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Recent Advances in Hypergraph Neural Networks

Murong Yang, Xin-Jian Xu

TL;DR

This survey addresses the problem of learning from data with higher-order relationships by organizing HGNN methods into a fivefold taxonomy: HGCNs, HGATs, HGAEs, HGRNs, and DHGGMs. It outlines spectral and spatial approaches for convolution, attention-based aggregation, unsupervised structure learning, temporal modeling, and three generative paradigms (variational, adversarial, and diffusion). Key contributions include a structured overview of practical mechanisms, representative models, and open problems across each category, plus discussion of applications and challenges such as oversmoothing, scalability, and explainability. The work serves as a comprehensive guide for researchers to navigate HGNN design choices and to identify promising directions for handling higher-order, heterogeneous, and temporal graph-structured data with practical impact in domains like vision, networks, and biology.

Abstract

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks, and natural language processing. This paper comprehensively reviews recent advances in HGNNs and presents a taxonomy of mainstream models based on their architectures: hypergraph convolutional networks (HGCNs), hypergraph attention networks (HGATs), hypergraph autoencoders (HGAEs), hypergraph recurrent networks (HGRNs), and deep hypergraph generative models (DHGGMs). For each category, we delve into its practical applications, mathematical mechanisms, literature contributions, and open problems. Finally, we discuss some common challenges and promising research directions.This paper aspires to be a helpful resource that provides guidance for future research and applications of HGNNs.

Recent Advances in Hypergraph Neural Networks

TL;DR

This survey addresses the problem of learning from data with higher-order relationships by organizing HGNN methods into a fivefold taxonomy: HGCNs, HGATs, HGAEs, HGRNs, and DHGGMs. It outlines spectral and spatial approaches for convolution, attention-based aggregation, unsupervised structure learning, temporal modeling, and three generative paradigms (variational, adversarial, and diffusion). Key contributions include a structured overview of practical mechanisms, representative models, and open problems across each category, plus discussion of applications and challenges such as oversmoothing, scalability, and explainability. The work serves as a comprehensive guide for researchers to navigate HGNN design choices and to identify promising directions for handling higher-order, heterogeneous, and temporal graph-structured data with practical impact in domains like vision, networks, and biology.

Abstract

The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks, and natural language processing. This paper comprehensively reviews recent advances in HGNNs and presents a taxonomy of mainstream models based on their architectures: hypergraph convolutional networks (HGCNs), hypergraph attention networks (HGATs), hypergraph autoencoders (HGAEs), hypergraph recurrent networks (HGRNs), and deep hypergraph generative models (DHGGMs). For each category, we delve into its practical applications, mathematical mechanisms, literature contributions, and open problems. Finally, we discuss some common challenges and promising research directions.This paper aspires to be a helpful resource that provides guidance for future research and applications of HGNNs.

Paper Structure

This paper contains 18 sections, 12 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Definitions of Hypergraphs
  4. Tasks of HGNNs
  5. Hypergraph Neural Networks
  6. Hypergraph Convolutional Networks
  7. Spectral HGCNs
  8. Spatial HGCNs
  9. Open Problems
  10. Hypergraph Attention Networks
  11. Hypergraph Autoencoders
  12. Hypergraph Recurrent Networks
  13. Deep Hypergraph Generative Models
  14. Variational Hypergraph Autoencoders
  15. Hypergraph Generative Adversarial Networks
  16. ...and 3 more sections

Figures (1)

  • Figure 1: The overall framework of HGNNs. The purpose of the hypergraph message passing block is to update the hypergraph structure $\mathbf{H}$ or features $\mathbf{X}$. It may involve various techniques, such as hypergraph convolution in HGCNs, attention-weighted aggregation in HGATs, encoding and decoding in HGAEs, recursive message passing in HGRNs, or hypergraph generation in DHGGMs.

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4