ON THE HYSTERESIS AND ROBUSTNESS OF HOPFIELD NEURAL NETWORKS

The effect of noise degradation on the Hopfield neural network is stud ied. The notion of a hysteresis network is defined. A noisy Hopfield n eural network is subsequently proven to be a hysteresis network. The e ffect of the hysteresis phenomenon on the robustness of the Hopfield n eural network to noise degradation is then investigated. An optimal Ho pfield neural network is defined as the Hopfield neural network which minimizes an upper-bound on the probability of error. The minimal robu stness indicator of a Hopfield neural network is defined. The upper bo und on the probability of error of a noisy Hopfield neural network is derived in terms of the minimal robustness indicator. We finally prove that an optimal Hopfield neural network is obtained when the minimal robustness indicator is maximized.