D. Schonfeld, ON THE HYSTERESIS AND ROBUSTNESS OF HOPFIELD NEURAL NETWORKS, IEEE transactions on circuits and systems. 2, Analog and digital signal processing, 40(11), 1993, pp. 745-748
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.