# Comparing Euclidean and Hyperbolic Embeddings on the WordNet Nouns Hypernymy Graph

arXiv: https://arxiv.org/abs/2109.07488 · HTML: https://mlsanity.com/paper/2109.07488/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 12 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [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)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Leveraging Hierarchical Representations for Preserving Privacy and Utility in Text](https://mlsanity.com/paper/1910.08917/) (2019)
- [Fine-Grained Entity Typing in Hyperbolic Space](https://mlsanity.com/paper/1906.02505/) (2019)

## Built on by (most cited first, 3 of 3)

- [Embedding Geometries of Contrastive Language-Image Pre-Training](https://mlsanity.com/paper/2409.13079/) (2024)
- [Minimax Rates for Hyperbolic Hierarchical Learning](https://mlsanity.com/paper/2601.20047/) (2026)
- [Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2607.05268/) (2026)

## Abstract (arXiv)

Nickel and Kiela (2017) present a new method for embedding tree nodes in the Poincare ball, and suggest that these hyperbolic embeddings are far more effective than Euclidean embeddings at embedding nodes in large, hierarchically structured graphs like the WordNet nouns hypernymy tree. This is especially true in low dimensions (Nickel and Kiela, 2017, Table 1). In this work, we seek to reproduce their experiments on embedding and reconstructing the WordNet nouns hypernymy graph. Counter to what they report, we find that Euclidean embeddings are able to represent this tree at least as well as Poincare embeddings, when allowed at least 50 dimensions. We note that this does not diminish the significance of their work given the impressive performance of hyperbolic embeddings in very low-dimensional settings. However, given the wide influence of their work, our aim here is to present an updated and more accurate comparison between the Euclidean and hyperbolic embeddings.