揭示GNN消息传递本质是高效矩阵乘法，打破黑箱认知
Demystifying MPNNs: Message Passing as Merely Efficient Matrix Multiplication
- 将多层GNN的消息传递机制解析为迭代矩阵乘法，解释其聚合邻域信息的原理
- 发现深层GNN在稀疏图中性能下降主因是梯度问题，而非仅过平滑
- 提供理论框架解释模型在结构与特征混合任务中的行为，适合研究者理解机制
尽管图神经网络（GNN）取得了显著成功，但其设计主要依赖经验直觉而非理论理解。本文从三个基本方面全面分析了GNN的行为：(1) 证明 $k$-层消息传递神经网络通过迭代计算高效聚合 $k$-跳邻域信息；(2) 分析不同循环结构对邻域计算的影响；(3) 探讨结构-特征混合任务与纯结构任务中的表现差异。针对深层GNN，我们发现梯度相关问题在稀疏图中会显著影响性能，而不仅限于过平滑现象。同时分析了不同归一化方案对模型性能的影响，并揭示了在统一节点特征下GNN如何做出预测。本研究构建了一个理论框架，弥合了经验成功与理论理解之间的鸿沟。
原文摘要 · Abstract (English)
While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three fundamental aspects: (1) we establish that \textbf{$k$-layer} Message Passing Neural Networks efficiently aggregate \textbf{$k$-hop} neighborhood information through iterative computation, (2) analyze how different loop structures influence neighborhood computation, and (3) examine behavior across structure-feature hybrid and structure-only tasks. For deeper GNNs, we demonstrate that gradient-related issues, rather than just over-smoothing, can significantly impact performance in sparse graphs. We also analyze how different normalization schemes affect model performance and how GNNs make predictions with uniform node features, providing a theoretical framework that bridges the gap between empirical success and theoretical understanding.
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