Graph Neural Network (GNN) aggregates the neighborhood of each node into the node embedding and shows its powerful capability for graph representation learning. However, most existing GNN variants aggregate the neighborhood information in a fixed non-injective fashion, which may map different graphs or nodes to the same embedding, reducing the model expressiveness. We present a theoretical framework to design a continuous injective set function for neighborhood aggregation in GNN. Using the framework, we propose expressive GNN that aggregates the neighborhood of each node with a continuous injective set function, so that a GNN layer maps similar nodes with similar neighborhoods to similar embeddings, different nodes to different embeddings and the equivalent nodes or isomorphic graphs to the same embeddings. Moreover, the proposed expressive GNN can naturally learn expressive representations for graphs with continuous node attributes. We validate the proposed expressive GNN (ExpGNN) for graph classification on multiple benchmark datasets including simple graphs and attributed graphs. The experimental results demonstrate that our model achieves state-of-the-art performances on most of the benchmarks.

翻译：Neural Network (GNN) 将每个节点的周围集合到节点嵌入中,并显示其强大的图形演示学习能力。 然而,大多数现有的 GNN 变量以固定的非定向方式将周边信息汇总起来, 它可以绘制不同的图形或节点到相同的嵌入中, 减少模型的表达性。 我们提出了一个理论框架, 用于设计 GNN 中邻居群集的连续定位设置功能。 使用这个框架, 我们提议表达式 GNN, 将每个节点的周围集中成一个连续的预测性功能, 以便让 GNNN 绘制一个类似相近于类似嵌入的节点、 不同嵌入中的不同节点和与相同嵌入中相同的节点或变形图。 此外, 提议的表达式 GNN 能够自然地学习具有连续节点属性的图形的表达式表达式。 我们验证了拟议的表达式 GNN (ExGN) 用于多个基准数据集的图表分类, 包括简单图表和可归的图表。 实验结果显示我们的模型在大多数基准上达到状态的状态表现。