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Hierarchical phrase-based translation with weighted finite state

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					H IERARCHICAL P HRASE -B ASED T RANSLATION WITH
     W EIGHTED F INITE S TATE T RANSDUCERS
                     Bill Byrne



               Department of Engineering
                University of Cambridge

               IWSLT 2010, Paris, France,
                   2 December 2010
Overview



     WFST formulation of Hiero-style translation
            Alternative implementation to Cube Pruning (CPH)
            Works with lattices rather than individual translation hypotheses
            Based on Google OpenFST toolkit
     Fast Hiero grammars
            language-specific grammars to avoid pruning, search errors, ...
     Fast linearized lattice based minimum Bayes risk decoding (LMBR) with weighted finite
     state transducers




                     `
 Joint work with Adria de Gispert, Gonzalo Iglesias, Graeme Blackwood, Juan Pino




   Department of Engineering     Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                               IWSLT 2010, Paris, France                              1 / 37
Hierarchical Phrase-based Translation


said

                                                                       R1 :   S→      X,X
                                                                       R2 :   S→      SX,SX
                                                                       R3 :   X→      s1 , said
       S                                                               R4 :   X→      s1 s2 , the president said
                                                                       R5 :   X→      s1 s2 s3 , Syrian president says
  R1                                                                   R6 :   X→      s2 , president
                                                                       R7 :   X→      s3 , the Syrian
                                                                       R8 :   X→      s4 , yesterday
       X                                                               R9 :   X→      s5 , that
  R3                                                                  R10 :   X→      s6 , would return
                                                                      R11 :   X→      s6 , he would return
    s1    s2     s3   s4   s5     s6
  wqAl Alr}ys Alswry Ams Anh syEwd
  (       

 
  
  
  )




   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                                 1 / 37
Hierarchical Phrase-based Translation


said president the Syrian yesterday that he would return
       S
                                                                             R1 :   S→      X,X
           ...




  R2             x5 times                                                    R2 :   S→      SX,SX
                                                                             R3 :   X→      s1 , said
       S                                                                     R4 :   X→      s1 s2 , the president said
                                                                             R5 :   X→      s1 s2 s3 , Syrian president says
  R1                                                                         R6 :   X→      s2 , president
                                                                             R7 :   X→      s3 , the Syrian
                                                                             R8 :   X→      s4 , yesterday
       X               X         X     X             X           X           R9 :   X→      s5 , that
  R3              R6        R7       R8         R9          R11             R10 :   X→      s6 , would return
                                                                            R11 :   X→      s6 , he would return
    s1    s2     s3   s4   s5     s6
  wqAl Alr}ys Alswry Ams Anh syEwd
  (       

 
  
  
  )




   Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                   IWSLT 2010, Paris, France                                 1 / 37
Hierarchical Phrase-based Translation


Syrian president says yesterday that he would return
       S
                                                                       R1 :   S→      X,X
           ...




  R2             x3 times                                              R2 :   S→      SX,SX
                                                                       R3 :   X→      s1 , said
       S                                                               R4 :   X→      s1 s2 , the president said
                                                                       R5 :   X→      s1 s2 s3 , Syrian president says
  R1                                                                   R6 :   X→      s2 , president
                                                                       R7 :   X→      s3 , the Syrian
                                                                       R8 :   X→      s4 , yesterday
       X                         X             X           X           R9 :   X→      s5 , that
                  R5           R8         R9           R11            R10 :   X→      s6 , would return
                                                                      R11 :   X→      s6 , he would return
    s1    s2     s3   s4   s5     s6
  wqAl Alr}ys Alswry Ams Anh syEwd
  (       

 
  
  
  )




   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                               1 / 37
Hierarchical Phrase-based Translation (2)


the Syrian president said yesterday that he would return
    S
                                                                           R1 : S→ X , X
                 x3 times
           ...



  R2                                                                       R2 : S→ S X , S X
       S                                                                   R3 : X→ s1 , said
  R1                                                                            ...
                                                                           R6 : X→ s2 , president
       X                                                                   R7 : X→ s3 , the Syrian
  R12                                                                      R8 : X→ s4 , yesterday
                    X                                                      R9 : X→ s5 , that
                 R13                                                      R10 : X→ s6 , would return
                               X        X          X           X          R11 : X→ s6 , he would return
                            R7     R8         R9          R11             R12 : X→ s1 X , X said
                                                                          R13 : X→ s2 X , X president
    s1    s2     s3   s4   s5     s6
  wqAl Alr}ys Alswry Ams Anh syEwd
  (       

 
  
  
  )




   Department of Engineering       Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                 IWSLT 2010, Paris, France                              2 / 37
Hierarchical Phrase-based Translation (2)


yesterday the Syrian president said that he would return
    S
                                                                            R1 : S→ X , X
  R2                                                                        R2 : S→ S X , S X
       S                                                                    R3 : X→ s1 , said
  R1                                                                             ...
                                                                            R6 : X→ s2 , president
       X                                                                    R7 : X→ s3 , the Syrian
  R14                                                                       R8 : X→ s4 , yesterday
                                                                            R9 : X→ s5 , that
    X1                         X2                               X          R10 : X→ s6 , would return
                                                                           R11 : X→ s6 , he would return
  R3                      R7                               R11             R14 : X→ X1 s2 X2 s4 s5 ,
                                                                                     y’day X2 president X1 that
    s1    s2     s3   s4   s5     s6
  wqAl Alr}ys Alswry Ams Anh syEwd
  (       

 
  
  
  )
       Each rule has a probability assigned by the Translation Model



   Department of Engineering        Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                  IWSLT 2010, Paris, France                              2 / 37
Keeping Track of All Derivations. CYK Grid
                                                                          R1 :   S→     X,X
   S            X                                                         R2 :   S→     SX,SX
                                                                          R3 :   X→     s1 , said
                                                                          R4 :   X→     s1 s2 , the president said
                               X                                          R5 :   X→     s1 s2 s3 , Syrian president says
                                                                          R6 :   X→     s2 , president
                                                                          R7 :   X→     s3 , the Syrian
                                    X                                     R8 :   X→     s4 , yesterday
                                                                          R9 :   X→     s5 , that
                                                                         R10 :   X→     s6 , would return
                                                 X
                                                                         R11 :   X→     s6 , he would return

                                                              X

                                                                           X



                s1             s2   s3           s4           s5           s6
            wqAl Alr}ys Alswry Ams                          Anh syEwd


   Department of Engineering        Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                  IWSLT 2010, Paris, France                               3 / 37
Keeping Track of All Derivations. CYK Grid
                                                                          R1 :   S→     X,X
   S            X                                                         R2 :   S→     SX,SX
                                                                          R3 :   X→     s1 , said
  R2                                                                      R4 :   X→     s1 s2 , the president said
                               X                                          R5 :   X→     s1 s2 s3 , Syrian president says
                                                                          R6 :   X→     s2 , president
  R2                                                                      R7 :   X→     s3 , the Syrian
                                    X                                     R8 :   X→     s4 , yesterday
                                                                          R9 :   X→     s5 , that
  R2
                                                                         R10 :   X→     s6 , would return
                                                 X
                                                                         R11 :   X→     s6 , he would return
  R1
               R5
  R2                                                          X
  R1
               R4
  R2                                                                      X
                                                                         R10
  R1           R3          R6       R7          R8           R9
                                                                         R11
                s1             s2   s3           s4           s5           s6
            wqAl Alr}ys Alswry Ams                          Anh syEwd


   Department of Engineering        Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                  IWSLT 2010, Paris, France                               3 / 37
Keeping Track of All Derivations. CYK Grid (2)
                                                                          R1 : S→ X , X
                                                                          R2 : S→ S X , S X
   S            X                                                         R3 : X→ s1 , said
                                                                               ...
                                                                          R6 : X→ s2 , president
                               X                                          R7 : X→ s3 , the Syrian
  R1                                                                      R8 : X→ s4 , yesterday
              R14
                                    X                                     R9 : X→ s5 , that
                                                                         R10 : X→ s6 , would return
                                                                         R11 : X→ s6 , he would return
                                                 X                       R14 : X→ X1 s2 X2 s4 s5 ,
                                                                                   y’day X2 president X1 that
               R5
                                                              X
               R4
                                                                          X
                                                                         R10
               R3          R6       R7          R8           R9
                                                                         R11
                s1             s2   s3           s4           s5           s6
            wqAl Alr}ys Alswry Ams                          Anh syEwd


   Department of Engineering        Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                  IWSLT 2010, Paris, France                              4 / 37
Cube Pruning Algorithm 1                                                                       S           X

                                                                                           x8420         x20
        The number of derivations can be vast
        Each derivation will produce a translation candidate
                                                                                            x420         x20
        Each candidate has a score
        Find best candidate                                                                  x20         x20         x20   x20
                                    argmax P(s|t) P(t)
                                      t ∈T
                                                                                                           s1        s2    s3

        Cube-Pruning Algorithm
             One-by-one processing of all derivations is not feasible
             Lists of k-best hypotheses are kept in each cell (k=104 )
             Local decisions based on Translation and Language Model
             Translation Model fits well in this grid representation
                                                   Q
           × Language Model does not: P(t) = In=1 p(tn |tn−1 )

           would return    ← p(return|would)×p(would|?)
           he would return ← p(return|would) × p(would|he)×p(he|?)

        In pruning, local decisions should be avoided!



  1
      Chiang, D. 2005. A Hierarchical Phrase-Based Model for Statistical Machine Translation. Proc. ACL.
      Department of Engineering       Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
      University of Cambridge                                 IWSLT 2010, Paris, France                                          4 / 37
Weighted Finite-State Acceptors (WFSAs) 2

         WFSAs are devices that compactly model a formal language
         A Weighted Acceptor of strings ‘a b c d’ and ‘a b b d’ :


                                       a/0.1                 b/0.3                  c/0.7                   d
                                   0                1                      2                      3                     4
                                                                                    b/0.2


                                                                                      x/w
         is defined by a set of states Q and a set of arcs : q → q

         Weighted Acceptors can assign costs to strings:
              - strings are associated with paths, which are sequences of arcs     N
              - weights are accumulated over paths by means of a product operation
                                                   w(p) = w(e1 ) ⊗ · · · ⊗ w(en )




   2
    Mohri, Mehryar, Fernando Pereira, and Michael Riley. 2002. Weighted finite-state transducers in speech recognition.
 Computer Speech and Language, v16
       Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
       University of Cambridge                                   IWSLT 2010, Paris, France                                  5 / 37
Weighted Finite-State Acceptors (WFSAs)


     WFSAs are devices that compactly model a formal language
     A Weighted Acceptor of strings ‘a b c d’ and ‘a b b d’ :


                                   a/0.1                 b/0.3                  c/0.7                   d
                               0                1                      2                      3                     4
                                                                                b/0.2


                                                                                  x/w
     is defined by a set of states Q and a set of arcs : q → q

     Weighted Acceptors can assign costs to strings:
          - strings are associated with paths, which are sequences of arcs     N
          - weights are accumulated over paths by means of a product operation
                                               w(p) = w(e1 ) ⊗ · · · ⊗ w(en )
        Probability Semiring: w(‘a b c d’) = 0.1 × 0.3 × 0.7 × 1.0 = 0.021 ← BEST
                              w(‘a b b d’) = 0.1 × 0.3 × 0.2 × 1.0 = 0.006




   Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                   IWSLT 2010, Paris, France                                  5 / 37
Weighted Finite-State Acceptors (WFSAs)


     WFSAs are devices that compactly model a formal language
     A Weighted Acceptor of strings ‘a b c d’ and ‘a b b d’ :


                                   a/0.1                 b/0.3                  c/0.7                   d
                               0                1                      2                      3                     4
                                                                                b/0.2


                                                                                  x/w
     is defined by a set of states Q and a set of arcs : q → q

     Weighted Acceptors can assign costs to strings:
          - strings are associated with paths, which are sequences of arcs     N
          - weights are accumulated over paths by means of a product operation
                                               w(p) = w(e1 ) ⊗ · · · ⊗ w(en )
        Tropical Semiring: w(‘a b c d’) = 0.1 + 0.3 + 0.7 + 0.0 = 1.1
                           w(‘a b b d’) = 0.1 + 0.3 + 0.2 + 0.0 = 0.6 ← BEST




   Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                   IWSLT 2010, Paris, France                                  5 / 37
WFSA Operations - Union
 A string x is accepted by A = A ∪ B if x is accepted by A or by B
                                                      M
                                  [[C]](x) = [[A]](x)   [[B]](x)


               red/0.5                                                                     green/0.4          1

                         green/0.3                blue                             0        blue/1.2
                  0                    1                           2
                                               yellow/0.6
                                                                                                              2

                                         A                                                       B




   Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                   IWSLT 2010, Paris, France                              6 / 37
WFSA Operations - Concatenation (or Product)
 A string x is accepted by C = A ⊗ B if x can be split into x = x1 x2 such that
 x1 is accepted by A and x2 is accepted by B
                                           M
                             [[C]](x) =           [[A]](x1 ) ⊗ [[B]](x2 )
                                                     x1 ,x2 : x=x1 x2



                red/0.5                                                                     green/0.4          1

                          green/0.3                blue                             0        blue/1.2
                   0                    1                           2
                                                yellow/0.6
                                                                                                               2

                                          A                                                       B




    Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
    University of Cambridge                                   IWSLT 2010, Paris, France                              7 / 37
WFSA Operations for Compactness

 WFSAs can be made compact with operations that:
     reduce their size in number of states/arcs
     accept the same distinct strings
     the cost of each string is respected according to the semiring



            a/0.4

            b/0.5       1      c/1
    0       a/0.5              c/2     3                  ⇒
            b/0.4       2



     WFSAs can represent compactly very, very large numbers of paths
     Processing a WFSA is much faster than processing all of the paths individually




   Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                   IWSLT 2010, Paris, France                              8 / 37
HiFST – Hierarchical Translation with WFSTs 3                                               4            S           X

                                                                                                      x8420      x20

         Keep all possible derivations in each cell
                                                                                                       x420      x20
         Efficiently explore largest T in
                                                        argmax P(s|t) P(t)                             x20       x20      x20   x20
                                                          t ∈T
                                                                                                                     s1   s2    s3
         Build a WFSA in each cell
                They compactly store millions of paths with Translation Model costs
                We can operate with them easily and faster than distinct hypotheses
                Applying a Language Model to a WFSA is a well-established task
                All parse information can be discarded



       In each cell, do:

            For each rule in the cell:                            N
               Build Rule WFSA by Concatenating target elements (   )
                                                                                         L
            Build Cell WFSA by Unioning Rule WFSAs (                                            )


   3
     Iglesias, G. et al. 2009. Hierarchical Phrase-Based Translation with Weighted Finite State Transducers. Proc. of
 NAACL-HLT.
   4
     de Gispert, et al. Hierarchical phrase-based translation with weighted finite state transducers and shallow-N grammars.
 Computational Linguistics, 36(3), 2010.
       Department of Engineering      Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
       University of Cambridge                                IWSLT 2010, Paris, France                                              9 / 37
Building Rule WFSAs by Concatenation

                                                                                                      R5
                                                                                                      R12




       R5 :




       R12 :


   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                              10 / 37
                    y
Building Cell WFSA by Union
                      R5 :


                      R12 :




     Can be made compact
     Target language model can be applied
     Search can be carried out efficiently




   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                              11 / 37
Delayed Translation




         Easy implementation with FST Replace operation
         Usual FST operations can be applied to skeleton → lattice size reduction

 Output has the form of a Recursive Transition Network (RTN) 5                 6


   5
     Woods, W. A. 1970. Transition network grammars for natural language analysis. Commun. ACM, 13(10):591–606.
   6
     Mohri, Mehryar. 1997. Finite-state transducers in language and speech processing. Computational Linguistics, v 23.
       Department of Engineering     Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
       University of Cambridge                               IWSLT 2010, Paris, France                                12 / 37
After expansion in the top cell, the result is a translation lattice
        Direct generation of translation lattices uses WFST operations
        Lattice contains all permissible hypotheses 7 under the grammar, with translation scores

               Translation lattice is denoted L(S, 1, J)
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           10


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        38/2.8457

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            543         38/4.5273
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                                                                                                                                                                                                                                                                                                                                48                                          4/0.69727                                                                            309                                                                                                                                                                                                                                                                 152                                                                                                                             175                       179                    184          187                                                                       215                                                                                                                                                                                                                                                                                                                                                                                                                                     5                         775/1.0488
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                                                                                                                                                                                                        23                                                                                                                                     7359                                                                                3                                            84                                                                                                                                                                                         153                157          163                 168         170         158                  164                 172                              15                                                                                                                                                                                                                                                                                                                                                                                                337          356        294                303                                                  2710/4.2734   332                                                                                                                              775                                                      38
                                                                          7/4.3574                                                                             21       1300                                                                 5614                          12316                                                                                                                                                                                                               309                                         95850/0.12402                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5                                                                                                                                                                                                                                                                                     368                            3848                                                                                                    374
                                                                                                                                                                                                                                        29                      36                                   43        7359                                                                                                                                               5                                                                                                                                                                                                                                                                                                                                                                                     4/0.9873                                                                                                                                                                                                                                                                                                                                                         63                                      10/0.21484                                                                                 342                                                                                                                                                11
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                                                                                                                                                                                                                                              39                                                                                                                                                                                                                                           58332/0.84375                                                                                                                                                               13267/3.3818                                                                                               7375/4.4355                                                                                                                                                   57/1.459                                                                                                             57/1.7461                                                                                                                                                                                       3                 140                                                                                                                                                                                                                                  438
                                                                                                             3                                                                                                                                                  56         12316                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  12                                                                                    4/0.9873
                                                                                                   3                     6          23                                                                                                                                                                                                                                                                                                                                                                                         101                                                                                                                       15/1.5693                                                                                                                                                        7375                                                                                                                                                                     185                  3                                                                                                                                                                                                                                                                                                                                             11/1.7031
                                                                                                                                                              1300                                      23                                                                                                    42/1.04                                                                                                                                                                                                                                            9                                     8716                                                                                                                                                                                                         177          180        16/6.084                                                                                                                                336   213                227                   242       90/4.8203                                                                                                                                                                                                                                                                                                                                              3848/1.75                        395
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                                                                                                                                                                        24                                                                                                                           58                                                                                                                            4                                                                                                            9                                                                                                                                     13267   142          147                                                                                                                                                                                                                                  57/1.459    197               202                                                                                       57                     50                                                                                                                        194             87           17                                                11/5.2559
                                                                                                                                                                                                                                                                                                                                                                                                    515/4.1318                                                                 100                                                                                                                                                                                                                                                   368                                                                 161                                                               20           1976           13              3           4854                                                                                                                                                                                                                                                                     296                    307          320        336   10/0.20996                                                                                                                                                                                                                                    11
                                                                                                                                                                                 23                                            3                                                                                                                                                            80                                                     3              5                                        95850/0.21289                                                                                                                                     16                                                                                                                                                                                                      181         183           186              189         192           198                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   419                                     81/0.38965
                                                                                                                                                                                                                                                                                                             42/1.3105                                                      4/0.52637                                                                                                                                                                                                                                                                                                                                                                         1001/1.9658                                                                                                                                                                                                                                                                                                                                                                                                                    63/0.29004                                                                       355                                                                        5/1.5518                                                    1579
                                                                                                                                     7                                                                            3580                                                                                                          51                                                                                    4            5                                                                                                                                        138    95850                                                                                   134                                                                         151                  176                                                                                                                                                                                   31/1.3125                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      569
                                                                                                                                                 1300                                                                                                                                                                                                                                                                                       98                                                                                                                                                                                                                                                                                                                                        5                                          15                                                                                                                                                                                                                                                                                                                                                                                                                               10/0.125                                                                                                                                                                                                                                                  632
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                                                                                                                                                                                                                                                                                                              42/1.04                                                                      58332    515/3.9678                                                                                                                                                                                                           8716                            15/2.5664                                                                                                                                        5                                                                                                                                                                                                           201                      212          90                                                                                                                                                                                                                                                                                   340    1579/6.1328                3/0.019531                                                                                                                 81                       143/0.37305
                                                                                                                                                                                                                                                                                                                                                                                                                                   3                    107       5                                                                                                                           127                                                137                                                                                                                                                                                                                                                                                                                                      193                                                                                                                                                                                                                                                                                                                           326
                                                                                                                                                                               4/2.5117                                                                                                                                    12272/1.9209                                                                                                                                                        309                                             121               9                                                                                                                                                                                                                                                                                      4/0.94141    20                                                                                                                                                                                                            235                                                                                                          29                                                                                                                                                                                                    381
                                                                                                                                                                         15                             25       3/2.1895                                                                                                                                                                                                                                                                                                                                                                           2035/4.6826                                          13267/5.418                                                                                                                                                                                                                                                                            63/6.7617                                                                                                                                                                                                                3029/2.8857   287                  295                                                                                                                                                                                                                                    1579                        775/2.917
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                                                                                                                                                                                 23                                                     27                     5614                      12316                                                                 62                                                                                                                                                                                                                                                                                                                     5108                 368                             12                                        1001             7375/5.1436                15                                                                                                                                                                                                                                                                                                       309          13                                                                194                                                                                                       2710/4.4717
                                                                                                                                                                                                                                                     34                      41                                                                                                                                                                                                                                                                                                                                                                                            144                      149             154                                                     171                 159                       165                 173                                                                                                                                                                     185                                                                                                        253            265                277       83                                                                                                                                                                                         369                                                         3996
                                                                                                                                                                                                                                                                                                     69                                                                                                                                                                                                                                                                                                                                                  15/2.5664                                                                                                                                                                                                                                                                                                                                           199                                                                                               3                                                                                                                                                     3                 140                                                                                                                                                                                     11/0.9668
                                                                                                                                                                                                                                                                                                                                                                                           58332                               515/3.8184   96                                  119                                                                                                 309                                   16                                                                                                                                                                                                                                                                                                                                                                    185/1.6523                         206         309         222          90                                                                                                                                                                                                                                                                                                             3                                                                                                                                                   81
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                                                                                                                                                                                                                                                                                                               7359                                                           58332                                            309/3.6953                                                        3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           5/4.6641                                                                                                                    63              87           17                                                                                                                                                                                                                                                                    485
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                                                                                                                                                                                                                                                                                                                                                                                                                                                        105                                                                                                                                            8716                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     13                                                           29
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                116                                                                                                                                                                                                                                                                                                                                                                                                                                                                 24/1.8857                                                                                                             264                276                                                                                                                                                                                                        348                                                                                                                                21/0.38281
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                                                                                                                                                                                                                                                                                                                                                                                                                     68                                                                                                       95850                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     240                                                                                                                                                                            140                                                                                                                                          1579
                                                                                                                                                                                                                                                                                                                                                                              58332                                                                                                                            115                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 236
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                               309                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 626/0.54102                                         505                      8                                                                                                                                                                                                                                                                                                                    1704
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      17         10/0.21484   304                       5/0.27246                                        3/5.5244                   3/2.3301                                                                                                                                            10/1.3828
                                                                                                                                                                                                                                                                                                                                                              58332                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        362                                    314                   325                                                                                                                                                                     347
                                                                                                                                                                                                                                                                                                                                                52                                          66                                                                                                                 309                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               3                                                                                8              3           309             13                 83                    29/0.15527         3029   285                                                                                                                     344
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                                                                                                                                                                                                                                                                                                                                                                                                                               755/3.9072               108                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  200                                                                                                      288                                                                                                          275                                                                                                                                                                                                                                                                                                     10
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   90/0.18164                                                                                                                                                                                         63/1.9453                                                                                                                  339
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             5/2.1689                                                                                                                                                                                                               1188/0.80762                                                                                                                                                                                                                         558
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            5

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            609




 Now need to apply the language model scores
  7
      If no pruning is applied
      Department of Engineering      Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
      University of Cambridge                                IWSLT 2010, Paris, France                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       13 / 37
Language Model Composition with L(S, 1, J)
 LMs are usually large: e.g. zero cut-off, stupid back-off LM estimated over all available English
      Implement a backoff LM as an acceptor and apply it via composition
 The following reviews a bigram implementation
                                       j
                          ˆ                p(wi , wj )    f (wi , wj ) > C
                          P(wj |wi ) =            ˆ
                                           α(wi )P(wj ) otherwise
                                       f (wi ,wj )
 where p(wi , wj ) = d(f (wi , wj ))      f (wi )
                                                   .
                                                                                                    w / p(w |w)
 - An arc for each pair of words w and w for which f (w, w ) > C : (w)                                   −→        (w )
                                                                                                   φ/ α(w)
 - A back-off arc from every word state (w) to the backoff state : (w) −→
      ‘failure transitions’ are crucial
                                                                                                     ˆ
                                                                                                  w /P(w )
 - A unigram arc from the back-off state to every word state (w ) :                                  −→         (w )
                                                        w /p(w , w)
                                (w)      φ/α(w)                          ˆ
                                                                      w /P (w )           (w )




 Approach developed for ASR ; very suitable for left-to-right application
 - Generalized Algorithms for Constructing Statistical Language Models. C. Allauzen, et al. ACL’03
    Department of Engineering    Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
    University of Cambridge                              IWSLT 2010, Paris, France                                        14 / 37
Language Model Composition with L(S, 1, J) - LM Servers

 A different approach:
   1 Extract 3/4/5-grams from L(S, 1, J) into a list
             Can be done very efficiently using transducers
   2 Query LM server(s) for probabilities P(w5 |w1 ) for the n-grams in the list
                                                 4

             We use Hadoop to serve raw n-gram counts
   3 Build a deterministic transducer with arcs
                                                                 4
                                                   4 w5 / p(w5 |w1 )          5
                                                 (w1 )    −→                (w2 )


             only add states and arcs for the n-grams in the list
             lower order histories starting with SENT START are handled separately
             deterministic WFST implementations of stupid backoff LMs are built on the fly
   4 Apply the LM transducer at L(S, 1, J) and prune based on complete scores
 Makes use of the compact representation of all translation hyps in L(S, 1, J)
      Unlike ASR and similar problems, the hypothesis space can be created before the
      language model is applied
      Simpler topology: many states and arcs, but no need for failure transitions
      Separates the computation of back-off n-gram probabilities from the WFST implementation

    Department of Engineering    Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
    University of Cambridge                              IWSLT 2010, Paris, France                              15 / 37
Top Level Pruning and Pruning in Search

 Final translation lattice L(S, 1, J) typically requires pruning
      Compose with target Language Model
      Perform likelihood-based pruning


 Pruning in Search
     For a CYK cell, if number of states, non-terminal category and source span meet certain
     conditions, then:
             Expand pointers in the translation lattice
             Compose with the language model
             Perform likelihood-based pruning of the resulting lattice
             Remove language model
      Only required for certain language pairs, e.g. Chinese→English
      Goal is to prune in search only when sublattices get large
             pruning triggers can vary based on cell height
      Use a ‘small’ LM too weak for translation but which is fine for pruning
             Or use an appropriated sized grammar which doesn’t need pruning in search - more on this later
 Much opportunity for improvement – need faster/better implementations



    Department of Engineering     Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
    University of Cambridge                               IWSLT 2010, Paris, France                              16 / 37
Translation Results into English. Contrast CP vs HiFST

         


                                  

                      





                                                                     
                      

   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                              17 / 37
Translation Results into English. Change in Semiring

                                                                                                 

  
        Changing the Semiring is easy
        Can have significant impact 8

                     Derivations D : E, F ← D


        Tropical Semiring: Viterbi likelihood
        - single most likely derivation :
                                                               argmax P(D|F )
                                                            D: E,F ←D

        Log Semiring: Marginal probability
        - sum over all derivations :                                   X
                                                      argmax                     P(D|F )
                                                           E      D: E,F ←D                                               
 

                                                                                                                       
 

        Additional gains with no extra programming effort


  8
      P. Blunsom et al. A discriminative latent variable model for statistical machine translation. ACL-HLT, 2008
      Department of Engineering         Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
      University of Cambridge                                   IWSLT 2010, Paris, France                               18 / 37
Translation Grammar Issues – Overgeneration
 Overgeneration: different translations arising from the same set of rules

                                 Translations of the source sequence s1 s2 s3


                      R1 : X → s1 X ,A X
                      R2 : X → X s3 ,X C
                      R3 : X → s2 ,B




      not necessarily a bad thing in that new translations can be synthesized from rules
      extracted from training data
      a strong target language model, such as a high order n-gram, is typically relied upon to
      discard unsuitable hypotheses
 Overgeneration complicates translation in that many hypotheses are introduced only to be
 subsequently discarded. These must be kept until the LM can be applied to discard them.

    Department of Engineering        Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
    University of Cambridge                                  IWSLT 2010, Paris, France                              19 / 37
Translation Grammar Issues – Spurious Ambiguity



 Spurious ambiguity (Chiang 2005):
     ... a situation where the decoder produces many derivations that are distinct yet have
     the same model feature vectors and give the same translation. This can result in
     n-best lists with very few different translations which is problematic for the
     minimum-error-rate training algorithm ...

     This is due in part to the cube pruning procedure (Chiang 2007) which enumerates all
     distinct hypotheses to a fixed depth by means of k-best hypothesis lists.
     If enumeration was not necessary, or if the lists could be arbitrarily deep, there might still
     be many duplicate derivations but at least the hypothesis space would not be
     impoverished.




   Department of Engineering   Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                             IWSLT 2010, Paris, France                              20 / 37
Translation Grammar Issues – Search Errors




     Any search procedure which relies on pruning during search is at risk of search errors
            the risk is made worse if the grammars tend to introduce many similar scoring hypotheses, many
            similar hypotheses, or repeated instances of hypotheses
     We have found that cube pruning is very prone to search errors, i.e. the hypotheses
     produced by cube pruning are not the top scoring hypotheses which should be found
     under the Hiero grammar




   Department of Engineering    Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                              IWSLT 2010, Paris, France                              21 / 37
Translation Grammar Issues – Grammars and Language Pairs




 Not all language pairs require the full power of the full Hiero grammar
         it may be that no language pairs require the full power of the full Hiero grammar ...
 Goal: For a given language pair, identify the (classes of) rules which matter
         interacts strongly with all previously mentioned issues:
         spurious ambiguity, overgeneration, search errors, ...

 Current work not discussed: Automatic Induction of Hiero Grammars 9




   9
     A de Gispert, J Pino, and W Byrne. Hierarchical phrase-based translation grammars extracted from alignment posterior
 probabilities. EMNLP 2010.
       Department of Engineering     Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
       University of Cambridge                               IWSLT 2010, Paris, France                                22 / 37
Grammar configurations: Shallow grammars 10
 Goal: avoid nested hierarchical rules of non-terminals

                              full hierarchical grammar
                              S→ X ,X                                         glue rule
                              S→ S X ,S X                                     glue rule
                              X → γ,α,∼ , γ, α ∈ {X ∪ T}+                     hiero rules of any level

         For Arabic-to-English, shallow-1 grammar performs as full hiero - but ∼20× faster
         Constrained search space, but can be built exactly and quickly - no pruning required
 Shallow-N grammars include special sets of non-terminals to control the degree of nesting

                           shallow-1 grammar
                           S→ X 1 ,X 1                                                  glue rule
                           S→ S X 1 ,S X 1                                              glue rule
                           X 1 → γ 0 ,α0 ,∼ , γ 0 , α0 ∈ {{X 0 } ∪ T}+                  hiero rules level 1
                           X 0 → γ p ,αp , γ p , αp ∈ T+                                regular phrases

         Fast and effective for European language translation


  10
    Iglesias, G. et al. 2009. Hierarchical Phrase-Based Translation with Weighted Finite State Transducers. Proc. of
 NAACL-HLT.
       Department of Engineering       Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
       University of Cambridge                                 IWSLT 2010, Paris, France                               23 / 37
Fast Hiero Grammars for Chinese-English SMT
 Baseline: full hierarchical grammar for the ZHEN task
     requires pruning in search (slow, search errors)
 Idea: faster grammars with fewer rule patterns
     these faster grammars can be (almost) fully explored in decoding
     better balance between time and performance
     same decoder – grammar design determines speed and translation performance

                               Preliminary results with Fast Hiero Grammars
                                        (training size 2M sent. pairs)
                                             BLEU        time         pruning
                                                       (seconds     (instances
                                                       per word)     per word)
                               baseline       34.2       12.0           2.7
                                fast-G1       33.8        0.6           0.0
                                fast-G2       34.0        0.9           0.0
                                fast-G3       34.0        2.0           0.1
                                fast-G4       34.6        7.2           0.9

     Syntax-based SMT can be useful, even if language pairs are very similar
     Syntactic systems can be fast enough for many research problems

   Department of Engineering      Hierarchical Phrase-Based Translation with Weighted Finite State Transducers
   University of Cambridge                                IWSLT 2010, Paris, France                              24 / 37
Translation lattice with translation and language model scores


         Lattice contains all permissible hypotheses 11 under the grammar
                paths weights contain translation scores and language model scores
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       38/2.8457

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