HYVINT: Intensity-Driven Hypergraph Generation with Variational Representations

TL;DR

HYVINT introduces an intensity-driven hypergraph generation framework that models higher-order interactions with interpretable latent representations, achieving high fidelity and diversity in synthetic and real-world data.

Contribution

It proposes a novel intensity-based incidence formation mechanism and a variational estimator for hypergraph generation, addressing interpretability and modeling limitations of prior methods.

Findings

HYVINT achieves strong fidelity in hypergraph generation.

It maintains substantial novelty and diversity.

The method provides theoretical error bounds and convergence rates.

Abstract

Hypergraphs provide a principled framework for modeling polyadic interactions, with applications in recommendation systems, social networks, and molecular modeling. Hypergraph generation remains challenging because incidence structures are discrete, sparse, and governed by heterogeneous higher-order interactions. Existing generators often rely on implicit latent spaces or continuous incidence decoders, which provide limited mechanistic interpretation of how node-hyperedge incidences arise. To address these limitations, we propose HYVINT, an intensity-driven hypergraph generative framework. Our key innovations are twofold: (i) we develop an intensity-driven incidence formation mechanism for hypergraphs that links latent interaction strength to binary incidence, and (ii) we derive a tractable lower-bound variational estimator for learning latent representations. We provide generation error bounds with asymptotic convergence rates and empirically show that HYVINT achieves strong fidelity while maintaining substantial novelty and diversity on synthetic and real-world hypergraphs.