Sparsely interconnected neural networks for associative memorieswith applications to cellular neural networks

摘要

We first present results for the analysis and synthesis of a classnof neural networks without any restrictions on the interconnectingnstructure. The class of neural networks which we consider have thenstructure of analog Hopfield nets and utilize saturation functions tonmodel the neurons. Our analysis results make it possible to locate in ansystematic manner all equilibrium points of the neural network and tondetermine the stability properties of the equilibrium points. Thensynthesis procedure makes it possible to design in a systematic mannernneural networks (for associative memories) which store all desirednmemory patterns as reachable memory vectors. We generalize the abovenresults to develop a design procedure for neural networks with sparsencoefficient matrices. Our results guarantee that the synthesized neuralnnetworks have predetermined sparse interconnection structures and storenany set of desired memory patterns as reachable memory vectors. We shownthat a sufficient condition for the existence of a sparse neural networkndesign is self feedback for every neuron in the network. We apply ournsynthesis procedure to the design of cellular neural networks fornassociative memories. Our design procedure for neural networks withnsparse interconnecting structure can take into account various problemsnencountered in VLSI realizations of such networks. For example, ournprocedure can be used to design neural networks with few or without anynline-crossings resulting from the network interconnections. Severalnspecific examples are included to demonstrate the applicability of thenmethodology advanced herein