Global convergence and suppression of spurious states of the Hopfield neural networks

Assuming that the output function of neurons is monotonic and differentiable at any interior point in the output range, the condition necessary for a vertex of a hypercube to become a local minimum of the Hopfield neural networks and the form of the convergence region to that minimum are clarified. Based on this, a method for analyzing and suppressing spurious states in the networks is derived. It is shown that all the spurious states of the traveling salesman problem (TSP) for the Hopfield original energy function can be suppressed by the method, and the validity of the method is demonstrated by computer simulations