  In this paper, we propose second-order graph-based neural dependency parsing
using message passing and end-to-end neural networks. We empirically show that
our approaches match the accuracy of very recent state-of-the-art second-order
graph-based neural dependency parsers and have significantly faster speed in
both training and testing. We also empirically show the advantage of
second-order parsing over first-order parsing and observe that the usefulness
of the head-selection structured constraint vanishes when using BERT embedding.
