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

TL;DR

EDEN is a plug-in encoding that enhances message-passing neural networks' ability to distinguish graph structures beyond the 1-WL test by leveraging interpretable distance matrix transformations.

Contribution

We introduce EDEN, a permutation-equivariant encoding that significantly improves GNN expressive power, reaching up to the 3-WL test, with practical benefits demonstrated on real datasets.

Findings

EDEN combined with GNNs surpasses recent advanced GNNs.

EDEN's expressive power reaches up to the 3-WL test.

Extensive experiments validate EDEN's effectiveness.

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.