Topology Optimization in Cellular Neural Networks

This paper presents a constrained combinatorial optimization approach to the design of cellular neural networks with sparse connectivity. The method applies to cases where maintaining links between neurons incurs a cost, which could possibly vary between these links. The interconnection topology of the cellular neural network is diluted without significantly degrading its performance, the latter quantified by the average recall probability for the desired patterns engraved into its associative memory. The dilution process selectively removes the links that contribute the least to a metric related to the size of system's desired memory pattern attraction regions. The metric used here is the magnitude of the network's nodes' stability parameters, which have been proposed as a measure for the quality of memorization. We demonstrate by means of an example that this method of network dilution produces cheaper associative memories that in general trade off performance for cost, and in many cases the performance of the diluted network is on par with the original system.