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An Exact and Direct Analytical Method for the Design of Optimally Robust CNN Templates
 IEEE TRANS. CIRCUITS & SYST.I
, 1999
"... 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 welldefined CNN tasks are characterized by a finit ..."
Abstract

Cited by 5 (2 self)
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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 welldefined 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.
Learning Algorithms For Cellular Neural Networks
 in Proc. IEEE Int. Symp. Circuits Systems
, 1998
"... A learning algorithm based on the decomposition of the Atemplate into symmetric and antisymmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusionlike and propagating behavior. 1. INTRODUCTION Cellular neural networks (CN ..."
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Cited by 1 (1 self)
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A learning algorithm based on the decomposition of the Atemplate into symmetric and antisymmetric parts is introduced. The performance of the algorithm is investigated in particular for coupled CNNs exhibiting diffusionlike 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 ijth cell for 1 # i # M,1# j # N and y = (x +1x 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 socalled Atemplate, the Btemplate and the bias I. In view of learning algorithms, since a CNN is a recurrent neural network, one can apply the lea...
An Analysis of CNN Settling Time
, 1998
"... The settling time of cellular neural networks (CNNs) is crucial for both simulation and applications of VLSI CNN chips. The computational effort for the numerical integration may be drastically reduced, and CNN programs can be optimized, if a priori knowledge on the settling time is available. Moreo ..."
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Cited by 1 (0 self)
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The settling time of cellular neural networks (CNNs) is crucial for both simulation and applications of VLSI CNN chips. The computational effort for the numerical integration may be drastically reduced, and CNN programs can be optimized, if a priori knowledge on the settling time is available. Moreover, this allows the parameters necessary to achieve higher processing speed to be tuned. For certain template classes, we present analytic solutions, while for others, tight upper bounds are given. 1. INTRODUCTION In this paper, we consider the class of singlelayer, spatially invariant cellular neural networks (CNNs) with neighborhood radius one, following the definition given in [1]. The dynamics of the network is governed by a system of n = MNdifferential equations, d x i (t) d t =x i (t) + X k#N i a k f (x k (t)) +b k u k + I + # i ,(1) where N i denotes the neighborhood of the cell C i , a k and b k the template parameters, and # i the contribution from the boundar...
Corrections to "Chaotic Complex Spreading Sequences for Asynchronous DSCDMAPart 1: System Modeling and Results"
, 1998
"... 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, t ..."
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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. PinedadeGyvez. B. Mirzai is with the Signal and Information Processing Laboratory, Swiss Federal Institute of Technology, Zurich, Switzerland (email: mirzai@isi.ee.ethz.ch). G. S. Moschytz ...
Automatic ChipSpecific CNN Template Optimization Using Adaptive Simulated Annealing
 IN PROCEEDINGS OF EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN (ECCTD’03), KRAKOW
, 2003
"... This paper describes a solution proposal for automatically tuning cellular neural network CNN templates for given CNN Universal Machine  CNNUM 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 CNNUM chi ..."
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This paper describes a solution proposal for automatically tuning cellular neural network CNN templates for given CNN Universal Machine  CNNUM 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 CNNUM chips. The approach uses measurements of actual CNNUM chips as part of the cost function for the adaptive simulated annealingASA 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 CNNUM 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 CNNUM chips enough reliability to compete with digital systems in terms of robustness in addition to advantages in speed.