We propose a headed span-based method for projective dependency parsing. In a projective tree, the subtree rooted at each word occurs in a contiguous sequence (i.e., span) in the surface order, we call the span-headword pair textit{headed span}. In this view, a projective tree can be regarded as a collection of headed spans. It is similar to the case in constituency parsing since a constituency tree can be regarded as a collection of constituent spans. Span-based methods decompose the score of a constituency tree sorely into the score of constituent spans and use the CYK algorithm for global training and exact inference, obtaining state-of-the-art results in constituency parsing. Inspired by them, we decompose the score of a dependency tree into the score of headed spans. We use neural networks to score headed spans and design a novel $O(n^3)$ dynamic programming algorithm to enable global training and exact inference. We evaluate our method on PTB, CTB, and UD, achieving state-of-the-art or comparable results.
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