EDEN: A Plug-in Equivariant Distance Encoding to Beyond the 1-WL Test

• URL: http://arxiv.org/abs/2211.10739v1
• Date: Sat, 19 Nov 2022 16:36:28 GMT
• Title: EDEN: A Plug-in Equivariant Distance Encoding to Beyond the 1-WL Test
• Authors: Chang Liu, Yuwen Yang, Yue Ding, Hongtao Lu
• Abstract summary: We propose a plug-in Equivariant Distance ENcoding (EDEN) for graph neural networks (MPNNs) EDEN is derived from a series of interpretable transformations on the graph's distance matrix. Experiments on real-world datasets show that combining EDEN with conventional GNNs surpasses recent advanced GNNs.
• Score: 17.027460848621434
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The message-passing scheme is the core of graph representation learning. While most existing message-passing graph neural networks (MPNNs) are permutation-invariant in graph-level representation learning and permutation-equivariant in node- and edge-level representation learning, their expressive power is commonly limited by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test. Recently proposed expressive graph neural networks (GNNs) with specially designed complex message-passing mechanisms are not practical. To bridge the gap, we propose a plug-in Equivariant Distance ENcoding (EDEN) for MPNNs. EDEN is derived from a series of interpretable transformations on the graph's distance matrix. We theoretically prove that EDEN is permutation-equivariant for all level graph representation learning, and we empirically illustrate that EDEN's expressive power can reach up to the 3-WL test. Extensive experiments on real-world datasets show that combining EDEN with conventional GNNs surpasses recent advanced GNNs.

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