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Topological Graph Neural Networks
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Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.
Forward citations
Cited by 2 Pith papers
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Heat Kernel Goes Topological
TopoHKS defines a weighted combinatorial-complex Laplacian and heat kernel descriptor, claiming maximal expressive power; the supporting uniqueness theorem is incorrect.
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CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learning
CellCLAT applies parameter-perturbation contrastive learning to cellular complexes and adaptively trims 2-cells to improve downstream graph classification.
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