  Phrase-level dense retrieval has shown many appealing characteristics in
downstream NLP tasks by leveraging the fine-grained information that phrases
offer. In our work, we propose a new task formulation of dense retrieval,
cross-lingual contextualized phrase retrieval, which aims to augment
cross-lingual applications by addressing polysemy using context information.
However, the lack of specific training data and models are the primary
challenges to achieve our goal. As a result, we extract pairs of cross-lingual
phrases using word alignment information automatically induced from parallel
sentences. Subsequently, we train our Cross-lingual Contextualized Phrase
Retriever (CCPR) using contrastive learning, which encourages the hidden
representations of phrases with similar contexts and semantics to align
closely. Comprehensive experiments on both the cross-lingual phrase retrieval
task and a downstream task, i.e, machine translation, demonstrate the
effectiveness of CCPR. On the phrase retrieval task, CCPR surpasses baselines
by a significant margin, achieving a top-1 accuracy that is at least 13 points
higher. When utilizing CCPR to augment the large-language-model-based
translator, it achieves average gains of 0.7 and 1.5 in BERTScore for
translations from X=>En and vice versa, respectively, on WMT16 dataset. Our
code and data are available at \url{https://github.com/ghrua/ccpr_release}.
