# From Hyperbolic Geometry Back to Word Embeddings

arXiv: https://arxiv.org/abs/2204.12481 · HTML: https://mlsanity.com/paper/2204.12481/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 26 Apr 2022.

## Builds on (most cited first, 13 of 13)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Analogies Explained: Towards Understanding Word Embeddings](https://mlsanity.com/paper/1901.09813/) (2019)
- [Towards Understanding Linear Word Analogies](https://mlsanity.com/paper/1810.04882/) (2018)
- [What the Vec? Towards Probabilistically Grounded Embeddings](https://mlsanity.com/paper/1805.12164/) (2018)
- [The Mechanism of Additive Composition](https://mlsanity.com/paper/1511.08407/) (2015)
- [Context Vectors are Reflections of Word Vectors in Half the Dimensions](https://mlsanity.com/paper/1902.09859/) (2019)

## Abstract (arXiv)

We choose random points in the hyperbolic disc and claim that these points are already word representations. However, it is yet to be uncovered which point corresponds to which word of the human language of interest. This correspondence can be approximately established using a pointwise mutual information between words and recent alignment techniques.