# Wasserstein Hypergraph Neural Network

arXiv: https://arxiv.org/abs/2506.09682 · HTML: https://mlsanity.com/paper/2506.09682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [Wasserstein Embedding for Graph Learning](https://mlsanity.com/paper/2006.09430/) (2020)
- [FSPool: Learning Set Representations with Featurewise Sort Pooling](https://mlsanity.com/paper/1906.02795/) (2019)
- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [Learning Wasserstein Embeddings](https://mlsanity.com/paper/1710.07457/) (2017)
- [Rep the Set: Neural Networks for Learning Set Representations](https://mlsanity.com/paper/1904.01962/) (2019)
- [Learnable Hypergraph Laplacian for Hypergraph Learning](https://mlsanity.com/paper/2106.05701/) (2021)
- [Learning Embeddings into Entropic Wasserstein Spaces](https://mlsanity.com/paper/1905.03329/) (2019)
- [Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design](https://mlsanity.com/paper/2310.07684/) (2023)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [Graph AI in Medicine](https://mlsanity.com/paper/2310.13767/) (2023)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)

## Abstract (arXiv)

The ability to model relational information using machine learning has driven advancements across various domains, from medicine to social science. While graph representation learning has become mainstream over the past decade, representing higher-order relationships through hypergraphs is rapidly gaining momentum. In the last few years, numerous hypergraph neural networks have emerged, most of them falling under a two-stage, set-based framework. The messages are sent from nodes to edges and then from edges to nodes. However, most of the advancement still takes inspiration from the graph counterpart, often simplifying the aggregations to basic pooling operations. In this paper we are introducing Wasserstein Hypergraph Neural Network, a model that treats the nodes and hyperedge neighbourhood as distributions and aggregate the information using Sliced Wasserstein Pooling. Unlike conventional aggregators such as mean or sum, which only capture first-order statistics, our approach has the ability to preserve geometric properties like the shape and spread of distributions. This enables the learned embeddings to reflect how easily one hyperedge distribution can be transformed into another, following principles of optimal transport. Experimental results demonstrate that applying Wasserstein pooling in a hypergraph setting significantly benefits node classification tasks, achieving top performance on several real-world datasets.