Part of Advances in Neural Information Processing Systems 2 (NIPS 1989)
O. Farotimi, Amir Dembo, Thomas Kailath
Given a set of input-output training samples, we describe a proce(cid:173) dure for determining the time sequence of weights for a dynamic neural network to model an arbitrary input-output process. We formulate the input-output mapping problem as an optimal con(cid:173) trol problem, defining a performance index to be minimized as a function of time-varying weights. We solve the resulting nonlin(cid:173) ear two-point-boundary-value problem, and this yields the training rule. For the performance index chosen, this rule turns out to be a continuous time generalization of the outer product rule earlier sug(cid:173) gested heuristically by Hopfield for designing associative memories. Learning curves for the new technique are presented.