AI 中文总结
针对图神经网络的过挤压问题，提出基于群论的Schreier-Coset图重连方法，可降低5%-40%有效电阻，缓解连接瓶颈并保持竞争力准确率。
AI 中文摘要
图神经网络（GNNs）的信息流受限于过挤压问题，结构瓶颈阻碍长程信息传播，图重连方法通过修改图拓扑缓解该问题，但现有方法常引入严重结构与计算瓶颈、无法保留原图关键属性且大幅增加边数。本文提出Schreier-Coset图重连（SCGR），这是一种基于群论的重连方法，利用特殊线性群衍生的Schreier-Coset图增强输入图，该方法有理论保证，生成的图具有谱隙和有界有效电阻，为长程通信创建低电阻旁路。实验评估显示，SCGR在各类学习任务中可降低5%-40%的有效电阻，在缓解连接瓶颈的同时保持了有竞争力的准确率。
英文摘要
The information flow in the graph neural networks (GNNs) is fundamentally constrained by over-squashing, where structural bottlenecks impede long range information propagation. Graph-rewiring methods, which modify graph topology, have been extensively used to alleviate this. However, existing approaches often introduce prohibitive structural and computational bottlenecks, fail to preserve the critical properties of original graphs, and increase the edge counts massively. We introduce a novel method Schreier-Coset Graph Rewiring , a group-theoretic rewiring method that augments the input graph with a Schreier-Coset graph derived from a special linear group. Our method provides theoretical guarantees, a graph that exhibits spectral gap and a bounded effective resistance, creating a low-resistance bypass for long-range communication. Empirical evaluations demonstrate that SCGR reduces effective resistance by 5-40% across various learning tasks, effectively mitigating connectivity bottlenecks while maintaining competitive accuracy.
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