Winner-Take-All Cellular Neural Networks

This paper presents an implementation of winner- take-all behavior in inputless cellular neural networks (CNN’s) which is defined as follows: The eventual output of the cell with the largest initial state is +1, while that of all other cells is -1. Although this basically requires a fully interconnected network, a simplified structure with only linear architectural complexity exists. Exact parameters are derived for winner-take-all CNN’s with an arbitrary number of cells, such that their robustness with respect to the simplified structure is maximum. A proof of functionality is given which encompasses both the nominal and the disturbed networks. It is found that accuracy requirements increase with the number of cells, such that the largest winner-take-all CNN’s that can be reliably implemented with current methods may consist of only about ten cells. The paper is also a thorough example of how to apply the robust design method introduced by Seiler, Schuler, and Nossek [2] to the exact determination of optimal CNN parameters and network robustness.