D. Liu et An. Michel, SPARSELY INTERCONNECTED NEURAL NETWORKS FOR ASSOCIATIVE MEMORIES WITHAPPLICATIONS TO CELLULAR NEURAL NETWORKS, IEEE transactions on circuits and systems. 2, Analog and digital signal processing, 41(4), 1994, pp. 295-307
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.