Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world tasks, limiting their practical impact. In contrast, global attention-based models such as graph transformers demonstrate strong performance in practice, but comparing their expressive power with the k-WL hierarchy remains challenging, particularly since these architectures rely on positional or structural encodings for their expressivity and predictive performance. To address this, we show that the recently proposed Edge Transformer, a global attention model operating on node pairs instead of nodes, has at least 3-WL expressive power. Empirically, we demonstrate that the Edge Transformer surpasses other theoretically aligned architectures regarding predictive performance while not relying on positional or structural encodings.

翻译：基于k维Weisfeiler-Leman（k-WL）层次的图学习架构在理论上具有良好理解的表达能力。然而，这类架构在实际任务中往往无法提供稳健的预测性能，限制了其实践影响力。相比之下，图Transformer等基于全局注意力的模型在实践中展现出强大性能，但将其表达能力与k-WL层次进行比较仍具挑战性，尤其因为这些架构依赖于位置编码或结构编码来实现其表达能力和预测性能。为应对这一问题，我们证明了近期提出的Edge Transformer（一种在节点对而非节点上操作的全局注意力模型）至少具有3-WL表达能力。实验结果表明，Edge Transformer在预测性能上超越了其他理论对齐的架构，同时不依赖任何位置编码或结构编码。