Tree-based Models. Dr. Mariana Neves (adapted from the original slides of Prof. Philipp Koehn) January 25th, 2016
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1 Tree-based Models Dr. Mariana Neves (adapted from the original slides of Prof. Philipp Koehn) January 25th, 2016 Mariana Neves Tree-based Models January 25th, / 75
2 Syntactic Decoding Inspired by monolingual syntactic chart parsing: During decoding of the source sentence, a chart with translations for the O(n 2 ) spans has to be filled Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Mariana Neves Tree-based Models January 25th, / 75
3 Syntax Decoding VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP German input sentence with tree Mariana Neves Tree-based Models January 25th, / 75
4 Syntax Decoding PRO she VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Purely lexical rule: filling a span with a translation (a constituent in the chart) Mariana Neves Tree-based Models January 25th, / 75
5 Syntax Decoding PRO she coffee VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Purely lexical rule: filling a span with a translation (a constituent in the chart) Mariana Neves Tree-based Models January 25th, / 75
6 Syntax Decoding PRO she coffee VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Purely lexical rule: filling a span with a translation (a constituent in the chart) Mariana Neves Tree-based Models January 25th, / 75
7 Syntax Decoding NP NP PP DET a cup PRO she coffee IN of VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Complex rule: matching underlying constituent spans, and covering words Mariana Neves Tree-based Models January 25th, / 75
8 Syntax Decoding VBZ wants VP TO to NP VP VB NP NP PP DET a cup PRO she coffee IN of VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Complex rule with reordering Mariana Neves Tree-based Models January 25th, / 75
9 Syntax Decoding S PRO VP VP VP VBZ wants TO to VB NP NP NP PP PRO she DET a cup IN of coffee VB drink Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Mariana Neves Tree-based Models January 25th, / 75
10 Bottom-Up Decoding For each span, a stack of (partial) translations are maintained Bottom-up: a higher stack is filled, once underlying stacks are complete Mariana Neves Tree-based Models January 25th, / 75
11 Naive Algorithm Input: Foreign sentence f = f 1,...f lf, with syntax tree Output: English translation e 1: for all spans [start,end] (bottom up) do 2: for all sequences s of hypotheses and words in span [start,end] do 3: for all rules r do 4: if rule r applies to chart sequence s then 5: create new hypothesis c 6: add hypothesis c to chart 7: end if 8: end for 9: end for 10: end for 11: return English translation e from best hypothesis in span [0,l f ] Mariana Neves Tree-based Models January 25th, / 75
12 Chart Organization Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF NP S VP Chart consists of cells that cover contiguous spans over the input sentence Each cell contains a set of hypotheses 1 Hypothesis = translation of span with target-side constituent 1 In the book, they are called chart entries. Mariana Neves Tree-based Models January 25th, / 75
13 Dynamic Programming Applying rule creates new hypothesis NP: a cup of coffee NP+P: a cup of apply rule: NP NP Kaffee ; NP NP+P coffee NP: coffee eine ART Tasse Kaffee trinken VVINF Mariana Neves Tree-based Models January 25th, / 75
14 Dynamic Programming Another hypothesis NP: a cup of coffee NP: a cup of coffee NP+P: a cup of apply rule: NP eine Tasse NP ; NP a cup of NP NP: coffee eine ART Tasse Kaffee trinken VVINF Both hypotheses are indistiguishable in future search can be recombined Mariana Neves Tree-based Models January 25th, / 75
15 Recombinable States Recombinable? NP: a cup of coffee NP: a cup of coffee NP: a mug of coffee Mariana Neves Tree-based Models January 25th, / 75
16 Recombinable States Recombinable? NP: a cup of coffee NP: a cup of coffee NP: a mug of coffee Yes, iff max. 2-gram language model is used Mariana Neves Tree-based Models January 25th, / 75
17 Recombinability Hypotheses have to match in span of input words covered output constituent label first n 1 output words last n 1 output words not properly scored, since they lack context still affect scoring of subsequently added words, just like in phrase-based decoding (n is the order of the n-gram language model) Mariana Neves Tree-based Models January 25th, / 75
18 Language Model Contexts When merging hypotheses, internal language model contexts are absorbed S (minister of Germany met with Condoleezza Rice) the foreign in Frankfurt NP (minister) the foreign of Germany VP (Condoleezza Rice) met with in Frankfurt relevant history plm(met of Germany) plm(with Germany met) un-scored words Mariana Neves Tree-based Models January 25th, / 75
19 Stack Pruning Number of hypotheses in each chart cell explodes need to discard bad hypotheses e.g., keep 100 best only Different stacks for different output constituent labels? Cost estimates translation model cost known language model cost for internal words known estimates for initial words outside cost estimate? (how useful will be a NP covering input words 3 5 later on?) Mariana Neves Tree-based Models January 25th, / 75
20 Naive Algorithm: Blow-ups Many subspan sequences for all sequences s of hypotheses and words in span [start,end] Many rules for all rules r Checking if a rule applies not trivial rule r applies to chart sequence s Unworkable Mariana Neves Tree-based Models January 25th, / 75
21 Solution Prefix tree data structure for rules Dotted rules Cube pruning Mariana Neves Tree-based Models January 25th, / 75
22 Storing Rules First concern: do they apply to span? have to match available hypotheses and input words Example rule np x 1 des x 2 np 1 of the nn 2 Check for applicability is there an initial sub-span that with a hypothesis with constituent label np? is it followed by a sub-span over the word des? is it followed by a final sub-span with a hypothesis with label nn? Sequence of relevant information np des nn np 1 of the nn 2 Mariana Neves Tree-based Models January 25th, / 75
23 Rule Applicability Check Trying to cover a span of six words with given rule NP des NP: NP of the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
24 Rule Applicability Check First: check for hypotheses with output constituent label np NP des NP: NP of the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
25 Rule Applicability Check Found np hypothesis in cell, matched first symbol of rule NP des NP: NP of the NP das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
26 Rule Applicability Check Matched word des, matched second symbol of rule NP des NP: NP of the NP das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
27 Rule Applicability Check Found a nn hypothesis in cell, matched last symbol of rule NP des NP: NP of the NP das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
28 Rule Applicability Check Matched entire rule apply to create a np hypothesis NP des NP: NP of the NP NP das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
29 Rule Applicability Check Look up output words to create new hypothesis (note: there may be many matching underlying np and nn hypotheses) NP des NP: NP of the NP: the house of the architect Frank Gehry NP: the house : architect Frank Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
30 Checking Rules vs. Finding Rules What we showed: given a rule check if and how it can be applied But there are too many rules (millions) to check them all Instead: given the underlying chart cells and input words find which rules apply Mariana Neves Tree-based Models January 25th, / 75
31 Prefix Tree for Rules NP DET NP NP: NP1... NP: NP1 IN2 NP3 NP: NP1 of DET2 NP3 NP: NP1 of IN2 NP3 PP VP des um VP NP: NP1 of the 2 NP: NP2 NP1 NP: NP1 of NP2... DET NP: DET das Haus NP: the house Highlighted Rules np np 1 det 2 nn 3 np 1 in 2 nn 3 np np 1 np 1 np np 1 des nn 2 np 1 of the nn 2 np np 1 des nn 2 np 2 np 1 np det 1 nn 2 det 1 nn 2 np das Haus the house Mariana Neves Tree-based Models January 25th, / 75
32 Dotted Rules: Key Insight If we can apply a rule like to a span p A B C x Then we could have applied a rule like q A B y to a sub-span with the same starting word We can re-use rule lookup by storing A B (dotted rule) Mariana Neves Tree-based Models January 25th, / 75
33 Finding Applicable Rules in Prefix Tree das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
34 Covering the First Cell das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
35 Looking up Rules in the Prefix Tree das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
36 Taking Note of the Dotted Rule das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
37 Checking if Dotted Rule has Translations DET: the DET: that das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
38 Applying the Translation Rules DET: the DET: that DET: that DET: the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
39 Looking up Constituent Label in Prefix Tree DET: that DET: the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
40 Add to Span s List of Dotted Rules DET: that DET: the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
41 Moving on to the Next Cell DET: that DET: the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
42 Looking up Rules in the Prefix Tree Haus ❸ DET: that DET: the das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
43 Taking Note of the Dotted Rule Haus ❸ DET: that DET: the house ❸ das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
44 Checking if Dotted Rule has Translations Haus ❸ : house NP: house DET: that DET: the house ❸ das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
45 Applying the Translation Rules Haus ❸ : house NP: house DET: that DET: the NP: house : house house ❸ das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
46 Looking up Constituent Label in Prefix Tree Haus ❸ ❹ NP ❺ DET: that DET: the NP: house : house house ❸ das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
47 Add to Span s List of Dotted Rules Haus ❸ ❹ NP ❺ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
48 More of the Same Haus ❸ ❹ NP ❺ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
49 Moving on to the Next Cell Haus ❸ ❹ NP ❺ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
50 Covering a Longer Span Cannot consume multiple words at once All rules are extensions of existing dotted rules Here: only extensions of span over das possible DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
51 Extensions of Span over das Haus ❸ ❹ NP ❺, NP, Haus?, NP, Haus? DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
52 Looking up Rules in the Prefix Tree Haus ❻ ❼ Haus ❽ ❾ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
53 Taking Note of the Dotted Rule Haus ❻ ❼ Haus ❽ ❾ DET ❾ DET Haus❽ das ❼ das Haus❻ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
54 Checking if Dotted Rules have Translations Haus ❻ NP: the house ❼ NP: the Haus ❽ NP: DET house ❾ NP: DET DET ❾ DET Haus❽ das ❼ das Haus❻ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
55 Applying the Translation Rules Haus ❻ NP: the house ❼ NP: the Haus ❽ NP: DET house ❾ NP: DET NP: that house NP: the house DET ❾ DET Haus❽ das ❼ das Haus❻ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
56 Looking up Constituent Label in Prefix Tree NP ❺ Haus ❻ NP: the house ❼ NP: the Haus ❽ NP: DET house ❾ NP: DET NP: that house NP: the house DET ❾ DET Haus❽ das ❼ das Haus❻ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
57 Add to Span s List of Dotted Rules NP ❺ Haus ❻ NP: the house ❼ NP: the Haus ❽ NP: DET house ❾ NP: DET NP: that house NP: the house DET ❾ DET Haus❽ das ❼ das Haus❻ NP❺ DET: that DET: the NP: house : house ❹ NP ❺ house ❸ IN: of DET: the des NP: architect : architect ❹ Architekten P: Frank P Frank P: Gehry P Gehry das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
58 Even Larger Spans Extend lists of dotted rules with cell constituent labels span s dotted rule list (with same start) plus neighboring span s constituent labels of hypotheses (with same end) das Haus des Architekten Frank Gehry Mariana Neves Tree-based Models January 25th, / 75
59 Reflections Complexity O(rn 3 ) with sentence length n and size of dotted rule list r may introduce maximum size for spans that do not start at beginning may limit size of dotted rule list (very arbitrary) Does the list of dotted rules explode? Yes, if there are many rules with neighboring target-side non-terminals such rules apply in many places rules with words are much more restricted Mariana Neves Tree-based Models January 25th, / 75
60 Difficult Rules Some rules may apply in too many ways Neighboring input non-terminals vp gibt x 1 x 2 gives np 2 to np 1 non-terminals may match many different pairs of spans especially a problem for hierarchical models (no constituent label restrictions) may be okay for syntax-models Three neighboring input non-terminals vp trifft x 1 x 2 x 3 heute meets np 1 today pp 2 pp 3 will get out of hand even for syntax models Mariana Neves Tree-based Models January 25th, / 75
61 Where are we now? We know which rules apply We know where they apply (each non-terminal tied to a span) But there are still many choices many possible translations each non-terminal may match multiple hypotheses number choices exponential with number of non-terminals Mariana Neves Tree-based Models January 25th, / 75
62 Rules with One Non-Terminal Found applicable rules pp des x... np... PP of NP PP by NP PP in NP PP on to NP the architect... NP architect Frank... NP the famous... NP Frank Gehry NP Non-terminal will be filled any of h underlying matching hypotheses Choice of t lexical translations Complexity O(ht) (note: we may not group rules by target constituent label, so a rule np des x the np would also be considered here as well) Mariana Neves Tree-based Models January 25th, / 75
63 Rules with Two Non-Terminals Found applicable rule np x 1 des x 2 np 1... np 2 a house a building the building a new house NP NP of NP NP NP by NP NP NP in NP NP NP on to NP the architect NP architect Frank... NP the famous... NP Frank Gehry NP Two non-terminal will be filled any of h underlying matching hypotheses each Choice of t lexical translations Complexity O(h 2 t) a three-dimensional cube of choices (note: rules may also reorder differently) Mariana Neves Tree-based Models January 25th, / 75
64 Cube Pruning 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house 2.6 Arrange all the choices in a cube (here: a square, generally a orthotope, also called a hyperrectangle) Mariana Neves Tree-based Models January 25th, / 75
65 Create the First Hypothesis 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: (0,0) Mariana Neves Tree-based Models January 25th, / 75
66 Add ( Pop ) Hypothesis to Chart Cell 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: ɛ Hypotheses in chart cell stack: (0,0) Mariana Neves Tree-based Models January 25th, / 75
67 Create Neighboring Hypotheses 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: (0,1), (1,0) Hypotheses in chart cell stack: (0,0) Mariana Neves Tree-based Models January 25th, / 75
68 Pop Best Hypothesis to Chart Cell 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: (0,1) Hypotheses in chart cell stack: (0,0), (1,0) Mariana Neves Tree-based Models January 25th, / 75
69 Create Neighboring Hypotheses 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: (0,1), (1,1), (2,0) Hypotheses in chart cell stack: (0,0), (1,0) Mariana Neves Tree-based Models January 25th, / 75
70 More of the Same 1.5 in the by architect by the of the... a house 1.0 a building 1.3 the building 2.2 a new house Hypotheses created in cube: (0,1), (1,2), (2,1), (2,0) Hypotheses in chart cell stack: (0,0), (1,0), (1,1) Mariana Neves Tree-based Models January 25th, / 75
71 Queue of Cubes Several groups of rules will apply to a given span Each of them will have a cube We can create a queue of cubes Always pop off the most promising hypothesis, regardless of cube May have separate queues for different target constituent labels Mariana Neves Tree-based Models January 25th, / 75
72 Bottom-Up Chart Decoding Algorithm 1: for all spans (bottom up) do 2: extend dotted rules 3: for all dotted rules do 4: find group of applicable rules 5: create a cube for it 6: create first hypothesis in cube 7: place cube in queue 8: end for 9: for specified number of pops do 10: pop off best hypothesis of any cube in queue 11: add it to the chart cell 12: create its neighbors 13: end for 14: extend dotted rules over constituent labels 15: end for Mariana Neves Tree-based Models January 25th, / 75
73 Outside Cost Estimation Which spans should be more emphasized in search? Initial decoding stage can provide outside cost estimates NP Sie PPER will VAFIN eine ART Tasse Kaffee trinken VVINF For instance, use of a restricted grammar Mariana Neves Tree-based Models January 25th, / 75
74 Summary Synchronous context free grammars Extracting rules from a syntactically parsed parallel corpus Bottom-up decoding Chart organization: dynamic programming, stacks, pruning Prefix tree for rules Dotted rules Cube pruning Mariana Neves Tree-based Models January 25th, / 75
75 Suggested reading Statistical Machine Translation, Philipp Koehn (chapter 11). Mariana Neves Tree-based Models January 25th, / 75
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