# Convergence of Generalized Belief Propagation Algorithm on Graphs with Motifs

arXiv: https://arxiv.org/abs/2112.06087 · HTML: https://mlsanity.com/paper/2112.06087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 18 references that are in the map.
- First posted on arXiv 11 Dec 2021.

## Builds on (most cited first, 1 of 1)

- [Fast Convergence of Belief Propagation to Global Optima: Beyond Correlation Decay](https://mlsanity.com/paper/1905.09992/) (2019)

## Abstract (arXiv)

Belief propagation is a fundamental message-passing algorithm for numerous applications in machine learning. It is known that belief propagation algorithm is exact on tree graphs. However, belief propagation is run on loopy graphs in most applications. So, understanding the behavior of belief propagation on loopy graphs has been a major topic for researchers in different areas. In this paper, we study the convergence behavior of generalized belief propagation algorithm on graphs with motifs (triangles, loops, etc.) We show under a certain initialization, generalized belief propagation converges to the global optimum of the Bethe free energy for ferromagnetic Ising models on graphs with motifs.