Given a set of input-output training samples, we describe a procedure 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 control problem, defining a performance index to be minimized as a function of time-varying weights. We solve the resulting nonlinear 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 suggested heuristically by Hopfield for designing associative memories. Learning curves for the new technique are presented.

Given a set of input-output training samples, we describe a procedure 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 control problem, defining a performance index to be minimized as a function of time-varying weights. We solve the resulting nonlinear 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 suggested heuristically by Hopfield for designing associative memories. Learning curves for the new technique are presented.

A rigorous analysis on the finite precision computational)Spects of neural network as a pattern classifier via a probabilistic approach is presented.

Given a set of input-output training samples, we describe a procedure fordetermining 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 control problem,defining a performance index to be minimized as a function of time-varying weights.

A"'ir Dembo Information Systems Laboratory, Stanford University Stanford, CA 94305 Ofer Zeitouni Laboratory for Information and Decision Systems MIT, Cambridge, MA 02139 ABSTRACT A class of high dens ity assoc iat ive memories is constructed, starting from a description of desired properties those should exhib it. These propert ies include high capac ity, controllable bas ins of attraction and fast speed of convergence. Fortunately enough, the resulting memory is implementable by an artificial Neural Net. I NfRODUCTION Most of the work on assoc iat ive memories has been structure oriented, i.e.. given a Neural architecture, efforts were directed towards the analysis of the resulting network. Issues like capacity, basins of attractions, etc. were the main objects to be analyzed cf., e.g.

A"'ir Dembo Information Systems Laboratory, Stanford University Stanford, CA 94305 Ofer Zeitouni Laboratory for Information and Decision Systems MIT, Cambridge, MA 02139 ABSTRACT A class of high dens ity assoc iat ive memories is constructed, starting from a description of desired properties those should exhib it. These propert ies include high capac ity, controllable bas ins of attraction and fast speed of convergence. Fortunately enough, the resulting memory is implementable by an artificial Neural Net. I NfRODUCTION Most of the work on assoc iat ive memories has been structure oriented, i.e.. given a Neural architecture, efforts were directed towards the analysis of the resulting network. Issues like capacity, basins of attractions, etc. were the main objects to be analyzed cf., e.g.

A"'ir Dembo Information Systems Laboratory, Stanford University Stanford, CA 94305 Ofer Zeitouni Laboratory for Information and Decision Systems MIT, Cambridge, MA 02139 ABSTRACT A class of high dens ity assoc iat ive memories is constructed, starting from a description of desired properties those should exhib it. These propert ies include high capac ity, controllable bas ins of attraction and fast speed of convergence. Fortunately enough, the resulting memory is implementable by an artificial Neural Net. I NfRODUCTION Most of the work on assoc iat ive memories has been structure oriented, i.e.. given a Neural architecture, efforts were directed towards the analysis of the resulting network. Issues like capacity, basins of attractions, etc. were the main objects to be analyzed cf., e.g.