Chaotic Boltzmann machines with two elements

TL;DR

This paper demonstrates that chaotic Boltzmann machines with only two elements can accurately produce samples from their associated probabilistic distributions, confirming their effectiveness in simple cases.

Contribution

It provides a proof that two-element chaotic Boltzmann machines generate correct probabilistic samples, clarifying their behavior in minimal configurations.

Findings

Chaotic Boltzmann machines with two elements produce correct samples.

Validation of chaotic Boltzmann machines' sampling accuracy in simple cases.

Clarification of the behavior of minimal chaotic Boltzmann machines.

Abstract

In this brief note, we show that chaotic Boltzmann machines truly yield samples from the probabilistic distribution of the corresponding Boltzmann machines if they are composed of only two elements. This note is an English translation (with slight modifications) of the article originally written in Japanese [H. Suzuki, Seisan Kenkyu 66 (2014), 315-316].