Users of machine translation (MT) may want to ensure the use of specific lexical terminologies. While there exist techniques for incorporating terminology constraints during inference for MT, current APE approaches cannot ensure that they will appear in the final translation. In this paper, we present both autoregressive and non-autoregressive models for lexically constrained APE, demonstrating that our approach enables preservation of 95% of the terminologies and also improves translation quality on English-German benchmarks. Even when applied to lexically constrained MT output, our approach is able to improve preservation of the terminologies. However, we show that our models do not learn to copy constraints systematically and suggest a simple data augmentation technique that leads to improved performance and robustness.
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