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Kai-Wei Chang Joint work with Scott Wen-tau Yih, Chris Meek Microsoft Research

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Build an intelligent system that can interact with human using natural language Research challenge Meaning representation of text Support useful inferential tasks Semantic word representation is the foundation Language is compositional Word is the basic semantic unit

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A lot of popular methods for creating word vectors! Vector Space Model [Salton & McGill 83] Latent Semantic Analysis [Deerwester+ 90] Latent Dirichlet Allocation [Blei+ 01] Deep Neural Networks [Collobert & Weston 08] Encode term co-occurrence information Measure semantic similarity well

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sunny rainy windy cloudy car wheel cab sad joy emotion feeling

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Tomorrow will be rainy. Tomorrow will be sunny.

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Can’t we just use the existing linguistic resources? Knowledge in these resources is never complete Often lack of degree of relations Create a continuous semantic representation that Leverages existing rich linguistic resources Discovers new relations Enables us to measure the degree of multiple relations (not just similarity)

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Introduction Background: Latent Semantic Analysis (LSA) Polarity Inducing LSA (PILSA) Multi-Relational Latent Semantic Analysis (MRLSA) Encoding multi-relational data in a tensor Tensor decomposition & measuring degree of a relation Experiments Conclusions

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Introduction Background: Latent Semantic Analysis (LSA) Polarity Inducing LSA (PILSA) Multi-Relational Latent Semantic Analysis (MRLSA) Encoding multi-relational data in a tensor Tensor decomposition & measuring degree of a relation Experiments Conclusions

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Data representation Encode single-relational data in a matrix Co-occurrence (e.g., from a general corpus) Synonyms (e.g., from a thesaurus) Factorization Apply SVD to the matrix to find latent components Measuring degree of relation Cosine of latent vectors

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Cosine Score Input: Synonyms from a thesaurus Joyfulness: joy, gladden Sad: sorrow, sadden joygladdensorrowsaddengoodwill Group 1: “joyfulness”11000 Group 2: “sad”00110 Group 3: “affection”00001 Target word: row-vectorTerm: column-vector

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terms

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LSA cannot distinguish antonyms [Landauer 2002] “Distinguishing synonyms and antonyms is still perceived as a difficult open problem.” [Poon & Domingos 09]

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Data representation Encode two opposite relations in a matrix using “polarity” Synonyms & antonyms (e.g., from a thesaurus) Factorization Apply SVD to the matrix to find latent components Measuring degree of relation Cosine of latent vectors

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joygladdensorrowsaddengoodwill Group 1: “joyfulness”11 0 Group 2: “sad” 110 Group 3: “affection”00001 Joyfulness: joy, gladden; sorrow, sadden Sad: sorrow, sadden; joy, gladden Inducing polarity Target word: row-vector

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joygladdensorrowsaddengoodwill Group 1: “joyfulness”11 0 Group 2: “sad” 110 Group 3: “affection”00001 Joyfulness: joy, gladden; sorrow, sadden Sad: sorrow, sadden; joy, gladden Inducing polarity Target word: row-vector

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Limitation of the matrix representation Each entry captures a particular type of relation between two entities, or Two opposite relations with the polarity trick Encoding other binary relations Is-A (hyponym) – ostrich is a bird Part-whole – engine is a part of car Encode multiple relations in a 3-way tensor (3-dim array)!

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Represent word relations using a tensor Each slice encodes a relation between terms and target words. 0000 0010 1000 0000 joy gladden sadden feeling joyfulness gladden sad anger gladden joy sadden feeling joyfulness gladden sad anger Synonym layer Antonym layer 1100 1100 0010 0000 Construct a tensor with two slices

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Can encode multiple relations in the tensor 0001 0000 0001 0001 gladden joy sadden feeling joyfulness gladden sad anger Hyponym layer 1100 1100 0010 0000 1100 1100 0010 0000

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Derive a low-rank approximation to generalize the data and to discover unseen relations Apply Tucker decomposition and reformulate the results ~ ~ × × latent representation of words

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~ ~ × × Derive a low-rank approximation to generalize the data and to discover unseen relations Apply Tucker decomposition and reformulate the results ~ ~ × × latent representation of words latent representation of a relation

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Data representation Encode multiple relations in a tensor Synonyms, antonyms, hyponyms (is-a), … (e.g., from a linguistic knowledge base) Factorization Apply tensor decomposition to the tensor to find latent components Measuring degree of relation Cosine of latent vectors after projection

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Similarity Cosine of the latent vectors Other relation (both symmetric and asymmetric) Take the latent matrix of the pivot relation (synonym) Take the latent matrix of the relation Cosine of the latent vectors after projection

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0000 0010 1000 0000 joy gladden sadden felling joyfulness gladden sad anger gladden joy sadden felling joyfulness gladden sad anger Synonym layer Antonym layer 1100 1100 0010 0000

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0000 0010 1000 0000 joy gladden sadden felling joyfulness gladden sad anger gladden joy sadden felling joyfulness gladden sad anger Synonym layer Antonym layer 1100 1100 0010 0000

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joy gladden sadden felling joyfulness gladden sad anger Synonym layer 1000 1100 0010 0000 0001 0000 0001 0001 gladden joy sadden feeling joyfulness gladden sad anger Hypernym layer

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Synonym layer The slice of the specific relation

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Cos (, ) ~ ~ × × ~ ~ ××

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Introduction Background: Latent Semantic Analysis (LSA) Polarity Inducing LSA (PILSA) Multi-Relational Latent Semantic Analysis (MRLSA) Encoding multi-relational data in a tensor Tensor decomposition & measuring degree of a relation Experiments Conclusions

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Encarta Thesaurus Record synonyms and antonyms of target words V ocabulary of 50k terms and 47k target words WordNet Has synonym, antonym, hyponym, hypernym relations V ocabulary of 149k terms and 117k target words Goals: MRLSA generalizes LSA to model multiple relations Improve performance by combing heterogeneous data

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TargetHigh Score Words inanimatealive, living, bodily, in-the-flesh, incarnate alleviateexacerbate, make-worse, in-flame, amplify, stir-up relishdetest, abhor, abominate, despise, loathe * Words in blue are antonyms listed in the Encarta thesaurus.

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Task: GRE closest-opposite questions Which is the closest opposite of adulterate ? (a) renounce (b) forbid (c) purify (d) criticize (e) correct Accuracy

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TargetHigh Score Words birdostrich, gamecock, nighthawk, amazon, parrot automobileminivan, wagon, taxi, minicab, gypsy cab vegetablebuttercrunch, yellow turnip, romaine, chipotle, chilli

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Accuracy

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Relational domain knowledge – the entity type Relation can only hold between the right types of entities Words having is-a relation have the same part-of-speech For relation born-in, the entity types are: (person, location) Leverage type information to improve MRLSA Idea #3: Change the objective function

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Continuous semantic representation that Leverages existing rich linguistic resources Discovers new relations Enables us to measure the degree of multiple relations Approaches Better data representation Matrix/Tensor decomposition Challenges & Future Work Capture more types of knowledge in the model Support more sophisticated inferential tasks

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