Hypergraph Neural Networks: A Comprehensive Survey on Modeling and Learning Higher-Order Interactions

Core Concepts

Hypergraph neural networks (HNNs) are powerful tools for representation learning on hypergraphs, which can effectively capture higher-order interactions (HOIs) in complex systems and applications.

Abstract

This survey provides an in-depth and step-by-step guide on HNNs. It first breaks down existing HNNs into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. It then examines how each component is designed to effectively model HOIs. The survey also overviews recent applications of HNNs in various domains, including recommendation, biological and medical science, time series analysis, and computer vision. Finally, it discusses the limitations and future directions of HNN research.
The survey starts by introducing the concept of HOIs and how they are mathematically expressed using hypergraphs. It then delves into the four design components of HNNs:

Input features: HNNs can leverage external features, structural features, and identity features to capture HOIs.
Input structures: HNNs can transform the input hypergraph structure using either reductive (e.g., clique expansion, adaptive expansion) or non-reductive (e.g., star expansion, line expansion, tensor representation) approaches.
Message passing: HNNs can aggregate messages from target nodes/hyperedges using fixed or learnable pooling functions, with target-agnostic or target-aware attention mechanisms.
Training objectives: HNNs can be trained using classification, contrastive, or generative learning approaches, especially when label supervision is weak or absent.

The survey also provides a comprehensive summary of existing HNN models and their key characteristics.

Stats

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications, such as physical systems, microbial communities, brain functions, and social networks.
Hypergraphs can mathematically express higher-order networks, or networks of HOIs, where nodes and hyperedges represent entities and their HOIs, respectively.
The number of peer-reviewed publications on hypergraph neural networks (HNNs) has grown exponentially, from 5 in 2019 to 150 in 2023.

Quotes

"Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications, and thus investigation of deep learning for HOIs has become a valuable agenda for the data mining and machine learning communities."
"Hypergraphs mathematically express higher-order networks, or networks of HOIs [13], where nodes and hyperedges respectively represent entities and their HOIs."
"As hypergraphs are extensively used, the demand grew to make predictions on them, such as node property estimation or missing hyperedge identification. Hypergraph neural networks (HNNs) have shown strong promise in solving such problems."

Key Insights Distilled From

A Survey on Hypergraph Neural Networks

by Sunwoo Kim,S... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.01039.pdf

Deeper Inquiries

How can HNNs be extended to handle dynamic, directed, or heterogeneous hypergraphs

To extend HNNs to handle dynamic hypergraphs, one approach is to incorporate temporal information into the model. This can be achieved by introducing time-dependent features for nodes and hyperedges, allowing the network to capture temporal dependencies and changes in the hypergraph structure over time. Additionally, recurrent neural networks (RNNs) or transformers can be integrated into the HNN architecture to process sequences of hypergraph snapshots.
For directed hypergraphs, modifications to the message passing mechanism can be made to consider the directionality of hyperedges. This can involve incorporating edge direction information into the aggregation process or designing specific attention mechanisms to capture the flow of information in directed hypergraphs.
Handling heterogeneous hypergraphs involves accommodating different types of nodes and hyperedges with distinct features and semantics. One way to address this is by introducing separate embedding spaces for different types of nodes and hyperedges, allowing the model to learn representations specific to each type. Additionally, attention mechanisms can be adapted to focus on relevant information from different types of entities in the hypergraph.

What are the theoretical limitations of HNNs in capturing higher-order interactions, and how can they be addressed

Theoretical limitations of HNNs in capturing higher-order interactions primarily stem from the complexity and scalability of modeling interactions beyond pairwise relationships. One key limitation is the curse of dimensionality, where the number of possible higher-order interactions grows exponentially with the order of interactions, making it challenging to learn and generalize effectively.
To address these limitations, techniques such as graph sampling and aggregation can be employed to reduce the computational complexity of capturing higher-order interactions. By sampling subgraphs or aggregating information at different granularities, HNNs can focus on relevant interactions while mitigating the computational burden.
Furthermore, incorporating domain knowledge and constraints into the model can help guide the learning process and improve the interpretability of higher-order interactions. By leveraging domain-specific information, HNNs can capture meaningful patterns and relationships in the data more effectively.

What are the potential applications of HNNs in emerging fields, such as quantum computing or neuroscience, where higher-order interactions play a crucial role

In emerging fields like quantum computing, HNNs can be applied to model complex interactions between quantum entities, such as qubits and quantum gates. By representing quantum systems as hypergraphs, HNNs can learn intricate relationships and dependencies, aiding in tasks like quantum state classification, error correction, and optimization of quantum circuits.
In neuroscience, HNNs can be utilized to analyze brain connectivity data represented as hypergraphs, capturing the intricate network of interactions between brain regions. This can help in understanding brain dynamics, identifying biomarkers for neurological disorders, and predicting brain states based on hypergraph representations of neural activity.
Overall, the potential applications of HNNs in these fields lie in their ability to model and analyze complex interactions at a higher level of abstraction, providing insights into the underlying structures and dynamics of systems where higher-order interactions play a crucial role.