Learning in analog Hopfield networks

The authors consider the problem of determining a symmetric weight matrix for which an n-neuron analog Hopfield network has energy minima at m prespecified patterns. Although these minima are zero-gradient points, their complete characterization is in general impossible for practical purposes. The authors give two formulations in the form of nonlinear programming problems, and two corresponding algorithms. Both approaches seek to minimize the energy gradient at the m patterns, and the second one in particular incorporates a heuristic for second-order characterization of minimality. Results on the successful learning of randomly generated patterns are provided