그래프 데이터를 위한 딥러닝 기법 탐색: 연속형 그래프 신경망부터 위상학적 신경망까지

초록

This paper reviews the latest advancements in Graph Neural Networks (GNNs), focusing on continuous GNNs and topological neural networks (TNNs). Continuous GNNs utilize diffusion techniques to address the issues of oversmoothing and oversquashing by interpreting graphs as discretized objects embedded in manifolds, explained through the concept of heat diffusion. TNNs, on the other hand, aim to analyze the high-dimensional and global features of graph data using simplicial complexes and persistent homology, although research in this area remains limited. The theoretical foundations, including differential equations and graph heat diffusion in continuous GNNs, as well as the mathematical tools adopted from topological data analysis for TNNs, are thoroughly examined. By introducing the latest deep learning models related to these approaches, this paper seeks to provide researchers with a comprehensive perspective on the GNN domain.

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