  Human annotation for syntactic parsing is expensive, and large resources are
available only for a fraction of languages. A question we ask is whether one
can leverage abundant unlabeled texts to improve syntactic parsers, beyond just
using the texts to obtain more generalisable lexical features (i.e. beyond word
embeddings). To this end, we propose a novel latent-variable generative model
for semi-supervised syntactic dependency parsing. As exact inference is
intractable, we introduce a differentiable relaxation to obtain approximate
samples and compute gradients with respect to the parser parameters. Our method
(Differentiable Perturb-and-Parse) relies on differentiable dynamic programming
over stochastically perturbed edge scores. We demonstrate effectiveness of our
approach with experiments on English, French and Swedish.
