Topology Optimization in Cellular Neural Networks

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Department of Mechanical Engineering, University of Delaware
This paper establishes a new constrained combinatorial optimization approach to the design of cellular neural networks with sparse connectivity. This strategy is applicable to cases where maintaining links between neurons incurs a cost, which could possibly vary between these links. The cellular neural network’s interconnection topology is diluted without significantly degrading its performance, the network 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. Further, the efficiency of the method is justified by comparing it with an alternative dilution approach based on probability theory and randomized algorithms. We demonstrate by means of an example that this method of network dilution based on combinatorial optimization 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. Also the randomized algorithm based method results in same network performance in terms of network recall probability.
Cellular neural networks, Optimization