# Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment

arXiv: https://arxiv.org/abs/2602.01828 · HTML: https://mlsanity.com/paper/2602.01828/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 64 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Characteristic Functions on Graphs: Birds of a Feather, from Statistical Descriptors to Parametric Models](https://mlsanity.com/paper/2005.07959/) (2020)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Tree! I am no Tree! I am a Low Dimensional Hyperbolic Embedding](https://mlsanity.com/paper/2005.03847/) (2020)
- [Graph Neural Networks Use Graphs When They Shouldn't](https://mlsanity.com/paper/2309.04332/) (2023)
- [Neural Collapse in the Intermediate Hidden Layers of Classification Neural Networks](https://mlsanity.com/paper/2308.02760/) (2023)
- [Riemannian Residual Neural Networks](https://mlsanity.com/paper/2310.10013/) (2023)
- [HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion](https://mlsanity.com/paper/1908.04895/) (2019)
- [Link prediction with hyperbolic geometry](https://mlsanity.com/paper/1903.08810/) (2019)

## Built on by (most cited first, 2 of 2)

- [Group-Equivariant Poincar'e Convolutional Networks](https://mlsanity.com/paper/2607.00556/) (2026)
- [Hyperbolic Graph Representation Learning for Differential Diagnosis on Biomedical Knowledge Graphs](https://mlsanity.com/paper/2609.18481/) (2026)

## Abstract (arXiv)

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely adopted as a principled choice for representation learning on tree-like graphs. In this work, we question this paradigm by proposing the additional condition of geometry--task alignment, i.e., whether the metric structure of the target follows that of the input graph. We theoretically and empirically demonstrate the capability of HGNNs to recover low-distortion representations on regression problems, and show that their geometric inductive bias becomes helpful when the problem requires preserving metric structure. By jointly analyzing predictive performance and embedding distortion, we further show that HGNNs gain an advantage on link prediction, a naturally geometry-aligned task, whereas this advantage largely disappears on standard node classification benchmarks, which are typically not geometry--aligned. Overall, our findings shift the focus from only asking "Is the graph hyperbolic?" to also questioning "Is the task aligned with hyperbolic geometry?", showing that HGNNs consistently outperform Euclidean models under such alignment, while their advantage vanishes otherwise.