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 WMT 2021 news translation tasks. We made submissions to 9 language directions, including English2Chinese, Japanese, Russian, Icelandic and English2Hausa tasks. Our primary systems are built on several effective variants of Transformer, e.g., Transformer-DLCL, ODE-Transformer. We also utilize back-translation, knowledge distillation, post-ensemble, and iterative fine-tuning techniques to enhance the model performance further.