Parsing to Noncrossing Dependency Graphs

Abstract

We study the generalization of maximum spanning tree dependency parsing to maximum acyclic subgraphs. Because the underlying optimization problem is intractable even under an arc-factored model, we consider the restriction to noncrossing dependency graphs. Our main contribution is a cubic-time exact inference algorithm for this class. We extend this algorithm into a practical parser and evaluate its performance on four linguistic data sets used in semantic dependency parsing. We also explore a generalization of our parsing framework to dependency graphs with pagenumber at most k and show that the resulting optimization problem is NP-hard for k ≥ 2.

Graph-Based Meaning Representations: Design and Processing

“…• Factorization-based methods (Flanigan et al, 2014;Kuhlmann and Jonsson, 2015;Peng et al, 2017;Dozat and Manning, 2018);…”

Neural Maximum Subgraph Parsing for Cross-Domain Semantic Dependency Analysis

“…Some recent work on parsing targets the graphstructured semantic representations that are more general than the tree representation. Existing approaches can be categorized into two dominant types: the transition-based (Zhang et al, 2016;Wang et al, 2018) and graph-based, i.e., Maximum Subgraph (Kuhlmann and Jonsson, 2015;Cao et al, 2017a), approaches. Previous investigations on transition-based string-to-semantic-graph parsing adopt many ideas from syntactic string-totree parsing, such as how to handle crossing arcs and how to perform neural disambiguation.…”

“…Dependency parsing, thus, can be formulated as the search for a maximum spanning tree (MST) from an arcweighted (complete) graph. For SDP where the target representation are no longer trees, Kuhlmann and Jonsson (2015) proposed to generalize the MST model to other types of subgraphs. In general, dependency parsing is formulated as the search for Maximum Subgraph regarding to a particular graph class, viz.…”

Generic Axiomatization of Families of Noncrossing Graphs in Dependency Parsing

“…Context-Free Properties Acyclicity and other important properties of noncrossing digraphs are expressible as unambiguous context-free sets of encoded noncrossing (2015) or Kuhlmann and Johnsson (2015), YJ = Yli-Jyrä (2012) digraphs. This facilitates the incorporation of property testing to dynamic programming algorithms that implement exact inference.…”

“…As this inference task is intractable (Guruswami et al, 2011), noncrossing digraphs have been studied instead, e.g. by Kuhlmann and Johnsson (2015) who provide a O(n 3 ) parser for maximum noncrossing acyclic subgraphs. Yli-Jyrä (2005) studied how to axiomatize dependency trees as a special case of noncrossing digraphs.…”