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I am wondering how the lexical ambiguity is addressed in phrase-based statistical machine translation?

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Well, a word like 'bank' that is ambiguous between 'financial institution' and 'side of a river' will often be disambiguated by context. So, the first sense is talked about near words like 'money', while the second sense is talked about near words like 'water'. An SMT model will pick up on this regularity, and when it sees something like "money....bank", it'll translate "bank" into "banco" (if we're translating into Spanish).

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