信仰传播是一种基本消息传递算法，用于机器学习中的许多应用。已知信仰传播算法精确在树图上。但是，在大多数应用程序中，信仰传播在循环图上运行。因此，了解对循环图中的信仰传播的行为一直是不同领域的研究人员的主要话题。在本文中，我们研究了在具有图案（三角形，循环等）图中的广义信仰传播算法的收敛行为我们在一定的初始化下显示，广义信仰传播会聚到铁磁性模型的贝特自由能的全球最优的最佳状态在与图案的图表上。

Multi-lingual language models (LM), such as mBERT, XLM-R, mT5, mBART, have been remarkably successful in enabling natural language tasks in low-resource languages through cross-lingual transfer from high-resource ones. In this work, we try to better understand how such models, specifically mT5, transfer *any* linguistic and semantic knowledge across languages, even though no explicit cross-lingual signals are provided during pre-training. Rather, only unannotated texts from each language are presented to the model separately and independently of one another, and the model appears to implicitly learn cross-lingual connections. This raises several questions that motivate our study, such as: Are the cross-lingual connections between every language pair equally strong? What properties of source and target language impact the strength of cross-lingual transfer? Can we quantify the impact of those properties on the cross-lingual transfer? In our investigation, we analyze a pre-trained mT5 to discover the attributes of cross-lingual connections learned by the model. Through a statistical interpretation framework over 90 language pairs across three tasks, we show that transfer performance can be modeled by a few linguistic and data-derived features. These observations enable us to interpret cross-lingual understanding of the mT5 model. Through these observations, one can favorably choose the best source language for a task, and can anticipate its training data demands. A key finding of this work is that similarity of syntax, morphology and phonology are good predictors of cross-lingual transfer, significantly more than just the lexical similarity of languages. For a given language, we are able to predict zero-shot performance, that increases on a logarithmic scale with the number of few-shot target language data points.