In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNN's) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

A learning algorithm based on the decomposition of the A-template into symmetric and anti-symmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusion-like and propagating behavior. 1. INTRODUCTION Cellular neural networks (CNNs) are examples of recurrent networks defined by the following system of differential equations dx ij (t) dt =-x ij (t) + # mn#N ij amn y mn (t) + # mn#N ij bmn u mn + I , where N ij denotes the neighborhood of the ij-th cell for 1 # i # M,1# j # N and y = (|x +1|-|x -1|)/2 . The state, input and output of a cell are defined by x ij , u ij and y ij , respectively. We assume a nearest neighborhood CNN. The output at an equilibrium point, when one exists, is denoted by y # ij .The parameters of a CNN are gathered into the so-called A-template, the B-template and the bias I. In view of learning algorithms, since a CNN is a recurrent neural network, one can apply the lea...

We investigate the issue of robustness and how it is effected by the choice of boundary values for a given template set. First we introduce a measure of robustness, and then we show that, in some cases, an appropriate choice of boundary value may increase the attainable robustness. In other cases, the boundary value may be varied within some interval without loss of robustness. I. INTRODUCTION Cellular neural networks (CNN's) constitute a class of recurrent networks that can be implemented in analog VLSI technology [1], [2]. The dynamics of each cell is governed by C dx ij (t) dt = 0 1 R x ij (t)+ kl 2N a ij;kl sat(x kl (t)) + kl 2N b ij;kl u kl + I (1) Manuscript received July 24, 1996; revised December 20, 1996 and April 28, 1997. This paper was recommended by Associate Editor J. Pineda-deGyvez. B. Mirzai is with the Signal and Information Processing Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland (e-mail: mirzai@isi.ee.ethz.ch). G. S. Moschytz ...

This paper describes a solution proposal for automatically tuning cellular neural network--- CNN templates for given CNN Universal Machine --- CNN-UM chips in order to make them respond in the same fashion as a simulator, i.e. to minimize or even eliminate the erroneous behavior of actual CNN-UM chips. The approach uses measurements of actual CNN-UM chips as part of the cost function for the adaptive simulated annealing---ASA algorithm to find an optimal template given an initial approximation, e.g. a template used for a simulator. The tuned templates are therefore customized versions that are expected to be much less sensitive to imperfections on the manufacturing process and other reasons of erroneous behavior of CNN-UM chips. Results are presented for the binary and gray scale input cases. The automatic tuning was able to find better templates for all considered tasks. It is expected that the maturity of this technique will give to CNN-UM chips enough reliability to compete with digital systems in terms of robustness in addition to advantages in speed.