Cellular Neural Networks

1. Cellular Neural Networks Survey of Techniques and Applications Max Pflueger CS 152: Neural Networks December 12, 2006

2. Cellular Neural Networks • Cells are given a spatial arrangement with connection between cells that are within a certain radius of each other • All the cells within the radius of cell (i,j) are the neighborhood of cell (i,j) • neighborhood with r = 1 • r = 2

3. Templates • Cell behavior is governed by the differential equation shown above • A template specifies values for A, B, and z that will be used throughout the CNN to achieve some effect • A, and B, are typically matrices of weights associated with the relative position of neighbors

4. The CNN Universal Machine • CNN with the ability to change templates during operation • Templates can be strung together, creating a programmable CNN • Instructions are similar to traditional microprocessor • Turing complete

5. Application of CNNs and the CNN-UM • Ocean modeling • 10,000 fps image recognition • Bionic eye • Face and eye detection • Template learning

6. Ocean Modeling • Exact solutions to fluid mechanics problems require solving systems of partial differential equations • Analytical solutions do not exist in most cases • Numerical solutions are very computationally intensive

7. Ocean Modeling • Nagy and Szolgay designed a simulation of a CNN-UM with modified cell architecture to model ocean currents • Simulation was run on a mid-size FPGA and an Athlon XP 1800+ for comparison • Athlon XP 1800+: 56 min • FPGA: 41 s • A larger FPGA could do the calculation in ~1 sec

8. Template Learning • It would be nice to use learning techniques to find useful templates for CNNs • Gradient descent is promising, except that it is difficult to compute the gradient for a CNN

9. Template Learning • Brendel, Roska, and Bartfai presented the equations for calculating the gradient of a CNN • They also showed that these equations have the same neighborhood and connectivity as the original CNN • Therefore, a CNN-UM can be used to compute the gradients for templates, making it possible to do fast on-line training with a CNN-UM

10. Face and Eye Detection • Detecting faces in images is a classic problem in computer science • Balya and Roska designed a CNN algorithm for recognizing and normalizing faces from color images. • Accurate • Runs in hardware, so it is very fast

11. References • Chua, Leon O. and Tamás Roska. Cellular Neural Networks and Visual Computing. Cambridge: Cambridge University Press, 2002. • Nagy, Z.; Szolgay, P., "Emulated digital CNN-UM implementation of a barotropic ocean model," Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on , vol.4, no.pp. 3137- 3142 vol.4, 25-29 July 2004 • Brendel, M., Roska, T., and Bártfai, G. 2002. Gradient Computation of Continuous-Time Cellular Neural/Nonlinear Networks with Linear Templates via the CNN Universal Machine. Neural Process. Lett. 16, 2 (Oct. 2002), 111-120. • Balya, D. and Roska, T. 1999. Face and Eye Detection by CNN Algorithms. J. VLSI Signal Process. Syst. 23, 2-3 (Nov. 1999), 497-511.