P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networks

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.