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.

翻译：信仰传播是机器学习中许多应用的基本信息传递算法。 众所周知, 信仰传播算法在树图中是精确的。 但是, 信仰传播在大多数应用中都在循环图中运行。 因此, 了解在循环图中传播信仰的行为是不同领域的研究人员的一个主要课题。 在本文中, 我们研究与motifs( 三角形、 循环等) 图表上普遍信仰传播算法的趋同行为 。 在某种初始化下, 我们显示, 普遍信仰传播会汇集到Bethe 免费能源用于使用motifs的铁磁岩模型的全球最佳状态 。