Cellular Nonlinear Networks

2. Teil des Moduls Einführung in die Theorie nichtlinearer Systeme (ET-12 08 07)

Lecturer

Dr. Alon Ascoli

Course Description

In view of the strongly-increasing impact that Digitalisation and Artificial Intelligence (AI)
will have on our lives in the years to come, research on non-von Neumann data processing architectures, allowing to implement in-memory computing paradigms robustly, is of utmost importance. In this respect Cellular Nonlinear Networks (CNNs) constitute one of the most promising platforms for the realisation of unconventional computing strategies, allowing to merge and distribute data sensing, processing, and storage, wherever and whenever necessary, as desirable to manage large data sets in various systems, e.g. for advanced driver assistance in automotive vehicles.

CNNs [1]-[2] consist of time-continuous processing elements, referred to as cells, which are discretely- yet regularly-spaced across a multi-dimensional lattice, are physically-coupled only to cells residing within a given local neighbourhood, and process information through the nonlinear dynamics of their states under predefined inputs, initial and boundary conditions, depending upon the parameters defining the operation of each cell and how it interacts with its neighbours.
Featuring a bio-inspired architecture, which allows to compute data in a massively-parallel
fashion, CNNs represent a powerful paradigm for modelling biological systems [3], e.g. the
brain, and for processing multivariate signals [4].
The capability of these cellular arrays to process a large data set in the multi-kHz rate range may be exploited to address time-critical issues for various applications, e.g. in the medical field, in the industry, and even for public or private security purposes. Universal Machines (UM) [5], implementing the CNN signal processing paradigm [6], are typically co-integrated with equal-sized sensor arrays to solve computing tasks in real time, directly where data acquisition takes place, which is of great appeal for Internet-of-Things (IoT) applications.

This course presents the robust system-theoretic foundations of the CNN paradigm, introducing the students to the tool kit necessary to analyse, design, and simulate cellular computing structures. It also provides an overview on the latest research developments in this field, especially on the benefits that the adoption of disruptive memristor technologies may provide to the performance of state-of-the-art purely-CMOS CNN-UMs [7].

References

[1] L.O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. On Circuits and Systems, vol. CAS-35, no. 10, pp. 1257-1272, 1988
[2] L.O. Chua and L. Yang, “Cellular Neural Networks: Applications,” IEEE Trans. On Circuits and Systems, vol. CAS-35, no. 10, pp. 1273-1290, 1988
[3] L.O. Chua, “CNN: A Paradigm for Complexity”, Word Scientific Series on Nonlinear Science, Series Editor: L.O. Chua, Series A, vol. 31, Word Scientific Publishing Co. Pte. Ltd., 1998, ISBN-13: 978-9810234836
[4] L.O. Chua, and T. Roska, “Cellular Neural Networks and Visual Computing: Foundations and Applications,” Cambridge University Press, ISBN-13: 978-0521652476
[5] T. Roska and L. O. Chua, “The CNN universal machine: An analogic array computer,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 40, no. 3, pp. 163–173, Mar. 1993
[6] A. Rodríguez-Vázquez, J. Fernández-Berni, J.A. Leñero-Bardallo, I. Vornicu, and R. Carmona-Galán, “CMOS Vision Sensors: Embedding Computer Vision at Imaging Front-Ends,” IEEE Circuits and Systems Magazine, vol. 18, no. 2, pp. 90-107, 2018
[7] A. Ascoli, R. Tetzlaff, Sung-Mo (Steve) Kang, and L.O. Chua, “Theoretical Foundations of
Memristor Cellular Nonlinear Networks: A DRM2-based Method to Design Memcomputers with Dynamic Memristors,” IEEE Trans. on Circuits and Systems–I: Regular Papers, 2020, DOI: 10.1109/TCSI.2020.2978460

Course Contents

• CNN Theory
  • Notation, Basic Definitions, Mathematical Framework
  • Theoretical Foundations
  • Classification of CNNs
  • Simulation of CNNs
  • The CNN Universal Machine
• Analysis, Design and Simulation of Time- and Space-Invariant CNNs
  • Standard Uncoupled CNNs
  • Non-standard Uncoupled CNNs with Nonlinear Synaptic Weights
  • Standard Coupled CNNs
  • Boolean CNNs
• Autonomous CNNs
  • Pattern Formation in Standard CNNs
  • Static Inhomogeneous Solutions and Nonlinear Waves in Reaction-Diffusion CNNs (RD-CNNs)
  • Application of the CNN paradigm to the modelling of biological systems
• Local Activity and the Genesis of Complexity
  • Definition of Local Activity
  • Local Activity Theorem
  • Local Activity Principle
  • Local Activity in RD-CNNs
• Memristor CNNs (M-CNNs)
  • Brief Introduction to Memristors
  • Mathematical Foundations and Applications of M-CNNs
  • Analysis and design techniques

Important Notice

The course will be offered on-line this winter semester. Lectures are scheduled as follows

• Tuesday at the 3rd hour (11:10am-12:40am) on even weeks
• Wednesday at the 3rd hour (11:10am-12:40am) each week

This time course held only on site at TOE 315 after 28.10.2021.

The lectures will be offered on site at TOE 315. After lecture student will received materials via E-mail.

Course material will be provided to the students after each lecture via OPAL or the TU Dresden Cloud Data Storage Service.

With regard to the exam format, it typically consists of a written test of 90 minutes, unless the number of examiners is lower than 5, in which case a 30-minute-long oral assessment is carried out.

Links

• OPAL Course
• Zoom conference (accessible after enrolment in OPAL)