Regularization methods applying input perturbation have drawn considerable attention and have been frequently explored for NMT tasks in recent years. Despite their simplicity and effectiveness, we argue that these methods are limited by the under-fitting of training data. In this paper, we utilize prediction difference for ground-truth tokens to analyze the fitting of token-level samples and find that under-fitting is almost as common as over-fitting. We introduce prediction difference regularization (PD-R), a simple and effective method that can reduce over-fitting and under-fitting at the same time. For all token-level samples, PD-R minimizes the prediction difference between the original pass and the input-perturbed pass, making the model less sensitive to small input changes, thus more robust to both perturbations and under-fitted training data. Experiments on three widely used WMT translation tasks show that our approach can significantly improve over existing perturbation regularization methods. On WMT16 En-De task, our model achieves 1.80 SacreBLEU improvement over vanilla transformer.

Although teacher forcing has become the main training paradigm for neural machine translation, it usually makes predictions only conditioned on past information, and hence lacks global planning for the future. To address this problem, we introduce another decoder, called seer decoder, into the encoder-decoder framework during training, which involves future information in target predictions. Meanwhile, we force the conventional decoder to simulate the behaviors of the seer decoder via knowledge distillation. In this way, at test the conventional decoder can perform like the seer decoder without the attendance of it. Experiment results on the Chinese-English, English-German and English-Romanian translation tasks show our method can outperform competitive baselines significantly and achieves greater improvements on the bigger data sets. Besides, the experiments also prove knowledge distillation the best way to transfer knowledge from the seer decoder to the conventional decoder compared to adversarial learning and L2 regularization.