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清晰的可表达性。然而，这类架构往往在实际任务中无法实现稳定的预测性能，限制了其实用价值。相比之下，基于全局注意力的模型（如图Transformer）在实践中表现出强劲性能，但将其表达能力与k-WL层次进行比较仍具挑战性，尤其是这些架构依赖位置或结构编码来实现其表达性和预测性能。为解决这一问题，我们证明了最近提出的Edge Transformer（一种作用于节点对而非节点的全局注意力模型）具有至少3-WL的表达能力。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或结构编码。