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Forest-Based Search Algorithms for Parsing and Machine Translation Liang Huang University of Pennsylvania Google Research, March 14th, 2008 Search in NLP is not trivial! I saw her duck. Aravind Joshi 2 Search in NLP is not trivial!

  1. Outline • Packed Forests and Hypergraph Framework • Exact k-best Search in the Forest (Solution 1) • Approximate Joint Search (Solution 2) with Non-Local Features TOP S • Forest Reranking NP VP . • Machine Translation PRP VBD NP PP . I saw DT NN IN NP • Decoding w/ Language Models the boy with DT NN a telescope bigram • Forest Rescoring held ... talk with ... Sharon • Future Directions VP 3, 6 PP 1, 3 25

  2. Why n -best reranking is bad? ... • too few variations (limited scope) • 41% correct parses are not in ~30-best (Collins, 2000) • worse for longer sentences • too many redundancies • 50-best usually encodes 5-6 binary decisions (2 5 <50<2 6 ) 26

  3. Reranking on a Forest? • with only local features • dynamic programming, tractable (Taskar et al. 2004; McDonald et al., 2005) • with non-local features • on-the-fly reranking at internal nodes • top k derivations at each node • use as many non-local features as possible at each node • chart parsing + discriminative reranking • we use perceptron for simplicity 27

  4. Generic Reranking by Perceptron • for each sentence s i , we have a set of candidates cand ( s i ) • and an oracle tree y i+ , among the candidates • a feature mapping from tree y to vector f ( y ) “decoder” feature representation (Collins, 2002) 28

  5. Features • a feature f is a function from tree y to a real number • f 1 ( y )=log Pr( y ) is the log Prob from generative parser • every other feature counts the number of times a particular configuration occurs in y our features are from TOP (Charniak & Johnson, 2005) S (Collins, 2000) NP VP . instances of Rule feature PRP VBD NP PP . f 100 ( y ) = f S → NP VP . ( y ) = 1 I saw DT NN IN NP f 200 ( y ) = f NP → DT NN ( y ) = 2 the boy with DT NN a telescope 29

  6. Local vs. Non-Local Features • a feature is local iff. it can be factored among local productions of a tree (i.e., hyperedges in a forest) • local features can be pre-computed on each hyperedge in the forest; non-locals can not TOP ParentRule is non-local S NP VP . PRP VBD NP PP . Rule is local I saw DT NN IN NP the boy with DT NN a telescope 30

  7. WordEdges (C&J 05) • a WordEdges feature classifies a node by its label, (binned) span length, and surrounding words • a POSEdges feature uses surrounding POS tags TOP f 400 ( y ) = f NP 2 saw with ( y ) = 1 S NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN 2 words a telescope 31

  8. WordEdges (C&J 05) • a WordEdges feature classifies a node by its label, (binned) span length, and surrounding words • a POSEdges feature uses surrounding POS tags WordEdges is local TOP f 400 ( y ) = f NP 2 saw with ( y ) = 1 S NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN 2 words a telescope 31

  9. WordEdges (C&J 05) • a WordEdges feature classifies a node by its label, (binned) span length, and surrounding words • a POSEdges feature uses surrounding POS tags WordEdges is local TOP f 400 ( y ) = f NP 2 saw with ( y ) = 1 S NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN 2 words a telescope 31

  10. WordEdges (C&J 05) • a WordEdges feature classifies a node by its label, (binned) span length, and surrounding words • a POSEdges feature uses surrounding POS tags WordEdges is local TOP f 400 ( y ) = f NP 2 saw with ( y ) = 1 S NP VP . POSEdges is non-local PRP VBD NP PP . f 800 ( y ) = f NP 2 VBD IN ( y ) = 1 I saw DT NN IN NP the boy with DT NN 2 words a telescope 31

  11. WordEdges (C&J 05) • a WordEdges feature classifies a node by its label, (binned) span length, and surrounding words • a POSEdges feature uses surrounding POS tags WordEdges is local TOP f 400 ( y ) = f NP 2 saw with ( y ) = 1 S NP VP . POSEdges is non-local PRP VBD NP PP . f 800 ( y ) = f NP 2 VBD IN ( y ) = 1 I saw DT NN IN NP the boy with DT NN local features comprise 2 words ~70% of all instances! a telescope 31

  12. Factorizing non-local features • going bottom-up, at each node • compute (partial values of) feature instances that become computable at this level • postpone those uncomputable to ancestors TOP unit instance of ParentRule S feature at the TOP node NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN a telescope 32

  13. Factorizing non-local features • going bottom-up, at each node • compute (partial values of) feature instances that become computable at this level • postpone those uncomputable to ancestors TOP unit instance of ParentRule S feature at the TOP node NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN a telescope 32

  14. Factorizing non-local features • going bottom-up, at each node • compute (partial values of) feature instances that become computable at this level • postpone those uncomputable to ancestors TOP unit instance of ParentRule S feature at the TOP node NP VP . PRP VBD NP PP . I saw DT NN IN NP the boy with DT NN a telescope 32

  15. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope 33

  16. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  17. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  18. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  19. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  20. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  21. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  22. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  23. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  24. NGramTree (C&J 05) • an NGramTree captures the smallest tree fragment that contains a bigram (two consecutive words) • unit instances are boundary words between subtrees A i,k TOP S B i,j C j,k NP VP . w i . . . w j − 1 w j . . . w k − 1 PRP VBD NP PP . unit instance of node A I saw DT NN IN NP the boy with DT NN a telescope Forest Reranking

  25. Heads (C&J 05, Collins 00) • head-to-head lexical dependencies • we percolate heads bottom-up • unit instances are between the head word of the head child and the head words of non-head children TOP/ saw S/ saw NP/ I VP/ saw ./ . PRP/ I VBD/ saw NP/ the PP/ with . NN/ boy I saw DT/ the IN/ with NP/ a NN/ telescope the boy with DT/ a a telescope 35

  26. Heads (C&J 05, Collins 00) • head-to-head lexical dependencies • we percolate heads bottom-up • unit instances are between the head word of the head child and the head words of non-head children TOP/ saw S/ saw NP/ I VP/ saw ./ . PRP/ I VBD/ saw NP/ the PP/ with . NN/ boy I saw DT/ the IN/ with NP/ a NN/ telescope the boy with DT/ a a telescope 35

  27. Heads (C&J 05, Collins 00) • head-to-head lexical dependencies • we percolate heads bottom-up • unit instances are between the head word of the head child and the head words of non-head children TOP/ saw unit instances at VP node saw - the ; saw - with S/ saw NP/ I VP/ saw ./ . PRP/ I VBD/ saw NP/ the PP/ with . NN/ boy I saw DT/ the IN/ with NP/ a NN/ telescope the boy with DT/ a a telescope 35

  28. Approximate Decoding • bottom-up, keeps top k derivations at each node • non-monotonic grid due to non-local features w · f N ( ) = 0.5 A i,k 1.0 3.0 8.0 B i,j C j,k 1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5 w i . . . w j − 1 w j . . . w k − 1 1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3 3.5 4.5 + 0.6 6.5 + 10.5 11.5 + 0.6 36

  29. Approximate Decoding • bottom-up, keeps top k derivations at each node • non-monotonic grid due to non-local features w · f N ( ) = 0.5 A i,k 1.0 3.0 8.0 B i,j C j,k 1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5 w i . . . w j − 1 w j . . . w k − 1 1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3 3.5 4.5 + 0.6 6.5 + 10.5 11.5 + 0.6 36

  30. Approximate Decoding • bottom-up, keeps top k derivations at each node • non-monotonic grid due to non-local features w · f N ( ) = 0.5 A i,k 1.0 3.0 8.0 B i,j C j,k 1.0 2.5 9.0 9.5 w i . . . w j − 1 w j . . . w k − 1 1.1 2.4 9.5 9.4 3.5 5.1 17.0 12.1 37

  31. Approximate Decoding • bottom-up, keeps top k derivations at each node • non-monotonic grid due to non-local features • priority queue for next-best • each iteration pops the best and pushes successors • extract unit non-local features on-the-fly A i,k 1.0 3.0 8.0 B i,j C j,k 1.0 2.5 9.0 9.5 1.1 2.4 9.5 9.4 w i . . . w j − 1 w j . . . w k − 1 3.5 5.1 17.0 12.1 38

  32. Algorithm 2 => Cube Pruning • process all hyperedges simultaneously! significant savings of computation VP hyperedge PP 1, 3 VP 3, 6 PP 1, 4 VP 4, 6 NP 1, 2 VP 2, 3 PP 3, 6 bottom-neck: the time for on-the-fly non-local feature extraction 39

  33. Forest vs. n-best Oracles • on top of Charniak parser (modified to dump forest) • forests enjoy higher oracle scores than n-best lists • with much smaller sizes 98.6 97.8 97.2 96.8 40

  34. Main Results • pre-comp. is for feature-extraction (can be parallelized) • # of training iterations is determined on the dev set • forest reranking outperforms both 50- and 100-best baseline: 1-best Charniak parser 89.72 features n or k pre-comp. training F 1 % local 50 1.4G / 25h 1 x 0.3h 91.01 all 50 2.4G / 34h 5 x 0.5h 91.43 all 100 5.3G / 77h 5 x 1.3h 91.47 local - 3 x 1.4h 91.25 1.2G / 5.1h all 4 x 11h 91.69 k =15 41

  35. Comparison with Others type system F 1 % Collins (2000) 89.7 Henderson (2004) 90.1 Charniak and Johnson (2005) 91.0 D updated (2006) 91.4 Petrov and Klein (2008) 88.3 this work 91.7 Bod (2000) 90.7 G Petrov and Klein (2007) 90.1 S McClosky et al. (2006) 92.1 best accuracy to date on the Penn Treebank 42

  36. Outline • Packed Forests and Hypergraph Framework • Exact k -best Search in the Forest TOP • Approximate Joint Search S with Non-Local Features NP VP . PRP VBD NP PP . • Forest Reranking I saw DT NN IN NP • Machine Translation the boy with DT NN a telescope • Decoding w/ Language Models bigram • Forest Rescoring held ... talk with ... Sharon • Future Directions VP 3, 6 PP 1, 3 43

  37. Statistical Machine Translation Spanish/English English Bilingual Text Text Statistical Analysis Statistical Analysis translation model (TM) language model (LM) Broken Spanish English competency fluency English What hunger have I Hungry I am so Have I that hunger Que hambre tengo yo I am so hungry I am so hungry How hunger have I ... (Knight and Koehn, 2003) 44

  38. Statistical Machine Translation Spanish/English English Bilingual Text Text Statistical Analysis Statistical Analysis translation model (TM) language model (LM) Broken Spanish English competency fluency English k -best rescoring (Algorithm 3) What hunger have I Hungry I am so Have I that hunger Que hambre tengo yo I am so hungry I am so hungry How hunger have I ... (Knight and Koehn, 2003) 44

  39. Statistical Machine Translation Spanish/English English Bilingual Text Text Statistical Analysis Statistical Analysis phrase-based TM translation model (TM) language model (LM) Broken n -gram LM Spanish English competency fluency English syntax-based decoder integrated decoder I am so hungry Que hambre tengo yo (LM-integrated) computationally challenging! ☹ 45

  40. Forest Rescoring Spanish/English English Bilingual Text Text Statistical Analysis Statistical Analysis phrase-based TM translation model (TM) language model (LM) Broken n -gram LM Spanish English competency fluency English syntax-based packed forest as non-local info decoder integrated decoder forest rescorer I am so hungry Que hambre tengo yo (LM-integrated) 46

  41. Syntax-based Translation • synchronous context-free grammars (SCFGs) • context-free grammar in two dimensions • generating pairs of strings/trees simultaneously • co-indexed nonterminal further rewritten as a unit PP (1) VP (2) , VP (2) PP (1) VP → VP juxing le huitan , held a meeting → PP yu Shalong , with Sharon → VP VP PP VP VP PP yu Shalong juxing le huitan held a meeting with Sharon 47

  42. Translation as Parsing • translation with SCFGs => monolingual parsing • parse the source input with the source projection • build the corresponding target sub-strings in parallel PP (1) VP (2) , VP (2) PP (1) VP → VP juxing le huitan , held a meeting → PP yu Shalong , with Sharon → VP 1, 6 VP 3, 6 PP 1, 3 yu Shalong juxing le huitan 48

  43. Translation as Parsing • translation with SCFGs => monolingual parsing • parse the source input with the source projection • build the corresponding target sub-strings in parallel PP (1) VP (2) , VP (2) PP (1) VP → VP juxing le huitan , held a meeting → held a talk with Sharon PP yu Shalong , with Sharon → VP 1, 6 with Sharon held a talk VP 3, 6 PP 1, 3 yu Shalong juxing le huitan 48

  44. Adding a Bigram Model • exact dynamic programming • nodes now split into +LM items • with English boundary words • search space too big for exact search • beam search: keep at most k +LM items each node • but can we do better? held ... Sharon S 1, 6 bigram held ... talk with ... Sharon +LM items VP 3, 6 PP 1, 3 49

  45. Non-Monotonic Grid ) ) ) n g n VP 1, 6 n o o r o r a a l a h h h S S S � � � g h h n t t o i VP 3, 6 PP 1, 3 i w l w 3 a 3 3 , , , 1 1 1 P P P P P P ( ( ( non-monotonicity due to LM combo costs 1.0 3.0 8.0 (VP held � meeting 1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5 ) 3,6 (VP held � talk 1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3 ) 3,6 (VP hold � conference 3.5 4.5 + 0.6 6.5 + 10.5 11.5 + 0.6 ) 3,6 50

  46. Non-Monotonic Grid ) ) ) n g n VP 1, 6 n o o r o r a a l a h h h S S S bigram ( meeting, with ) � � � g h h n t t o i VP 3, 6 PP 1, 3 i w l w 3 a 3 3 , , , 1 1 1 P P P P P P ( ( ( non-monotonicity due to LM combo costs 1.0 3.0 8.0 (VP held � meeting 1.0 2.0 + 0.5 4.0 + 5.0 9.0 + 0.5 ) 3,6 (VP held � talk 1.1 2.1 + 0.3 4.1 + 5.4 9.1 + 0.3 ) 3,6 (VP hold � conference 3.5 4.5 + 0.6 6.5 + 10.5 11.5 + 0.6 ) 3,6 50

  47. Algorithm 2 -Cube Pruning ) ) ) n g n VP 1, 6 n o o r o r a a l a h h h S S S � � � g h h n t t o i VP 3, 6 PP 1, 3 i w l w 3 a 3 3 , , , 1 1 1 P P P P P P ( ( ( 1.0 3.0 8.0 (VP held � meeting 1.0 2.5 9.0 9.5 ) 3,6 (VP held � talk 1.1 2.4 9.5 9.4 ) 3,6 (VP hold � conference 3.5 5.1 17.0 12.1 ) 3,6 51

  48. Algorithm 2 => Cube Pruning k -best Algorithm 2, with search errors VP hyperedge PP 1, 3 VP 3, 6 PP 1, 4 VP 4, 6 NP 1, 4 VP 4, 6 process all hyperedges simultaneously! significant savings of computation 52

  49. Phrase-based: Translation Accuracy speed ++ ~100 times faster quality++ Algorithm 2: 53

  50. Syntax-based: Translation Accuracy speed ++ quality++ Algorithm 2: Algorithm 3: 54

  51. Conclusion so far • General framework of DP on hypergraphs • monotonicity => exact 1-best algorithm • Exact k -best algorithms • Approximate search with non-local information • Forest Reranking for discriminative parsing • Forest Rescoring for MT decoding • Empirical Results • orders of magnitudes faster than previous methods • best Treebank parsing accuracy to date 55

  52. Impact • These algorithms have been widely implemented in • state-of-the-art parsers • Charniak parser • McDonald’s dependency parser • MIT parser (Collins/Koo), Berkeley and Stanford parsers • DOP parsers (Bod, 2006/7) • major statistical MT systems • Syntax-based systems from ISI, CMU, BBN, ... • Phrase-based system: Moses [underway] 56

  53. Future Directions

  54. Further work on Forest Reranking • Better Decoding Algorithms • pre-compute most non-local features • use Algorithm 3 cube growing • intra-sentence level parallelized decoding • Combination with Semi-supervised Learning • easy to apply to self-training (McClosky et al., 2006) • Deeper and deeper Decoding (e.g., semantic roles) • Other Machine Learning Algorithms • Theoretical and Empirical Analysis of Search Errors 58

  55. Machine Translation / Generation • Discriminative training using non-local features • local-features showed modest improvement on phrase-base systems (Liang et al., 2006) • plan for syntax-based (tree-to-string) systems • fast, linear-time decoding • Using packed parse forest for • tree-to-string decoding (Mi, Huang, Liu, 2008) • rule extraction (tree-to-tree) • Generation / Summarization: non-local constraints 59

  56. Thanks! THE END - Thanks! Questions? Comments? 60

  57. Speed vs. Search Quality tested on our faithful clone of Pharaoh speed ++ ( - log Prob ) quality ++ Huang and Chiang Forest Rescoring 61

  58. Speed vs. Search Quality tested on our faithful clone of Pharaoh speed ++ ( - log Prob ) quality ++ 32 times faster Huang and Chiang Forest Rescoring 61

  59. Speed vs. Search Quality tested on our faithful clone of Pharaoh speed ++ same parameters ( - log Prob ) quality ++ 32 times faster Huang and Chiang Forest Rescoring 61

  60. Syntax-based: Search Quality speed ++ ( - log Prob ) quality ++ 10 times faster 62

  61. Tree-to-String System • syntax-directed, English to Chinese (Huang, Knight, Joshi, 2006) • first parse input, and then recursively transfer synchronous tree- substitution grammars (STSG) VP (Galley et al., 2004; Eisner, 2003) VBD VP-C extended to translate was VP PP a packed-forest VBN PP IN NP-C instead of a tree (Mi, Huang, Liu, 2008) shot TO NP-C by DT NN to NN the police death 63

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