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Gaussian Mixture Latent Vector Grammars Yanpeng Zhao Liwen Zhang Kewei Tu School of Information Science and Technology ShanghaiTech University ACL 2018 PCFG Parsing & Limitations Constituency Parsing Grammars Prob.

  1. Gaussian Mixture Latent Vector Grammars Yanpeng Zhao Liwen Zhang Kewei Tu School of Information Science and Technology ShanghaiTech University ACL 2018

  2. PCFG Parsing & Limitations Constituency Parsing Grammars Prob. S → NP VP 1.0 VP → V NP 0.2 S NP → DT NP 0.5 PCFGs NP VP NP → NP NP 0.3 … … He found me P V NP P → He 1.0 P → me 1.0 P V → found 1.0 He found me … … � 2

  3. PCFG Parsing & Limitations Constituency Parsing Grammars Prob. S → NP VP 1.0 VP → V NP 0.2 S NP → DT NP 0.5 PCFGs NP VP NP → NP NP 0.3 … … He found me P V NP P → He 1.0 P → me 1.0 P V → found 1.0 He found me … … S T 1 = NP VP P V NP P He found me � 3

  4. PCFG Parsing & Limitations Constituency Parsing Grammars Prob. S → NP VP 1.0 VP → V NP 0.2 S NP → DT NP 0.5 PCFGs NP VP NP → NP NP 0.3 … … He found me P V NP P → He 1.0 P → me 1.0 P V → found 1.0 He found me … … S S T 1 = T 2 = NP VP NP VP P V NP P V NP P P He found me me found He � 4

  5. PCFG Parsing & Limitations Constituency Parsing Grammars Prob. S → NP VP 1.0 VP → V NP 0.2 S NP → DT NP 0.5 PCFGs NP VP NP → NP NP 0.3 … … He found me P V NP P → He 1.0 P → me 1.0 P V → found 1.0 He found me … … S S P ( T 1 ) = P ( T 2 ) T 1 = T 2 = NP VP NP VP P V NP P V NP He found me 6 = me found He P P limitations He found me me found He � 5

  6. Tree Annotation & Lexicalization SˆROOT S-found NPˆS VPˆS-BD-Z NP-He VP-found P-Z V-BD-Z NPˆVP-O P-He V-found NP-me P-O P-me He found me He found me [Johnson. 1998; Klein et al. 2003] [Collins. 1997; Charniak. 2000] Tree Annotation Lexicalization � 6

  7. Latent Variable Grammars (LVGs) [Matsuzaki et al. 2005; Petrov et al. 2007] S[ x 1 ] S 0 NP[ x 2 ] VP[ x 4 ] NP 2 VP 0 P[ x 3 ] V[ x 5 ] NP[ x 6 ] P 0 V 1 NP 2 P[ x 7 ] P 3 He found me He found me Annotated parse tree A subtype parse tree • Discrete latent variables x 1 , x 2 , x 3 . . . • Model a finite number of nonterminal subtypes � 7

  8. Refining Syntactic Category SˆROOT S-found S[ x 1 ] NPˆS VPˆS-BD-Z NP-He VP-found NP[ x 2 ] VP[ x 4 ] P-Z V-BD-Z NPˆVP-O P-He V-found NP-me P[ x 3 ] V[ x 5 ] NP[ x 6 ] P-O P-me P[ x 7 ] He found me He found me He found me Tree annotation Lexicalization LVGs [Klein et al. 2003] [Charniak. 2000] [Petrov et al. 2007] F1: 85.7 F1: 89.6 F1: 90.1 � 8

  9. Latent Vector Grammars (LVeGs) S[ x 1 ] S [0 . 05 , 0 . 2] NP[ x 2 ] VP[ x 4 ] NP [0 . 4 , 1 . 7] VP [3 . 4 , 0 . 9] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P [0 . 3 , 2 . 1] V [0 . 1 , 0 . 2] NP [1 . 3 , 0 . 7] P[ x 7 ] P [0 . 5 , 1 . 4] He found me He found me Annotated parse tree A subtype parse tree • Continuous latent vectors x 1 , x 2 , x 3 . . . • Model an infinite number of nonterminal subtypes � 9

  10. LVGs vs LVeGs (Latent Variable Grammars) (Latent Vector Grammars) S[ x 1 ] S[ x 1 ] NP[ x 2 ] VP[ x 4 ] NP[ x 2 ] VP[ x 4 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 7 ] P[ x 7 ] He found me He found me � 10

  11. LVGs vs LVeGs (Latent Variable Grammars) (Latent Vector Grammars) S[ x 1 ] S[ x 1 ] NP[ x 2 ] VP[ x 4 ] NP[ x 2 ] VP[ x 4 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 7 ] P[ x 7 ] He found me He found me Discrete latent variables Continuous latent vectors x 1 , x 2 , x 3 . . . x 1 , x 2 , x 3 . . . Annotated rule NP[ x 2 ] � P[ x 3 ] Annotated rule NP[ x 2 ] � P[ x 3 ] � 11

  12. LVGs vs LVeGs (Latent Variable Grammars) (Latent Vector Grammars) S[ x 1 ] S[ x 1 ] NP[ x 2 ] VP[ x 4 ] NP[ x 2 ] VP[ x 4 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 7 ] P[ x 7 ] He found me He found me Discrete latent variables Continuous latent vectors x 1 , x 2 , x 3 . . . x 1 , x 2 , x 3 . . . Annotated rule Annotated rule NP[ x 2 ] � P[ x 3 ] NP[ x 2 ] � P[ x 3 ] A finite set of subtype rules An infinite set of subtype rules Subtype rule Subtype rule NP [2 . 3 , 1 . 7] � P [0 . 4 , 1 . 3] NP 0 � P 1 � 12

  13. LVGs vs LVeGs (Latent Variable Grammars) (Latent Vector Grammars) S[ x 1 ] S[ x 1 ] NP[ x 2 ] VP[ x 4 ] NP[ x 2 ] VP[ x 4 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 7 ] P[ x 7 ] He found me He found me Discrete latent variables Continuous latent vectors x 1 , x 2 , x 3 . . . x 1 , x 2 , x 3 . . . Annotated rule Annotated rule NP[ x 2 ] � P[ x 3 ] NP[ x 2 ] � P[ x 3 ] A finite set of subtype rules An infinite set of subtype rules Subtype rule Subtype rule NP [2 . 3 , 1 . 7] � P [0 . 4 , 1 . 3] NP 0 � P 1 Prob. of the subtype rule: Weight density of the subtype rule: W NP � P ( x 2 = [2 . 3 , 1 . 7] , x 3 = [0 . 4 , 1 . 3]) W NP � P ( x 2 = 0 , x 3 = 1) � 13

  14. LVGs as Special Case of LVeGs S[ x 1 ] Discrete Variables NP[ x 2 ] VP[ x 4 ] P[ x 3 ] V[ x 5 ] NP[ x 6 ] P[ x 7 ] One-hot Vectors He found me � 14

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