WL-Tree: a New Tool for Analyzing Graph Neural Networks

Liping Liu, Jiaxing He, Jacob Boerma, Xiaohui Chen

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: graph learning, graph neural networks, 1-WL, color refinement, node representation

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TL;DR: A new computation model for graph neural networks.

Abstract: The 1-WL algorithm provides a clean algorithmic model for graph neural networks (GNNs) that run with a message-passing architecture. Previous work compares a GNN against the 1-WL algorithm to analyze its expressiveness, and develops new GNN variants under the guidance of the comparison. In this work, we propose WL-Trees, a new algorithmic model of GNNs. We compute WL-trees using Breadth-First-Searches on the input graph. We show that WL-trees are equivalent to colors computed from the 1-WL algorithm. Despite the equivalence, WL-trees deepen the understanding of a graph’s structural information encoded in node representations. They also serve as an algorithmic model for improved GNNs to analyze their expressiveness from a new angle.

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Submission Number: 2059