Martin Hänggi

An exact and direct analytical method for the design of optimally robust CNN templates

In this paper, we present an analytical design approach for the class of bipolar cellular neural networks (CNNs) which yields optimally robust template parameters. We give a rigorous definition of absolute and relative robustness and show that all well-defined CNN tasks are characterized by a finite set of linear and homogeneous inequalities. This system of inequalities can be analytically solved for the most robust template by simple matrix algebra. For the relative robustness of a task, a theoretical upper bound exists and is easily derived, whereas the absolute robustness can be arbitrarily increased by template scaling. A series of examples demonstrates the simplicity and broad applicability of the proposed method.

Simplicial RTD-based cellular nonlinear networks

Recently, a novel structure called the simplicial cellular neural network (CNN) has been introduced , which permits one to implement any Boolean/Gray-level function of any number of variables. This paper is devoted to explore novel circuit architectures for the implementation of the simplicial CNN based on resonant tunneling diodes. The final objective is to implement a fully programmable CNN in a hardware platform based on nanoelectronic devices.

Genetic optimization of cellular neural networks

The operation of a cellular neural network (CNN) is defined by a set of 19 parameters. There is no known general method for finding these parameters; analytic design methods are available for a small class of problems only. Standard learning algorithms cannot be applied due to the lack of gradient information. The authors propose a genetic algorithm as a generally applicable global learning method. In order to be useful for real CNN VLSI chips, the parameters have to be insensitive to small perturbations Therefore, after the parameters are learnt they are optimized with respect to robustness in a second genetic processing step. As the simulation of CNNs necessitates the numerical integration of large systems of nonlinear differential equations, the evaluation of the fitness functions is computationally very expensive; a massively parallel supercomputer is used to achieve acceptable run times.

SIMULATION AND VISUALIZATION OF CNN DYNAMICS

A new simulator for Cellular Neural Networks (CNNs) is presented. In contrast to other simulators, the CNN cells are visualized in a grid structure, the values of input and states being represented by colors. Input and initial images can easily be generated and changed even while the integration of the system is in progress, and an oscilloscope function allows the quantitative study of CNN transients, thus providing insight into the dynamics of the network. For those who are new to the world of CNNs, a series of predefined templates set and demonstrations are available, which makes the simulator a valuable educational tool. Advanced users and CNN expert can examine manually-entered and parametrized templates and carry out experiments in a very broad spectrum of CNN theory and applications, including quantitative behavior, robustness aspects, settling time, state limitations, different output functions and numerical integration methods. The simulator is written in Java and publicly available on WWW and will run on any Web browser of the newer generations.

Stochastic and hybrid approaches toward robust templates

We propose and compare different methods of synthesizing robust templates for cellular neural networks. In the first approach, genetic algorithms are used for both template learning and optimization with respect to robustness. The evaluation of the fitness functions in the optimization step is computationally very expensive; a massively parallel supercomputer is used to achieve acceptable run times. As alternative approaches, a steepest-ascent method and an averaging approach are presented, the latter being computationally inexpensive. To overcome their respective drawbacks, these algorithms are combined into a hybrid approach which is shown to be efficient even for complex problems.

A compact and universal cellular neural network cell based on resonant tunneling diodes: circuit, model, and functional capabilities

A novel cellular neural network (CNN) cell and its circuit realization are proposed. The theory of the multi-nested universal cell is applied, and the nonmonotonic current-voltage characteristic of resonant tunneling diodes (RTD) is exploited to achieve a high functionality. The proposed cell has the potential of implementing arbitrary local Boolean functions with n inputs. The cell has a complexity of only O(n) in the number of devices and template elements. For comparison, the digital n-to-1 multiplexor, a functionally equivalent system has a complexity of O(2/sup n/). A simple, piecewise-linear mathematical model is derived and used to evaluate the functional capabilities of the RTD-CNN cell. The model was proved to be accurate enough, and only minor tuning of some of the parameters is necessary to achieve the same functionality using a Spice simulation of the same circuit, which is based on more refined physical device models.

Unifying results in CNN theory using delta operator

By means of the delta operator, a new type of CNN, the (/spl delta/,c)-CNN, is introduced. It is a superclass of continuous-time (CT) and discrete-time (DT) CNNs with any saturation-, high-gain-, or hardlimiting sign-nonlinearity. It is shown that the (/spl delta/,c)-CNN allows continuous transition between different types of nonlinearities and between CT- and DT-CNNs, providing a unifying framework for CNN theory. In particular, the problem of optimally robust template design can be dealt with in a unified manner.

CNN Settling Time

When discussing and comparing signal processing devices, their processing speed is always of particular interest. In the case of a nonlinear dynamical system, the processing speed is defined by its settling time, i.e., the time it takes the system to reach its equilibrium state. In this chapter, the settling time of locally regular CNNs is defined and investigated.

Robust Template Design

The problem of template design or template learning is a key topic in CNN research; the methods which have been investigated since the inception of the CNN may be classified as analytical methods [17–20], local learning algorithms [21–23], and global learning algorithms [24,25]. The analytical approaches are based upon a set of local rules (see 2.6) characterizing the dynamics of a cell, depending on its neighboring cells. These rules are transformed into an affine set of inequalities that has to be solved to get correctly operating templates.

Locally Regular CNNS

The distinction between different types of CNNs depending on the existence of intercell feedback has proven to be very helpful in the last decade. In uncoupled CNNs, where the parameters in the feedback template A are zero except for the self-feedback a 5, the cells are isolated from each other. These networks can be analyzed in all details and are well-understood. Coupled CNNs, which have at least one non-zero off-center entry in the A template, may exhibit complex dynamical behavior which is not fully tractable analytically. For example, there is no necessary and sufficient condition on the (feedback) template elements for stability.