On the hysteresis and robustness of Hopfield neural networks

The effect of noise degradation on the Hopfield neural network is studied. The notion of a hysteresis network is defined. A noisy Hopfield neural network is subsequently proven to be a hysteresis network. The effect of the hysteresis phenomenon on the robustness of the Hopfield neural network to noise degradation is then investigated. An optimal Hopfield neural network is defined as the Hopfield neural network which minimizes an upper-bound on the probability of error. The minimal robustness indicator of a Hopfield neural network is defined. The upper bound 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