Belief propagation in monoidal categories

TL;DR

This paper presents a categorical formulation of the belief propagation algorithm, demonstrating its equivalence across different algorithms and emphasizing the computational perspective within monoidal categories.

Contribution

It introduces a categorical framework for belief propagation, unifying various algorithms and highlighting their computational structure in monoidal categories.

Findings

Categorical formulation of belief propagation established.

Proof of equivalence among similar algorithms.

Emphasis on computational aspects in monoidal categories.

Abstract

We discuss a categorical version of the celebrated belief propagation algorithm. This provides a way to prove that some algorithms which are known or suspected to be analogous, are actually identical when formulated generically. It also highlights the computational point of view in monoidal categories.