  Graph representation learning has made major strides over the past decade.
However, in many relational domains, the input data are not suited for simple
graph representations as the relationships between entities go beyond pairwise
interactions. In such cases, the relationships in the data are better
represented as hyperedges (set of entities) of a non-uniform hypergraph. While
there have been works on principled methods for learning representations of
nodes of a hypergraph, these approaches are limited in their applicability to
tasks on non-uniform hypergraphs (hyperedges with different cardinalities). In
this work, we exploit the incidence structure to develop a hypergraph neural
network to learn provably expressive representations of variable sized
hyperedges which preserve local-isomorphism in the line graph of the
hypergraph, while also being invariant to permutations of its constituent
vertices. Specifically, for a given vertex set, we propose frameworks for (1)
hyperedge classification and (2) variable sized expansion of partially observed
hyperedges which captures the higher order interactions among vertices and
hyperedges. We evaluate performance on multiple real-world hypergraph datasets
and demonstrate consistent, significant improvement in accuracy, over
state-of-the-art models.
