Geometric graphs are a special kind of graph with geometric features,which are vital to model many scientific problems.Unlike generic graphs,geometric graphs often exhibit physical symmetries of translations,rotations...Geometric graphs are a special kind of graph with geometric features,which are vital to model many scientific problems.Unlike generic graphs,geometric graphs often exhibit physical symmetries of translations,rotations,and reflections,making them ineffectively processed by current Graph Neural Networks(GNNs).To address this issue,researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs.Given the current progress in this field,it is imperative to conduct a comprehensive survey of data structures,models,and applications related to geometric GNNs.In this paper,based on the necessary but concise mathematical preliminaries,we formalize geometric graph as the data structure,on top of which we provide a unified view of existing models from the geometric message passing perspective.Additionally,we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey.展开更多
基金supported by the following projects:The National Natural Science Foundation of China(Grant Nos.62376276 and 62172422)Beijing Nova Program(Grant No.20230484278)+1 种基金the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China(Grant No.23XNKJ19)Tencent AI Lab Rhino-Bird Focused Research Program.
文摘Geometric graphs are a special kind of graph with geometric features,which are vital to model many scientific problems.Unlike generic graphs,geometric graphs often exhibit physical symmetries of translations,rotations,and reflections,making them ineffectively processed by current Graph Neural Networks(GNNs).To address this issue,researchers proposed a variety of geometric GNNs equipped with invariant/equivariant properties to better characterize the geometry and topology of geometric graphs.Given the current progress in this field,it is imperative to conduct a comprehensive survey of data structures,models,and applications related to geometric GNNs.In this paper,based on the necessary but concise mathematical preliminaries,we formalize geometric graph as the data structure,on top of which we provide a unified view of existing models from the geometric message passing perspective.Additionally,we summarize the applications as well as the related datasets to facilitate later research for methodology development and experimental evaluation.We also discuss the challenges and future potential directions of geometric GNNs at the end of this survey.
