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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 ..."
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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.
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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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...
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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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...