Equivariant Heterogeneous Graph Networks

Many real-world datasets include multiple distinct types of entities and relations, and so they are naturally best represented by heterogeneous graphs. However, the most common forms of neural networks operating on graphs either assume that their input graphs are homogeneous, or they convert heterogeneous graphs into homogeneous ones, losing valuable information in the process. Any neural network that acts on graph data should be equivariant or invariant to permutations of nodes, but this is complicated when there are multiple distinct node and edge types. With this as motivation, we design graph neural networks that are composed of linear layers that are maximally expressive while being equivariant only to permutations of nodes within each type. We demonstrate their effectiveness on heterogeneous graph node classification and link prediction benchmarks.