We investigate the representation power of graph neural networks in the
semi-supervised node classification task under heterophily or low homophily,
i.e., in networks where connected nodes may have different class labels and
dissimilar features. Many popular GNNs fail to generalize to this setting, and
are even outperformed by models that ignore the graph structure (e.g.,
multilayer perceptrons). Motivated by this limitation, we identify a set of key
designs -- ego- and neighbor-embedding separation, higher-order neighborhoods,
and combination of intermediate representations -- that boost learning from the
graph structure under heterophily. We combine them into a graph neural network,
H2GCN, which we use as the base method to empirically evaluate the
effectiveness of the identified designs. Going beyond the traditional
benchmarks with strong homophily, our empirical analysis shows that the
identified designs increase the accuracy of GNNs by up to 40% and 27% over
models without them on synthetic and real networks with heterophily,
respectively, and yield competitive performance under homophily.

该研究通过节约和邻居嵌入、高阶邻居和中间表示的结合，设计出一种草图神经网络（H2GCN），并通过实验表明其在半监督节点分类任务下，具有比传统模型更高的预测准确率，尤其对于异质性网络（即一对连接的节点可能具有不同的类别标签和不同的特征）表现更出色。