Quantized Wasserstein Procrustes Alignment of Word Embedding Spaces

In natural language processing (NLP), the problem of aligning monolingual embedding spaces to induce a shared cross-lingual vector space has been shown not only to be useful in a variety of tasks such as bilingual lexicon induction (BLI) (Mikolov et al., 2013; Barone, 2016; Artetxe et al., 2017; Aboagye et al., 2022), machine translation (Artetxe et al., 2018b), cross-lingual information retrieval (Vulić & Moens, 2015), but it plays a crucial role in facilitating the cross-lingual transfer of language technologies from high resource languages to low resource languages. Cross-lingual word embeddings (CLWEs) represent words from two or more languages in a shared cross-lingual vector space in which words with similar meanings obtain similar vectors regardless of their language. There has been a flurry of work dominated by the so-called projection-based CLWE models (Mikolov et al., 2013; Artetxe et al., 2016, 2017, 2018a; Smith et al., 2017; Ruder et al., 2019), which aim to improve CLWE model performance significantly. Projection-based CLWE models learn a transfer function or mapper between two independently trained monolingual word vector spaces with limited or no cross-lingual supervision. Famous among projection-based CLWE models are the unsupervised projection-based CLWE models (Artetxe et al., 2017; Lample et al., 2018; Alvarez-Melis & Jaakkola, 2018;