  Several recent papers have recently shown that higher order graph neural
networks can achieve better accuracy than their standard message passing
counterparts, especially on highly structured graphs such as molecules. These
models typically work by considering higher order representations of subgraphs
contained within a given graph and then perform some linear maps between them.
We formalize these structures as permutation equivariant tensors, or P-tensors,
and derive a basis for all linear maps between arbitrary order equivariant
P-tensors. Experimentally, we demonstrate this paradigm achieves state of the
art performance on several benchmark datasets.
