# A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space

arXiv: https://arxiv.org/abs/2407.16641 · HTML: https://mlsanity.com/paper/2407.16641/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 20 of 20)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings](https://mlsanity.com/paper/1902.00913/) (2019)
- [Large-Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/1806.00437/) (2018)
- [Robust Large-Margin Learning in Hyperbolic Space](https://mlsanity.com/paper/2004.05465/) (2020)
- [Skip-gram word embeddings in hyperbolic space](https://mlsanity.com/paper/1809.01498/) (2018)
- [Specialising Word Vectors for Lexical Entailment](https://mlsanity.com/paper/1710.06371/) (2017)
- [Gradient descent in hyperbolic space](https://mlsanity.com/paper/1805.08207/) (2018)

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

- [H4G: Unlocking Faithful Inference for Zero-Shot Graph Learning in Hyperbolic Space](https://mlsanity.com/paper/2510.12094/) (2025)
- [Beyond Distributions: Geometric Action Control for Continuous Reinforcement Learning](https://mlsanity.com/paper/2511.08234/) (2025)

## Abstract (arXiv)

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm.