Graph tasks are ubiquitous, with applications ranging from recommendation systems, to language understanding, to automation with environmental awareness and molecular synthesis. A fundamental challenge in applying machine learning to these tasks has been encoding (representing) the graph structure in a way that ML models can easily exploit the relational information in the graph, including node and edge features. Until recently, this encoding has been performed by factor models (a.k.a. graph embeddings), which originated in 1904 with Spearman's common factors. Recently, however, graph neural networks have introduced a new powerful way to encode graphs for machine learning models. In my talk, I will describe these two approaches and then introduce a unifying mathematical framework that connects them. Using this novel framework, I will introduce new practical guidelines to generating and using node embeddings and graph representations, which fixes significant shortcomings of the standard operating procedures used today.

Joint work with Ryan Murphy, Bala Shrinivasan, and Vinayak Rao.