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

TL;DR

This paper introduces a hypergraph neural network that learns expressive, permutation-invariant representations of variable-sized hyperedges, enabling better modeling of higher-order relationships in complex relational data.

Contribution

It develops a novel hypergraph neural network framework that effectively handles non-uniform hypergraphs with variable hyperedge sizes, improving over existing methods.

Findings

Significant accuracy improvements over state-of-the-art models.

Effective hyperedge classification and higher-order interaction capture.

Robust performance on multiple real-world hypergraph datasets.

Abstract

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.