Topological Graph Neural Networks

• URL: http://arxiv.org/abs/2102.07835v1
• Date: Mon, 15 Feb 2021 20:27:56 GMT
• Title: Topological Graph Neural Networks
• Authors: Max Horn, Edward De Brouwer, Michael Moor, Yves Moreau, Bastian Rieck, Karsten Borgwardt
• Abstract summary: We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. Augmenting GNNs with our layer leads to beneficial predictive performance, both on synthetic data sets and on real-world data.
• Score: 14.349152231293928
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 of the Weisfeiler--Lehman test of isomorphism. Augmenting GNNs with our layer leads to beneficial predictive performance, both on synthetic data sets, which can be trivially classified by humans but not by ordinary GNNs, and on real-world data.

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