An Extended GHKM Algorithm for Inducing λ -SCFG

1. An Extended GHKM Algorithm forInducing λ-SCFG Peng Li pengli09@gmail.com Tsinghua University

2. Semantic Parsing • Mapping natural language (NL) sentence to its computable meaning representation (MR) NL: Every boy likes a star MR: predicate variable

3. Motivation • Common way: inducing probabilistic grammar PCFG: Probabilistic Context Free Grammar

4. Motivation • Common way: inducing probabilistic grammar CCG: Combinatory Categorial Grammar

5. Motivation • Common way: inducing probabilistic grammar SCFG: Synchronous Context Free Grammar

6. Motivation • State of the art: SCFG + λ-calculus (λ-SCFG) • Major challenge: grammar induction • It is much harder to find the correspondence between NL sentence and MR than between NL sentences • SCFG rule extraction is well-studied in MT • GHKM is the most widely used algorithm • We want to adapt GHKM to semantic parsing • Experimental results show that we get the state-of-the-art performance

7. Background • State of the art: SCFG + λ-calculus (λ-SCFG) • λ-calculus • λ-expression: • β-conversion: bound variable substitution • α-conversion: bound variable renaming

8. λ-SCFG Rule Extraction • Outline • Building training examples • Transforming logical forms to trees • Aligning trees with sentences • Identifying frontier nodes • Extracting minimal rules • Extracting composed rules

9. Building Training Examples NL: Every boy likes a star MR:

10. Building Training Examples

11. Building Training Examples

12. Building Training Examples boy human pop like

13. Building Training Examples boy human pop like Every boy likes a star

14. Identifying Frontier Nodes

15. Identifying Frontier Nodes

16. Identifying Frontier Nodes

17. Identifying Minimal Frontier Tree

18. Identifying Minimal Frontier Tree

19. Identifying Minimal Frontier Tree

20. Identifying Minimal Frontier Tree

21. Minimal Rule Extraction X X

22. Minimal Rule Extraction X X

23. Minimal Rule Extraction X X

24. Composed Rule Extraction

25. λ-SCFG Rule Extraction • Outline • Building training examples • Transforming logical forms to trees • Aligning trees with sentences • Identifying frontier nodes • Extracting minimal rules • Extracting composed rules

26. Modeling • Log-linear model + MERT training • Target

27. Experiments • Dataset: GEOQUERY • 880 English questions with corresponding Prolog logical form • Metric

28. Experiments CCG PCFG SCFG

29. Experiments • F-measure for different languages * en - English, ge - German, el - Greek, th - Thai

30. Experiments

31. Experiments