  Back-translation (BT) is an effective semi-supervised learning framework in
neural machine translation (NMT). A pre-trained NMT model translates
monolingual sentences and makes synthetic bilingual sentence pairs for the
training of the other NMT model, and vice versa. Understanding the two NMT
models as inference and generation models, respectively, the training method of
variational auto-encoder (VAE) was applied in previous works, which is a
mainstream framework of generative models. However, the discrete property of
translated sentences prevents gradient information from flowing between the two
NMT models. In this paper, we propose the categorical reparameterization trick
(CRT) that makes NMT models generate differentiable sentences so that the VAE's
training framework can work in an end-to-end fashion. Our BT experiment
conducted on a WMT benchmark dataset demonstrates the superiority of our
proposed CRT compared to the Gumbel-softmax trick, which is a popular
reparameterization method for categorical variable. Moreover, our experiments
conducted on multiple WMT benchmark datasets demonstrate that our proposed
end-to-end training framework is effective in terms of BLEU scores not only
compared to its counterpart baseline which is not trained in an end-to-end
fashion, but also compared to other previous BT works. The code is available at
the web.
