# Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design

arXiv: https://arxiv.org/abs/2310.07684 · HTML: https://mlsanity.com/paper/2310.07684/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 64 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [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)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Self-Supervised Multi-Channel Hypergraph Convolutional Network for Social Recommendation](https://mlsanity.com/paper/2101.06448/) (2021)
- [Breaking the Limits of Message Passing Graph Neural Networks](https://mlsanity.com/paper/2106.04319/) (2021)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [The Total Variation on Hypergraphs - Learning on Hypergraphs Revisited](https://mlsanity.com/paper/1312.5179/) (2013)
- [Inhomogeneous Hypergraph Clustering with Applications](https://mlsanity.com/paper/1709.01249/) (2017)
- [Grale: Designing Networks for Graph Learning](https://mlsanity.com/paper/2007.12002/) (2020)
- [Self-supervised Hypergraph Representation Learning for Sociological Analysis](https://mlsanity.com/paper/2212.11440/) (2022)
- [Preventing Over-Smoothing for Hypergraph Neural Networks](https://mlsanity.com/paper/2203.17159/) (2022)
- [Classification of Edge-dependent Labels of Nodes in Hypergraphs](https://mlsanity.com/paper/2306.03032/) (2023)
- [EvolveHypergraph: Group-Aware Dynamic Relational Reasoning for Trajectory Prediction](https://mlsanity.com/paper/2208.05470/) (2022)

## Built on by (most cited first, 15 of 15)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks](https://mlsanity.com/paper/2410.06530/) (2024)
- [Training-Free Message Passing for Learning on Hypergraphs](https://mlsanity.com/paper/2402.05569/) (2024)
- [Recent Advances in Hypergraph Neural Networks](https://mlsanity.com/paper/2503.07959/) (2025)
- [Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs](https://mlsanity.com/paper/2510.04727/) (2025)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)
- [Analysing the Behaviour of Tree-Based Neural Networks in Regression Tasks](https://mlsanity.com/paper/2406.11437/) (2024)
- [Wasserstein Hypergraph Neural Network](https://mlsanity.com/paper/2506.09682/) (2025)
- [Hypergraph Pattern Machine: Compositional Tokenization for Higher-Order Interactions](https://mlsanity.com/paper/2605.16527/) (2026)
- [Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation](https://mlsanity.com/paper/2607.07330/) (2026)
- [Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning](https://mlsanity.com/paper/2608.15388/) (2026)
- [Byzantine-Resilient Federated Large Language Model via Hypergraph Message Passing](https://mlsanity.com/paper/2610.12711/) (2026)
- [PANDA: Prior-guided Attentional Dual-path Architecture](https://mlsanity.com/paper/2610.13635/) (2026)

## Abstract (arXiv)

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This paper attempts to confront some pending questions in that regard: Q1 Can the concept of homophily play a crucial role in Hypergraph Neural Networks (HNNs)? Q2 Is there room for improving current HNN architectures by carefully addressing specific characteristics of higher-order networks? Q3 Do existing datasets provide a meaningful benchmark for HNNs? To address them, we first introduce a novel conceptualization of homophily in higher-order networks based on a Message Passing (MP) scheme, unifying both the analytical examination and the modeling of higher-order networks. Further, we investigate some natural, yet mostly unexplored, strategies for processing higher-order structures within HNNs such as keeping hyperedge-dependent node representations, or performing node/hyperedge stochastic samplings, leading us to the most general MP formulation up to date -MultiSet-, as well as to an original architecture design, MultiSetMixer. Finally, we conduct an extensive set of experiments that contextualize our proposals and successfully provide insights about our inquiries.