Several models for inducing cross-lingual embeddings have been proposed, each requiring a different form of cross-lingual supervision -some can use document-level alignments (Vulić and Moens, 2015), others need alignments at the sentence (Hermann and Blunsom, 2014; or word level (Faruqui and Dyer, 2014;Gouws and Søgaard, 2015), while some require both sentence and word alignments (Luong et al., 2015).
a systematic comparison of these models is missing from the literature, making it difficult to analyze which approach is suitable for a particular NLP task.