On the interconnection constants of Hopfield nets

Hopfield nets are a class of neural networks that are often applied to optimisation problems. The role played by certain constants appearing in the interconnections are crucial to the computations. A bad choice of constant values results in the convergence of the system to states that represent extraneous results. This paper examines a discrete model of the nets which allows a better characterisation of the constants. The formal approach followed in this paper allows the specification of values to the constants that ensure convergence of the system to states that represent results that are not extraneous. Using the Hopfield nets terminology, we have identified methods to remove extraneous energy minima in the discrete version of the system. Since any simulation study of Hopfield nets on real computers must use discretised approximations to analog values, the results are of interest in a practical domain as well.