用线性变换统一聚合图中直接与间接邻居，提升信息传递效率。
Aggregating Direct and Indirect Neighbors through Graph Linear Transformations
- 基于图结构设计单一线性算子，实现直接与多跳邻居特征融合。
- 在同质与异质数据集上表现优于传统消息传递GNN和动态邻域模型。
- 可解释性强，不同构造方式对应不同传播偏好，如选边或平滑结构。
图神经网络通常依赖局部消息传递机制，需增加深度才能捕捉长程依赖。本文提出图线性变换（Graph Linear Transformations），通过图结构导出的单一明确线性算子，实现图上直接与间接邻居的特征混合。将图视为行走可求和的高斯图模型，利用高斯信念传播计算该变换，使每个节点无需显式枚举多跳路径即可聚合远端信息。我们发现，底层精度矩阵的不同构造会引发不同且可解释的传播偏差，从选择性边级交互到均匀结构平滑。实验表明，该方法在同质与异质基准数据集上均达到或超过局部消息传递GNN及动态邻域聚合模型的性能。
原文摘要 · Abstract (English)
Graph neural networks (GNN) typically rely on localized message passing, requiring increasing depth to capture long range dependencies. In this work, we introduce Graph Linear Transformations, a linear transformation that realizes direct and indirect feature mixing on graphs through a single, well-defined linear operator derived from the graph structure. By interpreting graphs as walk-summable Gaussian graphical models, we compute these transformations via Gaussian Belief Propagation, enabling each node to aggregate information from both direct and indirect neighbors without explicit enumeration of multi-hop paths. We show that different constructions of the underlying precision matrix induce distinct and interpretable propagation biases, ranging from selective edge-level interactions to uniform structural smoothing, and that Graph Linear Transformations can achieve competitive or superior performance compared to both local message-passing GNNs and dynamic neighborhood aggregation models across homophilic and heterophilic benchmark datasets.
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