ERROR TOLERANCE IN CNNs . APPLICATION TO THE DESIGN OF ROBUST CNNs

This paper deals with the obtention of robust parameter configurations for DT-CNNs and for a class of CT-CNNs (here called CT-CNNs with Discrete Configurations, DC-CT-CNN), in the presence of additive and multiplicative implementation errors. Expressions that characterize the tolerance to both multiplicative and additive errors caused by circuit inaccuracies in DT-CNNs and DC-CT-CNNs VLSI implementation are first deduced. Taking into account those expressions it is proposed to obtain robust parameter configurations, by using a design process based on local rules, as the solution of a single linear programming problem. The process is applied to the generation of robust configuration for some tasks. The tolerance to errors of these configurations has been corroborated by simulations. The differences in parameter values and tolerance to errors, between the robust configuration obtained for solving a particular task in DT-CNNs and that obtained in DC-CT-CNNs, are given. 1.INTRODUCTION The Cellular Neural Network model proposed by L. O. Chua and L. Yang [1] has been widely used for image processing tasks [2]. The time evolution of the state of a cell (neuron or pixel) c in an NxM-cell CNN is described by the differential equation [1]: where n denotes a generic cell belonging to the neighbourhood of cell c, NR(c), with radius equal to R (for example, N1(c) is the set of 3x3 cells centred on c, N1(c)={ c-N-1, c-N, c-N+1, c-1, c, c+1, c+N-1, c+N, c+N+1}). xc is the state of cell c, yn and un are the output and the input, respectively, of the cell n, I is an offset term, and the matrices A and B are called feedback and control templates respectively. Some authors have proposed [3] a discrete-time (DT) version of CNN obtained by applying the Euler integration algorithm to discretise the cell state equation. The state of a cell c in an NxM-cell DT-CNN is described