  We investigate the use of hierarchical phrase-based SMT lattices in
end-to-end neural machine translation (NMT). Weight pushing transforms the
Hiero scores for complete translation hypotheses, with the full translation
grammar score and full n-gram language model score, into posteriors compatible
with NMT predictive probabilities. With a slightly modified NMT beam-search
decoder we find gains over both Hiero and NMT decoding alone, with practical
advantages in extending NMT to very large input and output vocabularies.
