Several recent papers have proposed increasing the expressive power of graph neural networks by exploiting subgraphs or other topological structures. In parallel, researchers have investigated higher order permutation equivariant networks. In this paper we tie these two threads together by providing a general framework for higher order permutation equivariant message passing in subgraph neural networks. In this paper we introduce a new type of mathematical object called $P$-tensors, which provide a simple way to define the most general form of permutation equivariant message passing in both the above two categories of networks. We show that the P-Tensors paradigm can achieve state-of-the-art performance on benchmark molecular datasets.

翻译：近期多篇论文提出通过利用子图或其他拓扑结构来增强图神经网络的表达能力。与此同时，研究者们也在探索高阶置换等变网络。本文通过为子图神经网络中的高阶置换等变消息传递提供一个通用框架，将这两个研究方向结合起来。我们引入了一种称为$P$-张量的新型数学对象，它能够以简洁的方式定义上述两类网络中最通用的置换等变消息传递形式。实验表明，P-张量范式在基准分子数据集上能够达到最先进的性能。