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Synchronous Forest Substitution Grammars Andreas Maletti Institute for Natural Language Processing University of Stuttgart, Germany maletti@ims.uni-stuttgart.de Porquerolles Island, France (CAI 2013) A. Maletti Synchronous Forest Substitution

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Synchronous Forest Substitution Grammars

Andreas Maletti

Institute for Natural Language Processing University of Stuttgart, Germany maletti@ims.uni-stuttgart.de

Porquerolles Island, France (CAI 2013)

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013

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Outline

Motivation Main model Results

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013

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Machine translation

Translation

◮ Input:

Official forecasts predicted just 3 percent, Bloomberg said.

◮ Reference:

Offizielle Prognosen sind von nur 3 Prozent ausgegangen, meldete Bloomberg. [official] [forecasts] [are] [of] [only] [3 percent] [assumed] [reported] [Bloomberg]

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Synchronous Forest Substitution Grammars September 4, 2013

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Machine translation

Translation

◮ Input:

Official forecasts predicted just 3 percent, Bloomberg said.

◮ Reference:

Offizielle Prognosen sind von nur 3 Prozent ausgegangen, meldete Bloomberg. [official] [forecasts] [are] [of] [only] [3 percent] [assumed] [reported] [Bloomberg]

◮ Google Translate (translate.google.com):

Offizielle Prognosen vorhergesagt nur 3 Prozent, sagte Bloomberg. [official] [forecasts] [*predicted] [only] [3 percent] [said] [Bloomberg]

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013

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Machine translation

Translation

◮ Input:

The ECB wants to hold inflation to under two percent,

  • r somewhere in that vicinity.

◮ Reference:

Die EZB ist bestrebt, die Inflationsrate unter zwei Prozent, [the] [ECB] [is] [desire] [the] [inflation rate] [below] [two percent]

  • der zumindest knapp an der Zwei-Prozent-Marke zu halten.

[or] [at least] [close] [at] [the] [two percent mark] [to keep]

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Machine translation

Translation

◮ Input:

The ECB wants to hold inflation to under two percent,

  • r somewhere in that vicinity.

◮ Reference:

Die EZB ist bestrebt, die Inflationsrate unter zwei Prozent, [the] [ECB] [is] [desire] [the] [inflation rate] [below] [two percent]

  • der zumindest knapp an der Zwei-Prozent-Marke zu halten.

[or] [at least] [close] [at] [the] [two percent mark] [to keep]

◮ Google Translate (translate.google.com):

Die EZB will die Inflation unter zwei Prozent zu halten , [the] [ECB] [wants] [the] [inflation] [below] [two percent] [*to keep]

  • der irgendwo in der Nähe.

[or] [somewhere] [in] [the] [vicinity]

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Syntax-based machine translation

Architecture

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

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Syntax-based machine translation

Architecture

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

Formalisms

◮ Parser = weighted tree automaton ◮ Translation system = some tree transducer ◮ Language model = weighted string automaton

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Resources

Input

◮ Parallel text (English and German)

EUROPARL

◮ Parsers

BITPAR, CHARNIAK, BERKELEY

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Synchronous Forest Substitution Grammars September 4, 2013

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Resources

Input

◮ Parallel text (English and German)

EUROPARL

◮ Parsers

BITPAR, CHARNIAK, BERKELEY

Example

◮ “We must bear in mind the Community as a whole.” ◮ “Wir müssen uns davor hüten, alles vergemeinschaften zu wollen.”

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Resources

Input

◮ Parallel text (English and German)

EUROPARL

◮ Parsers

BITPAR, CHARNIAK, BERKELEY

Example

◮ “We must bear in mind the Community as a whole.” ◮ “Wir müssen uns davor hüten, alles vergemeinschaften zu wollen.”

EUROPARL German-English parallel data:

◮

1, 920, 209 parallel sentences

◮ 44, 548, 491 words in German ◮ 47, 818, 827 words in English

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First step: word alignment

Alignments by GIZA++ [OCH, NEY ’03]:

We must bear in mind the Community as a whole Wir müssen uns davor hüten , alles vergemeinschaften zu wollen

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First step: word alignment

Alignments by GIZA++ [OCH, NEY ’03]:

We must bear in mind the Community as a whole Wir müssen uns davor hüten , alles vergemeinschaften zu wollen

We can help countries catch up , but not by putting their neighbours

  • n

hold Wir können Ländern beim Aufholen helfen , aber nicht , indem wir ihre Nachbarn in den Wartesaal schicken

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Second step: parsing

CHARNIAK parser:

[CHARNIAK, JOHNSON ’05]

TOP S NP PRP We VP MD must VP VB bear PP IN in NP NN mind NP NP DT the NN Community PP IN as NP DT a NN whole . .

BitPar parser:

[SCHMID ’06]

TOP S-TOP NP-SB/Pl PPER-HD-Nom.Pl Wir VMFIN-HD-Pl müssen VP-OC/inf NP-DA PPER-HD-Dat.Pl uns PP-OP/V PROAV-PH davor VVINF-HD hüten $, , VP-OC/zu VP-OC/inf NP-OA PIS-HD-Acc.Sg.Neut alles VVINF-HD vergemeinschaften VZ-HD PTKZU-PM zu VMINF-HD wollen $. .

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Full example

Parallel text

Yugoslav President Voislav signed for Serbia.

  • Transliteration: w twlY AltwqyE En SrbyA Alr}ys AlywgwslAfy fwyslAf.

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

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

Below are the male and female winners in the different categories.

  • Transliteration: w hnA Al>wA}l w Al>wlyAt fy mxtlf Alf}At.
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Full example

Alignment

Yugoslav President Voislav signed for Serbia w twlY AltwqyE En SrbyA Alr}ys AlywgwslAfy fwyslAf

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Third step: 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

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Third step: 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

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Third step: 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

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Third step: 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

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Third step: 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

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Third step: 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 qNP qVP

qS

— S CONJ w VP qVP qVP qNP

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Third step: 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 qNP qVP

qS

— S CONJ w VP qVP qVP qNP VP VBD signed qPP

qVP

— PV twlY NP-OBJ NP DET-NN AltwqyE qPP

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Last step: evaluation

English to German [BRAUNE et al., 2013]

Model BLEU STSG (tree-to-tree) 12.60 GHKM (tree-to-string) 12.72 MBOT (tree-to-tree) 13.06

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Last step: evaluation

English to German [BRAUNE et al., 2013]

Model BLEU STSG (tree-to-tree) 12.60 GHKM (tree-to-string) 12.72 MBOT (tree-to-tree) 13.06

Chinese to English [SUN et al., 2009]

Model BLEU FST (string-to-string) 23.86 STSG (tree-to-tree) 25.92 MBOT (tree-to-tree) 26.56 SFSG (tree-to-tree) 26.53

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Outline

Motivation Main model Results

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RTG — Syntax

Definition (BRAINERD, 1969)

Regular tree grammar (RTG) is tuple G = (Q, Σ, I, P)

◮ alphabet Q

nonterminals

◮ alphabet Σ

terminals

◮ I ⊆ Q

initial nonterminals

◮ finite set P ⊆ Q × TΣ(Q)

productions

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RTG — Syntax

Definition (BRAINERD, 1969)

Regular tree grammar (RTG) is tuple G = (Q, Σ, I, P)

◮ alphabet Q

nonterminals

◮ alphabet Σ

terminals

◮ I ⊆ Q

initial nonterminals

◮ finite set P ⊆ Q × TΣ(Q)

productions

Remark

Instead of (q, r) we write q → r

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RTG — Syntax

Example

◮ Q = {q0, q1, q2, q3, q4, q5, q6} ◮ Σ = {VP, NP, S, . . . } ◮ I = {q0} ◮ and the following productions:

q4 → VP q5 NP q2 q3 q0 → S NP q1 q4 q0 → S q6 VP q2 q4

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RTG — Semantics

Definition (Derivation semantics)

Sentential forms: t, u ∈ TΣ(Q) t ⇒G u if there exist position w ∈ pos(t) and production q → r ∈ P

◮ t = t[q]w ◮ u = t[r]w

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RTG — Semantics

Definition (Derivation semantics)

Sentential forms: t, u ∈ TΣ(Q) t ⇒G u if there exist position w ∈ pos(t) and production q → r ∈ P

◮ t = t[q]w ◮ u = t[r]w

Definition (Recognized tree language)

L(G) = {t ∈ TΣ | ∃q ∈ I : q ⇒∗

G t}

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RTG — Semantics

Example (Productions)

q4 → VP q5 NP q2 q3 q0 → S NP q1 q4 q0 → S q6 VP q2 q4

Example (Derivation)

q0 ⇒G S NP q1 q4 ⇒G S NP q1 VP q5 NP q2 q3

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RTG — Semantics

Example (Productions)

q4 → VP q5 NP q2 q3 q0 → S NP q1 q4 q0 → S q6 VP q2 q4

Example (Derivation)

q0 ⇒G S NP q1 q4 ⇒G S NP q1 VP q5 NP q2 q3

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RTG — Semantics

Example (Productions)

q4 → VP q5 NP q2 q3 q0 → S NP q1 q4 q0 → S q6 VP q2 q4

Example (Derivation)

q0 ⇒G S NP q1 q4 ⇒G S NP q1 VP q5 NP q2 q3

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Synchronous Grammar

Intuition

◮ Productions that consist of several RTG productions ◮ Synchronous = several RTG productions are applied at once ◮ typically at least two RTG productions

input/output side

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Synchronous Grammar

Intuition

◮ Productions that consist of several RTG productions ◮ Synchronous = several RTG productions are applied at once ◮ typically at least two RTG productions

input/output side

◮ but even several RTG productions per side possible

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Synchronous Grammar

Intuition

◮ Productions that consist of several RTG productions ◮ Synchronous = several RTG productions are applied at once ◮ typically at least two RTG productions

input/output side

◮ but even several RTG productions per side possible

Definition

Given RTG (Q, Σ, I, P) and q ∈ Q let Pq = {q → r | q → r ∈ P}

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SFSG — Syntax

Definition (RAOULT, 1997 and SUN et al., 2009)

Synchronous forest substitution grammar (SFSG) is tuple G = (Q, Σ, I, P, R)

◮ (Q, Σ, I, P) is RTG

basic productions

◮ R ⊆ ( q∈I Pq × Pq) ∪ ( q∈Q\I P∗ q × P∗ q) finite

aligned rules

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SFSG — Syntax

Definition (RAOULT, 1997 and SUN et al., 2009)

Synchronous forest substitution grammar (SFSG) is tuple G = (Q, Σ, I, P, R)

◮ (Q, Σ, I, P) is RTG

basic productions

◮ R ⊆ ( q∈I Pq × Pq) ∪ ( q∈Q\I P∗ q × P∗ q) finite

aligned rules

Definition (ARNOLD & DAUCHET, 1982)

Multi bottom-up tree transducer (MBOT) is SFSG with R ⊆

q∈Q Pq × P∗ q

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SFSG — Syntax

Example

RTG (Q, Σ, {q0}, P)

◮ Q = {q0, q, q′} and Σ = {α, γ1, γ2, σ} ◮ P contains the productions:

ρ0 : q0 → σ(q, q′, q) ρ2 : q → γ1(q) ρ4 : q → γ2(q) ρ6 : q → α ρ1 : q0 → σ(q′, α, q′) ρ3 : q′ → γ1(q′) ρ5 : q′ → γ2(q′) ρ7 : q′ → α

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SFSG — Syntax

Example

RTG (Q, Σ, {q0}, P)

◮ Q = {q0, q, q′} and Σ = {α, γ1, γ2, σ} ◮ P contains the productions:

ρ0 : q0 → σ(q, q′, q) ρ2 : q → γ1(q) ρ4 : q → γ2(q) ρ6 : q → α ρ1 : q0 → σ(q′, α, q′) ρ3 : q′ → γ1(q′) ρ5 : q′ → γ2(q′) ρ7 : q′ → α

SFSG G = (Q, Σ, {q0}, P, R)

R = {(ρ0, ρ1), (ρ2ρ2, ε), (ρ4ρ4, ε), (ρ6ρ6, ε), (ρ3, ρ3ρ3), (ρ5, ρ5ρ5) (ρ7, ρ7ρ7)}

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SFSG — Syntax

Example

RTG (Q, Σ, {q0}, P)

◮ Q = {q0, q, q′} and Σ = {α, γ1, γ2, σ} ◮ P contains the productions:

ρ0 : q0 → σ(q, q′, q) ρ2 : q → γ1(q) ρ4 : q → γ2(q) ρ6 : q → α ρ1 : q0 → σ(q′, α, q′) ρ3 : q′ → γ1(q′) ρ5 : q′ → γ2(q′) ρ7 : q′ → α

SFSG G = (Q, Σ, {q0}, P, R)

R = {(ρ0, ρ1), (ρ2ρ2, ε), (ρ4ρ4, ε), (ρ6ρ6, ε), (ρ3, ρ3ρ3), (ρ5, ρ5ρ5) (ρ7, ρ7ρ7)}

G is no MBOT

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SFSG — Syntax

q0 →

  • σ

q q′ q , σ q′ α q′

  • q →

γ1 q γ1 q , ε

  • q →

γ2 q γ2 q , ε

  • q →
  • α α , ε
  • q′ →
  • α , α α
  • q′ →

γ1 q′ , γ1 q′ γ1 q′

  • q′ →

γ2 q′ , γ2 q′ γ2 q′

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SFSG — Semantics

Definition

Pre-translation for SFSG G = (Q, Σ, I, P, R) is triple t, q, u

◮ q ∈ Q

(governing) nonterminal

◮

t, u ∈ T ∗

Σ

input and output tree sequences

Definition

Pre-translations PT(G) generated by G are smallest set T

  • ℓθ , q ,

rθ′ ∈ PT(G) for all χ = q → ( ℓ, r) ∈ R, maps θ, θ′ : var(χ) → T ∗

Σ and q′ ∈ var(χ) ◮ |θ(q′)| = |posq′(

ℓ)| and |θ′(q′)| = |posq′( r)|

◮ θ(q′), q′, θ′(q′) ∈ T

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SFSG — Semantics

q0 →

  • σ

q q′ q , σ q′ α q′

  • ( t , t ) , q , ε

u , q′ , ( u , u )

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SFSG — Semantics

Definition

SFSG G = (Q, Σ, I, P, R) computes the tree translation τG ⊆ TΣ × TΣ τG =

q∈I{(t, u) | t, q, u ∈ PT(G)}

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SFSG — Semantics

Definition

SFSG G = (Q, Σ, I, P, R) computes the tree translation τG ⊆ TΣ × TΣ τG =

q∈I{(t, u) | t, q, u ∈ PT(G)}

Definition

◮ SFSG = translations computable by SFSG ◮ MBOT = translations computable by MBOT

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Outline

Motivation Main model Results

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One-symbol normal form

Definition

MBOT (Q, Σ, I, P, R) is in one-symbol normal form if |posΣ(ℓ)| ≤ 1 for every q → (ℓ, r) ∈ R

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One-symbol normal form

Definition

MBOT (Q, Σ, I, P, R) is in one-symbol normal form if |posΣ(ℓ)| ≤ 1 for every q → (ℓ, r) ∈ R

Lemma (ENGELFRIET et al., 2009)

Every MBOT can be transformed into one-symbol normal form

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Simple properties

Theorem

  • 1. SFSG = SFSG−1
  • 2. Domain dom(τ) and range ran(τ) of τ ∈ SFSG

are not necessarily regular

  • 3. MBOT SFSG
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Decomposition

Theorem (RAOULT, 1997)

For every SFSG G there exist two (deterministic) MBOT G1 and G2 τG = τ −1

G1 ; τG2

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Decomposition

Theorem (RAOULT, 1997)

For every SFSG G there exist two (deterministic) MBOT G1 and G2 τG = τ −1

G1 ; τG2

Theorem (Bimorphism characterization)

SFSG = d-MBOT−1 ; RTG ; d-MBOT

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Composition

Theorem

MBOT−1 ; MBOT ⊆ SFSG

Proof.

◮ Decompose MBOT into bimorphisms (d1, L1, τG′

1) and (d2, L2, τG′ 2)

◮ Apply

L′

1 ∩ L′ 2

L1 L2 e2 e1 τG′

1

d1 d2 τG′

2

◮ Use SFSG bimorphism characterization

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Characterization

Corollary

SFSG = MBOT−1 ; MBOT

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Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

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Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

Proof.

SFSG ; SFSG ⊆ (MBOT−1 ; MBOT) ; (MBOT−1 ; MBOT)

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Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

Proof.

SFSG ; SFSG ⊆ (MBOT−1 ; MBOT) ; (MBOT−1 ; MBOT) ⊆ MBOT−1 ; SFSG ; MBOT

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Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

Proof.

SFSG ; SFSG ⊆ (MBOT−1 ; MBOT) ; (MBOT−1 ; MBOT) ⊆ MBOT−1 ; SFSG ; MBOT ⊆ MBOT−1 ; (MBOT−1 ; MBOT) ; MBOT

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Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

Proof.

SFSG ; SFSG ⊆ (MBOT−1 ; MBOT) ; (MBOT−1 ; MBOT) ⊆ MBOT−1 ; SFSG ; MBOT ⊆ MBOT−1 ; (MBOT−1 ; MBOT) ; MBOT ⊆ MBOT−1 ; MBOT

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013

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SLIDE 61

Immediate consequences

Theorem (RADMACHER, 2008)

SFSG is not closed under composition

Corollary

MBOT ; MBOT−1 ⊆ SFSG.

Proof.

SFSG ; SFSG ⊆ (MBOT−1 ; MBOT) ; (MBOT−1 ; MBOT) ⊆ MBOT−1 ; SFSG ; MBOT ⊆ MBOT−1 ; (MBOT−1 ; MBOT) ; MBOT ⊆ MBOT−1 ; MBOT = SFSG

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013

slide-62
SLIDE 62

Immediate consequences

problem string level tree level Parsing O(|G| · (|w1| · |w2|)2 rk(G)+2) O(|G| · |t1| · |t2|) Translation O(|G| · |w1|2 rk(G)+2) O(|G| · |t1|)

  • A. Maletti

Synchronous Forest Substitution Grammars September 4, 2013