Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in Transformer can be described as a higher-order solution to ODE. Inspired by this, we design a new architecture, ODE Transformer, which is analogous to the Runge-Kutta method that is well motivated in ODE. As a natural extension to Transformer, ODE Transformer is easy to implement and efficient to use. Experimental results on the large-scale machine translation, abstractive summarization, and grammar error correction tasks demonstrate the high genericity of ODE Transformer. It can gain large improvements in model performance over strong baselines (e.g., 30.77 and 44.11 BLEU scores on the WMT’14 English-German and English-French benchmarks) at a slight cost in inference efficiency.

This paper describes NiuTrans neural machine translation systems of the WMT20 news translation tasks. We participated in Japanese<->English, English->Chinese, Inuktitut->English and Tamil->English total five tasks and rank first in Japanese<->English both sides. We mainly utilized iterative back-translation, different depth and widen model architectures, iterative knowledge distillation and iterative fine-tuning. And we find that adequately widened and deepened the model simultaneously, the performance will significantly improve. Also, iterative fine-tuning strategy we implemented is effective during adapting domain. For Inuktitut->English and Tamil->English tasks, we built multilingual models separately and employed pretraining word embedding to obtain better performance.