Projection method formulations of Hopfield-type associative memory neural networks

We study certain neural network architectures, which admit to optical implementations, from the point of view of projection methods. This approach enables us to uncover some interesting facts about the stable states of such networks. For example, a Hopfield-type associative content-addressable memory (ACAM) using a hard-limiter nonlinearity has three kinds of possible stable states. If the hard-limiter is replaced by a unity-slope saturation nonlinearity, there are only two kinds of stable states. These and other results demonstrate the utility of using projection methods in analyzing the dynamic behavior of neural networks.