The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet rarely adopted when developing expressive GNNs. This paper proposes to maximize the expressivity of GNNs by graph canonization, then the power of such GNNs is studies from the perspective of model stability. A stable GNN will map similar graphs to close graph representations in the vectorial space, and the stability of GNNs is critical to generalize their performance to unseen graphs. We theoretically reveal the trade-off of expressivity and stability in graph-canonization-enhanced GNNs. Then we introduce a notion of universal graph canonization as the general solution to address the trade-off and characterize a widely applicable sufficient condition to solve the universal graph canonization. A comprehensive set of experiments demonstrates the effectiveness of the proposed method. In many popular graph benchmark datasets, graph canonization successfully enhances GNNs and provides highly competitive performance, indicating the capability and great potential of proposed method in general graph representation learning. In graph datasets where the sufficient condition holds, GNNs enhanced by universal graph canonization consistently outperform GNN baselines and successfully improve the SOTA performance up to $31\%$, providing the optimal solution to numerous challenging real-world graph analytical tasks like gene network representation learning in bioinformatics.

翻译：图神经网络（GNN）的表达能力近年被广泛研究，以揭示设计更强大GNN的原则。图规范化是区分非同构图的典型方法，但在开发具有表达能力的GNN时却鲜少采用。本文提出通过图规范化最大化GNN的表达能力，进而从模型稳定性的角度研究此类GNN的能力。稳定的GNN会将相似图映射到向量空间中相近的图表示，而GNN的稳定性对其泛化到未见图上的性能至关重要。我们从理论上揭示了图规范化增强型GNN中表达能力与稳定性的权衡关系。随后引入通用图规范化的概念作为解决这一权衡的通用方案，并刻画了实现通用图规范化的普适充分条件。大量实验证明了所提方法的有效性。在许多流行的图基准数据集中，图规范化成功增强了GNN并提供了极具竞争力的性能，表明所提方法在通用图表示学习中具有强大能力与巨大潜力。在满足充分条件的图数据集中，通用图规范化增强型GNN始终优于GNN基线，并成功将当前最优性能提升高达31%，为生物信息学中基因网络表示学习等众多具有挑战性的真实图分析任务提供了最优解。