How would randomly shuffling feature vectors among nodes from the same class
affect graph neural networks (GNNs)? The feature shuffle, intuitively, perturbs
the dependence between graph topology and features (A-X dependence) for GNNs to
learn from. Surprisingly, we observe a consistent and significant improvement
in GNN performance following the feature shuffle. Having overlooked the impact
of A-X dependence on GNNs, the prior literature does not provide a satisfactory
understanding of the phenomenon. Thus, we raise two research questions. First,
how should A-X dependence be measured, while controlling for potential
confounds? Second, how does A-X dependence affect GNNs? In response, we (i)
propose a principled measure for A-X dependence, (ii) design a random graph
model that controls A-X dependence, (iii) establish a theory on how A-X
dependence relates to graph convolution, and (iv) present empirical analysis on
real-world graphs that aligns with the theory. We conclude that A-X dependence
mediates the effect of graph convolution, such that smaller dependence improves
GNN-based node classification.

如何通过对节点之间的特征向量进行随机洗牌来影响图神经网络 (GNNs)? 我们观察到特征洗牌会显著提高 GNN 的性能，并提出一种度量 A-X 依赖关系、设计控制 A-X 依赖关系的随机图模型、建立 A-X 依赖关系与图卷积之间的理论联系，并通过实证分析验证了该理论。我们的研究表明 A-X 依赖关系在图卷积中起到调节的作用，较小的依赖关系会提高基于 GNN 的节点分类。