We study robustness properties of a large class of artificial feedback
neural networks for associative memories by addressing the following
question: given a neural network with specified stable memories (speci
fied asymptotically stable equilibria), under what conditions will a p
erturbed model of the neural network possess stable memories that are
close (in distance) to the stable memories of the unperturbed neural n
etwork model? In arriving at our results, we establish robustness stab
ility results for the perturbed neural network models considered and w
e determine conditions that ensure the existence of asymptotically sta
ble equilibria of the perturbed neural network model that are near the
asymptotically stable equilibria of the original unperturbed neural n
etwork. These results involve quantitative estimates of the distance b
etween the corresponding equilibrium points of the unperturbed and per
turbed neural network models.