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

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

Distributed Representations for Compositional Semantics

The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional approaches --- meaning distributed representations that exploit co-occurrence statistics of large corpora --- have proved popular and successful across a number of tasks. However, natural language usually comes in structures beyond the word level, with meaning arising not only from the individual words but also the structure they are contained in at the phrasal or sentential level. Modelling the compositional process by which the meaning of an utterance arises from the meaning of its parts is an equally fundamental task of NLP. This dissertation explores methods for learning distributed semantic representations and models for composing these into representations for larger linguistic units. Our underlying hypothesis is that neural models are a suitable vehicle for learning semantically rich representations and that such representations in turn are suitable vehicles for solving important tasks in natural language processing. The contribution of this thesis is a thorough evaluation of our hypothesis, as part of which we introduce several new approaches to representation learning and compositional semantics, as well as multiple state-of-the-art models which apply distributed semantic representations to various tasks in NLP.Comment: DPhil Thesis, University of Oxford, Submitted and accepted in 201

Inferring unobserved co-occurrence events in Anchored Packed Trees

Anchored Packed Trees (APTs) are a novel approach to distributional semantics that takes distributional composition to be a process of lexeme contextualisation. A lexeme’s meaning, characterised as knowledge concerning co-occurrences involving that lexeme, is represented with a higher-order dependency-typed structure (the APT) where paths associated with higher-order dependencies connect vertices associated with weighted lexeme multisets. The central innovation in the compositional theory is that the APT’s type structure enables the precise alignment of the semantic representation of each of the lexemes being composed. Like other count-based distributional spaces, however, Anchored Packed Trees are prone to considerable data sparsity, caused by not observing all plausible co-occurrences in the given data. This problem is amplified for models like APTs, that take the grammatical type of a co-occurrence into account. This results in a very sparse distributional space, requiring a mechanism for inferring missing knowledge. Most methods face this challenge in ways that render the resulting word representations uninterpretable, with the consequence that distributional composition becomes difficult to model and reason about. In this thesis, I will present a practical evaluation of the Apt theory, including a large-scale hyperparameter sensitivity study and a characterisation of the distributional space that APTs give rise to. Based on the empirical analysis, the impact of the problem of data sparsity is investigated. In order to address the data sparsity challenge and retain the interpretability of the model, I explore an alternative algorithm — distributional inference — for improving elementary representations. The algorithm involves explicitly inferring unobserved co-occurrence events by leveraging the distributional neighbourhood of the semantic space. I then leverage the rich type structure in APTs and propose a generalisation of the distributional inference algorithm. I empirically show that distributional inference improves elementary word representations and is especially beneficial when combined with an intersective composition function, which is due to the complementary nature of inference and composition. Lastly, I qualitatively analyse the proposed algorithms in order to characterise the knowledge that they are able to infer, as well as their impact on the distributional APT space

RELPRON: A Relative Clause Evaluation Data Set for Compositional Distributional Semantics

This article introduces RELPRON, a large data set of subject and object relative clauses, for the evaluation of methods in compositional distributional semantics. RELPRON targets an intermediate level of grammatical complexity between content-word pairs and full sentences. The task involves matching terms, such as “wisdom,” with representative properties, such as “quality that experience teaches.” A unique feature of RELPRON is that it is built from attested properties, but without the need for them to appear in relative clause format in the source corpus. The article also presents some initial experiments on RELPRON, using a variety of composition methods including simple baselines, arithmetic operators on vectors, and finally, more complex methods in which argument-taking words are represented as tensors. The latter methods are based on the Categorial framework, which is described in detail. The results show that vector addition is difficult to beat—in line with the existing literature—but that an implementation of the Categorial framework based on the Practical Lexical Function model is able to match the performance of vector addition. The article finishes with an in-depth analysis of RELPRON, showing how results vary across subject and object relative clauses, across different head nouns, and how the methods perform on the subtasks necessary for capturing relative clause semantics, as well as providing a qualitative analysis highlighting some of the more common errors. Our hope is that the competitive results presented here, in which the best systems are on average ranking one out of every two properties correctly for a given term, will inspire new approaches to the RELPRON ranking task and other tasks based on linguistically interesting constructions.Laura Rimell and Stephen Clark were supported by EPSRC grant EP/I037512/1. Jean Maillard is supported by an EPSRC Doctoral Training Grant and a St. John’s Scholarship. Laura Rimell, Tamara Polajnar, and Stephen Clark are supported by ERC Starting Grant DisCoTex (306920)

Mathematical linguistics

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