可扩展的子图采样：基于电阻曲率

中文摘要 AI 辅助

子图采样降低了大规模图神经网络训练成本，但采样准则可能忽略边的几何作用。我们提出一个基于电阻曲率的采样框架，其核心是ERC-LG，一种适用于大规模图的曲率近似方法。ERC-LG将Johnson-Lindenstrauss投影与正则化的多GPU批量共轭梯度求解器相结合，避免了显式的拉普拉斯伪逆计算和完整嵌入存储。由此得到的曲率信息用于构建节点和边的采样概率，以生成GNN训练子图。实验表明，该方法与基于伪逆的曲率数值上一致，且相比仅用共轭梯度计算，运行时间更短。基于ERC-LG的采样变体在七个真实世界数据集的六个中，在下游节点分类任务上取得了最高平均准确率。

英文摘要

Subgraph sampling reduces the training cost of large-scale graph neural networks, but sampling criteria may overlook the geometric roles of edges. We propose a resistance-curvature-guided sampling framework built on ERC-LG, a curvature approximation method for large-scale graphs. ERC-LG combines Johnson-Lindenstrauss projections with regularized multi-GPU batched conjugate gradient solvers, avoiding explicit Laplacian pseudoinverse computation and full embedding storage. The resulting curvature informs node- and edge-sampling probabilities for constructing GNN training subgraphs. Experiments show numerical agreement with pseudoinverse-based curvature and reduced runtime compared with CG-only computation. ERC-LG-based sampling variants achieve the highest mean accuracy on six of seven real-world datasets in downstream node classification.

发表机构

• South China Normal University（华南师范大学）
• Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）

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