Robustness analysis and design of sparsely interconnected neural networks

We first conduct an analysis of the robustness properties of a class of neural networks with applications to associative memories. Specifically, for a network with nominal parameters storing a set of desired bipolar memories, we establish sufficient conditions under which the same set of bipolar memories is also stored in the network with perturbed parameters. This result enables us to establish a design procedure for neural networks whose stored memories are invariant under perturbations. Our design procedure is capable of generating artificial neural networks with prespecified sparsity constraints and in particular, is applicable in the design of cellular neural networks for associative memories