P-Tensors: a General Formalism for Constructing Higher Order Message Passing Networks
This provides a foundational advancement for researchers in graph representation learning, particularly in domains like molecular modeling, by unifying and generalizing existing approaches.
The paper tackles the problem of limited expressive power in graph neural networks by introducing P-tensors, a general framework for higher-order permutation equivariant message passing in subgraph neural networks, achieving state-of-the-art performance on benchmark molecular datasets.
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.