Sparsely interconnected neural networks for associative memories with applications 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 structure. 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 systematic manner all equilibrium points of the neural network and to determine the stability properties of the equilibrium points. The synthesis procedure makes it possible to design in a systematic manner neural networks (for associative memories) which store all desired memory patterns as reachable memory vectors. We generalize the above results to develop a design procedure for neural networks with sparse coefficient matrices. Our results guarantee that the synthesized neural networks have predetermined sparse interconnection structures and store any set of desired memory patterns as reachable memory vectors. We show that a sufficient condition for the existence of a sparse neural network design is self feedback for every neuron in the network. We apply our synthesis procedure to the design of cellular neural networks for associative memories. Our design procedure for neural networks with sparse interconnecting structure can take into account various problems encountered in VLSI realizations of such networks. For example, our procedure can be used to design neural networks with few or without any line-crossings resulting from the network interconnections. Several specific examples are included to demonstrate the applicability of the methodology advanced herein