A generalized updating rule for modified Hopfield neural network

In this paper, a generalized updating rule (GUR) for the modified Hopfield neural network (MHNN) is presented. It is proved that with the GUR, for any given sequence of updating modes the network monotonously converges to a fixed point. An upper bound on the gradient of the energy function at the fixed point is given. All conventional MHNN algorithms are shown to be instances of the GUR. It is shown that the class of wide sense sequential updating modes guarantee the network to converge to the local minimum points of the energy function