[논문 리뷰] Hyperbolic Graph Neural Networks: A Review of Methods and Applications

Meng‐Lin Yang, Min Zhou외 6명|arXiv (Cornell University)|2022. 02. 28.

Advanced Graph Neural Networks인용 수 29

한 줄 요약

This paper surveys Hyperbolic Graph Neural Networks (HGNNs), unifying methods into a framework and detailing their algorithms and diverse applications, while outlining key challenges and future directions.

ABSTRACT

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world data, particularly for datasets exhibiting a highly non-Euclidean latent anatomy or power-law distributions. Hyperbolic geometry, with its constant negative curvature and exponential growth property, naturally accommodates such structures, offering a promising alternative for learning rich graph representations. This survey paper provides a comprehensive review of the rapidly evolving field of Hyperbolic Graph Learning (HGL). We systematically categorize and analyze existing methods broadly dividing them into (1) hyperbolic graph embedding-based techniques, (2) graph neural network-based hyperbolic models, and (3) emerging paradigms. Beyond methodologies, we extensively discuss diverse applications of HGL across multiple domains, including recommender systems, knowledge graphs, bioinformatics, and other relevant scenarios, demonstrating the broad applicability and effectiveness of hyperbolic geometry in real-world graph learning tasks. Most importantly, we identify several key challenges that serve as directions for advancing HGL, including handling complex data structures, developing geometry-aware learning objectives, ensuring trustworthy and scalable implementations, and integrating with foundation models, e.g., large language models. We highlight promising research opportunities in this exciting interdisciplinary area. A comprehensive repository can be found at https://github.com/digailab/awesome-hyperbolic-graph-learning.

연구 동기 및 목표

• Survey and unify HGNN methods within a general framework.
• Detail the variations of each HGNN module (initialization, transformation, aggregation, activation).
• Categorize and review HGNN applications across domains.
• Highlight theoretical and empirical analyses and identify open challenges and opportunities for future work.

제안 방법

• Present a unified HGNN framework that encompasses hyperbolic initialization, feature transformation, neighborhood aggregation, and non-linear activation.
• Discuss tangent-space and fully hyperbolic transformation approaches for layer operations.
• Summarize matrix-vector multiplications and bias addition in hyperbolic space with models like Poincaré ball and Lorentz.
• Describe various hyperbolic neighborhood aggregation strategies including structure, feature, and distance-based weights.
• Explain mean aggregation methods in hyperbolic space such as tangent-space, Einstein midpoint, and Lorentzian centroid.
• Outline practical architectures and their operational equations within hyperbolic geometry.

실험 결과

연구 질문

• RQ1 What constitute the core components of HGNNs and how can they be unified into a general framework?
• RQ2 What are the main methods for initializing, transforming, and aggregating in hyperbolic space?
• RQ3 How do HGNNs apply to different application domains like recommender systems, knowledge graphs, and molecules?
• RQ4 What challenges impede HGNN development and what opportunities exist for future research?

주요 결과

• Hyperbolic space offers advantages for tree-like or hierarchical graph data and can yield high-quality representations with lower embedding dimensions.
• HGNNs can be analyzed and implemented within a unified framework covering initialization, transformation, aggregation, and activation in hyperbolic geometry.
• A variety of neighborhood weighting strategies exist, leveraging structure, features, and hyperbolic distances to enhance aggregation.
• Multiple mean-aggregation methods (tangent-space, Einstein midpoint, Lorentzian centroid) address manifold constraints in hyperbolic space.
• The survey consolidates HGNN methodologies and maps them to diverse applications, while outlining current challenges and future directions.