Transforming Dependency Structures to LTAG Derivation Trees 13th International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+13) Caio Corro Joseph Le Roux September 1, 2017 Laboratoire Informatique de Paris Nord (LIPN), Universit´ e Paris 13 (France), CNRS UMR 7030
Introduction
Lexicalized Tree Adjoining Grammar (LTAG) S Why LTAGs? NP VP • Constituency structure VBZ NP NP • Linguistically plausible walks NN • Built-in bi-lexical relations • Deep syntax dog S Weighted grammars NP VP • Disambiguation/Preference � VBZ NP • Robustness: NP walks • Unknown words NN • Errors river 1
LTAG parsing CKY-type algorithm • Deduction-rule based • Bottom-up Complexity O ( n 6 max( n , g ) gt ): n : sentence length t : maximum number of nodes in an elementary tree g : maximum ambiguity ⇒ O ( n 7 ) asymptotically w.r.t. the sentence length [Eisner et al., 2000] 2
LTAG parsing problem Lexical ambiguity Non-trivial dependency Combination structure constraints 3
Supertagging approach (1) Lexical ambiguity Non-trivial dependency Combination structure constraints 4
Supertagging approach (2) She walks the dog 5
Supertagging approach (2) S NP VP NP VBZ NP NN She walks the dog 5
Supertagging approach (2) S NP VP NP VBZ NP NN She walks the dog 5
Supertagging approach (2) S NP VP NP VBZ NP NN She walks the dog She walks, despite her hatred for quadruped mammals, the dog 5
Supertagging approach (2) S NP VP NP VBZ NP NN She walks the dog S NP VP NP VBZ NN She walks, despite her hatred for quadruped mammals, the dog 5
Supertagging approach (2) S NP VP NP VBZ NP NN She walks the dog S ? NP VP NP VBZ NN She walks, despite her hatred for quadruped mammals, the dog 5
Supertagging approach (3) Pipeline 1. Supertagging 2. Constraint LTAG parsing Downsides • Long distance relationship • 2nd step complexity: O ( n 7 t ) ⇒ No lexical ambiguity 6
Phrase structure tree VS Dependency tree ”. . . One should always distinguish the type of representation [. . . ] from the content of the representation...” [Rambow, 2010] Syntactic content Representation types • Syntactic dependency • Dependency tree • Syntactic phrase/constituency structure • Hierarchy structure tree ⇒ Syntactic phrase-structure parsing as a dependency structure parsing task 7
LTAG derivation tree S NP VP NP VBZ NP NP PRP VP walks NP NN She ADVP VP* DET NP ∗ dog RB the deliberately Bottom-up construction of the syntactic phrase structure v 3 1 1 2 1 . . 2 . 2 τ 3 1 . 1 v 1 v 5 τ 1 τ 5 v 2 v 4 τ 2 τ 4 She deliberately walks the dog Representation alternative: the LTAG derivation tree is a dependency tree [Rambow et al., 1997] 8
Proposed approach (1) Lexical ambiguity Non-trivial dependency Combination structure constraints 9
Proposed approach (1) Lexical ambiguity Non-trivial dependency Combination constraints structure 9
Proposed approach (2) v 3 v 3 1 . 1 1 . 2 . 2 1 . 2 τ 3 dog ⇒ v 1 v 5 v 1 1 . 1 v 5 v 2 v 4 τ 1 v 2 v 4 τ 5 τ 2 τ 4 deliberately deliberately dog She walks the She walks the Alternative pipeline 1. Bi-lexical dependency parsing: long distance relationships 2. LTAG parse labeler Downsides • 1st step complexity: O ( n 7 ) [G´ omez-Rodr´ ıguez et al., 2009] • 2nd step complexity? 10
Proposed approach (2) v 3 v 3 1 . 2 . 2 1 . 1 1 . 2 τ 3 dog ⇒ v 1 v 5 v 1 v 5 1 . 1 v 2 v 4 v 2 v 4 τ 1 τ 5 τ 2 τ 4 She deliberately walks the She deliberately walks the dog Alternative pipeline 1. Bi-lexical dependency parsing: long distance relationships 2. LTAG parse labeler Downsides • 1st step complexity: O ( n 7 ) [G´ omez-Rodr´ ıguez et al., 2009] ⇒ Efficient decoding in practice via Lagrangian relaxation [Corro et al., 2016] • 2nd step complexity? ⇒ This contribution! 10
Table of contents 1. Introduction 2. Characterization of LTAG derivation trees 3. Outline of the algorithm 4. Complexity 5. Conclusion 11
Characterization of LTAG derivation trees
LTAG derivation trees Structural properties [Bodirsky et al., 2005] • Arborescence (directed tree) • 2-bounded block degree • Well-nestedness 2-bounded block degree • Maximum 1 gap in the yield of a sub-arborescence ⇒ Due to wrapping adjunction Well-nestedness • Sub-arborescences must not interleave (not used in this presentation) 12
Yield Yield of a vertex v : set of all nodes reachable from v 0 2 4 1 3 s 0 s 1 s 2 s 3 s 4 13
Yield Yield of a vertex v : set of all nodes reachable from v Yield (0) = { 0 , 1 , 2 , 3 , 4 } 0 0 2 2 4 4 1 1 3 3 s 0 s 1 s 2 s 3 s 4 13
Yield Yield of a vertex v : set of all nodes reachable from v Yield (0) = { 0 , 1 , 2 , 3 , 4 } 0 Yield (1) = { 1 } 2 4 1 1 3 s 0 s 1 s 2 s 3 s 4 13
Yield Yield of a vertex v : set of all nodes reachable from v Yield (0) = { 0 , 1 , 2 , 3 , 4 } 0 Yield (1) = { 1 } 2 2 4 4 Yield (2) = { 1 , 2 , 3 , 4 } 1 1 3 3 s 0 s 1 s 2 s 3 s 4 13
Yield Yield of a vertex v : set of all nodes reachable from v Yield (0) = { 0 , 1 , 2 , 3 , 4 } 0 Yield (1) = { 1 } 2 4 Yield (2) = { 1 , 2 , 3 , 4 } 1 Yield (3) = { 3 } 3 3 s 0 s 1 s 2 s 3 s 4 13
Yield Yield of a vertex v : set of all nodes reachable from v Yield (0) = { 0 , 1 , 2 , 3 , 4 } 0 Yield (1) = { 1 } 2 4 4 Yield (2) = { 1 , 2 , 3 , 4 } 1 1 Yield (3) = { 3 } 3 3 Yield (4) = { 1 , 3 , 4 } s 0 s 1 s 2 s 3 s 4 13
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 v 2 v 3 v 1 v 4 s 0 s 1 s 2 s 3 s 4 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 v 2 v 3 v 3 v 1 v 1 v 4 v 4 s 0 s 1 s 2 s 3 s 4 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 Yield (1) = [1] ∪ [4] BD (1) = 2 v 3 v 1 v 1 v 4 v 4 s 0 s 1 s 2 s 3 s 4 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 v 2 Yield (1) = [1] ∪ [4] BD (1) = 2 v 3 v 3 v 1 Yield (2) = [2 . . . 3] BD (2) = 1 v 4 s 0 s 1 s 2 s 3 s 4 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 Yield (1) = [1] ∪ [4] BD (1) = 2 v 3 v 3 v 1 Yield (2) = [2 . . . 3] BD (2) = 1 v 4 Yield (3) = [3] BD (3) = 1 s 0 s 1 s 2 s 3 s 4 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 Yield (1) = [1] ∪ [4] BD (1) = 2 v 3 v 1 Yield (2) = [2 . . . 3] BD (2) = 1 v 4 v 4 Yield (3) = [3] BD (3) = 1 s 0 s 1 s 2 s 3 s 4 Yield (4) = [4] BD (4) = 1 14
2-bounded block degree Bound degree • Vertex: number of contiguous intervals described by its yield • Arborescence: the maximal block degree of its vertices 2 Bounded degree arborescence • Arborescence with a bound degree less or equal to 2 v 0 Yield (0) = [0 . . . 4] BD (0) = 1 v 2 Yield (1) = [1] ∪ [4] BD (1) = 2 v 3 v 1 v 1 Yield (2) = [2 . . . 3] BD (2) = 1 v 4 v 4 Yield (3) = [3] BD (3) = 1 s 0 s 1 s 2 s 3 s 4 Yield (4) = [4] BD (4) = 1 Intuition • Auxiliary tree anchored at s 1 adjoined via wrapping adjunction • Anchors s 2 and s 3 attached below the foot node 14
Parsing Dynamic programming [G´ omez-Rodr´ ıguez et al., 2009] • Complexity: O ( n 7 ), intractable on long sentences ⇒ Asymptotically equivalent to LTAG parsing! Combinatorial optimization [Corro et al., 2016] • Complexity: exponential • Practically: fast ⇒ ”Simple” optimization problem as there is no constraint on combination operations Intuition 1. Non-trivial dependency structure parsing tackled via combinatorial optimization 2. Complexity of parse tree labeling? 15
Outline of the algorithm
Parse tree labeling Lexical ambiguity Non-trivial dependency Combination structure constraints 16
Parse tree labeling Lexical ambiguity Non-trivial dependency Combination structure constraints 16
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