# Characterizing Departures from Linearity in Word Translation

arXiv: https://arxiv.org/abs/1806.04508 · HTML: https://mlsanity.com/paper/1806.04508/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2018.

## Built on by (most cited first, 7 of 7)

- [IsoVec: Controlling the Relative Isomorphism of Word Embedding Spaces](https://mlsanity.com/paper/2210.05098/) (2022)
- [Bilingual Lexicon Induction for Low-Resource Languages using Graph Matching via Optimal Transport](https://mlsanity.com/paper/2210.14378/) (2022)
- [Towards Multi-Sense Cross-Lingual Alignment of Contextual Embeddings](https://mlsanity.com/paper/2103.06459/) (2021)
- [Cross-lingual alignments of ELMo contextual embeddings](https://mlsanity.com/paper/2106.15986/) (2021)
- [Learning a Reversible Embedding Mapping using Bi-Directional Manifold Alignment](https://mlsanity.com/paper/2107.00124/) (2021)
- [An Analysis of Euclidean vs. Graph-Based Framing for Bilingual Lexicon Induction from Word Embedding Spaces](https://mlsanity.com/paper/2109.12640/) (2021)
- [ProMap: Effective Bilingual Lexicon Induction via Language Model Prompting](https://mlsanity.com/paper/2310.18778/) (2023)

## Abstract (arXiv)

We investigate the behavior of maps learned by machine translation methods. The maps translate words by projecting between word embedding spaces of different languages. We locally approximate these maps using linear maps, and find that they vary across the word embedding space. This demonstrates that the underlying maps are non-linear. Importantly, we show that the locally linear maps vary by an amount that is tightly correlated with the distance between the neighborhoods on which they are trained. Our results can be used to test non-linear methods, and to drive the design of more accurate maps for word translation.