Designing template is the most important stage for design and make CNN chip that gives mathematical logic architecture basing on each problem. CNN researchers have many methods to design template corresponding to solutions. This paper review some ways which is used commonly in solving PDE using CNN. The paper has 3 parts, part 1 introduction CNN technology; next part introduces some common ways to design template; part 3 give some illustrations and the last is conclusion and future trends.
Vũ Đức Thái Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 116 (02): - DESIGN TEMPLATE IN CELLULAR NEURAL NETWORK Vu Duc Thai1*, Sonxay Phanthavong2 College of Information and Communication Technology - TNU Ha Noi-Vieng Chan Friendship Vocational School – PDR Lao SUMMARY Designing template is the most important stage for design and make CNN chip that gives mathematical logic architecture basing on each problem CNN researchers have many methods to design template corresponding to solutions This paper review some ways which is used commonly in solving PDE using CNN The paper has parts, part introduction CNN technology; next part introduces some common ways to design template; part give some illustrations and the last is conclusion and future trends Keywords: Template Design, Partial Differential Equation, Cellular Neural Network, Lyapunov Function, Taylor Expansion INTRODUCTION* The theory of CNN has been proposed by L.O Chua an L Yang in 1988 and developed to hardware architecture on CNN Universal Machine (CNN-UM) by L.O Chua and R Tamas [1,2] The CNN is the physical paralleled computing with array of processor called cell Depending on particular problem, the numbers of cell can expand from 10,000 to 100,000 cells CNN is applied in many fields like image processing; scientific computing; robot and economic at high speed processing From 1988, many researchers have been developed the CNN in theory and application as prof the stability and condition constrains for CNN chip The International Conferences of CNN applicationare organized every two years The 13th CNNA was organized from 29-31 August, at Turin, Italy with topics like: Theoretical advances of CNNs; Sensory integration; New spatial-temporal algorithms; Biological relevance of CNNs; Applications on FPGAs and GPUs; Emerging new Cellular Wave Computing Technologies In Vietnam, there are some groups in IT Institute- Vietnam Academy of Science and Technology; Hanoi National University; * Tel: 0985 158998, Email: vdthai@ictu.edu.vn Hanoi Poly technique University and especially in University of Information & Communication Technology -Thai Nguyen University (ICTU), the lecturers have taken researches in image processing; Solving PDE; CNN chaos in data encryption Up to now, they have had more than 10 papers on Vietnamese and International scientific and technology journals Cellular neural networks is made of a massive aggregate of regularly spaced circuit clones, called cells, which communicate with each other directly only through its nearest neighbors Each cell is made of a linear capacitor, a nonlinear voltage-controlled current source, and a few resistive linear circuit elements The basic circuit unit of a cellular neural network is called a cell It contains linear and nonlinear circuit ele-ments, which typically are linear capacitors, linearresistors, linearandnonlinear controlled sources, and independent sources The structure of cellular neuralnetworksissimilar to that found in cellular automata Each cell in a cellular neural network is connected only to its neighbor cells Adjacent cells can interact direct with each other Cells not directly connected together may affect each other indirectly because of the propagation effects of the continuoustime dynamics of the network The state equation of cell C(i,j) is given by the following equation: Vũ Đức Thái Đtg C xij t xij R Tạp chí KHOA HỌC & CƠNG NGHỆ A(i, j; k , l ) ykl 116 (02): - B(i, j; k , l )ukl C ( k ,l ) S r ( i , j ) zij C ( k ,l ) S r ( i , j ) (1) here, R, C is the linear resistor and capacitor respectively A(i,j;kl) is the feedback operator parameter; B(i,j;kl) is the control operator parameter and zij is the bias value of the cell C(i,j) On the CNN system, (A, B, z) are the local connective weight values of each cell C(i,j) to its neighbors vuij vyij vxij I Rx C Eij Ry Ixu(ij,kl) Ixy(ij,kl) Iyx Fig Structure inside of the cell uij B ukl x(t) z dt + yij f (.) - yij A ykl Fig The processing model of cell The output of the cell C(i,j) is modeled by: DESIGNING CNN TEMPLATES METHODS template These masks are used for A template for CNN chip like average, erosion, dilation Analyzing the dynamic of CNN chip to create templates: This method is analyze the operating of processing into detail interactive tasks to find local rules then base on the CNN state equations and relevance between state variables and the first its derivatives on DP chart to find templates Direct template design: This method is often used for uncouple CNN, in which the A template has only center particle having zero off center values, but others are zero, this only applied for process binary image and simple processing Using mask in image processing technique: This method using some types of mask like in classical process on PC to create CNN Using GA and Fuzzy: This method is new and developing and only applying for some special CNN architectures v yij (t ) (| v xij (t ) | | v xij (t ) |) (2) i M ;1 j N The CNN program the series of templates in steps as design, so the templates are actual instructions for CNN chip The programmers find the templates then design architecture CNN chip follow algorithm analyzed Running CNN program is in steps as follow: Set up the initial state Load and run the template automatically by the electronic operations inside circuit (do the instructions coded) Get the output as the result Vũ Đức Thái Đtg Tạp chí KHOA HỌC & CƠNG NGHỆ Learning method: This method to find connection weight, the input is image need to process and desired image at output compare between input and output one can compute the variable values to find weight matrix then having correspondent template Using Taylor Difference: This method bases on difference the differential model by Taylor formula After differencing original equation by refine difference grid then compare to CNN state equation one has templates which describe the operation of CNN chip This method is very useful for solving DPE and advanced image processing Example of using Taylor Difference: 116 (02): - Give an assume partial differential equation follow: u t u x u t u ( x, t ) u x f ( x, t ) u ( x, t ) (4) f ( x, t ) with boundary and initial conditions satisfied, after differencing, one has: ui t ui u i i i ui x 1 fi We the templates for this equation like A [ x ( R ) x ] B [0 0] z =0 Fig Architectural design of CNN chip for Equation(4) 0denote a zero synaptic weight denote a positive or zero synaptic weight denote a negative synaptic weight a denote any value Fig Templates with different stable state patterns of CNN chip Vũ Đức Thái Đtg Tạp chí KHOA HỌC & CƠNG NGHỆ THE STABILITY OF CNN TEMPLATES After finding templates, one knows the dynamic behavior among cells, and then we need to assure that the circuit works steadily, mean that voltage and current are in working ranges The designer must to demonstrate that found templates are accepted for making circuit We have some ways to prove the stability of designed diagram Using Chua method [3,4]: A CNN with MxN cells and a x A template for arbitrary B-template, arbitrary threshold z is completely stable of the following three condition are satisfied: + The A template is sign symmetric 116 (02): - Define the scalar function (6) where θ denotes any number such that f(∞)