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.

Non-autoregressive models achieve significant decoding speedup in neural machine translation but lack the ability to capture sequential dependency. Directed Acyclic Transformer (DA-Transformer) was recently proposed to model sequential dependency with a directed acyclic graph. Consequently, it has to apply a sequential decision process at inference time, which harms the global translation accuracy. In this paper, we present a Viterbi decoding framework for DA-Transformer, which guarantees to find the joint optimal solution for the translation and decoding path under any length constraint. Experimental results demonstrate that our approach consistently improves the performance of DA-Transformer while maintaining a similar decoding speedup.