Neural networks with chaotic recursive nodes: design of associative memories, performance analysis, and contrast with traditional Hopfield architectures

This paper addresses the coding and storage of information in neural architectures with bifurcating recursive nodes that exhibit chaotic dynamics. It describes architectures of coupled recursive processing elements (RPEs) used to store binary strings, discusses the choices of network parameters related to the coding of zeros and ones, and analyzes several aspects of the network operation in implementing associative memories through populations of logistic maps. Experiments for the performance evaluation of these memories are described, and results addressing the operation under digital noise (flipped bits) and analog noise added to the prompting pattern are presented and analyzed. In the initial sections of the paper, several quantitative aspects related to the representation of binary strings in terms of cyclic states of the network are equated, and then related to the planning and analysis of the experiments discussed in the following sections. A simple pre-processing procedure useful in situations of prompting conditions with analog noise is discussed and the resultant improvements in recovery performance are presented. Finally the performance of the associative network based in RPEs is contrasted with the performance of traditional Hopfield associative networks, and the situations where the RPEs network presents significant superiority are identified.