AbstractIn this paper, we propose a probabilistic parsing model that defines a proper conditional probability distribution over non-projective dependency trees for a given sentence, using neural representations as inputs. The neural network architecture is based on bi-directional LSTMCNNs, which automatically benefits from both word- and character-level representations, by using a combination of bidirectional LSTMs and CNNs. On top of the neural network, we introduce a probabilistic structured layer, defining a conditional log-linear model over non-projective trees. By exploiting Kirchhoff’s Matrix-Tree Theorem (Tutte, 1984), the partition functions and marginals can be computed efficiently, leading to a straightforward end-to-end model training procedure via back-propagation. We evaluate our model on 17 different datasets, across 14 different languages. Our parser achieves state-of-the-art parsing performance on nine datasets.