Title: SuperHype: Hypergraph Generation via Graph-Superposition Decomposition
Primary area: learning on graphs and other geometries & topologies
Keywords: graph, hypergraph, diffusion model

Abstract: Hypergraphs are graph generalizations with key applications in domains such as healthcare, where strict data privacy requirements apply, or bioinformatics, where testing new compounds is costly. However, research into hypergraph synthesis is limited, and state-of-the-art approaches yield limited generation quality in terms of overall structural patterns and graph-level validity. This is caused by the hypergraph's combinatorial structure, which is composed of a number of possible hyperedges that is factorial in the number of nodes. In fact, current solutions rely on diffusion models denoising graph projections, which are exact but inefficient, or lightweight but approximate. To address such shortcomings, we introduce SuperHype, the first hypergraph diffusion model with tractable and exact modeling. To tackle the complexity of hypergraph representation, we introduce graph superposition, a novel representation that embeds a hypergraph into a multilayer graph. Superposition enables a tractable representation that maintains exactness. To generate new samples from such representations, we introduce a Graph-Superposition Transformer that treats the superposition as an interconnected sequence of layers. We optimize the model architecture to learn low-level patterns within individual graphs in the superposition and high-level patterns between the different graphs of the same superposition. Moreover, we enhance the model's performance with hypergraph-specific auxiliary features and triplet aggregation of indirect node interactions. Our evaluation on five datasets shows that \algo generally reproduces local and global connectivity patterns with superior fidelity to state-of-the-art baselines.