Systematic design of associative memory networks: equilibrium confinement, exponential stability and gradient descent learning

Basic results from a qualitative analysis of the exponential stability and equilibrium characterization of a class of dynamical neural networks intended to serve as associative memories are presented. A simple learning rule tailored to efficiently minimize the deviation between the stable equilibrium points of the network and the desired memory vectors to be stored is proposed and is established as a descent procedure for minimizing the deviation. The results are developed for asymmetric interconnection matrices and hence considerably enlarge the scope of the associative memory design compared to existing procedures