Improving Continuous Hopfield Network Stability Using Runge-Kutta Method

Abstract

Continuous Hopfield network is a recurring network that has shown its ability to solve important optimization problems. Continuous Hopfield network dynamic system is characterized by a differential equation. This equation is difficult to solve, especially for large problems. This led researchers to discretize the differential equation using Euler’s method. However, this method generally does not converge to a good solution because it is sensitive to the step size decision and initial conditions. In this work, we discretize the dynamic system of continuous Hopfield network by a new method of Runge-Kutta. This method is strong in terms of stability and performance in order to converge to a better solution. This new method introduces two phases for better network stability. The first phase targets to solve the dynamic equation by the Euler method, while the second phase allows refining the solution found in the first phase. Experimental results on benchmarks show that the proposed approach can effectively improve Hopfield neural network performance.