# HYVINT: Intensity-Driven Hypergraph Generation with Variational Embeddings

arXiv: https://arxiv.org/abs/2605.16836 · HTML: https://mlsanity.com/paper/2605.16836/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 16 May 2026.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Molecular Hypergraph Grammar with its Application to Molecular Optimization](https://mlsanity.com/paper/1809.02745/) (2018)
- [Multimodal Representations Learning and Adversarial Hypergraph Fusion for Early Alzheimer's Disease Prediction](https://mlsanity.com/paper/2107.09928/) (2021)
- [LLM-Guided Multi-View Hypergraph Learning for Human-Centric Explainable Recommendation](https://mlsanity.com/paper/2401.08217/) (2024)
- [Evolution of Real-world Hypergraphs: Patterns and Models without Oracles](https://mlsanity.com/paper/2008.12729/) (2020)
- [A Survey on Hypergraph Mining: Patterns, Tools, and Generators](https://mlsanity.com/paper/2401.08878/) (2024)
- [Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes](https://mlsanity.com/paper/2203.03060/) (2022)
- [HYGENE: A Diffusion-based Hypergraph Generation Method](https://mlsanity.com/paper/2408.16457/) (2024)
- [Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model](https://mlsanity.com/paper/2112.11671/) (2021)
- [A General Latent Embedding Approach for Modeling Non-uniform High-dimensional Sparse Hypergraphs with Multiplicity](https://mlsanity.com/paper/2410.12108/) (2024)
- [Denoising Diffused Embeddings: a Generative Approach for Hypergraphs](https://mlsanity.com/paper/2501.01541/) (2025)
- [Effective and Efficient Attributed Hypergraph Embedding on Nodes and Hyperedges](https://mlsanity.com/paper/2508.08807/) (2025)

## Abstract (arXiv)

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.