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Graph representation learning has made major strides over the past decade.However, in many relational domains, the input data are not suited for simplegraph representations as the relationships between entities go beyond pairwiseinteractions. In such cases, the relationships in the data are betterrepresented as hyperedges (set of entities) of a non-uniform hypergraph. Whilethere have been works on principled methods for learning representations ofnodes of a hypergraph, these approaches are limited in their applicability totasks on non-uniform hypergraphs (hyperedges with different cardinalities). Inthis work, we exploit the incidence structure to develop a hypergraph neuralnetwork to learn provably expressive representations of variable sizedhyperedges which preserve local-isomorphism in the line graph of thehypergraph, while also being invariant to permutations of its constituentvertices. Specifically, for a given vertex set, we propose frameworks for (1)hyperedge classification and (2) variable sized expansion of partially observedhyperedges which captures the higher order interactions among vertices andhyperedges. We evaluate performance on multiple real-world hypergraph datasetsand demonstrate consistent, significant improvement in accuracy, overstate-of-the-art models.

Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Tasks