Synchronous Grammars
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- Ginger Chase
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1 ynchronous Grammars
2 ynchronous grammars are a way of simultaneously generating pairs of recursively related strings ynchronous grammar w wʹ
3 ynchronous grammars were originally invented for programming language compilation ynchronous grammar for i := 1 to 10 do begin n := n + i end mov ax, 1 loop: add bx, ax cmp ax, 10 jle loop
4 ynchronous grammars have been proposed as a way of doing semantic interpretation ynchronous grammar I open the box open (me, box )
5 ynchronous grammars have been used for syntax-based machine translation ynchronous grammar I open the box watashi wa hako wo akemasu
6 ynchronous grammars can do much fancier transformations than finite-state methods The boy stated that the student said that the teacher danced shoonen ga gakusei ga sensei ga odotta to itta to hanashita boy student teacher danced that said that stated
7 ynchronous grammars can do much fancier transformations than finite-state methods that John saw Peter help the children swim dat Jan Piet de kinderen zag helpen zwemmen John Peter the children saw help swim
8 Overview Definitions Properties Algorithms Extensions
9 Definitions
10 Context-free grammars NP P NP I NP the box P NP open NP P I NP open the box
11 Context-free grammars NP P NP watashi wa NP hako wo P NP akemasu NP P watashi wa NP hako wo akemasu
12 ynchronous CFGs NP 1 P 2 NP 1 P 2 NP I NP watashi wa NP the box NP hako wo P 1 NP 2 P NP 2 1 open akemasu
13 ynchronous CFGs NP 1 P 2, NP 1 P 2 NP I, watashi wa NP the box, hako wo P 1 NP 2, NP 2 1 open, akemasu
14 ynchronous CFGs 1 1 NP 2 P 3 NP 2 P 3 I 4 NP 5 watashi wa NP 5 4 open the box hako wo akemasu
15 Adding probabilities 0.3 NP 1 P 2, NP 1 P NP I, watashi wa 0.6 NP the box, hako wo 0.5 P 1 NP 2, NP open, akemasu
16 ynchronous CFGs 1 1 NP 2 P 3 NP 2 P 3 I 4 NP 5 watashi wa NP 5 4 open the box hako wo akemasu Derivation probability:
17 Other notations P ( 1 NP 2, NP 2 1 ) yntax directed translation schema (Aho and Ullman; Lewis and tearns) (P 1 NP 2, P NP 2 1 ) P NP Inversion transduction grammar (Wu) P [1,2] ( NP ) [2,1] NP Multitext grammar (Melamed)
18 Properties
19 Chomsky normal form X Y Z X a
20 Chomsky normal form A (((B C) D) E) F rank 5
21 Chomsky normal form A [[[B C] D] E] F rank 5 A 1 F 1 2 E 2 3 D rank 2 3 B C
22 A hierarchy of synchronous CFGs 1-CFG 2-CFG = 3-CFG = 4-CFG = 1-CFG 2-CFG = 3-CFG 4-CFG = = ITG (Wu, 1997)
23 ynchronous CNF? A (B 1 [C 2 D 3 ], [C 2 D 3 ] B 1 ) rank 3
24 ynchronous CNF? A (B 1 [C 2 D 3 ], [C 2 D 3 ] B 1 ) rank 3 A (B 1 1 2, 1 2 B 1 ) 1 (C 1 D 2, C 1 D 2 ) rank 2
25 ynchronous CNF? A (B 1 C 2 D 3 E 4, C 2 E 4 B 1 D 3 ) rank 4 A ([B 1 C 2 ] D 3 E 4, [C 2 E 4 B 1 ] D 3 ) A (B 1 [C 2 D 3 ] E 4, [C 2 E 4 B 1 D 3 ]) A (B 1 C 2 [D 3 E 4 ], C 2 [E 4 B 1 D 3 ])
26 ynchronous CNF? A (B 1 C 2 D 3, C 2 D 3 B 1 ) 1 B 2 C 3 D B A (B 1 C 2 D 3 E 4, C 2 E 4 B 1 D 3 ) 2 C 3 D 4 E
27 A hierarchy of synchronous CFGs 1-CFG 2-CFG = 3-CFG = 4-CFG = 1-CFG 2-CFG = 3-CFG 4-CFG = = ITG (Wu, 1997)
28 Algorithms
29 Overview Translation Bitext parsing
30 Review: CKY NP P NP I NP the box P NP open NP I open the box
31 Review: CKY NP P NP I NP the box P NP open NP NP I open the box
32 Review: CKY NP P NP I NP the box P NP open NP P NP I open the box
33 Review: CKY NP P NP I NP the box P NP open NP P I open the box
34 Review: CKY NP P NP I NP the box P NP open I open the box
35 Review: CKY 2 NP 3 2 P 4 open the box O(n 3 ) ways of matching
36 Translation NP 1 P 2 I 3 NP 4 open the box O(n 3 ) I open the box
37 Translation O(n) NP 1 P 2 NP 1 P 2 I 3 NP 4 watashi wa NP 4 3 open the box hako wo akemasu O(n 3 ) O(n) I open the box watashi wa hako wo akemasu
38 Translation What about A B C D E O(n 5 ) ways of combining?
39 1 A Translation A B C D E 2 B C D E flatten O(n) translate O(n) A C E D B parse O(n 3 )
40 Bitext parsing NP 1 P 2 NP 1 P 2 I 3 NP 4 watashi wa NP 4 3 open the box hako wo O(n? ) akemasu I open the box watashi wa hako wo akemasu
41 Bitext parsing NP 1 NP 1 3 NP 4 NP 4 3 I open the box watashi wa hako wo akemasu Consider rank-2 synchronous CFGs for now
42 Bitext parsing NP 1 P 2 NP 1 P 2 3 NP 4 NP 4 3 I open the box watashi wa hako wo akemasu
43 Bitext parsing NP 1 P 2 NP 1 P 2 I open the box watashi wa hako wo akemasu
44 Bitext parsing I open the box watashi wa hako wo akemasu
45 Bitext parsing P 2 P 2 3 NP 4 NP 4 3 open the box hako wo akemasu O(n 6 ) ways of matching
46 Bitext parsing A A B 1 C 2 D 3 E 4 C 2 E 4 B 1 D 3 O(n 10 ) ways of combining!
47 Algorithms Translation: easy Bitext parsing: polynomial in n but worst-case exponential in rank
48 Algorithms Translation with an n-gram language model Offline rescoring Intersect grammar and LM (Wu 1996; Huang et al. 2005): slower Hybrid approaches (Chiang 2005; Zollman and enugopal 2006)
49 Extensions
50 Limitations of synchronous CFGs NP P NP P John NP Marie PP misses Mary manque P NP à Jean
51 One solution 1 NP 2 misses NP 3 1 NP 3 manque à NP 2 John Mary Marie Jean
52 ynchronous tree substitution grammars NP 1 NP P NP 2 P John NP 2 PP NP Jean misses manque P NP 1 NP NP à Mary Marie
53 ynchronous tree substitution grammars NP 1 P NP 2 P John NP 2 Marie PP misses Mary manque P NP 1 à Jean
54 Limitations of synchronous TGs dat Jan Piet de kinderen zag helpen zwemmen that John saw Peter help the children swim This pattern extends to n nouns and n verbs
55 Limitations of synchronous TGs NP 1 P NP 1 P John 2 Jan 2 saw? zag? Piet de kinderen helpen zwemmen Peter help the children swim
56 Tree-adjoining grammar NP P zwemmen NP P helpen de kinderen Piet * t t
57 zwemmen NP P zwemmen NP P helpen de kinderen t NP P helpen Piet Piet * NP P t t de kinderen t
58 ynchronous TAG 1 1 NP 2 P 3 NP 2 P 3 zwemmen the children de kinderen swim t
59 1 1 NP 2 P 3 NP 2 P 3 zwemmen the children de kinderen swim t 1 1 NP 2 P 3 NP 2 P 3 helpen Peter * Piet * help t
60 1 1 zwemmen NP 2 P 3 NP 2 P 3 helpen Peter Piet help NP 4 P 5 NP 4 P 5 t the children de kinderen swim t
61 1 NP 2 P 3 Peter 1 zwemmen help NP 4 P 5 NP 2 P 3 helpen the children Piet swim NP 4 P 5 t 1 de kinderen 1 NP 2 P 3 John saw * t NP 2 P 3 Jan * t zag
62 1 NP 2 P 3 zwemmen John 1 helpen saw NP 4 P 5 NP 2 P 3 zag Peter Jan help NP 6 P 7 NP 4 P 5 t the children swim Piet NP 6 P 7 t de kinderen t
63 ummary ynchronous grammars are useful for various tasks including translation ome rules in the wild (Chiang, 2005): X (de, s) X (X 1 de X 2, the X 2 of X 1) X (X 1 de X 2, the X 2 that) X (zai X 1 xia, under X 1 ) X (zai X 1 qian, before X 1 ) X (X 1 zhiyi, one of X 1 )
64 ummary ynchronous context-free grammars vary in power depending on rank Translation is easy; bitext parsing is exponential in rank
65 ummary Beyond synchronous CFGs, synchronous TGs allow multilevel rules synchronous TAGs allow discontinuous constituents
This kind of reordering is beyond the power of finite transducers, but a synchronous CFG can do this.
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