图神经网络的同态计数：关键在于基
Homomorphism Counts for Graph Neural Networks: All About That Basis
AI总结：
本文提出将目标模式基中所有结构的同态计数纳入图神经网络，在不增加计算开销的前提下提升表达能力，并通过理论和实验验证其优于现有子图或同态计数方法。
摘要：
大量工作研究了图神经网络的性质，并指出了若干局限性，尤其是其表达能力方面的不足。这种不足的核心在于它们无法对图中的某些模式（例如环）进行计数，因为许多需要学习的函数都依赖于对这类模式进行计数的能力。两种主流范式试图通过用子图或同态模式计数来丰富图特征，以解决这一局限性。在这项工作中，我们表明这两种方法在某种意义上都是次优的，并主张采用一种更细粒度的方法，即将目标模式的“基”中所有结构的同态计数纳入其中。与现有方法相比，这在不增加任何额外计算复杂度开销的情况下，产生了严格更具表达能力的架构。我们证明了关于节点级和图级motif参数的一系列理论结果，并在标准基准数据集上对其进行了实证验证。
英文摘要：
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.
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