  Semantic dependency parsing aims to identify semantic relationships between
words in a sentence that form a graph. In this paper, we propose a second-order
semantic dependency parser, which takes into consideration not only individual
dependency edges but also interactions between pairs of edges. We show that
second-order parsing can be approximated using mean field (MF) variational
inference or loopy belief propagation (LBP). We can unfold both algorithms as
recurrent layers of a neural network and therefore can train the parser in an
end-to-end manner. Our experiments show that our approach achieves
state-of-the-art performance.
