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.
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