发表机构
Vellore Institute of Technology (VIT-AP)（维洛尔理工大学（VIT-AP））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究图神经网络长距离传播问题，提出谱流证书（SFCs），通过图的归一化拉普拉斯矩阵快速计算单个标量，无需训练和标记数据，能在训练前预测精度，为图神经网络部署提供初步筛选，解释能力强。
AI 中文摘要
图神经网络通过局部消息传递传播信息，但图拓扑结构可能会妨碍长距离任务的解决。在部署图神经网络时，目前没有低成本方法在训练前了解图结构是否能使信息在远距离节点间有效传播。本文提出谱流证书（SFCs），它由图的归一化拉普拉斯矩阵在数秒内计算得出，无需模型训练和标记数据。SFC将图的代数连通性与选定的消息传递深度融合为一个数字，衡量在可用深度预算内可穿越关键谱瓶颈的程度。与原始谱隙不同，SFC随层数增加而变化，携带更多诊断信息。与经典结构统计量相比，SFC在解释训练后的图神经网络长距离精度方差方面能力更强。在多个合成图族和真实分子图拓扑上的实验表明，SFC能在计算梯度前预测训练精度，为图神经网络部署提供了原则性的初步筛选。
英文摘要
Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks. When we deploy GNNs on new graphs, there is currently no inexpensive way to know, before training begins, whether the graphs' structures will allow information to travel far enough between distant nodes. We address this gap by proposing Spectral Flow Certificates (SFCs), single scalars computed from the graphs' normalised Laplacians in seconds, requiring no model training and no labelled data. An SFC fuses a graph's algebraic connectivity with the chosen message-passing depth into one number that measures how much of the critical spectral bottleneck can be traversed within the available depth budget. Unlike raw spectral gaps, which are static and depth-agnostic, SFCs adapt as the number of layers increases and therefore carry strictly more diagnostic information when depths vary. Compared with classical structural statistics such as average effective resistance and graph diameter, SFCs explain more than twice as much variance in trained GNN long-range accuracy. Across twenty-five synthetic graph families spanning paths, cycles, grids, regular graphs, and random graphs, SFCs predict trained accuracy before any gradients are computed, achieving explanatory power above ninety percent at all tested depths. The same predictive relationships hold on one hundred fifty real molecular graph topologies drawn from three independent benchmark datasets, confirming that the findings are not artefacts of their synthetic construction. Taken together, these results show that a single eigenvalue computation is sufficient to flag topology-limited graphs before committing to expensive training pipelines, providing a principled first filter for GNN deployments.
Comments16 pages, 15 figures
