从消息传递反馈中学习传播几何

中文摘要 AI 辅助

学习局部几何使图神经网络（GNNs）能够自适应地比较和整合邻域信息。然而，从聚合表示中估计几何可能会忽略单个消息之间的差异以及特征维度之间的依赖关系。我们提出了GeoF，一个通过消息传递反馈联合演化节点特征和传播几何的循环框架。每个节点维护一个局部对称正定几何，该几何从结构感知的原型图集初始化，并以块对数三角坐标参数化。在每一步，几何决定邻域权重，而三角框架传输将变换后的源消息映射到目标节点的局部坐标后再进行聚合。对齐消息与变换后的目标状态之间的残差的加权二阶统计量捕获方向变化和块内依赖，产生几何更新目标。一个共享控制器通过任务监督学习互补的修正。一个有界的对数三角更新结合这些修正、目标和先前的几何状态，同时保持正定性。该几何指导后续传播，从而闭合反馈循环。由于参数在循环步骤间共享，任务特定的读出支持节点分类、链接预测和图分类。在基准数据集上的实验表明，GeoF始终优于最先进的GNN基线。

英文摘要

Learning local geometry enables graph neural networks (GNNs) to adapt how they compare and integrate neighborhood information. However, estimating geometry from aggregated representations can overlook variation among individual messages and dependencies across feature dimensions. We propose GeoF, a recurrent framework that jointly evolves node features and propagation geometry through message-passing feedback. Each node maintains a local symmetric positive-definite geometry, initialized from a structure-aware prototype atlas and parameterized in block log-triangular coordinates. At each step, the geometry determines neighborhood weights, while triangular frame transport maps transformed source messages into the target node's local coordinates before aggregation. Weighted second-order statistics of residuals between aligned messages and the transformed target state capture directional variation and within-block dependencies, yielding a geometric update target. A shared controller learns complementary corrections through task supervision. A bounded log-triangular update combines these corrections, the target, and the previous geometric state while preserving positive definiteness. The geometry governs subsequent propagation, closing the feedback loop. With parameters shared across recurrent steps, task-specific readouts support node classification, link prediction, and graph classification. Experiments on benchmark datasets show that GeoF consistently outperforms state-of-the-art GNN baselines.

发表机构

• The Chinese University of Hong Kong（香港中文大学）
• The Education University of Hong Kong（香港教育大学）
• National University of Defense Technology（国防科技大学）
• Hebei University of Technology（河北工业大学）
• City University of Hong Kong（香港城市大学）
• Huazhong University of Science and Technology（华中科技大学）

机构由 AI 辅助整理，请以论文原文为准。