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, Over-squashing, oversmoothing

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

Abstract:

Famously, the ability of Message Passing Neural Networks (MPNN) to distinguish between graphs is limited to graphs separable by the Weisfeiler-Lemann (WL) graph isomorphism test, and the strongest MPNNs, in terms of separation power, are WL-equivalent.
However, it was demonstrated 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 outputs. This phenomenon can be explained by the recent observation that standard MPNNs are not lower-Lipschitz.
This paper addresses this issue by introducing FSW-GNN, the first MPNN that is fully bi-Lipschitz with respect to standard WL-equivalent graph metrics. Empirically, we show that our MPNN is competitive with standard MPNNs for several graph learning tasks and is far more accurate in long-range tasks, due to its ability to avoid oversmoothing and oversquashing.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 65