A variety of globally stable periodic orbits in permutation binary neural networks

TL;DR

This paper investigates globally stable periodic orbits in permutation binary neural networks, identifying all such orbits in 7-dimensional cases using standard permutation connections, which aids in understanding network dynamics and potential applications.

Contribution

The paper introduces a method to classify all globally stable periodic orbits in permutation binary neural networks using standard permutation connections, providing a comprehensive analysis of network stability.

Findings

Identified all globally stable periodic orbits in 7-dimensional networks.

Developed a classification method using standard permutation connections.

Provided a foundation for further analysis and engineering applications.

Abstract

The permutation binary neural networks are characterized by global permutation connections and local binary connections. Although the parameter space is not large, the networks exhibit various binary periodic orbits. Since analysis of all the periodic orbits is not easy, we focus on globally stable binary periodic orbits such that almost all initial points fall into the orbits. For efficient analysis, we define the standard permutation connection that represents multiple equivalent permutation connections. Applying the brute force attack to 7-dimensional networks, we present the main result: a list of standard permutation connections for all the globally stable periodic orbits. These results will be developed into detailed analysis of the networks and its engineering applications.