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的不变函数的架构。大量研究探讨了图神经网络的特性，并指出了若干限制，特别是其表达能力方面的局限。无法计数图中某些模式（如环）是这些限制的核心原因，因为许多待学习函数依赖于计数此类模式的能力。两种主流范式通过用子图或同态模式计数增强图特征来应对这一局限。在本工作中，我们表明这两种方法在某种意义上是次优的，并主张采用更细粒度的方案，该方案将目标模式“基”中所有结构的同态计数纳入考量。相较于现有方法，这在不增加额外计算复杂度的前提下，产生了严格更具表达力的架构。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。