A hill-climbing learning method for Hopfield networks

In this paper, we propose a hill-climbing learning method for Hopfield networks in which the energy of the network is intentionally raised in the weight space so that the network can escape from local minima. This learning method involves repeated updating of the Hopfield network in state space and modification of the weights in weight space if it settles into a local minimum, so that the energy is raised. Shifting of the global minimum during learning can be avoided by updating the state on the unlearned Hopfield network in state space, using equilibrium states obtained from learning as the initial state. Simulations using this learning method show that the Hopfield network can escape from a local minimum which depends on the initial state. A simulation experiment is first conducted with a two-variable Hopfield network, and the convergence of learning and the change of the domain from a local minimum to a global minimum are demonstrated. Then, using an example of the traveling-salesman problem, a simulation is performed using concrete numerical values, and the validity of the method is demonstrated.