Hysteresis and Robustness of Hopfield Neural Networks

The effect of noise degradation on the Hopfield neural netwerk is s t u d i e d The notion of a hysteresis nefwork is defined. A noisy HephsSi =urd network is subsequently proven to be a hysteresis network. The effect of the hysteresis phentmenon on the robustness of the HoppeM neural network to noise degradation is then investigated. An eptiraal Heefield neural network is defined as the Hopfield neural network which minimizes an upper-bound on the probability of error. The minimal reindicator of a Hopfield neural network is defined. The upper bound on the probability of error of a noisy Hopfield neural network is &rived io terms of the minimal robustness indicator. We h d l y prove that an eptimal HopfieM neural network is obtained when the miniid robustness indicator is maximized.