Explorations of Fitness Landscapes of a Hopfield Associative Memory with Random and Evolutionary Walks

We apply evolutionary computations to the Hopfield's neural network model of associative memory. In the model, some of the appropriate configurations of the synaptic weights give the network a function of associative memory. One of our goals is to obtain the distribution of these optimal configurations as the global optima in the synaptic weight space as well as the information of local optima created together. In other words, our aim is to know a geometry of fitness landscapes defined on weight space. As a step toward this goal, we concentrate in this paper mainly on the local optima. Hence, we use a walk by the Gaussian mutation to explore the fitness landscape, rather than more effective evolutionary walks, expecting its high probability to be trapped at the local optima. I. Introduction Associative memory is a dynamical system which has a number of stable states with a domain of attraction around them (Koml'os et al. 1988). If the system starts at any state in the domain, it will ..