Abstract
We consider a Cellular Neural Network (CNN) with a bias term $z$ in the integer lattice $Z^2$ on the plane $R^2$. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, $a$ and $c$, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic patterns, and the parameter space $(z, a; c)$ can be completely characterized. This, in turn, addresses the so-called "Learning Problem" in CNNs. The complexities of mosaic is also studied.
Information
Published: 1 January 1999
First available in Project Euclid: 18 November 2014
zbMATH: 1193.34098
Rights: Copyright © 1999, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
