On the Utilization of Unique Node Identifiers in Graph Neural Networks

TL;DR

This paper explores the use of permutation-equivariant unique node identifiers in graph neural networks, proposing a regularization method that improves generalization, extrapolation, and training efficiency, achieving state-of-the-art results.

Contribution

It introduces a novel regularization approach for UID models to maintain permutation-equivariance, enhancing GNN performance and theoretical understanding.

Findings

Improved generalization and extrapolation in GNNs with UID regularization.

Faster training convergence compared to baseline models.

State-of-the-art performance on BREC expressiveness benchmark.

Abstract

Graph Neural Networks have inherent representational limitations due to their message-passing structure. Recent work has suggested that these limitations can be overcome by using unique node identifiers (UIDs). Here we argue that despite the advantages of UIDs, one of their disadvantages is that they lose the desirable property of permutation-equivariance. We thus propose to focus on UID models that are permutation-equivariant, and present theoretical arguments for their advantages. Motivated by this, we propose a method to regularize UID models towards permutation equivariance, via a contrastive loss. We empirically demonstrate that our approach improves generalization and extrapolation abilities while providing faster training convergence. On the recent BREC expressiveness benchmark, our proposed method achieves state-of-the-art performance compared to other random-based approaches.