  This paper describes a parsing model that combines the exact dynamic
programming of CRF parsing with the rich nonlinear featurization of neural net
approaches. Our model is structurally a CRF that factors over anchored rule
productions, but instead of linear potential functions based on sparse
features, we use nonlinear potentials computed via a feedforward neural
network. Because potentials are still local to anchored rules, structured
inference (CKY) is unchanged from the sparse case. Computing gradients during
learning involves backpropagating an error signal formed from standard CRF
sufficient statistics (expected rule counts). Using only dense features, our
neural CRF already exceeds a strong baseline CRF model (Hall et al., 2014). In
combination with sparse features, our system achieves 91.1 F1 on section 23 of
the Penn Treebank, and more generally outperforms the best prior single parser
results on a range of languages.
