This report describes our VolcTrans system for the WMT22 shared task on large-scale multilingual machine translation. We participated in the unconstrained track which allows the use of external resources. Our system is a transformer-based multilingual model trained on data from multiple sources including the public training set from the data track, NLLB data provided by Meta AI, self-collected parallel corpora, and pseudo bitext from back-translation. Both bilingual and monolingual texts are cleaned by a series of heuristic rules. On the official test set, our system achieves $17.3$ BLEU, $21.9$ spBLEU, and $41.9$ chrF2++ on average over all language pairs. Averaged inference speed is $11.5$ sentences per second using a single Nvidia Tesla V100 GPU.

Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can help improve predictive accuracy. However, designing good constraints often relies on domain expertise. In this paper, we study the problem of learning such constraints. We frame the problem as that of training a two-layer rectifier network to identify valid structures or substructures, and show a construction for converting a trained network into a system of linear constraints over the inference variables. Our experiments on several NLP tasks show that the learned constraints can improve the prediction accuracy, especially when the number of training examples is small.