Recent advances in cross-lingual word embeddings have primarily relied on mapping-based methods, which project pretrained word embeddings from different languages into a shared space through a linear transformation. However, these approaches assume word embedding spaces are isomorphic between different languages, which has been shown not to hold in practice (S{\o}gaard et al., 2018), and fundamentally limits their performance. This motivates investigating joint learning methods which can overcome this impediment, by simultaneously learning embeddings across languages via a cross-lingual term in the training objective. We propose a bilingual extension of the CBOW method which leverages sentence-aligned corpora to obtain robust cross-lingual word and sentence representations. Our approach significantly improves cross-lingual sentence retrieval performance over all other approaches while maintaining parity with the current state-of-the-art methods on word-translation. It also achieves parity with a deep RNN method on a zero-shot cross-lingual document classification task, requiring far fewer computational resources for training and inference. As an additional advantage, our bilingual method leads to a much more pronounced improvement in the the quality of monolingual word vectors compared to other competing methods.
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