Cellular Neural/nonlinear Networks Research Articles

Robust Design for Local Concave CNN

This paper proposes a robust design theorem for a kind of cellular neural/nonlinear networks (CNNs) to detect images with local concave properties and then gives a general method for determining template of such a kind of CNN. One theorem provides parameter inequalities for determining parameter intervals for implementing prescribed image processing function. Moreover, the numerical simulation is carried out, proved its practical applications.

FPGA-Based Real Time, Multichannel Emulated-Digital Retina Model Implementation

The function of the low-level image processing that takes place in the biological retina is to compress only the relevant visual information to a manageable size. The behavior of the layers and different channels of the neuromorphic retina has been successfully modeled by cellular neural/nonlinear networks (CNNs). In this paper, we present an extended, application-specific emulated-digital CNN-universal machine (UM) architecture to compute the complex dynamic of this mammalian retina in video real time. The proposed emulated-digital implementation of multichannel retina model is compared to the previously developed models from three key aspects, which are processing speed, number of physical cells, and accuracy. Our primary aim was to build up a simple, real-time test environment with camera input and display output in order to mimic the behavior of retina model implementation on emulated digital CNN by using low-cost, moderate-sized field-programmable gate array (FPGA) architectures.

Stochastic optimization of spin-glasses on cellular neural/nonlinear network based processors

Nowadays, Cellular Neural/Nonlinear Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. It is important also for physicists to be aware that such computers are appropriate for implementing in an elegant manner practically important algorithms, which are extremely slow on the classical digital architecture. Here, CNN is used for optimization of spin-glass systems. We prove, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type spin-glass system. Using the properties of CNN we show that one single operation on the CNN chip would yield a local minimum of the spin-glass energy function. By using this property a fast optimization method, similar to simulated annealing, can be built. After estimating the simulation time needed for this algorithm on CNN based computers, and comparing it with the time needed on normal digital computers using the classical simulated annealing algorithm, the results look promising: a speed-up of the order 10 12 is expected already at 50×50 lattice sizes. Hardwares realized nowadays are of 128×128 size. Also, there seem to be no technical difficulties adapting CNN chips for such problems and the needed local control of the parameters could be fully developed in the near future.

Statistical physics on cellular neural network computers

The computational paradigm represented by Cellular Neural/nonlinear Networks (CNN) and the CNN Universal Machine (CNN-UM) as a Cellular Wave Computer, gives new perspectives also for computational statistical physics. Thousands of locally interconnected cells working in parallel, analog signals giving the possibility of generating truly random numbers, continuity in time and the optical sensors included on the chip are just a few important advantages of such computers. Although CNN computers are mainly used and designed for image processing, here we argue that they are also suitable for solving complex problems in computational statistical physics. This study presents two examples of stochastic simulations on CNN: the site-percolation problem and the two-dimensional Ising model. Promising results are obtained using an ACE16K chip with 128×128 cells. In the second part of the work we discuss the possibility of using the CNN architecture in studying problems related to spin-glasses. A CNN with locally variant parameters is used for developing an optimization algorithm on spin-glass type models. Speed of the algorithms and further trends in developing the CNN chips are discussed.

Emulated digital CNN‐UM solution of partial differential equations

AbstractWe present here new cellular neural/non‐linear networks (CNN)‐based emulated digital architectures specifically designed for the solution of different partial differential equations (PDE). The array structure and local connectivity of the CNN paradigm make it a natural framework to describe the behaviour of locally interconnected dynamical systems. Solution of the PDE is carried out by a spatio‐temporal dynamics, which can be computed in real‐time on analogue CNN‐UM chips, but the accuracy of the solution is low. Additionally, solution of PDEs on a CNN‐UM architecture often requires a multi‐layer structure and non‐linear templates which is partially or not supported on the current analogue VLSI CNN‐UM chips. To overcome these obstacles while preserving high computing performance a configurable emulated digital CNN‐UM can be used where the main parameters (accuracy, template size and number of layers) are configurable. Additionally, the symmetry of the finite difference operators makes it possible to specialize the emulated digital CNN‐UM architecture to solve a specific type of PDE, which results in higher performance. Emulated digital CNN‐UM processors use fixed‐point numbers to carry out computations, and by decreasing the precision the speed of the computations can be improved. Hence, a simple algorithm is introduced to determine the optimal fixed‐point precision and maximize computing performance. Copyright © 2006 John Wiley & Sons, Ltd.

Object comparison using PDE‐based wave metric on cellular neural networks

AbstractThe paper investigates PDE‐based dynamic phenomena for comparing objects and introduces a spatio‐temporal non‐linear wave metric. This metric is capable of comparing both binary and grey‐scale object pairs in a parallel way. Spatio‐temporal waves are initialized and controlled to explore the quantitative properties of objects. In addition to spatial data, even ‘hidden’, time‐related information is also extracted and used for evaluating differences and similarities. The detailed analysis of the proposed metric shows that this wave‐based approach can outperform well‐known metrics such as Hausdorff and Hamming metrics in selectivity and sensitivity. The approach in question can be efficiently implemented on massively parallel architectures, e.g. on Cellular Neural/Non‐linear Networks (CNN), providing solutions either for real time applications. Copyright © 2006 John Wiley & Sons, Ltd.

Stochastic simulations on the cellular wave computers

The computational paradigm represented by Cellular Neural/nonlinear Networks (CNN) and the CNN Universal Machine (CNN-UM) as a Cellular Wave Computer, gives new perspectives for computational physics. Many numerical problems and simulations can be elegantly addressed on this fully parallelized and analogic architecture. Here we study the possibility of performing stochastic simulations on this chip. First a realistic random number generator is implemented on the CNN-UM, and then as an example the two-dimensional Ising model is studied by Monte Carlo type simulations. The results obtained on an experimental version of the CNN-UM with 128 * 128 cells are in good agreement with the results obtained on digital computers. Computational time measurements suggests that the developing trend of the CNN-UM chips - increasing the lattice size and the number of local logic memories - will assure an important advantage for the CNN-UM in the near future.

STABILITY OF MULTI-LAYER CELLULAR NEURAL/NONLINEAR NETWORKS

We have found a formalism that lets us present generalizations of several stability theorems (see Chua & Roska, 1990; Chua & Wu, 1992; Gilli, 1993; Forti, 2002] on Multi-Layer Cellular Neural/Nonlinear Networks (MLCNN) formerly claimed for Single-Layer Cellular Neural/Nonlinear Networks (CNN). The theorems were selected with special regard to usefulness in engineering applications. Hence, in contrast to many works considering stability on recurrent neural networks, the criteria of the new theorems have clear indications that are easy to verify directly on the template values. Proofs of six new theorems on 2-Layer CNNs (2LCNN) related to symmetric, τ-symmetric, nonsymmetric, τ-nonsymmetric, and sign-symmetric cases are given. Furthermore, a theorem with a proof on a MLCNN with arbitrary template size and arbitrary layer number in relation to the sign-symmetric theorem is given, along with a conjecture for the one-dimensional, two-layer, nonreciprocal case.

On stability of cellular neural networks with polynomial interactions.

Cellular neural/nonlinear networks (CNNs) are analog dynamic processor arrays, that present local interconnections. CNN models with polynomial interactions among the cells (Polynomial type CNNs) have been recently introduced. They are useful for solving some complex computational problems and for real-time implementation of PDE-based algorithms. This manuscript provides some simple and rigorous sufficient conditions for stability of polynomial type CNNs. A particular emphasis is given to conditions that can be expressed in terms of template elements, since they can be exploited for design purposes.

New results and measurements related to some tasks in object-oriented dynamic image coding using CNN universal chips

Cellular neural/nonlinear networks (CNN) are considered for efficient implementation of the most computationally intensive steps of dynamic image coding. Several analogic CNN algorithms are presented for the generation of binary image masks and image decomposition. Measurement results for the first CNN universal chips executing an analogic algorithm for a reconstruction operator are also presented. Based on measured execution times, the viability of the CNN implementation of efficient but computationally expensive compression algorithms such as dynamic image coding is assessed.