  Sequence-to-sequence learning with neural networks has become the de facto
standard for sequence prediction tasks. This approach typically models the
local distribution over the next word with a powerful neural network that can
condition on arbitrary context. While flexible and performant, these models
often require large datasets for training and can fail spectacularly on
benchmarks designed to test for compositional generalization. This work
explores an alternative, hierarchical approach to sequence-to-sequence learning
with quasi-synchronous grammars, where each node in the target tree is
transduced by a node in the source tree. Both the source and target trees are
treated as latent and induced during training. We develop a neural
parameterization of the grammar which enables parameter sharing over the
combinatorial space of derivation rules without the need for manual feature
engineering. We apply this latent neural grammar to various domains -- a
diagnostic language navigation task designed to test for compositional
generalization (SCAN), style transfer, and small-scale machine translation --
and find that it performs respectably compared to standard baselines.
