  Neural unsupervised parsing (UP) models learn to parse without access to
syntactic annotations, while being optimized for another task like language
modeling. In this work, we propose self-training for neural UP models: we
leverage aggregated annotations predicted by copies of our model as supervision
for future copies. To be able to use our model's predictions during training,
we extend a recent neural UP architecture, the PRPN (Shen et al., 2018a) such
that it can be trained in a semi-supervised fashion. We then add examples with
parses predicted by our model to our unlabeled UP training data. Our
self-trained model outperforms the PRPN by 8.1% F1 and the previous state of
the art by 1.6% F1. In addition, we show that our architecture can also be
helpful for semi-supervised parsing in ultra-low-resource settings.
