FOR NEURAL NETWORKS, FUNCTION DETERMINES FORM

This article shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under weak genericity assumptions, the following is true: Assume given two nets, whose neurons all have the same nonlinear activation function sigma; if the two nets have equal behaviors as ''black boxes'' then necessarily they must have the same number of neurons and-except at most for sign reversals at each node-the same weights. Moreover, even if the activations are not a priori known to coincide, they are shown to be also essentially determined from the external measurements.