Robustness and perturbation analysis of a class of artificial neural networks

Abstract 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 (specified asymptotically stable equilibria), under what conditions will a perturbed model of the neural network possess stable memories that are close (in distance) to the stable memories of the unperturbed neural network model? In arriving at our results, we establish robustness stability results for the perturbed neural network models considered and we determine conditions that ensure the existence of asymptotically stable equilibria of the perturbed neural network model that are near the asymptoitically stable equilibria of the original unperturbed neural network. These results involve quantitative estimates of the distance between the corresponding equilibrium points of the unperturbed and pertubed neural network models.