  Dependency parsing is a crucial step towards deep language understanding and,
therefore, widely demanded by numerous Natural Language Processing
applications. In particular, left-to-right and top-down transition-based
algorithms that rely on Pointer Networks are among the most accurate approaches
for performing dependency parsing. Additionally, it has been observed for the
top-down algorithm that Pointer Networks' sequential decoding can be improved
by implementing a hierarchical variant, more adequate to model dependency
structures. Considering all this, we develop a bottom-up-oriented Hierarchical
Pointer Network for the left-to-right parser and propose two novel
transition-based alternatives: an approach that parses a sentence in
right-to-left order and a variant that does it from the outside in. We
empirically test the proposed neural architecture with the different algorithms
on a wide variety of languages, outperforming the original approach in
practically all of them and setting new state-of-the-art results on the English
and Chinese Penn Treebanks for non-contextualized and BERT-based embeddings.
