FSW-GNN: A Bi-Lipschitz WL-Equivalent Graph Neural Network

Yonatan Sverdlov, Yair Davidson, Nadav Dym, Tal Amir

Keywords: Bi-Lipschitzness, Weisfeiler Leman, Graph Embedding, Graph Neural Network, MPNN

TL;DR: We propose the first bi-Lipschitz graph neural network and Euclidean embedding for graphs equivalent to the 1-WL test

Abstract:

Many of the most popular graph neural networks fall into the category of Message Passing Neural Networks (MPNNs). Famously, MPNNs ability to distinguish between graphs is limited to graphs separable by the Weisfeiler-Leman (WL) graph isomorphism test, and the strongest MPNNs, in terms of separation power, are those which are WL-equivalent.

Recently, it was shown that the quality of separation provided by standard WL-equivalent MPNN can be very low, resulting in WL-separable graphs being mapped to very similar, hardly distinguishable features.

This paper addresses this issue by seeking bi-Lipschitz continuity guarantees for MPNNs. We demonstrate that, in contrast with standard summation-based MPNNs, which lack bi-Lipschitz properties, our proposed model provides a bi-Lipschitz graph embedding with respect to two standard graph metrics. Empirically, we show that our MPNN is competitive with standard MPNNs for several graph learning tasks, and is far more accurate on long-range tasks.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 2592