Can Latent Alignments Improve Autoregressive Machine Translation?

Latent alignment objectives such as CTC and AXE significantly improve non-autoregressive machine translation models. Can they improve autoregressive models as well? We explore the possibility of training autoregressive machine translation models with latent alignment objectives, and observe that, in practice, this approach results in degenerate models. We provide a theoretical explanation for these empirical results, and prove that latent alignment objectives are incompatible with teacher forcing.