SPARSELY INTERCONNECTED NEURAL NETWORKS FOR ASSOCIATIVE MEMORIES WITHAPPLICATIONS TO CELLULAR NEURAL NETWORKS

We first present results for the analysis and synthesis of a class of neural networks without any restrictions on the interconnecting struct ure. The class of neural networks which we consider have the structure of analog Hopfield nets and utilize saturation functions to model the neurons. Our analysis results make it possible to locate in a systema tic manner all equilibrium points of the neural network and to determi ne the stability properties of the equilibrium points. The synthesis p rocedure makes it possible to design in a systematic manner neural net works (for associative memories) which store all desired memory patter ns as reachable memory vectors. We generalize the above results to dev elop a design procedure for neural networks with sparse coefficient ma trices. Our results guarantee that the synthesized neural networks hav e predetermined sparse interconnection structures and store any set of desired memory patterns as reachable memory vectors. We show that a s ufficient condition for the existence of a sparse neural network desig n is self feedback for every neuron in the network. We apply our synth esis procedure to the design of cellular neural networks for associati ve memories. Our design procedure for neural networks with sparse inte rconnecting structure can take into account various problems encounter ed in VLSI realizations of such networks. For example, our procedure c an be used to design neural networks with few or without any line-cros sings resulting from the network interconnections. Several specific ex amples are included to demonstrate the applicability of the methodolog y advanced herein.