A Context-theoretic Framework for Compositionality in Distributional Semantics

Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a framework for natural language semantics in which words, phrases and sentences are all represented as vectors, based on a theoretical analysis which assumes that meaning is determined by context. In the theoretical analysis, we define a corpus model as a mathematical abstraction of a text corpus. The meaning of a string of words is assumed to be a vector representing the contexts in which it occurs in the corpus model. Based on this assumption, we can show that the vector representations of words can be considered as elements of an algebra over a field. We note that in applications of vector spaces to representing meanings of words there is an underlying lattice structure; we interpret the partial ordering of the lattice as describing entailment between meanings. We also define the context-theoretic probability of a string, and, based on this and the lattice structure, a degree of entailment between strings. We relate the framework to existing methods of composing vector-based representations of meaning, and show that our approach generalises many of these, including vector addition, component-wise multiplication, and the tensor product.Comment: Submitted to Computational Linguistics on 20th January 2010 for revie

Efficiency in ambiguity: two models of probabilistic semantics for natural language

This paper explores theoretical issues in constructing an adequate probabilistic semantics for natural language. Two approaches are contrasted. The first extends Montague Semantics with a probability distribution over models. It has nice theoretical properties, but does not account for the ubiquitous nature of ambiguity; moreover inference is NP hard. An alternative approach is described in which a sequence of pairs of sentences and truth values is generated randomly. By sacrificing some of the nice theoretical properties of the first approach it is possible to model ambiguity naturally; moreover inference now has polynomial time complexity. Both approaches provide a compositional semantics and account for the gradience of semantic judgements of belief and inference

The Mechanism of Additive Composition

Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this article, we prove an upper bound for the bias of additive composition, which is the first theoretical analysis on compositional frameworks from a machine learning point of view. The bound is written in terms of collocation strength; we prove that the more exclusively two successive words tend to occur together, the more accurate one can guarantee their additive composition as an approximation to the natural phrase vector. Our proof relies on properties of natural language data that are empirically verified, and can be theoretically derived from an assumption that the data is generated from a Hierarchical Pitman-Yor Process. The theory endorses additive composition as a reasonable operation for calculating meanings of phrases, and suggests ways to improve additive compositionality, including: transforming entries of distributional word vectors by a function that meets a specific condition, constructing a novel type of vector representations to make additive composition sensitive to word order, and utilizing singular value decomposition to train word vectors.Comment: More explanations on theory and additional experiments added. Accepted by Machine Learning Journa

Using Ontology-Based Approaches to Representing Speech Transcripts for Automated Speech Scoring

Text representation is a process of transforming text into some formats that computer systems can use for subsequent information-related tasks such as text classification. Representing text faces two main challenges: meaningfulness of representation and unknown terms. Research has shown evidence that these challenges can be resolved by using the rich semantics in ontologies. This study aims to address these challenges by using ontology-based representation and unknown term reasoning approaches in the context of content scoring of speech, which is a less explored area compared to some common ones such as categorizing text corpus (e.g. 20 newsgroups and Reuters). From the perspective of language assessment, the increasing amount of language learners taking second language tests makes automatic scoring an attractive alternative to human scoring for delivering rapid and objective scores of written and spoken test responses. This study focuses on the speaking section of second language tests and investigates ontology-based approaches to speech scoring. Most previous automated speech scoring systems for spontaneous responses of test takers assess speech by primarily using acoustic features such as fluency and pronunciation, while text features are less involved and exploited. As content is an integral part of speech, the study is motivated by the lack of rich text features in speech scoring and is designed to examine the effects of different text features on scoring performance. A central question to the study is how speech transcript content can be represented in an appropriate means for speech scoring. Previously used approaches from essay and speech scoring systems include bag-of-words and latent semantic analysis representations, which are adopted as baselines in this study; the experimental approaches are ontology-based, which can help improving meaningfulness of representation units and estimating importance of unknown terms. Two general domain ontologies, WordNet and Wikipedia, are used respectively for ontology-based representations. In addition to comparison between representation approaches, the author analyzes which parameter option leads to the best performance within a particular representation. The experimental results show that on average, ontology-based representations slightly enhances speech scoring performance on all measurements when combined with the bag-of-words representation; reasoning of unknown terms can increase performance on one measurement (cos.w4) but decrease others. Due to the small data size, the significance test (t-test) shows that the enhancement of ontology-based representations is inconclusive. The contributions of the study include: 1) it examines the effects of different representation approaches on speech scoring tasks; 2) it enhances the understanding of the mechanisms of representation approaches and their parameter options via in-depth analysis; 3) the representation methodology and framework can be applied to other tasks such as automatic essay scoring

A Defense of Pure Connectionism

Connectionism is an approach to neural-networks-based cognitive modeling that encompasses the recent deep learning movement in artificial intelligence. It came of age in the 1980s, with its roots in cybernetics and earlier attempts to model the brain as a system of simple parallel processors. Connectionist models center on statistical inference within neural networks with empirically learnable parameters, which can be represented as graphical models. More recent approaches focus on learning and inference within hierarchical generative models. Contra influential and ongoing critiques, I argue in this dissertation that the connectionist approach to cognitive science possesses in principle (and, as is becoming increasingly clear, in practice) the resources to model even the most rich and distinctly human cognitive capacities, such as abstract, conceptual thought and natural language comprehension and production. Consonant with much previous philosophical work on connectionism, I argue that a core principle—that proximal representations in a vector space have similar semantic values—is the key to a successful connectionist account of the systematicity and productivity of thought, language, and other core cognitive phenomena. My work here differs from preceding work in philosophy in several respects: (1) I compare a wide variety of connectionist responses to the systematicity challenge and isolate two main strands that are both historically important and reflected in ongoing work today: (a) vector symbolic architectures and (b) (compositional) vector space semantic models; (2) I consider very recent applications of these approaches, including their deployment on large-scale machine learning tasks such as machine translation; (3) I argue, again on the basis mostly of recent developments, for a continuity in representation and processing across natural language, image processing and other domains; (4) I explicitly link broad, abstract features of connectionist representation to recent proposals in cognitive science similar in spirit, such as hierarchical Bayesian and free energy minimization approaches, and offer a single rebuttal of criticisms of these related paradigms; (5) I critique recent alternative proposals that argue for a hybrid Classical (i.e. serial symbolic)/statistical model of mind; (6) I argue that defending the most plausible form of a connectionist cognitive architecture requires rethinking certain distinctions that have figured prominently in the history of the philosophy of mind and language, such as that between word- and phrase-level semantic content, and between inference and association