We address two fundamental questions about graph neural networks (GNNs).
First, we prove that several important graph properties cannot be computed by
GNNs that rely entirely on local information. Such GNNs include the standard
message passing models, and more powerful spatial variants that exploit local
graph structure (e.g., via relative orientation of messages, or local port
ordering) to distinguish neighbors of each node. Our treatment includes a novel
graph-theoretic formalism. Second, we provide the first data dependent
generalization bounds for message passing GNNs. This analysis explicitly
accounts for the local permutation invariance of GNNs. Our bounds are much
tighter than existing VC-dimension based guarantees for GNNs, and are
comparable to Rademacher bounds for recurrent neural networks.

本研究关注图神经网络的本质问题：无法仅仅依靠局部信息计算多个重要的图形特征；同时提出了信息传递图神经网络的第一个数据相关泛化界限，这一分析专门考虑了 GNN 局部置换不变性，该边界比现有的基于 VC 维度的 GNN 保证要紧密，与循环神经网络的 Rademacher 界限相当。