are derived by simply satisfying a rank condition on the output of the hidden layer. The weights for the hidden layer can be chosen almost arbitrarily, and the weights for the output layer are found by solving p linear equations.