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

Understand

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.