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	トポロジカル深層学習	グラフニューラルネットワーク
分野	位相幾何学	ネットワーク分析
系統	Machine learning	Process / pipeline
提唱年	2023	2017–2018 (major variants)
提唱者	Topological deep learning literature	—
種類	Higher-order message-passing framework	Deep learning on graph-structured data
原典	Hajij, M., et al. (2023). Topological deep learning: Going beyond graph data. arXiv preprint.	Kipf, T.N. & Welling, M. (2017). Semi-Supervised Classification with Graph Convolutional Networks. International Conference on Learning Representations (ICLR).
別名	TDL, Topological Neural Networks, Higher-Order Deep Learning, Topolojik Derin Öğrenme	GNN, GCN, GAT, GraphSAGE
関連	3	5
概要	Topological Deep Learning (TDL) is a framework that extends deep learning beyond graphs to higher-order topological domains such as simplicial complexes, cell complexes, and hypergraphs. Formalized by Hajij et al. (2023), TDL provides a unified mathematical language for defining message-passing schemes across cells of different ranks, enabling neural networks to model multi-way interactions that pairwise graph edges cannot capture. It is relevant to researchers working with relational, geometric, or biological data exhibiting group-level dependencies.	A Graph Neural Network (GNN) is a deep learning architecture that operates directly on graph-structured data by combining node features with structural information through iterative neighborhood message passing. The three canonical variants — the Graph Convolutional Network (GCN) introduced by Kipf and Welling in 2017, the Graph Attention Network (GAT) introduced by Veličković et al. in 2018, and GraphSAGE — differ in how they aggregate neighbor information: GCN applies a spectral convolution over the full adjacency, GAT weights neighbors by learned attention scores, and GraphSAGE samples and aggregates local neighborhoods inductively, enabling generalization to unseen nodes.