On the Convergence Properties of the Hopfield Model

We will review the three known results and prove that the fully parallel mode of operation is a special case of the serial mode of operation for which we present an elementary proof. The elementary proof (one which does not involve the concept of an energy function) follows from the relations between the model and cuts in the graph. We also prove that the three known cases are the only interesting ones by exhibiting exponential lower bounds on the length of the cycles in the other cases."