# Are Hyperbolic Representations in Graphs Created Equal?

arXiv: https://arxiv.org/abs/2007.07698 · HTML: https://mlsanity.com/paper/2007.07698/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [AMCAD: Adaptive Mixed-Curvature Representation based Advertisement Retrieval System](https://mlsanity.com/paper/2203.14683/) (2022)
- [Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures](https://mlsanity.com/paper/2308.09250/) (2023)
- [Knowledge-based Multiple Adaptive Spaces Fusion for Recommendation](https://mlsanity.com/paper/2308.15244/) (2023)

## Abstract (arXiv)

Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node classification and link prediction we compute hyperbolic embeddings and conclude that for tasks that require global prediction consistency it might be useful to use non-Euclidean embeddings, while for other tasks Euclidean models are superior. To do so we first fix an issue of the existing models associated with the optimization process at zero curvature. Current hyperbolic models deal with gradients at the origin in ad-hoc manner, which is inefficient and can lead to numerical instabilities. We solve the instabilities of kappa-Stereographic model at zero curvature cases and evaluate the approach of embedding graphs into the manifold in several graph representation learning tasks.