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 genericky assumptions, the following is true: Assume given two nets, whose neurons all have the same nonlinear activation function a; 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.