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Generally, machine translation is translating a sentence from an original language to a target language. However, for a specific origin sentence, the target sentence is not unique. Now, I have multiple target sentences for a single original sentence. Is there any possible way to train a multi-label machine translation model?

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Generally, machine translation is translating a sentence from an original language to a target language.

To be more precise, in the context of statistical or neural machine translation, the goal is to

  1. Model the conditional distribution $p(y|x)$ where $x$ is the source sentence and $y$ the target.

  2. At test time, sample a high quality result from this distribution, so that you can actually use the translation model.

Under the maximum likelihood framework (which most neural translation models are trained with), (1) simply reduces to finding $\theta^* = \text{argmax}_\theta \sum_i \log p(y_i|x_i; \theta)$ where $(x_i, y_i)$ are pairs of source and target sentences. But notice this doesn't assume anything about the pairs, including whether each source sentence has only a single corresponding target sentence or not.

So it is possible to train a "multi-label machine translation model", and in fact most models will work perfectly fine without any changes.

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