Survey of deep learning techniques for graph data: from continuous graph neural networks to topological deep learning
Seongmin Yun, Hyoung-Jun Kim, Seung Jun Shin · Korean Journal of Applied Statistics · 2025
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.