How to train your multi bottom-up tree transducer
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1 How to train your multi bottom-up tree transducer Andreas Maletti Universität tuttgart Institute for Natural Language Processing tuttgart, Germany Portland, OR June 22, 2011 How to train your multi bottom-up tree transducer A. Maletti 1
2 ynchronous Tree ubstitution Grammar Used rule Next rule CONJ wa How to train your multi bottom-up tree transducer A. Maletti 2
3 ynchronous Tree ubstitution Grammar CONJ wa Used rule Next rule CONJ wa 1 p 2 p 1 2 How to train your multi bottom-up tree transducer A. Maletti 2
4 ynchronous Tree ubstitution Grammar 1 CONJ p 2 wa p 1 2 Used rule Next rule 1 p 1 2 V saw p V ra aa p 2 How to train your multi bottom-up tree transducer A. Maletti 2
5 ynchronous Tree ubstitution Grammar 1 V saw 2 CONJ wa V ra aa 1 2 Used rule Next rule V saw p V ra aa DT r 1 r the How to train your multi bottom-up tree transducer A. Maletti 2
6 ynchronous Tree ubstitution Grammar CONJ DT r V 2 wa V 2 the saw ra aa r Used rule Next rule DT r 1 r the N boy r N atefl How to train your multi bottom-up tree transducer A. Maletti 2
7 ynchronous Tree ubstitution Grammar CONJ DT N V 2 wa V 2 the boy saw ra aa N atefl Used rule Next rule N boy r N atefl DT r 2 r the How to train your multi bottom-up tree transducer A. Maletti 2
8 ynchronous Tree ubstitution Grammar CONJ DT N V wa V the boy saw DT r ra aa N r the atefl Used rule Next rule DT r 2 r the N door r N albab How to train your multi bottom-up tree transducer A. Maletti 2
9 ynchronous Tree ubstitution Grammar CONJ DT N V wa V the boy saw DT N ra aa N N the door atefl albab Used rule Next rule N door r N albab How to train your multi bottom-up tree transducer A. Maletti 2
10 ynchronous Tree ubstitution Grammar Rule shape states can occur only once in lhs and rhs states in rhs = states in lhs exactly one lhs and one rhs bijective synchronization relation 1 p 1 2 p 2 How to train your multi bottom-up tree transducer A. Maletti 3
11 ynchronous Tree ubstitution Grammar Rule shape states can occur only once in lhs and rhs states in rhs = states in lhs exactly one lhs and one rhs bijective synchronization relation 1 p 1 2 p 2 How to train your multi bottom-up tree transducer A. Maletti 3
12 ynchronous Tree ubstitution Grammar Rule shape states can occur only once in lhs and rhs states in rhs = states in lhs exactly one lhs and one rhs bijective synchronization relation Notes version with states (instead of locality tests) euivalent to linear nondeleting extended tree transducers implemented in TIBURON [May, Knight 2006] How to train your multi bottom-up tree transducer A. Maletti 3
13 Multi Bottom-up Tree Transducer Used rule Next rule p wa p p How to train your multi bottom-up tree transducer A. Maletti 4
14 Multi Bottom-up Tree Transducer p wa p p Used rule Next rule p wa p p signed r p twly -OBJ r AltwyE How to train your multi bottom-up tree transducer A. Maletti 4
15 Multi Bottom-up Tree Transducer wa signed r twly -OBJ r AltwyE Used rule Next rule signed r p twly -OBJ r AltwyE -BJ p Voislav -BJ p fwyslaf How to train your multi bottom-up tree transducer A. Maletti 4
16 Multi Bottom-up Tree Transducer -BJ wa p Voislav signed r twly -OBJ -BJ r p AltwyE fwyslaf Used rule Next rule -BJ p Voislav -BJ p fwyslaf NML Yugoslav President p Alr}ys AlywgwslAfy How to train your multi bottom-up tree transducer A. Maletti 4
17 Multi Bottom-up Tree Transducer -BJ wa NML Voislav signed r twly -OBJ -BJ Yugoslav President r... AltwyE Alr}ys AlywgwslAfy Used rule Next rule PP PP Yugoslav NML President p Alr}ys AlywgwslAfy for erbia r en rbya How to train your multi bottom-up tree transducer A. Maletti 4
18 Multi Bottom-up Tree Transducer -BJ NML Voislav Yugoslav President signed PP for erbia wa twly -OBJ... PP AltwyE en rbya Used rule Next rule PP for erbia r PP en rbya How to train your multi bottom-up tree transducer A. Maletti 4
19 Multi Bottom-up Tree Transducer Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: bijective synchronization relation MBOT: inverse synchronization relation is functional p wa p p How to train your multi bottom-up tree transducer A. Maletti 5
20 Multi Bottom-up Tree Transducer Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: bijective synchronization relation MBOT: inverse synchronization relation is functional p wa p p How to train your multi bottom-up tree transducer A. Maletti 5
21 Multi Bottom-up Tree Transducer Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: bijective synchronization relation MBOT: inverse synchronization relation is functional signed r p twly -OBJ AltwyE r How to train your multi bottom-up tree transducer A. Maletti 5
22 Multi Bottom-up Tree Transducer Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: bijective synchronization relation MBOT: inverse synchronization relation is functional p wa p p How to train your multi bottom-up tree transducer A. Maletti 5
23 TG vs. MBOT property TG MBOT simple and natural? symmetric preserves regularity inverse pres. regularity binarizable closed under composition input parsing O( M n x ) O( M n 3 ) output parsing O( M n x ) O( M n y ) where x = 2 rk(m) + 5 and y = 2 rk(m) + 2 How to train your multi bottom-up tree transducer A. Maletti 6
24 Additional Expressive Power Finite copying { t, σ(t, t) t T Σ } desirable [ATANLP participants, 2010] e.g., for cross-serial dependencies harms preservation of regularity Non-contiguous rules BLEU [un, Zhang, Tan, 2009] do not harm preservation of regularity How to train your multi bottom-up tree transducer A. Maletti 7
25 Additional Expressive Power Finite copying { t, σ(t, t) t T Σ } desirable [ATANLP participants, 2010] e.g., for cross-serial dependencies harms preservation of regularity Non-contiguous rules BLEU [un, Zhang, Tan, 2009] do not harm preservation of regularity How to train your multi bottom-up tree transducer A. Maletti 7
26 Approach Old approach 1 extract TG rules 2 train TG 3 convert to MBOT 4 work with MBOT New approach 1 extract (restricted) MBOT rules 2 train MBOT 3 work with MBOT How to train your multi bottom-up tree transducer A. Maletti 8
27 Approach Old approach 1 extract TG rules 2 train TG 3 convert to MBOT 4 work with MBOT New approach 1 extract (restricted) MBOT rules 2 train MBOT 3 work with MBOT How to train your multi bottom-up tree transducer A. Maletti 8
28 Roadmap 1 Motivation 2 Relation to TG 3 Rule Extraction and Training 4 Preservation of Recognizability How to train your multi bottom-up tree transducer A. Maletti 9
29 ynchronous Tree-euence ubstitution Grammar Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: (no restriction) TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: (no restriction) TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: (no restriction) How to train your multi bottom-up tree transducer A. Maletti 10
30 ynchronous Tree-euence ubstitution Grammar Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: (no restriction) TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: (no restriction) TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: (no restriction) How to train your multi bottom-up tree transducer A. Maletti 10
31 ynchronous Tree-euence ubstitution Grammar Rule shape TG: states can occur only once in lhs and rhs MBOT: states can occur only once in lhs TG: (no restriction) TG: states in rhs = states in lhs MBOT: states in rhs states in lhs TG: (no restriction) TG: exactly one lhs and one rhs MBOT: exactly one lhs TG: (no restriction) How to train your multi bottom-up tree transducer A. Maletti 10
32 Expressive Power Corollary TG MBOT TG Theorem TG MBOT TG Claim MBOT 1 ; MBOT = TG How to train your multi bottom-up tree transducer A. Maletti 11
33 Expressive Power Corollary TG MBOT TG Theorem TG MBOT TG Claim MBOT 1 ; MBOT = TG How to train your multi bottom-up tree transducer A. Maletti 11
34 Expressive Power Corollary TG MBOT TG Theorem TG MBOT TG Claim MBOT 1 ; MBOT = TG How to train your multi bottom-up tree transducer A. Maletti 11
35 TG vs. MBOT vs. TG property TG MBOT TG simple and natural??? symmetric preserves regularity inverse pres. regularity binarizable closed under composition input parsing O( M n x ) O( M n 3 ) O( M n y ) output parsing O( M n x ) O( M n y ) O( M n y ) where x = 2 rk(m) + 5 and y = 2 rk(m) + 2 How to train your multi bottom-up tree transducer A. Maletti 12
36 Roadmap 1 Motivation 2 Relation to TG 3 Rule Extraction and Training 4 Preservation of Recognizability How to train your multi bottom-up tree transducer A. Maletti 13
37 Rule Extraction Input parallel bi-text parses for input and output word alignment Output MBOT rules How to train your multi bottom-up tree transducer A. Maletti 14
38 Rule Extraction Input parallel bi-text parses for input and output word alignment Output MBOT rules How to train your multi bottom-up tree transducer A. Maletti 14
39 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 15
40 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 15
41 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 15
42 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 15
43 -BJ NML N VBD PP JJ N Voislav signed IN Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 15
44 Rule Extraction JJ -BJ NML N N Voislav VBD PP signed IN V P CONJ w V P V P Yugoslav President for N erbia rbya AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ How to train your multi bottom-up tree transducer A. Maletti 16
45 Rule Extraction JJ -BJ NML N N Voislav VBD PP signed IN V P CONJ w V P V P Yugoslav President for N erbia rbya VBD P P AltwyE En NN-PROP Alr}ys AlywgwslAfy fwyslaf signed DET-NN PREP DET-NN DET-ADJ NN-PROP twly PP w PV -OBJ -BJ CONJ V P PV twly -OBJ P P DET-NN AltwyE How to train your multi bottom-up tree transducer A. Maletti 16
46 Extracted Rules TG rule MBOT rules TG rule PV -OBJ twly P P VBD P P DET-NN signed AltwyE How to train your multi bottom-up tree transducer A. Maletti 17
47 Extracted Rules TG rule MBOT rules TG rule PV -OBJ twly P P VBD P P DET-NN signed AltwyE V P V P V P -OBJ PV P P VBD P P V P twly DET-NN signed AltwyE How to train your multi bottom-up tree transducer A. Maletti 17
48 Extracted Rules TG rule MBOT rules TG rule PV -OBJ twly P P VBD P P DET-NN signed AltwyE V P V P V P -OBJ PV P P VBD P P V P twly DET-NN signed AltwyE VBD signed IN PV for twly DET-NN AltwyE PREP En How to train your multi bottom-up tree transducer A. Maletti 17
49 Training Definition A tree language is regular if it can be represented by a TG (with states). Example is not regular. {σ(t, t) t T Σ } How to train your multi bottom-up tree transducer A. Maletti 18
50 Training Theorem The set of derivations of an MBOT is regular. Conclusion Minimal adaptation of [Graehl, Knight, May 2008] can be used. How to train your multi bottom-up tree transducer A. Maletti 19
51 Training Theorem The set of derivations of an MBOT is regular. Conclusion Minimal adaptation of [Graehl, Knight, May 2008] can be used. How to train your multi bottom-up tree transducer A. Maletti 19
52 Roadmap 1 Motivation 2 Relation to TG 3 Rule Extraction and Training 4 Preservation of Recognizability How to train your multi bottom-up tree transducer A. Maletti 20
53 Preservation of Regularity Input MBOT M regular tree language L Question Is M(L) = {t s L: s, t M} regular? Example M = { t, σ(t, t) t T Σ } infinite, but regular tree language L T Σ Then M(L) = {σ(t, t) t L} is not regular. How to train your multi bottom-up tree transducer A. Maletti 21
54 Preservation of Regularity Input MBOT M regular tree language L Question Is M(L) = {t s L: s, t M} regular? Example M = { t, σ(t, t) t T Σ } infinite, but regular tree language L T Σ Then M(L) = {σ(t, t) t L} is not regular. How to train your multi bottom-up tree transducer A. Maletti 21
55 Preservation of Regularity Why desired? easy and efficient representation of output languages allows intersection with (regular) language model allows bucket-brigade algorithms [May, Knight, Vogler, 2010] How to train your multi bottom-up tree transducer A. Maletti 22
56 Rule Composition Input rules Output rule V P VBD P P signed V P V P V P PV twly -OBJ DET-NN AltwyE P P VBD P P signed PV twly -OBJ DET-NN AltwyE P P How to train your multi bottom-up tree transducer A. Maletti 23
57 Rule Composition Power MBOT M k = {R 1 R k R 1,..., R k M} Explanation M k contains k-fold composed rules composition fails if states do not match composition succeeds (with no effect) if no matchable states present How to train your multi bottom-up tree transducer A. Maletti 24
58 Finitely Collapsing Definition M is finitely collapsing if there exists k N such that every state occurs at most once in rhs of every rule of M k. Example V P V P V P -OBJ PV P P VBD P P V P twly DET-NN signed AltwyE PV -OBJ twly P P VBD P P DET-NN signed AltwyE How to train your multi bottom-up tree transducer A. Maletti 25
59 Finite ynchronization Definition M has finite synchronization if there exists k N such that all occurrences of a state occur in the same tree in the rhs of every rule of M k. Theorem (Raoult, 1997) MBOT with finite synchronization and finitely collapsing MBOT preserve regularity. How to train your multi bottom-up tree transducer A. Maletti 26
60 Finite ynchronization Definition M has finite synchronization if there exists k N such that all occurrences of a state occur in the same tree in the rhs of every rule of M k. Theorem (Raoult, 1997) MBOT with finite synchronization and finitely collapsing MBOT preserve regularity. How to train your multi bottom-up tree transducer A. Maletti 26
61 Copy-free Definition M is copy-free if there exists k N such that for every rule of M k and all occurrences w of a state: w is the root of a tree in the rhs or w belongs to a fixed tree in the rhs. Example (not copy-free) X x X c X c X a X a X X b X b X σ How to train your multi bottom-up tree transducer A. Maletti 27
62 Copy-free Definition M is copy-free if there exists k N such that for every rule of M k and all occurrences w of a state: w is the root of a tree in the rhs or w belongs to a fixed tree in the rhs. Example (copy-free) X Y Z X X X X X X X X Y X How to train your multi bottom-up tree transducer A. Maletti 27
63 Main Result Theorem Copy-free MBOT preserve regularity. Theorem finitely collapsing finite synchronization copy-free Note All 3 restrictions can be guaranteed during rule extraction. How to train your multi bottom-up tree transducer A. Maletti 28
64 Main Result Theorem Copy-free MBOT preserve regularity. Theorem finitely collapsing finite synchronization copy-free Note All 3 restrictions can be guaranteed during rule extraction. How to train your multi bottom-up tree transducer A. Maletti 28
65 Main Result Theorem Copy-free MBOT preserve regularity. Theorem finitely collapsing finite synchronization copy-free Note All 3 restrictions can be guaranteed during rule extraction. How to train your multi bottom-up tree transducer A. Maletti 28
66 Thank you for your attention! How to train your multi bottom-up tree transducer A. Maletti 29
67 References 1 ARNOLD, DAUCHET: Morphismes et bimorphismes d arbres. Theoret. Comput. ci., ATANLP participants: Desired properties of syntax-based MT systems. ACL workshop, GRAEHL, KNIGHT, MAY: Training tree transducers. Computational Linguistics, MAY, KNIGHT: TIBURON A weighted tree automata toolkit. In CIAA, MAY, KNIGHT, VOGLER: Efficient Inference through Cascades of Weighted Tree Transducers. In ACL, RAOULT: Rational tree relations. Bull. Belg. Math. oc. imon tevin, UN, ZHANG, TAN: A non-contiguous tree seuence alignment-based model for statistical machine translation. In ACL, 2009 How to train your multi bottom-up tree transducer A. Maletti 30
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