an introduction to compositional models in distributional semantics

www.insight-centre.org

An Introduction to Compositional Models in Distributional Semantics

André FreitasSupervisor: Edward Curry

Reading GroupFriday (22/11/2013)


Based on: Baroni et al. (2012)

Frege in Space: A Program for Compositional Distributional Semantics


The Paper

• Comprehensive (107 pages) introduction and overview of compositional distributional models.

3


Semantics for a Complex World

• Most semantic models have dealt with particular types of constructions, and have been carried out under very simplifying assumptions, in true lab conditions.

• If these idealizations are removed it is not clear at all that modern semantics can give a full account of all but the simplest sentences.

Sahlgren, 2013

4


Goal behind Compositional Distributional Models

• Principled and effective semantic models for coping with real world semantic conditions.

• Focus on semantic approximation.

• Applications– Semantic search.– Approximate semantic inference.– Paraphrase detection.– Semantic anomaly detection.– ...

5


Paraphrase Detection

• I find it rather odd that people are already trying to tie the Commission's hands in relation to the proposal for a directive, while at the same calling on it to present a Green Paper on the current situation with regard to optional and supplementary health insurance schemes.

• I find it a little strange to now obliging the Commission to a motion for a resolution and to ask him at the same time to draw up a Green Paper on the current state of voluntary insurance and supplementary sickness insurance.

=?

6


Solving the Problem: The Data-driven Way

• Distributional– Use vast corpora to extract the meaning of content words.– Provide a principled representation of distributional

meaning.

• Compositional– These representations should be objects that compose

together to form more complex meanings.– Content words should be able to combine with

grammatical roles, in ways that account for the importance of structure in sentence meaning.

7


Distributional Semantics

8


Distributional Semantics

• “Words occurring in similar (linguistic) contexts are semantically similar.”

• Practical way to automatically harvest word “meanings” on a large-scale.

• meaning = linguistic context.• This can then be used as a surrogate of its

semantic representation.

99


Vector Space Model

c1

child

husbandspouse

cn

c2

function (number of times that the words occur in c1)

10

0.7

0.5


Semantic Similarity/Relatedness

θ

11

c1

child

husbandspouse

cn

c2


Similarity

• Distributional vectors allow a precise quantification of similarity.

• Measured by the distance of the corresponding vectors on the Cartesian plane.

12


Semantic Approximation (Video)


CompositionalModel


Compositional Semantics

• Can we extend DS to account for the meaning of phrases and sentences?

15


Compositionality

• The meaning of a complex expression is a function of the meaning of its constituent parts.

carnivorous plants

digest slowly

16


Compositionality Principles

Words in which the meaning is directly determined by their distributional behaviour (e.g., nouns).

Words that act as functions transforming the distributional profile of other words (e.g., verbs, adjectives, …).

dogs

old

17


Compositionality Principles• Take the syntactic structure to constitute the backbone

guiding the assembly of the semantic representations of phrases.

• A correspondence between syntactic categories and distributional objects.

18


Mixture-based Models

• Mitchell and Lapata (2010)• Proposed two broad classes of composition

models. – Additive.– Multiplicative.

19


Additive Model

20


Additive Model

• Limitations with the additive model:– The input vectors contribute to the composed

expression in the same way. – Linguistic intuition would suggest that the

composition operation is asymmetric (head of the phrase should have greater weight).

21


Multiplicative Model

22


Analysis

• Multiplicative models perform quite well in the task of predicting human similarity judgments about adjective-noun, noun-noun, verb-noun and noun-verb phrases.

23


Criticism of Mixture Models

• Some words have an intrinsic functional behaviour:

“lice on dogs”, “lice and dogs”

• Lack of recursion.

• To address these limitations function-based models were introduced.

24


Mixture vs Function

25


Distributional Functions

• Composition as function application.• Nouns are still represented as vectors.• Adjectives, verbs, determiners, prepositions,

conjunctions and so forth are all modelled by distributional functions.

(ON(dogs))(lice)AND(lice, dogs)

26


Distributional functions as linear transformations

• Distributional functions are linear transformations on semantic vector/tensor spaces.

• Matrix: First-order, one argument distributional functions.• Used to represent adjectives and intransitive verbs.

27


Example: Adjective + Noun

• Adjective = a function from nouns to nouns,

28


Measuring similarity of tensors

• Two matrices (or tensors) are similar when they have a similar weight distribution, i.e., they perform similar input-to-output component mappings.

• DECREPIT, OLD might dampen the “runs” component of a noun.

29


Inducing distributional functions from corpus data

- Distributional functions are induced from input to output transformation examples - Regression techniques commonly used in machine learning.

old

30


31


Socher, 2012• Recursive neural network (RNN) model that learns

compositional vector representations for phrases and sentences.

• State of the art performance on three different experiments sentiment analysis and cause-effect semantic relations.

32


Main Challenges• Challenge I: Lack of sufficient examples of their inputs and

outputs.– Possible Solution: Extend the training sets exploiting

similarities between linguistic expressions to ‘share’ training examples across distributional functions.

• Challenge II: Computational power and space– Grefenstette et al., 2013.– Nouns live in 300-dimensional spaces, a transitive verb is a

(300 × 300) × 300 tensor, that is, it contains 27 million components.

– Relative pronoun: (300 × 300) × (300 × 300) tensor, contains 8.1 billion components.

33


Categorial Grammar

• Provides the syntax-semantics interface.• Tight connection between syntax and semantics.• Motivated by the principle of compositionality.• View that syntactic constituents should generally

combine as functions or according to a function-argument relationship.

34


Categorial Grammar

ApplyInference

rules

The string is a sentence ((the (bad boy)) (made (that mess)))

35


Local compositions

BARK x dogs

vector matrix

36


Local compositions

(CHASE × cats) × dogs.

3rd order tensor vector

vector

(CHASE × cats)

37


Syntax-Semantics interfacefor a English fragment

38


Other Compositional Models

• Coecke et al. (2010): Category theory and Lambek calculus.

• Grefenstette et al. (2013): Simulating Logical Calculi with Tensors.

• Novacek et al. ISWC (2011), Freitas et al. ICSC (2011) : Semantic Web & Distributional Semantics.

39


Conclusion

• Distributional semantics brings a promising approach for building computational models that work in the real world.

• Semantic approximation as a built-in construct.• Compositionality is still an open problem but

classical (formal) works have been leveraged and adapted to DSMs.

• Exciting time to be around!

40

an introduction to compositional models in distributional semantics

Education

distributional vectors

distributional functions

distributional behaviour

distributional objects

compositional models

distributional profile

effective semantic models

multiplicative models