# Implicit Hypergraph Neural Network

arXiv: https://arxiv.org/abs/2508.14101 · HTML: https://mlsanity.com/paper/2508.14101/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 16 Aug 2025.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Labeling Trick: A Theory of Using Graph Neural Networks for Multi-Node Representation Learning](https://mlsanity.com/paper/2010.16103/) (2020)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [EIGNN: Efficient Infinite-Depth Graph Neural Networks](https://mlsanity.com/paper/2202.10720/) (2022)
- [Clustering in graphs and hypergraphs with categorical edge labels](https://mlsanity.com/paper/1910.09943/) (2019)
- [Optimization-Induced Graph Implicit Nonlinear Diffusion](https://mlsanity.com/paper/2206.14418/) (2022)
- [Session-based Recommendation with Hypergraph Attention Networks](https://mlsanity.com/paper/2112.14266/) (2021)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [Convergent Graph Solvers](https://mlsanity.com/paper/2106.01680/) (2021)
- [A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs](https://mlsanity.com/paper/2102.06825/) (2021)
- [Efficient and Effective Implicit Dynamic Graph Neural Network](https://mlsanity.com/paper/2406.17894/) (2024)
- [A Hypergraph-Based Machine Learning Ensemble Network Intrusion Detection System](https://mlsanity.com/paper/2211.03933/) (2022)

## Abstract (arXiv)

Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which rely on message-passing between nodes over hyperedges to learn latent representations, have emerged as the method of choice for predictive tasks in many of these domains. These approaches typically perform only a small number of message-passing rounds to learn the representations, which they then utilize for predictions. The small number of message-passing rounds comes at a cost, as the representations only capture local information and forego long-range high-order dependencies. However, as we demonstrate, blindly increasing the message-passing rounds to capture long-range dependency also degrades the performance of hyper-graph neural networks. Recent works have demonstrated that implicit graph neural networks capture long-range dependencies in standard graphs while maintaining performance. Despite their popularity, prior work has not studied long-range dependency issues on hypergraph neural networks. Here, we first demonstrate that existing hypergraph neural networks lose predictive power when aggregating more information to capture long-range dependency. We then propose Implicit Hypergraph Neural Network (IHNN), a novel framework that jointly learns fixed-point representations for both nodes and hyperedges in an end-to-end manner to alleviate this issue. Leveraging implicit differentiation, we introduce a tractable projected gradient descent approach to train the model efficiently. Extensive experiments on real-world hypergraphs for node classification demonstrate that IHNN outperforms the closest prior works in most settings, establishing a new state-of-the-art in hypergraph learning.