Hyperbolic Graph Neural Networks

By Qi Liu, Maximilian Nickel, Douwe Kiela. Neural Information Processing Systems, 2019

499 citations recorded by the source corpus.

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we propose a novel GNN architecture for learning representations on Riemannian manifolds with differentiable exponential and logarithmic maps. We develop a scalable algorithm for modeling the structural properties of graphs, comparing Euclidean and hyperbolic geometry. In our experiments, we show that hyperbolic GNNs can lead to substantial improvements on various benchmark datasets.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/784b018c87c7dcbbe772374e45d5191bae9938ee

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In Artificial Intelligence

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Artificial Neural Networks and Machine Learning – ICANN 2021: 30th International Conference on Artificial Neural Networks, Bratislava, Slovakia, September 14–17, 2021, Proceedings, Part III (2021, background): “The works [29,6] have empirically shown that the hyperbolic setting is better suited for representation learning on real-world graphs with scale-free or hierarchical structure.”
Differentiating through the Fréchet Mean (2020, background): “recent work has focused specifically on developing neural networks that exploit the structure of hyperbolic space (Ganea et al., 2018; Tifrea et al., 2019; Chami et al., 2019; Liu et al., 2019).”
A Survey on Heterogeneous Graph Embedding: Methods, Techniques, Applications and Sources (2020, unknown): “Some attempts have been made towards hyperbolic HG embedding, and the results are rather promising [62], [121], [122].”
Understanding over-squashing and bottlenecks on graphs via curvature (2021, background): “It offers an appealing framework to study the properties of graphs, in particular arguing that graphs, like manifolds, exhibit curvature that makes them more suitable to be realized in spaces with hyperbolic geometry (Liu et al., 2019; Chami et al., 2019; Boguna et al., 2021).”
Low-Dimensional Hyperbolic Knowledge Graph Embeddings (2020, methodology): “Our approach maps hyperbolic representations to tangent space representations, x E = log c 0 ( x H ) and y E = log c 0 ( y H ) , and computes attention scores: We then compute a weighted average using the recently proposed tangent space average (Chami et al., 2019; Liu et al., 2019):”
Hyperbolic Graph Convolutional Neural Networks (2019, methodology): “Additionally, while [26] demonstrates strong performance on graph classification tasks and provides an elegant extension to dynamic graph embeddings, we focus on link prediction and node classification.”
Machine Learning on Graphs: A Model and Comprehensive Taxonomy (2020, background): “Hyperbolic Graph Convolutional Neural Networks Hyperbolic Graph Convolution Networks (HGCN) [22] and Hyperbolic Graph Neural Networks (HGNN) [75] apply graph convolutions in hyperbolic space by leveraging the Euclidean tangent space, which provides a first-order approximation of the hyperbolic manif”
HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation (2026, unknown): “…tree-like structures (Yang et al., 2023; Peng et al., 2021), which enhances performance in various tasks, including molecular generation (Liu et al., 2019), recommendation (Yang et al., 2021; Li et al., 2021), image retrieval (Khrulkov et al., 2020; Wei et al., 2024; Bui et al., 2025),…”