Conventional knowledge distillation (KD) methods require access to the internal information of teachers, e.g., logits. However, such information may not always be accessible for large pre-trained language models (PLMs). In this work, we focus on decision-based KD for PLMs, where only teacher decisions (i.e., top-1 labels) are accessible. Considering the information gap between logits and decisions, we propose a novel method to estimate logits from the decision distributions. Specifically, decision distributions can be both derived as a function of logits theoretically and estimated with test-time data augmentation empirically. By combining the theoretical and empirical estimations of the decision distributions together, the estimation of logits can be successfully reduced to a simple root-finding problem. Extensive experiments show that our method significantly outperforms strong baselines on both natural language understanding and machine reading comprehension datasets.

While neural machine translation (NMT) has achieved remarkable success, NMT systems are prone to make word omission errors. In this work, we propose a contrastive learning approach to reducing word omission errors in NMT. The basic idea is to enable the NMT model to assign a higher probability to a ground-truth translation and a lower probability to an erroneous translation, which is automatically constructed from the ground-truth translation by omitting words. We design different types of negative examples depending on the number of omitted words, word frequency, and part of speech. Experiments on Chinese-to-English, German-to-English, and Russian-to-English translation tasks show that our approach is effective in reducing word omission errors and achieves better translation performance than three baseline methods.