1. A trainable optical neural network in combination with apparatus for training the neural network, comprising: a neural network, the neural network comprising: an array of input terminals to receive a plurality of optical signals defining an input vector; an array of weighting means for applying preset adjustable weights to signals applied to the input terminals and for obtaining weighted signals, the weighting means including control input terminals to permit adjustment of the preset weights; and an output terminal for outputting an output vector obtained in response to the weighted signals obtained from the weighting means; and training apparatus external to the neural network for training the neural network, the training apparatus comprising: means for repetitively applying a series of training vectors to the input terminals; error logging means coupled to the output terminal for receiving a series of output vectors produced in response to the series of training vectors and for comparing the output vectors with target vectors to determine mismatches so as to produce an average mismatch value as a function of the number of occasions that mismatches occur for the series of input vectors; and control means responsive to the average mismatch value for a series of input training vectors, for applying weight adjustment signals to the control input terminals of at least one of the weighting means, for tending to reduce the average mismatch value for the application of the next series of training vectors, and for determining when training is completed.