Generating Probability Distributions using Multivalued Stochastic Relay Circuits

TL;DR

This paper explores how multivalued relay circuits can be designed to generate any probability distribution efficiently, extending previous two-state relay work and introducing a universal generator with robustness to errors.

Contribution

It generalizes existing two-state relay results to multivalued relays, establishes a duality property, and designs a universal probability generator for arbitrary distributions.

Findings

Networks can generate arbitrary rational probability distributions.

The proposed networks are robust to errors.

A universal probability generator is designed for binary distributions.

Abstract

The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions from unbiased bits. An equally interesting, but less studied aspect is the structural component of random number generation as opposed to the algorithmic aspect. That is, given a network structure imposed by nature or physical devices, how can we build networks that generate arbitrary probability distributions in an optimal way? In this paper, we study the generation of arbitrary probability distributions in multivalued relay circuits, a generalization in which relays can take on any of N states and the logical 'and' and 'or' are replaced with 'min' and 'max' respectively. Previous work was done on two-state relays. We generalize these results, describing a duality property and networks that generate arbitrary rational probability distributions. We prove that these networks are robust to errors and design a universal probability generator which takes input bits and outputs arbitrary binary probability distributions.