This work provides the first unifying theoretical framework for node
(positional) embeddings and structural graph representations, bridging methods
like matrix factorization and graph neural networks. Using invariant theory, we
show that the relationship between structural representations and node
embeddings is analogous to that of a distribution and its samples. We prove
that all tasks that can be performed by node embeddings can also be performed
by structural representations and vice-versa. We also show that the concept of
transductive and inductive learning is unrelated to node embeddings and graph
representations, clearing another source of confusion in the literature.
Finally, we introduce new practical guidelines to generating and using node
embeddings, which fixes significant shortcomings of standard operating
procedures used today.

该研究提出了第一个统一的理论框架，将节点嵌入和结构图表示相结合，通过不变量理论证明了结构表示和节点嵌入之间的关系，证明了能够使用节点嵌入执行的所有任务也都可以通过结构表示执行，并且介绍了新的指南来生成和使用节点嵌入，修复了现有标准操作程序的显著缺点。