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

Abstract

For the extended sigmoid function which is monotonic and differentiable at any interior point in the output range, the author clarifies the condition that a vertex of a hypercube becomes a local minimum of the Hopfield neural networks and a monotonic convergence region to that minimum. Based on this, a method of analyzing and suppressing spurious states in the networks is derived. It is shown that all the spurious states of the traveling salesman problem for the Hopfield original energy function can be suppressed by the proposed method, and its validity is demonstrated by computer simulations.<>