Capabilities of a three layer feedforward neural network

Mapping capabilities of a three-layer feedforward neural network with a finite number of hidden units which have sigmoid functions as their nonlinearities are discussed. It is proved that sigmoid functions of a hidden layer of the network can raise the dimension of the input space up to the number of the hidden units. From this result, it is concluded that a three-layer feedforward neural network with N hidden units can assign arbitrary analog values to N arbitrary input vectors