# Learning a Reversible Embedding Mapping using Bi-Directional Manifold Alignment

arXiv: https://arxiv.org/abs/2107.00124 · HTML: https://mlsanity.com/paper/2107.00124/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [FastText.zip: Compressing text classification models](https://mlsanity.com/paper/1612.03651/) (2016)
- [A Survey Of Cross-lingual Word Embedding Models](https://mlsanity.com/paper/1706.04902/) (2017)
- [Loss in Translation: Learning Bilingual Word Mapping with a Retrieval Criterion](https://mlsanity.com/paper/1804.07745/) (2018)
- [On the Limitations of Unsupervised Bilingual Dictionary Induction](https://mlsanity.com/paper/1805.03620/) (2018)
- [Bilingual Lexicon Induction with Semi-supervision in Non-Isometric Embedding Spaces](https://mlsanity.com/paper/1908.06625/) (2019)
- [Cross-lingual Alignment vs Joint Training: A Comparative Study and A Simple Unified Framework](https://mlsanity.com/paper/1910.04708/) (2019)
- [LNMap: Departures from Isomorphic Assumption in Bilingual Lexicon Induction Through Non-Linear Mapping in Latent Space](https://mlsanity.com/paper/2004.13889/) (2020)
- [Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach](https://mlsanity.com/paper/1808.08773/) (2018)
- [Unsupervised Cross-lingual Transfer of Word Embedding Spaces](https://mlsanity.com/paper/1809.03633/) (2018)
- [Revisiting Adversarial Autoencoder for Unsupervised Word Translation with Cycle Consistency and Improved Training](https://mlsanity.com/paper/1904.04116/) (2019)
- [Beyond Offline Mapping: Learning Cross Lingual Word Embeddings through Context Anchoring](https://mlsanity.com/paper/2012.15715/) (2020)
- [Characterizing Departures from Linearity in Word Translation](https://mlsanity.com/paper/1806.04508/) (2018)
- [Consistent Alignment of Word Embedding Models](https://mlsanity.com/paper/1702.07680/) (2017)

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

- [Improving Word Translation via Two-Stage Contrastive Learning](https://mlsanity.com/paper/2203.08307/) (2022)
- [Bilingual Lexicon Induction for Low-Resource Languages using Graph Matching via Optimal Transport](https://mlsanity.com/paper/2210.14378/) (2022)

## Abstract (arXiv)

We propose a Bi-Directional Manifold Alignment (BDMA) that learns a non-linear mapping between two manifolds by explicitly training it to be bijective. We demonstrate BDMA by training a model for a pair of languages rather than individual, directed source and target combinations, reducing the number of models by 50%. We show that models trained with BDMA in the "forward" (source to target) direction can successfully map words in the "reverse" (target to source) direction, yielding equivalent (or better) performance to standard unidirectional translation models where the source and target language is flipped. We also show how BDMA reduces the overall size of the model.