On a Novel Application of Wasserstein-Procrustes for Unsupervised Cross-Lingual Learning

The emergence of unsupervised word embeddings, pre-trained on very large monolingual text corpora, is at the core of the ongoing neural revolution in Natural Language Processing (NLP). Initially introduced for English, such pre-trained word embeddings quickly emerged for a number of other languages. Subsequently, there have been a number of attempts to align the embedding spaces across languages, which could enable a number of cross-language NLP applications. Performing the alignment using unsupervised cross-lingual learning (UCL) is especially attractive as it requires little data and often rivals supervised and semi-supervised approaches. Here, we analyze popular methods for UCL and we find that often their objectives are, intrinsically, versions of the Wasserstein-Procrustes problem. Hence, we devise an approach to solve Wasserstein-Procrustes in a direct way, which can be used to refine and to improve popular UCL methods such as iterative closest point (ICP), multilingual unsupervised and supervised embeddings (MUSE) and supervised Procrustes methods. Our evaluation experiments on standard datasets show sizable improvements over these approaches. We believe that our rethinking of the Wasserstein-Procrustes problem could enable further research, thus helping to develop better algorithms for aligning word embeddings across languages. Our code and instructions to reproduce the experiments are available at https://github.com/guillemram97/wp-hungarian.