Cayley Graph Propagation（凯莱图传播）
Cayley Graph Propagation
AI总结：
针对图神经网络的过挤压问题，提出在完整凯莱图结构上传播信息的CGP方法，避免截断破坏扩张特性，在多个真实数据集上性能优于EGP，且比肩或超越高复杂度图重连技术。
摘要：
尽管图神经网络（GNN）在建模图结构数据方面已有大量成功案例，但它们极易出现过挤压（over-squashing）问题——当任务需要在远距离节点对之间混合信息时，该问题就会凸显。为解决这一问题，已有研究提出通过重连图结构来改善信息流；另有大量研究致力于发现并预计算无瓶颈的图结构，以缓解过挤压问题。在数学领域，一类广受认可的无瓶颈图是扩张图（expander graph），此前的研究Expander Graph Propagation（EGP，扩张图传播）提出将一类知名的扩张图族——特殊线性群$\text{SL}(2,\text{Z}_n)$的凯莱图——用作GNN的计算模板。但EGP中使用的计算图会被截断，以匹配给定的输入图。本研究表明，这种截断会破坏扩张图备受重视的扩张特性。我们提出CGP方法，该方法在完整的凯莱图结构上传播信息，从而确保图结构无瓶颈，更好地缓解过挤压问题。我们在多个真实世界数据集上的实验证据表明，CGP不仅相比EGP实现了显著的性能提升，而且性能与计算复杂度较高的图重连技术相当甚至更优。
英文摘要：
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 -- Expander Graph Propagation (EGP) -- proposing the use of a well-known expander graph family -- the Cayley graphs of the $\mathrm{SL}(2,\mathbb{Z}_n)$ special linear group -- 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.
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