Tree Transducers in Machine Translation Andreas Maletti Universitt - - PowerPoint PPT Presentation

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Tree Transducers in Machine Translation Andreas Maletti Universitt Stuttgart Institute for Natural Language Processing andreas.maletti@ims.uni-stuttgart.de Szeged November 29, 2011 Tree Transducers in MT A. Maletti 1 Machine

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SLIDE 1

Tree Transducers in Machine Translation

Andreas Maletti

Universität Stuttgart Institute for Natural Language Processing andreas.maletti@ims.uni-stuttgart.de

Szeged — November 29, 2011

Tree Transducers in MT

  • A. Maletti

· 1

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SLIDE 2

Machine translation

Applications

Technical manuals

Example (An mp3 player)

The synchronous manifestation of lyrics is a procedure for can broadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the equipments that synchronous function of support up broadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that broadcast. That procedure returns offerings to have to modify, and delete, and stick top , keep etc. edit function.

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 3

Machine translation

Applications

Technical manuals

Example (An mp3 player)

The synchronous manifestation of lyrics is a procedure for can broadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the equipments that synchronous function of support up broadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that broadcast. That procedure returns offerings to have to modify, and delete, and stick top , keep etc. edit function.

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 4

Machine translation

Applications

Technical manuals

Example (An mp3 player)

The synchronous manifestation of lyrics is a procedure for can broadcasting the music, waiting the mp3 file at the same time showing the lyrics. With the this kind method that the equipments that synchronous function of support up broadcast to make use of document create setup, you can pass the LCD window way the check at the document contents that broadcast. That procedure returns offerings to have to modify, and delete, and stick top , keep etc. edit function.

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 5

Machine translation

Applications

Technical manuals TripAdvisor R

  • Example (Hotel Uppsala, Sweden)

Wir hatten die Zimmer eingestuft wird als “Superior” weil sie renoviert wurde im letzten Jahr oder zwei. Unsere Zimmer hatten Parkettboden und waren sehr geräumig. Man musste allerdings nicht musste seitwärts bewegen.

Tree Transducers in MT

  • A. Maletti

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SLIDE 6

Machine translation

Applications

Technical manuals TripAdvisor R

  • Example (Hotel Uppsala, Sweden)

Nos alojamos en habitaciones clasificado como “superior” porque se lo habían renovado en el año pasado o dos. Nuestras habitaciones tenían suelos de madera y eran

  • espaciosas. No te tenías que caminar arriba

para movernos por allí.

Tree Transducers in MT

  • A. Maletti

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SLIDE 7

Machine translation

Applications

Technical manuals TripAdvisor R

  • Example (Hotel Uppsala, Sweden)

Wir hatten die Zimmer eingestuft wird als “Superior” weil sie renoviert wurde im letzten Jahr oder zwei. Unsere Zimmer hatten Parkettboden und waren sehr geräumig. Man musste allerdings nicht musste seitwärts bewegen. — We stayed in rooms classified as “superior” because they had been renovated in the last year or two. Our rooms had wood floors and were roomy. You didn’t have to walk sideways to move around.

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 8

Machine translation

Applications

Technical manuals TripAdvisor R

  • Military

Example (JONES, SHEN, HERZOG 2009)

Soldier: Okay, what is your name? Local: Abdul. Soldier: And your last name? Local: Al Farran.

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 9

Machine translation

Applications

Technical manuals TripAdvisor R

  • Military

Example (JONES, SHEN, HERZOG 2009)

Soldier: Okay, what is your name? Local: Abdul. Soldier: And your last name? Local: Al Farran. Speech-to-text machine translation Soldier: Okay, what’s your name? Local: milk a mechanic and I am here I mean yes

Tree Transducers in MT

  • A. Maletti

· 2

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SLIDE 10

Machine translation

Applications

Technical manuals TripAdvisor R

  • Military

Example (JONES, SHEN, HERZOG 2009)

Soldier: Okay, what is your name? Local: Abdul. Soldier: And your last name? Local: Al Farran. Speech-to-text machine translation Soldier: Okay, what’s your name? Local: milk a mechanic and I am here I mean yes Soldier: What is your last name? Local: every two weeks my son’s name is ismail

Tree Transducers in MT

  • A. Maletti

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SLIDE 11

Machine translation

Applications

Technical manuals TripAdvisor R

  • Military

MSDN, Knowledge Base . . .

Tree Transducers in MT

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SLIDE 12

Machine translation (cont’d)

Systems

GOOGLE translate

translate.google.com

BING translator

www.microsofttranslator.com

LANGUAGE WEAVER + SDL

www.freetranslation.com

. . .

Tree Transducers in MT

  • A. Maletti

· 3

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SLIDE 13

Machine translation (cont’d)

Systems

GOOGLE translate

translate.google.com

BING translator

www.microsofttranslator.com

LANGUAGE WEAVER + SDL

www.freetranslation.com

. . .

Try them!

Tree Transducers in MT

  • A. Maletti

· 3

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SLIDE 14

Machine translation (cont’d)

History

1

Dark age (60s–90s)

◮ rule-based systems (e.g., SYSTRAN) ◮ CHOMSKYAN approach ◮ perfect translation, poor coverage 2

Reformation (1991–present)

◮ word-based, phrase-based, syntax-based systems ◮ statistical approach ◮ cheap, automatically trained 3

Potential future

◮ semantics-based systems (e.g., FRAMENET) ◮ semi-supervised, statistical approach ◮ basic understanding of translated text Tree Transducers in MT

  • A. Maletti

· 4

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SLIDE 15

Machine translation (cont’d)

History

1

Dark age (60s–90s)

◮ rule-based systems (e.g., SYSTRAN) ◮ CHOMSKYAN approach ◮ perfect translation, poor coverage 2

Reformation (1991–present)

◮ word-based, phrase-based, syntax-based systems ◮ statistical approach ◮ cheap, automatically trained 3

Potential future

◮ semantics-based systems (e.g., FRAMENET) ◮ semi-supervised, statistical approach ◮ basic understanding of translated text Tree Transducers in MT

  • A. Maletti

· 4

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SLIDE 16

Machine translation (cont’d)

History

1

Dark age (60s–90s)

◮ rule-based systems (e.g., SYSTRAN) ◮ CHOMSKYAN approach ◮ perfect translation, poor coverage 2

Reformation (1991–present)

◮ word-based, phrase-based, syntax-based systems ◮ statistical approach ◮ cheap, automatically trained 3

Potential future

◮ semantics-based systems (e.g., FRAMENET) ◮ semi-supervised, statistical approach ◮ basic understanding of translated text Tree Transducers in MT

  • A. Maletti

· 4

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SLIDE 17

Machine translation (cont’d)

Schema

Input − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 5

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SLIDE 18

Machine translation (cont’d)

Schema

Input − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 5

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SLIDE 19

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: And then the matter was decided , and everything was put in place Output:

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 20

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: then the matter was decided , and everything was put in place Output:

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 21

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output:

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 22

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output: f

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 23

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output: f kAn

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 24

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output: f kAn

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 25

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output: f kAn

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 26

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was decided , and everything was put in place Output: f kAn

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 27

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter , and everything was put in place Output: f kAn An tm AlHsm

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 28

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter and everything was put in place Output: f kAn An tm AlHsm

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 29

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter everything was put in place Output: f kAn An tm AlHsm w

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 30

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was put in place Output: f kAn An tm AlHsm w

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 31

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter was put in place Output: f kAn An tm AlHsm w

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 32

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: the matter in place Output: f kAn An tm AlHsm w wDEt

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 33

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: in place Output: f kAn An tm AlHsm w wDEt Al>mwr

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 34

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: place Output: f kAn An tm AlHsm w wDEt Al>mwr fy

Tree Transducers in MT

  • A. Maletti

· 6

slide-35
SLIDE 35

Word-based system (FST)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: Output: f kAn An tm AlHsm w wDEt Al>mwr fy nSAb hA

Tree Transducers in MT

  • A. Maletti

· 6

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SLIDE 36

Phrase-based machine translation

Schema

Input − → Machine translation system − → Language model − → Output

Phrase-based systems

Input − → Segmenter − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 7

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SLIDE 37

Phrase-based machine translation

Schema

Input − → Machine translation system − → Language model − → Output

Phrase-based systems

Input − → Segmenter − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 7

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SLIDE 38

Phrase-based system (FST+Perm)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input: And then the matter was decided , and everything was put in place Output:

Tree Transducers in MT

  • A. Maletti

· 8

slide-39
SLIDE 39

Phrase-based system (FST+Perm)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input:

And then

1 the matter 5 was decided 2 , and everything 3 was put 4 in place 6

Output:

Tree Transducers in MT

  • A. Maletti

· 8

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SLIDE 40

Phrase-based system (FST+Perm)

And then the matter was decided , and everything was put in place

  • f
  • kAn
  • An
  • tm
  • AlHsm
  • w
  • wDEt
  • Al>mwr
  • fy
  • nSAb
  • hA

Derivation

Input:

And then

1 the matter 5 was decided 2 , and everything 3 was put 4 in place 6

Output:

f kAn

1 An tm AlHsm 2 w 3 wDEt 4 Almwr 5 fy nSAb hA 6 Tree Transducers in MT

  • A. Maletti

· 8

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SLIDE 41

Machine translation (cont’d)

Phrase-based systems

Input − → Segmenter − → Machine translation system − → Language model − → Output

Syntax-based systems

Input − → Parser − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 9

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SLIDE 42

Machine translation (cont’d)

Phrase-based systems

Input − → Segmenter − → Machine translation system − → Language model − → Output

Syntax-based systems

Input − → Parser − → Machine translation system − → Language model − → Output

Tree Transducers in MT

  • A. Maletti

· 9

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SLIDE 43

Parser

S S CC And ADVP RB then NP-SBJ-9 DT the NN matter VP VBD was VP VBN decided NP-9 , CC and S NP-SBJ-1 NN everything VP VBD was VP VBN put NP-1 * PP IN in NP NN place And then the matter was decided , and everything was put in place

(thanks to KEVIN KNIGHT for the data)

Tree Transducers in MT

  • A. Maletti

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SLIDE 44

S S CC And ADVP RB then NP-SBJ-9 DT the NN matter VP VBD was VP VBN decided NP-9 , CC and S NP-SBJ-1 NN everything VP VBD was VP VBN put NP-1 * PP IN in NP NN place S CONJ f VP PV kAn NP-SBJ * SBAR SUB An S S VP PV tm NP-SBJ DET-NN AlHsm CONJ w S VP PV wDEt NP-SBJ1 DET-NN Almwr NP-OBJ1 * PP PREP fy NP NN nSAb NP POSS hA

Tree Transducers in MT

  • A. Maletti

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SLIDE 45

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

Tree Transducers in MT

  • A. Maletti

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SLIDE 46

Contents

1

Machine Translation

2

Extended Top-down Tree Transducers

3

Multi Bottom-up Tree Transducers

4

Synchronous Tree-Adjoining Grammars

Tree Transducers in MT

  • A. Maletti

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SLIDE 47

Weight structure

Definition

Commutative semiring (C, +, ·, 0, 1) if (C, +, 0) and (C, ·, 1) commutative monoids · distributes over finite (incl. empty) sums

Example

BOOLEAN semiring ({0, 1}, max, min, 0, 1) Semiring (R≥0, +, ·, 0, 1) of probabilities Tropical semiring (N ∪ {∞}, min, +, ∞, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring

Tree Transducers in MT

  • A. Maletti

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slide-48
SLIDE 48

Weight structure

Definition

Commutative semiring (C, +, ·, 0, 1) if (C, +, 0) and (C, ·, 1) commutative monoids · distributes over finite (incl. empty) sums

Example

BOOLEAN semiring ({0, 1}, max, min, 0, 1) Semiring (R≥0, +, ·, 0, 1) of probabilities Tropical semiring (N ∪ {∞}, min, +, ∞, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring

Tree Transducers in MT

  • A. Maletti

· 14

slide-49
SLIDE 49

Weight structure

Definition

Commutative semiring (C, +, ·, 0, 1) if (C, +, 0) and (C, ·, 1) commutative monoids · distributes over finite (incl. empty) sums

Example

BOOLEAN semiring ({0, 1}, max, min, 0, 1) Semiring (R≥0, +, ·, 0, 1) of probabilities Tropical semiring (N ∪ {∞}, min, +, ∞, 0) Any field, ring, etc. Most of the talk: BOOLEAN semiring

Tree Transducers in MT

  • A. Maletti

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SLIDE 50

Syntax

Definition (ARNOLD, DAUCHET 1976, GRAEHL, KNIGHT 2004)

Extended top-down tree transducer (XTOP) M = (Q, Σ, ∆, I, R) with finitely many rules q Σ x1 . . . xk → ∆ q′(xi) . . . p(xj) q, q′, p ∈ Q are states i, j ∈ {1, . . . , k}

Tree Transducers in MT

  • A. Maletti

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slide-51
SLIDE 51

Syntax (cont’d)

Definition (ROUNDS 1970, THATCHER 1970)

Top-down tree transducer (TOP) if all rules q σ x1 . . . xk → ∆ q′(xi) . . . p(xj) linear if no variable occurs twice in r for all rules l → r nondeleting if var(l) = var(r) for all rules l → r

Tree Transducers in MT

  • A. Maletti

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slide-52
SLIDE 52

Syntax (cont’d)

Definition (ROUNDS 1970, THATCHER 1970)

Top-down tree transducer (TOP) if all rules q σ x1 . . . xk → ∆ q′(xi) . . . p(xj) linear if no variable occurs twice in r for all rules l → r nondeleting if var(l) = var(r) for all rules l → r

Tree Transducers in MT

  • A. Maletti

· 16

slide-53
SLIDE 53

Syntax (cont’d)

Definition (ROUNDS 1970, THATCHER 1970)

Top-down tree transducer (TOP) if all rules q σ x1 . . . xk → ∆ q′(xi) . . . p(xj) linear if no variable occurs twice in r for all rules l → r nondeleting if var(l) = var(r) for all rules l → r

Tree Transducers in MT

  • A. Maletti

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slide-54
SLIDE 54

Semantics

Example

States {qS, qV, qNP} of which only qS is initial qS S x1 x2 → S′ qV x2 qNP x1 qNP x2 qV VP x1 x2 → qV x1 qNP VP x1 x2 → qNP x2

Derivation

qS S t1 VP t2 t3 ⇒ S′ qV VP t2 t3 qNP t1 qNP VP t2 t3 ⇒ S′ qV t2 qNP t1 qNP VP t2 t3 ⇒ S′ qV t2 qNP t1 qNP t3

Tree Transducers in MT

  • A. Maletti

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slide-55
SLIDE 55

Semantics (cont’d)

Definition

Computed transformation: τM = {(t, u) ∈ TΣ × T∆ | ∃q ∈ I : q(t) ⇒∗ u}

Tree Transducers in MT

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slide-56
SLIDE 56

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

Tree Transducers in MT

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· 19

slide-57
SLIDE 57

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

Tree Transducers in MT

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SLIDE 58

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

Tree Transducers in MT

  • A. Maletti

· 19

slide-59
SLIDE 59

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

Tree Transducers in MT

  • A. Maletti

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SLIDE 60

Rule extraction

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1

Tree Transducers in MT

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slide-61
SLIDE 61

Rule extraction

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1 q NP-SBJ x1 NNP Voislav → NP-SBJ q x1 NP NN-PROP fwyslAf

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SLIDE 62

Rule extraction

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1 q NP-SBJ x1 NNP Voislav → NP-SBJ q x1 NP NN-PROP fwyslAf q NML JJ Yugoslav NNP President → NP DET-NN Alr}ys DET-ADJ AlywgwslAfy

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SLIDE 63

Symmetry

Original rule

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1

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SLIDE 64

Symmetry

Original rule

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1

Inverted rule

q S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1 → S q x1 VP VBD signed q x2

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SLIDE 65

Symmetry

Original rule

q S x1 VP VBD signed x2 → S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1

Inverted rule

q S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE q x2 q x1 → S q x1 VP VBD signed q x2

Linear nondeleting XTT can be inverted

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SLIDE 66

Preservation of regularity

Schematics

Input − → Parser − → XTT − → Language model − → Output

Parse trees

best parse tree n-best parses all parses Can all be represented by regular tree language

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SLIDE 67

Preservation of regularity

Schematics

Input − → Parser − → Parse trees − → XTT − → . . .

Parse trees

best parse tree n-best parses all parses Can all be represented by regular tree language

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SLIDE 68

Preservation of regularity

Schematics

Input − → Parser − → Parse trees − → XTT − → . . .

Parse trees

best parse tree n-best parses all parses Can all be represented by regular tree language

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SLIDE 69

Preservation of regularity

Schematics

Input − → Parser − → Parse trees − → XTT − → . . .

Parse trees

best parse tree n-best parses all parses Can all be represented by regular tree language

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SLIDE 70

Preservation of regularity (cont’d)

Schematics

Regular language − → XTT − → Regular language?

Approach

Input restriction Project to output

Result

Linear XTT preserve regularity

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SLIDE 71

Preservation of regularity (cont’d)

Schematics

Regular language − → XTT − → Regular language?

Approach

Input restriction Project to output

Result

Linear XTT preserve regularity

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SLIDE 72

Preservation of regularity (cont’d)

Schematics

Regular language − → XTT − → Regular language?

Approach

Input restriction Project to output

Result

Linear XTT preserve regularity

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SLIDE 73

Composition

Schematics

Parse trees − → XTT − → . . .

Example (YAMADA, KNIGHT 2002)

Reorder Insert words Translate words

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SLIDE 74

Composition

Schematics

Parse trees − → Stage 1 XTT − → Stage 2 XTT − → Stage 3 XTT − → . . .

Example (YAMADA, KNIGHT 2002)

Reorder Insert words Translate words

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SLIDE 75

Composition

Schematics

Parse trees − → Composed XTT − → . . .

Example (YAMADA, KNIGHT 2002)

Reorder Insert words Translate words

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SLIDE 76

Composition (cont’d)

Example (ARNOLD, DAUCHET 1982)

σ t1 δ t2 t3 δ tn−4 tn−3 δ tn−2 tn−1 tn ⇒∗ σ t1 σ t2 σ t3 σ t4 σ tn−3 σ tn−2 σ tn−1 tn ⇒∗ δ t2 t1 δ t4 t3 δ tn−2 tn−3 σ tn−1 tn

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SLIDE 77

Summary

Model \ Criterion EXPR SYM PRES PRES−1 COMP Linear nondeleting TOP ✗ ✗ ✓ ✓ ✓ Linear TOP ✗ ✗ ✓ ✓ ✗ Linear TOPR ✗ ✗ ✓ ✓ ✓ General TOP ✗ ✗ ✗ ✓ ✗ General TOPR ✓ ✗ ✗ ✓ ✗ Linear nondeleting XTOP ✓ ✓ ✓ ✓ ✗ Linear XTOP ✓ ✗ ✓ ✓ ✗ Linear XTOPR ✓ ✗ ✓ ✓ ✗ General XTOP ✓ ✗ ✗ ✓ ✗ General XTOPR ✓ ✗ ✗ ✓ ✗

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SLIDE 78

Summary

Model \ Criterion EXPR SYM PRES PRES−1 COMP Linear nondeleting TOP ✗ ✗ ✓ ✓ ✓ Linear TOP ✗ ✗ ✓ ✓ ✗ Linear TOPR ✗ ✗ ✓ ✓ ✓ General TOP ✗ ✗ ✗ ✓ ✗ General TOPR ✓ ✗ ✗ ✓ ✗ Linear nondeleting XTOP ✓ ✓ ✓ ✓ ✗ Linear XTOP ✓ ✗ ✓ ✓ ✗ Linear XTOPR ✓ ✗ ✓ ✓ ✗ General XTOP ✓ ✗ ✗ ✓ ✗ General XTOPR ✓ ✗ ✗ ✓ ✗

  • Comp. closure ln-XTOP

✓ ✓ ✓ ✓ ✓ “composable” ln-XTOP ? ? ✓ ✓ ✓

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SLIDE 79

Implementation

TIBURON [MAY, KNIGHT 2006]

Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation

Algorithms

Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP)

Example

qNP.NP(DT(the) N(boy)) -> NP(N(atefl))

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SLIDE 80

Implementation

TIBURON [MAY, KNIGHT 2006]

Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation

Algorithms

Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP)

Example

qNP.NP(DT(the) N(boy)) -> NP(N(atefl))

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SLIDE 81

Implementation

TIBURON [MAY, KNIGHT 2006]

Implements XTOP (and tree automata; everything also weighted) Framework with command-line interface Optimized for machine translation

Algorithms

Application of XTOP to input tree/language Backward application of XTOP to output language Composition (for some XTOP)

Example

qNP.NP(DT(the) N(boy)) -> NP(N(atefl))

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SLIDE 82

Multi Bottom-up Tree Transducers

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 83

Syntax

Definition

Extended multi bottom-up tree transducer (XMBOT) is M = (Q, Σ, ∆, F, R) with finitely many rules

Σ q′ x1 . . . xℓ . . . p xm . . . xn → q ∆ xi . . . xj . . . ∆ xi′ . . . xj′

q′, p, q ∈ Q are now ranked states F ⊆ Q1 final states

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SLIDE 84

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e

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SLIDE 85

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e ⇒ a b b q e e

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SLIDE 86

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e ⇒ a b b q e e ⇒ a b q b e b e

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SLIDE 87

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e ⇒ a b b q e e ⇒ a b q b e b e ⇒ a q b b e b b e

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SLIDE 88

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e ⇒ a b b q e e ⇒ a b q b e b e ⇒ a q b b e b b e ⇒ q a b b e a b b e

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SLIDE 89

Example

States {f (1), q(2)} with final state f and rules

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

Example (Derivation)

a b b e ⇒ a b b q e e ⇒ a b q b e b e ⇒ a q b b e b b e ⇒ q a b b e a b b e ⇒ f σ a b b e a b b e

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SLIDE 90

Semantics

Definition

Computed transformation: τM = {(t, u) ∈ TΣ × T∆ | ∃q ∈ F : t ⇒∗ q(u)}

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SLIDE 91

Semantics

Definition

Computed transformation: τM = {(t, u) ∈ TΣ × T∆ | ∃q ∈ F : t ⇒∗ q(u)}

Example

τM = {t, σ(t, t) | t ∈ TΣ}

e → q e e a q x1 x2 → q a x1 a x2 b q x1 x2 → q b x1 b x2 q x1 x2 → f σ x1 x2

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SLIDE 92

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 93

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 94

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 95

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 96

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 97

Rule extraction

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

S q x1 p x2 x3 → q S CONJ w VP x2 x3 x1

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SLIDE 98

Rule extraction

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

S q x1 p x2 x3 → q S CONJ w VP x2 x3 x1 VP VBD signed q x1 → p PV twlY NP-OBJ NP DET-NN AltwqyE x1

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SLIDE 99

One-symbol normal form

Definition

Rule in one-symbol normal form if it contains at most one symbol

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SLIDE 100

One-symbol normal form

Definition

Rule in one-symbol normal form if it contains at most one symbol

Example (ENGELFRIET, LILIN, ∼ 2009)

b q x1 x2 → q b x1 b x2

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SLIDE 101

One-symbol normal form

Definition

Rule in one-symbol normal form if it contains at most one symbol

Example (ENGELFRIET, LILIN, ∼ 2009)

b q x1 x2 → q b x1 b x2

In one-symbol normal form

b q x1 x2 → q1 x1 x2 q1 x1 x2 → q2 b x1 x2 q2 x1 x2 → q x1 b x2

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SLIDE 102

Basic properties

Example (Copying translation)

τM = {t, σ(t, t) | t ∈ TΣ}

Consequences

XMBOT are not symmetric XMBOT do not preserve regularity but they can be composed

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SLIDE 103

Basic properties

Example (Copying translation)

τM = {t, σ(t, t) | t ∈ TΣ}

Consequences

XMBOT are not symmetric XMBOT do not preserve regularity but they can be composed

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SLIDE 104

Basic properties

Example (Copying translation)

τM = {t, σ(t, t) | t ∈ TΣ}

Consequences

XMBOT are not symmetric XMBOT do not preserve regularity but they can be composed

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SLIDE 105

Composition

σ q1 x1 x2 q2 → q x2 σ q1 p1 p2 x1 x2 q2 → q p2 x1 x2

Simple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975]

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SLIDE 106

Composition

σ q1 x1 x2 q2 → q x2 σ q1 p1 p2 x1 x2 q2 → q p2 x1 x2 p1 → p α q1 p1 p2 x1 x2 → q1 p α p2 x1 x2

Simple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975]

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SLIDE 107

Composition

σ q1 x1 x2 q2 → q x2 σ q1 p1 p2 x1 x2 q2 → q p2 x1 x2 p1 → p α q1 p1 p2 x1 x2 → q1 p α p2 x1 x2 q1 x1 x2 → q γ x2 γ p2 x1 x2 → p x2 q1 p1 p2 x1 x2 → q p x2

Simple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975]

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SLIDE 108

Composition

σ q1 x1 x2 q2 → q x2 σ q1 p1 p2 x1 x2 q2 → q p2 x1 x2 p1 → p α q1 p1 p2 x1 x2 → q1 p α p2 x1 x2 q1 x1 x2 → q γ x2 γ p2 x1 x2 → p x2 q1 p1 p2 x1 x2 → q p x2

Simple composition works in the typical cases [BAKER 1979, ENGELFRIET 1975]

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SLIDE 109

Summary

Model \ Criterion EXPR SYM PRES PRES−1 COMP Linear nondeleting TOP ✗ ✗ ✓ ✓ ✓ Linear nondeleting XTOP ✓ ✓ ✓ ✓ ✗ Linear nondeleting XMBOT ✓ ✗ ✗ ✓ ✓ Linear XMBOT ✓ ✗ ✗ ✓ ✓ General XMBOT ✓ ✗ ✗ ✓ ✗ reg.-preserving linear XMBOT ✓ ✗ ✓ ✓ ✓ invertable linear XMBOT ✓ ✓ ✓ ✓ ✓

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SLIDE 110

Summary

Model \ Criterion EXPR SYM PRES PRES−1 COMP Linear nondeleting TOP ✗ ✗ ✓ ✓ ✓ Linear nondeleting XTOP ✓ ✓ ✓ ✓ ✗ Linear nondeleting XMBOT ✓ ✗ ✗ ✓ ✓ Linear XMBOT ✓ ✗ ✗ ✓ ✓ General XMBOT ✓ ✗ ✗ ✓ ✗ reg.-preserving linear XMBOT ✓ ✗ ✓ ✓ ✓ invertable linear XMBOT ✓ ✓ ✓ ✓ ✓

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SLIDE 111

Implementation

No implementation yet,

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SLIDE 112

Implementation

No implementation yet, but stay tuned

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SLIDE 113

Synchronous Tree-Adjoining Grammars

S NP-SBJ NML JJ Yugoslav NNP President NNP Voislav VP VBD signed PP IN for NP NNP Serbia S CONJ w VP PV twlY NP-OBJ NP DET-NN AltwqyE PP PREP En NP NN-PROP SrbyA NP-SBJ NP DET-NN Alr}ys DET-ADJ AlywgwslAfy NP NN-PROP fwyslAf

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SLIDE 114

Syntax

Definition (SHIEBER, SCHABES 1990)

Synchronous tree-adjoining grammar (STAG) is G = (N, Σ, ∆, S, R) with a finite set R of substitution rules adjunction rules

Example (Substitution rule)

X Σ X1 . . . Xk — X ∆ Xi . . . Xj

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SLIDE 115

Syntax

Definition (SHIEBER, SCHABES 1990)

Synchronous tree-adjoining grammar (STAG) is G = (N, Σ, ∆, S, R) with a finite set R of substitution rules adjunction rules

Example (Adjunction rule)

X Σ X⋆ — X ∆ X⋆

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SLIDE 116

Example

S S

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SLIDE 117

Example

S NP VP S NP VP

Used substitution rule

S NP VP — S NP VP

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SLIDE 118

Example

S NP 1 VP V NP 2 S NP 1 VP V NP 2

Used substitution rule

VP V NP — VP V NP

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SLIDE 119

Example

S NP 1 VP V likes NP 2 S NP 1 VP V aime NP 2

Used substitution rule

V likes — V aime

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SLIDE 120

Example

S NP VP V likes NP N S NP VP V aime NP DT les N

Used substitution rule

NP N — NP DT les N

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SLIDE 121

Example

S NP VP V likes NP N candies S NP VP V aime NP DT les N bonbons

Used substitution rule

N candies — N bonbons

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SLIDE 122

Example

S NP VP V likes NP N ADJ N candies S NP VP V aime NP DT les N N bonbons ADJ

Used adjunction rule

N ADJ N⋆ — N N⋆ ADJ

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SLIDE 123

Example

S NP VP V likes NP N ADJ red N candies S NP VP V aime NP DT les N N bonbons ADJ rouges

Used substitution rule

ADJ red — ADJ rouges

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SLIDE 124

Semantics

Definition

Computed transformation: τG = {(t, u) ∈ TΣ × T∆ | (S, S) ⇒∗ (t, u)}

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SLIDE 125

Relation to tree transducers

Illustration

HOM HOM eval eval STSG STAG EMB EMB

Definition (SHIEBER 2006)

embedded tree transducer is a macro tree transducer: linear, nondeleting, deterministic, total 1-parameter: linear, nondeleting

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SLIDE 126

Relation to tree transducers

Illustration

HOM HOM eval eval STSG STAG EMB EMB

Definition (SHIEBER 2006)

embedded tree transducer is a macro tree transducer: linear, nondeleting, deterministic, total 1-parameter: linear, nondeleting

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SLIDE 127

Copying example

Example

S T c — S T c S S a S T c a — S a S S T c a S S S b S a S T c a b — S a S b S S S T c a b

Example

S T c — S T c S S a S⋆ a — S a S S⋆ a S S b S⋆ b — S b S S⋆ b S S⋆ — S S⋆

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SLIDE 128

Copying example

Example

S T c — S T c S S a S T c a — S a S S T c a S S S b S a S T c a b — S a S b S S S T c a b

String translation

{(wcwR, wcw) | w ∈ {a, b}∗}

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SLIDE 129

Basic properties

Example (Copying translation)

τG = {(wcwR, wcw) | w ∈ {a, b}∗}

Consequences

STAG are symmetric STAG do not preserve regularity (neither direction)

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SLIDE 130

Basic properties

Example (Copying translation)

τG = {(wcwR, wcw) | w ∈ {a, b}∗}

Consequences

STAG are symmetric STAG do not preserve regularity (neither direction)

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SLIDE 131

Summary

Model \ Criterion EXPR SYM PRES PRES−1 COMP Linear nondeleting TOP ✗ ✗ ✓ ✓ ✓ Linear nondeleting XTOP ✓ ✓ ✓ ✓ ✗ Linear nondeleting XMBOT ✓ ✗ ✗ ✓ ✓ Linear XMBOT ✓ ✗ ✗ ✓ ✓ General XMBOT ✓ ✗ ✗ ✓ ✗ reg.-preserving linear XMBOT ✓ ✗ ✓ ✓ ✓ invertable linear XMBOT ✓ ✓ ✓ ✓ ✓ STAG ✓ ✓ ✗ ✗ ✗

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SLIDE 132

Implementation

XTAG [THE XTAG PROJECT 2008]

Implements TAG, STAG Optimized for natural language applications Application of STAG http://www.cis.upenn.edu/~xtag/

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SLIDE 133

Implementation

XTAG [THE XTAG PROJECT 2008]

Implements TAG, STAG Optimized for natural language applications Application of STAG http://www.cis.upenn.edu/~xtag/

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SLIDE 134

References

ARNOLD, DAUCHET: Bi-transductions de forêts. ICALP 1976 BERSTEL, REUTENAUER: Recognizable formal power series on

  • trees. Theor. Comput. Sci. 18, 1982

ENGELFRIET: Top-down tree transducers with regular look-ahead.

  • Math. Systems Theory 10, 1977

GALLEY, HOPKINS, KNIGHT, MARCU: What’s in a translation rule? HLT-NAACL 2004 GRAEHL, KNIGHT: Training tree transducers. HLT-NAACL 2004 MAY, KNIGHT: TIBURON — a weighted tree automata toolkit. CIAA 2006 ROUNDS: Mappings and grammars on trees. Math. Systems Theory 4, 1970 THATCHER Generalized 2 sequential machine maps. J. Comput. System Sci. 4, 1970

Tree Transducers in MT

  • A. Maletti

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