Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional graph representations. Graph neural networks (GNNs) are currently the most popular model in graph embedding approaches. However, standard GNNs in the neighborhood aggregation paradigm suffer from limited discriminative power in distinguishing \emph{high-order} graph structures as opposed to \emph{low-order} structures. To capture high-order structures, researchers have resorted to motifs and developed motif-based GNNs. However, existing motif-based GNNs still often suffer from less discriminative power on high-order structures. To overcome the above limitations, we propose Motif Graph Neural Network (MGNN), a novel framework to better capture high-order structures, hinging on our proposed motif redundancy minimization operator and injective motif combination. First, MGNN produces a set of node representations w.r.t. each motif. The next phase is our proposed redundancy minimization among motifs which compares the motifs with each other and distills the features unique to each motif. Finally, MGNN performs the updating of node representations by combining multiple representations from different motifs. In particular, to enhance the discriminative power, MGNN utilizes an injective function to combine the representations w.r.t. different motifs. We further show that our proposed architecture increases the expressive power of GNNs with a theoretical analysis. We demonstrate that MGNN outperforms state-of-the-art methods on seven public benchmarks on both node classification and graph classification tasks.

翻译：图可以建模实体间复杂的相互作用，这种相互作用自然出现在许多重要应用中。这些应用通常可归结为标准图学习任务，其中关键步骤是学习低维图表示。图神经网络（GNN）是目前图嵌入方法中最流行的模型。然而，标准GNN在邻域聚合范式中，区分高阶图结构与低阶结构的能力有限。为捕捉高阶结构，研究者转向使用模体并开发了基于模体的GNN。但现有基于模体的GNN在高阶结构上仍常缺乏足够区分力。为克服上述局限，我们提出主题图神经网络（MGNN），这是一种依托于所提模体冗余最小化算子和单射模体组合的全新框架，能更有效捕捉高阶结构。首先，MGNN为每个模体生成一组节点表示。下一阶段是所提的模体间冗余最小化，该步骤比较不同模体并蒸馏出各模体特有的特征。最后，MGNN通过组合来自不同模体的多重表示来更新节点表示。特别地，为增强区分力，MGNN采用单射函数组合不同模体的表示。我们进一步通过理论分析证明所提架构增强了GNN的表达能力。实验表明，在节点分类和图分类任务的七个公开基准上，MGNN性能优于当前最先进方法。