Patrick Thiran

Pattern formation properties of autonomous Cellular Neural Networks

We use the Cellular Neural Network (CNN) to study the pattern formation properties of large scale spatially distributed systems. We have found that the Cellular Neural Network can produce patterns similar to those found in Ising spin glass systems, discrete bistable systems, and the reaction-diffusion system. A thorough analysis of a 1-D CNN whose cells are coupled to immediate neighbors allows us to completely characterize the patterns that can exist as stable equilibria, and to measure their complexity thanks to an entropy function. In the 2-D case, we do not restrict the symmetric coupling between cells to be with immediate neighbors only or to have a special diffusive form. When larger neighborhoods and generalized diffusion coupling are allowed, it is found that some new and unique patterns can be formed that do not fit the standard ferro-antiferromagnetic paradigms. We have begun to develop a theoretical generalization of these paradigms which can be used to predict the pattern formation properties of given templates. We give many examples. It is our opinion that the Cellular Neural Network model provides a method to control the critical instabilities needed for pattern formation without obfuscating parameterizations, complex nonlinearities, or high-order cell states, and which will allow a general and convenient investigation of the essence of the pattern formation properties of these systems. >

An analytic method for designing simple cellular neural networks

A method is proposed for synthesizing cellular neural networks (CNNs) designed for simple applications. Based on the comparison principle for ordinary differential equations, this method leads to a set of inequalities that must be satisfied by the parameters of the cloning template defining the cellular neural network in order to guarantee correct operation for the network. The authors review the architecture of CNNs, compute the bounds of the state and output of a cell, and illustrate how to use this technique to design CNNs for shadowing, motion detection, and hole filling. >

CHARACTERIZATION AND DYNAMICS OF PATTERN FORMATION IN CELLULAR NEURAL NETWORKS

We study some properties of pattern formation arising in large arrays of locally coupled first-order nonlinear dynamical systems, namely Cellular Neural Networks (CNNs). We will present exact results to analyze spatial patterns for symmetric coupling and to analyze spatio-temporal patterns for anti-symmetric coupling in one-dimensional lattices, which will then be completed by approximative results based on a spatial and/or temporal frequency approach. We will discuss the validity of these approximations, which bring a lot of insight. This spectral approach becomes very convenient for the two-dimensional lattice, as exact results get more complicated to establish. In this second part, we will only consider a symmetric coupling between cells. We will show what kinds of motifs can be found in the patterns generated by 3×3 templates. Then, we will discuss the dynamics of pattern formation starting from initial conditions which are a small random noise added to the unstable equilibrium: this can generally be well predicted by the spatial frequency approach. We will also study whether a defect in a pure pattern can propagate or not through the whole lattice, starting from initial conditions being a localized perturbation of a stable pattern: this phenomenon is no longer correctly predicted by the spatial frequency approach. We also show that patterns such as spirals and targets can be formed by “seed” initial conditions — localized, non-random perturbations of an unstable equilibrium. Finally, the effects on the patterns formed of a bias term in the dynamics are demonstrated.

Quantization effects in digitally behaving circuit implementations of Kohonen networks

Implementing a neural network on a digital or mixed analog and digital chip yields the quantization of the synaptic weights dynamics. This paper addresses this topic in the case of Kohonens self-organizing maps. We first study qualitatively how the quantization affects the convergence and the properties, and deduce from this analysis the way to choose the parameters of the network (adaptation gain and neighborhood). We show that a spatially decreasing neighborhood function is far more preferable than the usually rectangular neighborhood function, because of the weight quantization. Based on these results, an analog nonlinear network, integrated in a standard CMOS technology, and implementing this spatially decreasing neighborhood function is then presented. It can be used in a mixed analog and digital circuit implementation.

Detecting moving and standing objects using cellular neural networks

The general framework of motion detection based on discrete time samples of the moving image is defined. Four types of motion detection problem are studied. the simplest one is a model resembling the famous Hubel-Wiesel experiment with a cats retina for detecting the motion of an object having a given speed in a given direction. the most complicated case is the determination of the vertical and horizontal velocity components of a moving image. n n n nVarious cloning template sequences are proposed for detecting different types of motion. In the sampled mode the consecutive black-and-white snapshots are fed to the input and to the initial state nodes of the cellular neural network respectively. After the transients have decayed, the output gives the information necessary for detecting the presence or absence of a specific motion as well as for estimating the direction and magnitude of the velocity vector. In continuous mode the sampling process is eliminated by the use of delay-type templates. n n n nConditions are analysed under which the detection is correct. the circuit realization of some motion detectors is discussed and the use of a programmable dual-CNN structure is proposed.

Self-organization of a one-dimensional Kohonen network with quantized weights and inputs

Abstract If a self-organizing neural network has to be implemented on a digital (or mixed analog and digital) circuit realization, with on-chip learning, all the input signals and the weight values have to be quantized. It is therefore crucial to study whether this quantization does not annihilate the self-organization property of the weights. This paper provides necessary and sufficient conditions on the parameters of a one-dimensional network, which ensure the organization of the weights for any one-dimensional input probability distribution. These results are rigorously proved using the Markovian formulation of Kohonens algorithm.

Design, Implementation, and Test of a Multi-Model Systolic Neural-Network Accelerator

Keywords: neurone ; Non-Linear Modelling ; Neural Network Reference LANOS-CONF-1994-018 Record created on 2004-12-03, modified on 2016-08-08

Information storage using stable and unstable oscillations : an overview

Keywords: Non-Linear Modelling ; Neural Network Reference LANOS-ARTICLE-1996-004View record in Web of Science Record created on 2004-12-03, modified on 2017-05-12

Information storage and retrieval in an associative memory based on one-dimensional maps†

In this paper, we show how to synthethize a dynamical system based on a method proposed by Dmitriev et al. (1991) for storing and retrieving information as stable limit cycles of one-dimensional maps in a simple case.