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Analysis of the relationship between weight parameters and stability of solutions in Hopfield networks form dynamic systems viewpoint

A study of the stability properties of the set of equilibrium points that are solutions for a given constraint satisfaction or optimization problem mapped to Hopfield network dynamics is presented. Specifically, the relation between constraint weight parameter values and the stability of solutions of optimization problems mapped to Hopfield networks is investigated. A theoretical development relating constraint weight parameter values to solution stability is presented. Employing an abstract optimization problem, the dependency of solution stability on constraint weight parameter values is shown. The empirical evidence as observed by many earlier researchers indicated that the selection of constraint weight parameters often had an effect on the stability of solution equilibrium points. This paper clearly identifies the reasons for that effect from a theoretical viewpoint.