Limit cycles of a perceptron

TL;DR

This paper investigates the periodic behaviors of boolean perceptrons, analyzing their cycle lengths both analytically and numerically, revealing similarities to properties of rational numbers.

Contribution

It provides a detailed analysis of the cycle length spectrum of boolean perceptrons, combining analytical and numerical methods to uncover their properties.

Findings

Cycle lengths have a spectrum similar to rational number properties

Analytical and numerical methods reveal the structure of perceptron cycles

Boolean perceptrons generate periodic bit sequences with predictable cycles

Abstract

An artificial neural network can be used to generate a series of numbers. A boolean perceptron generates bit sequences with a periodic structure. The corresponding spectrum of cycle lengths is investigated analytically and numerically; it has similarities with properties of rational numbers.