Analysis of neural networks by statistical linearization

Summary form only given, as follows. The author considers an adaptive neural network of n units, of which k are input, m are outputs, and n-m-k are hidden units, where m>or=k. Using the known approximation techniques of n units, of which k are inputs, m are outputs, and statistical linearization, it is demonstrated for the class of analog networks studied by Pineda that the asymmetric synaptic weight matrix W can be trained to remember at most k linearly independent associations between input patterns and prespecified output patterns, but there is a massive ambiguity in the corresponding correctly trained weights W; in fact, there is a q-parameter family of allowable weights W, where q=(n-k)/sup 2/+k/sup 2/.<>