AN ANALOG FEEDBACK ASSOCIATIVE MEMORY

Most of the neural network associative memory models deal with the storage of binary vectors. We consider the Hopfield continuous-time network, and develop a new method for the storage of analog vectors, i.e., vectors whose components are real-valued. An important requirement is that each memory vector has to be an asymptotically stable (i.e., attractive) equilibrium of the network. We point out some of the limitations of the continuous Hopfield model on the set of vectors that can be stored. These limitations can be relieved by choosing a network containing visible as well as hidden units. We have chosen an architecture consisting of several hidden layers and a visible layer, connected in a circular fashion. We prove that the two-layer case of such an architecture is guaranteed to store any number of given analog vectors provided their number does not exceed 1 + the number of neurons in the hidden layer. We have developed a learning algorithm, which results in correctly adjusting the locations of the equilibria, as well as guaranteeing their asymptotic stability. Simulation results confirm the effectiveness of the new method.