2,012 research outputs found
Experimental Support for a Categorical Compositional Distributional Model of Meaning
Modelling compositional meaning for sentences using empirical distributional
methods has been a challenge for computational linguists. We implement the
abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using
data from the BNC and evaluate it. The implementation is based on unsupervised
learning of matrices for relational words and applying them to the vectors of
their arguments. The evaluation is based on the word disambiguation task
developed by Mitchell and Lapata (2008) for intransitive sentences, and on a
similar new experiment designed for transitive sentences. Our model matches the
results of its competitors in the first experiment, and betters them in the
second. The general improvement in results with increase in syntactic
complexity showcases the compositional power of our model.Comment: 11 pages, to be presented at EMNLP 2011, to be published in
Proceedings of the 2011 Conference on Empirical Methods in Natural Language
Processin
Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus
The Distributional Compositional Categorical (DisCoCat) model is a
mathematical framework that provides compositional semantics for meanings of
natural language sentences. It consists of a computational procedure for
constructing meanings of sentences, given their grammatical structure in terms
of compositional type-logic, and given the empirically derived meanings of
their words. For the particular case that the meaning of words is modelled
within a distributional vector space model, its experimental predictions,
derived from real large scale data, have outperformed other empirically
validated methods that could build vectors for a full sentence. This success
can be attributed to a conceptually motivated mathematical underpinning, by
integrating qualitative compositional type-logic and quantitative modelling of
meaning within a category-theoretic mathematical framework.
The type-logic used in the DisCoCat model is Lambek's pregroup grammar.
Pregroup types form a posetal compact closed category, which can be passed, in
a functorial manner, on to the compact closed structure of vector spaces,
linear maps and tensor product. The diagrammatic versions of the equational
reasoning in compact closed categories can be interpreted as the flow of word
meanings within sentences. Pregroups simplify Lambek's previous type-logic, the
Lambek calculus, which has been extensively used to formalise and reason about
various linguistic phenomena. The apparent reliance of the DisCoCat on
pregroups has been seen as a shortcoming. This paper addresses this concern, by
pointing out that one may as well realise a functorial passage from the
original type-logic of Lambek, a monoidal bi-closed category, to vector spaces,
or to any other model of meaning organised within a monoidal bi-closed
category. The corresponding string diagram calculus, due to Baez and Stay, now
depicts the flow of word meanings.Comment: 29 pages, pending publication in Annals of Pure and Applied Logi
The role of syntactic dependencies in compositional distributional semantics
This article provides a preliminary semantic framework for Dependency Grammar in which lexical words are semantically defined as contextual distributions (sets of contexts) while syntactic dependencies are compositional operations on word distributions. More precisely, any syntactic dependency uses the contextual distribution of the dependent word to restrict the distribution of the head, and makes use of the contextual distribution of the head to restrict that of the dependent word. The interpretation of composite expressions and sentences, which are analyzed as a tree of binary dependencies, is performed by restricting the contexts of words dependency by dependency in a left-to-right incremental way. Consequently, the meaning of the whole composite expression or sentence is not a single representation, but a list of contextualized senses, namely the restricted distributions of its constituent (lexical) words. We report the results of two large-scale corpus-based experiments on two different natural language processing applications: paraphrasing and compositional translationThis work is funded by Project TELPARES, Ministry of Economy and Competitiveness (FFI2014-51978-C2-1-R), and the program “Ayuda Fundación BBVA a Investigadores y Creadores Culturales 2016”S
Lexical and Derivational Meaning in Vector-Based Models of Relativisation
Sadrzadeh et al (2013) present a compositional distributional analysis of
relative clauses in English in terms of the Frobenius algebraic structure of
finite dimensional vector spaces. The analysis relies on distinct type
assignments and lexical recipes for subject vs object relativisation. The
situation for Dutch is different: because of the verb final nature of Dutch,
relative clauses are ambiguous between a subject vs object relativisation
reading. Using an extended version of Lambek calculus, we present a
compositional distributional framework that accounts for this derivational
ambiguity, and that allows us to give a single meaning recipe for the relative
pronoun reconciling the Frobenius semantics with the demands of Dutch
derivational syntax.Comment: 10 page version to appear in Proceedings Amsterdam Colloquium,
updated with appendi
Category-Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics
This thesis is about the problem of compositionality in distributional
semantics. Distributional semantics presupposes that the meanings of words are
a function of their occurrences in textual contexts. It models words as
distributions over these contexts and represents them as vectors in high
dimensional spaces. The problem of compositionality for such models concerns
itself with how to produce representations for larger units of text by
composing the representations of smaller units of text.
This thesis focuses on a particular approach to this compositionality
problem, namely using the categorical framework developed by Coecke, Sadrzadeh,
and Clark, which combines syntactic analysis formalisms with distributional
semantic representations of meaning to produce syntactically motivated
composition operations. This thesis shows how this approach can be
theoretically extended and practically implemented to produce concrete
compositional distributional models of natural language semantics. It
furthermore demonstrates that such models can perform on par with, or better
than, other competing approaches in the field of natural language processing.
There are three principal contributions to computational linguistics in this
thesis. The first is to extend the DisCoCat framework on the syntactic front
and semantic front, incorporating a number of syntactic analysis formalisms and
providing learning procedures allowing for the generation of concrete
compositional distributional models. The second contribution is to evaluate the
models developed from the procedures presented here, showing that they
outperform other compositional distributional models present in the literature.
The third contribution is to show how using category theory to solve linguistic
problems forms a sound basis for research, illustrated by examples of work on
this topic, that also suggest directions for future research.Comment: DPhil Thesis, University of Oxford, Submitted and accepted in 201
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