  We treat projective dependency trees as latent variables in our probabilistic
model and induce them in such a way as to be beneficial for a downstream task,
without relying on any direct tree supervision. Our approach relies on Gumbel
perturbations and differentiable dynamic programming. Unlike previous
approaches to latent tree learning, we stochastically sample global structures
and our parser is fully differentiable. We illustrate its effectiveness on
sentiment analysis and natural language inference tasks. We also study its
properties on a synthetic structure induction task. Ablation studies emphasize
the importance of both stochasticity and constraining latent structures to be
projective trees.
