Parsing has been a central problem in Natural Language Processing, further
improved with pre-trained language models and neural networks. I will present
two advances made in significantly improving the speed of dependency parsing
(EMNLP, 2021) and significantly improving the accuracy of unsupervised
constituency parsing (Findings of ACL, 2022).

In the first part of the talk, I will mainly show how a simple modification to
the weights of a learned model can make dependency parsing asymptotically
optimal, with a quadratic complexity for parsing (rather than cubic).

In the second part of the talk, I will show how co-training and intuitions from
spectral learning combine with pre-trained language models to get effective
multilingual unsupervised parsing.

Joint work with Miloš Stanojević and Nickil Maveli.