On the Utilization of Unique Node Identifiers in Graph Neural Networks
This work addresses a fundamental problem in graph learning for researchers and practitioners by providing an incremental improvement to enhance model expressiveness while maintaining desirable properties.
The paper tackles the representational limitations of Graph Neural Networks by addressing the loss of permutation-equivariance when using unique node identifiers, proposing a regularization method that improves generalization and extrapolation with faster training convergence, achieving state-of-the-art performance on the BREC benchmark.
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.