图神经网络扩展的理论比较
A Theoretical Comparison of Graph Neural Network Extensions
摘要：
我们研究并比较了不同的图神经网络扩展，这些扩展提高了GNN的表达能力，超出了Weisfeiler-Leman测试。我们专注于（i）基于高阶WL方法的GNNs，（ii）预处理图中的小子结构的GNNs，（iii）预处理图到小半径的GNNs，以及（iv）稍微扰动图以计算嵌入的GNNs。首先，我们对最后一个扩展做了一个简单的改进，它严格地提高了GNN变体的表达能力。然后，作为我们的主要结果，我们通过一系列的例子，可以区分的扩展，但不是由另一个结构，这些扩展的表达能力相互比较。我们还展示了负面的例子，是特别具有挑战性的每个扩展，我们证明了几个索赔的能力，这些扩展计算集团和周期图。
英文摘要：
We study and compare different Graph Neural Network extensions that increase the expressive power of GNNs beyond the Weisfeiler-Leman test. We focus on (i) GNNs based on higher order WL methods, (ii) GNNs that preprocess small substructures in the graph, (iii) GNNs that preprocess the graph up to a small radius, and (iv) GNNs that slightly perturb the graph to compute an embedding. We begin by presenting a simple improvement for this last extension that strictly increases the expressive power of this GNN variant. Then, as our main result, we compare the expressiveness of these extensions to each other through a series of example constructions that can be distinguished by one of the extensions, but not by another one. We also show negative examples that are particularly challenging for each of the extensions, and we prove several claims about the ability of these extensions to count cliques and cycles in the graph.
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