Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

翻译：图神经网络（GNNs）是图学习问题中流行的模型。GNNs在许多实际任务中展现出强大的实证性能，但其理论性质尚未完全阐明。本文从GNNs表达能力的角度，探究了GNNs能否利用图结构。在分析中，我们考虑了由隐藏节点特征控制的图生成过程，这些隐藏特征包含了图结构的所有信息。该框架的一个典型示例是基于隐藏特征构建的kNN图。我们的主要结果表明，即使所有节点特征（包括隐藏特征本身和任何间接线索）均不可用，GNNs也能仅从输入图中恢复隐藏节点特征。GNNs还可将恢复的节点特征用于下游任务。这些结果表明，GNNs能够自主充分利用图结构，实际上GNNs可以同时利用隐藏和显式节点特征处理下游任务。在实验中，我们通过使用基于理论分析构建的GNN架构成功恢复隐藏特征，验证了结果的正确性。