Graph neural networks are architectures for learning invariant functions over graphs. A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at the heart of such limitations, since many functions to be learned rely on the ability of counting such patterns. Two prominent paradigms aim to address this limitation by enriching the graph features with subgraph or homomorphism pattern counts. In this work, we show that both of these approaches are sub-optimal in a certain sense and argue for a more fine-grained approach, which incorporates the homomorphism counts of all structures in the "basis" of the target pattern. This yields strictly more expressive architectures without incurring any additional overhead in terms of computational complexity compared to existing approaches. We prove a series of theoretical results on node-level and graph-level motif parameters and empirically validate them on standard benchmark datasets.

翻译：图神经网络是学习图上不变函数的架构。大量研究已探讨了图神经网络的性质，并指出了若干限制，尤其是其表达能力方面。图神经网络无法计数图中的某些模式（如环）是这些限制的核心原因，因为许多待学习函数依赖于此类模式的计数能力。两种主流范式通过子图或同态模式计数来增强图特征，试图解决这一限制。在本工作中，我们证明这两种方法在某种意义上均非最优，并主张采用一种更精细的方法，即将目标模式“基元”中所有结构的同态计数纳入考量。与现有方法相比，这在不增加计算复杂度额外负担的情况下，产生了表达能力严格更强的架构。我们在节点级和图级模体参数上证明了一系列理论结果，并在标准基准数据集上进行了实证验证。