In spite of the plethora of success stories with graph neural networks (GNNs) on modelling graph-structured data, they are notoriously vulnerable to over-squashing, whereby tasks necessitate the mixing of information between distance pairs of nodes. To address this problem, prior work suggests rewiring the graph structure to improve information flow. Alternatively, a significant body of research has dedicated itself to discovering and precomputing bottleneck-free graph structures to ameliorate over-squashing. One well regarded family of bottleneck-free graphs within the mathematical community are expander graphs, with prior work$\unicode{x2014}$Expander Graph Propagation (EGP)$\unicode{x2014}$proposing the use of a well-known expander graph family$\unicode{x2014}$the Cayley graphs of the $\mathrm{SL}(2,\mathbb{Z}_n)$ special linear group$\unicode{x2014}$as a computational template for GNNs. However, in EGP the computational graphs used are truncated to align with a given input graph. In this work, we show that truncation is detrimental to the coveted expansion properties. Instead, we propose CGP, a method to propagate information over a complete Cayley graph structure, thereby ensuring it is bottleneck-free to better alleviate over-squashing. Our empirical evidence across several real-world datasets not only shows that CGP recovers significant improvements as compared to EGP, but it is also akin to or outperforms computationally complex graph rewiring techniques.

翻译：尽管图神经网络（GNN）在建模图结构数据方面取得了诸多成功，但它们普遍易受过度挤压的影响，即任务需要混合距离较远的节点对之间的信息。为解决此问题，先前的研究建议对图结构进行重布线以改善信息流。此外，大量研究致力于发现并预计算无瓶颈的图结构以缓解过度挤压。在数学界，一类备受推崇的无瓶颈图是扩展图，先前工作——扩展图传播（EGP）——提出使用一个著名的扩展图族，即特殊线性群 $\mathrm{SL}(2,\mathbb{Z}_n)$ 的凯莱图，作为GNN的计算模板。然而，在EGP中，所使用的计算图被截断以与给定的输入图对齐。本文中，我们证明截断会损害所期望的扩展性质。相反，我们提出了CGP，一种在完整的凯莱图结构上传播信息的方法，从而确保其无瓶颈，以更好地缓解过度挤压。我们在多个真实世界数据集上的实证证据不仅表明CGP相较于EGP恢复了显著的性能提升，而且其效果与计算复杂的图重布线技术相当甚至更优。