# Equivariant Hypergraph Diffusion Neural Operators

arXiv: https://arxiv.org/abs/2207.06680 · HTML: https://mlsanity.com/paper/2207.06680/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 81 of its 135 references that are in the map.
- First posted on arXiv 14 Jul 2022.

## Builds on (most cited first, 30 of 81)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [A Review of Relational Machine Learning for Knowledge Graphs](https://mlsanity.com/paper/1503.00759/) (2015)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [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)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)

## Built on by (most cited first, 30 of 47)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs](https://mlsanity.com/paper/2404.00638/) (2024)
- [Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design](https://mlsanity.com/paper/2310.07684/) (2023)
- [Hypergraph Transformer for Semi-Supervised Classification](https://mlsanity.com/paper/2312.11385/) (2023)
- [Molecular Hypergraph Neural Networks](https://mlsanity.com/paper/2312.13136/) (2023)
- [Training-Free Message Passing for Learning on Hypergraphs](https://mlsanity.com/paper/2402.05569/) (2024)
- [Polynomial Width is Sufficient for Set Representation with High-dimensional Features](https://mlsanity.com/paper/2307.04001/) (2023)
- [LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100× Faster Inference](https://mlsanity.com/paper/2402.04296/) (2024)
- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [UniG-Encoder: A Universal Feature Encoder for Graph and Hypergraph Node Classification](https://mlsanity.com/paper/2308.01650/) (2023)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding](https://mlsanity.com/paper/2501.00712/) (2025)
- [Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs](https://mlsanity.com/paper/2510.04727/) (2025)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [HGFormer: Topology-Aware Vision Transformer with HyperGraph Learning](https://mlsanity.com/paper/2504.02440/) (2025)
- [Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach](https://mlsanity.com/paper/2603.15696/) (2026)
- [Hypergraph Neural Diffusion: A PDE-Inspired Framework for Hypergraph Message Passing](https://mlsanity.com/paper/2604.10955/) (2026)
- [BHyGNN+: Unsupervised Representation Learning for Heterophilic Hypergraphs](https://mlsanity.com/paper/2602.14919/) (2026)
- [A Unified View on Neural Message Passing with Opinion Dynamics for Social Networks](https://mlsanity.com/paper/2310.01272/) (2023)
- [DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions](https://mlsanity.com/paper/2410.06969/) (2024)
- [Explaining Hypergraph Neural Networks: From Local Explanations to Global Concepts](https://mlsanity.com/paper/2410.07764/) (2024)
- [Handling Heterophily in Recommender Systems with Wavelet Hypergraph Diffusion](https://mlsanity.com/paper/2501.14399/) (2025)
- [Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification](https://mlsanity.com/paper/2510.21462/) (2025)
- [Weisfeiler and Lehman Go Categorical](https://mlsanity.com/paper/2602.06787/) (2026)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [Enhancing Node Representations for Real-World Complex Networks with Topological Augmentation](https://mlsanity.com/paper/2402.13033/) (2024)
- [Hypergraph Diffusion for High-Order Recommender Systems](https://mlsanity.com/paper/2501.16722/) (2025)

## Abstract (arXiv)

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2%uparrow in prediction accuracy over four datasets therein.