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We present lambeq, the first high-level Python library for Quantum Natural Language Processing (QNLP). The open-source toolkit offers a detailed hierarchy of modules and classes implementing all stages of a pipeline for converting sentences to string diagrams, tensor networks, and quantum circuits ready to be used on a quantum computer. lambeq supports syntactic parsing, rewriting and simplification of string diagrams, ansatz creation and manipulation, as well as a number of compositional models for preparing quantum-friendly representations of sentences, employing various degrees of syntax sensitivity. We present the generic architecture and describe the most important modules in detail, demonstrating the usage with illustrative examples. Further, we test the toolkit in practice by using it to perform a number of experiments on simple NLP tasks, implementing both classical and quantum pipelines.

Quantum Natural Language Processing (QNLP) deals with the design and implementation of NLP models intended to be run on quantum hardware. In this paper, we present results on the first NLP experiments conducted on Noisy Intermediate-Scale Quantum (NISQ) computers for datasets of size greater than 100 sentences. Exploiting the formal similarity of the compositional model of meaning by Coecke, Sadrzadeh and Clark (2010) with quantum theory, we create representations for sentences that have a natural mapping to quantum circuits. We use these representations to implement and successfully train NLP models that solve simple sentence classification tasks on quantum hardware. We conduct quantum simulations that compare the syntax-sensitive model of Coecke et al. with two baselines that use less or no syntax; specifically, we implement the quantum analogues of a "bag-of-words" model, where syntax is not taken into account at all, and of a word-sequence model, where only word order is respected. We demonstrate that all models converge smoothly both in simulations and when run on quantum hardware, and that the results are the expected ones based on the nature of the tasks and the datasets used. Another important goal of this paper is to describe in a way accessible to AI and NLP researchers the main principles, process and challenges of experiments on quantum hardware. Our aim in doing this is to take the first small steps in this unexplored research territory and pave the way for practical Quantum Natural Language Processing., Comment: 38 pages

Word embedding techniques heavily rely on the abundance of training data for individual words. Given the Zipfian distribution of words in natural language texts, a large number of words do not usually appear frequently or at all in the training data. In this paper we put forward a technique that exploits the knowledge encoded in lexical resources, such as WordNet, to induce embeddings for unseen words. Our approach adapts graph embedding and cross-lingual vector space transformation techniques in order to merge lexical knowledge encoded in ontologies with that derived from corpus statistics. We show that the approach can provide consistent performance improvements across multiple evaluation benchmarks: in-vitro, on multiple rare word similarity datasets, and in-vivo, in two downstream text classification tasks., Comment: Accepted for presentation at AAAI 2019

The ability to compose parts to form a more complex whole, and to analyze a whole as a combination of elements, is desirable across disciplines. This workshop bring together researchers applying compositional approaches to physics, NLP, cognitive science, and game theory. Within NLP, a long-standing aim is to represent how words can combine to form phrases and sentences. Within the framework of distributional semantics, words are represented as vectors in vector spaces. The categorical model of Coecke et al. [2010], inspired by quantum protocols, has provided a convincing account of compositionality in vector space models of NLP. There is furthermore a history of vector space models in cognitive science. Theories of categorization such as those developed by Nosofsky [1986] and Smith et al. [1988] utilise notions of distance between feature vectors. More recently G\"ardenfors [2004, 2014] has developed a model of concepts in which conceptual spaces provide geometric structures, and information is represented by points, vectors and regions in vector spaces. The same compositional approach has been applied to this formalism, giving conceptual spaces theory a richer model of compositionality than previously [Bolt et al., 2018]. Compositional approaches have also been applied in the study of strategic games and Nash equilibria. In contrast to classical game theory, where games are studied monolithically as one global object, compositional game theory works bottom-up by building large and complex games from smaller components. Such an approach is inherently difficult since the interaction between games has to be considered. Research into categorical compositional methods for this field have recently begun [Ghani et al., 2018]. Moreover, the interaction between the three disciplines of cognitive science, linguistics and game theory is a fertile ground for research. Game theory in cognitive science is a well-established area [Camerer, 2011]. Similarly game theoretic approaches have been applied in linguistics [J\"ager, 2008]. Lastly, the study of linguistics and cognitive science is intimately intertwined [Smolensky and Legendre, 2006, Jackendoff, 2007]. Physics supplies compositional approaches via vector spaces and categorical quantum theory, allowing the interplay between the three disciplines to be examined.

This paper addresses the problem of mapping natural language text to knowledge base entities. The mapping process is approached as a composition of a phrase or a sentence into a point in a multi-dimensional entity space obtained from a knowledge graph. The compositional model is an LSTM equipped with a dynamic disambiguation mechanism on the input word embeddings (a Multi-Sense LSTM), addressing polysemy issues. Further, the knowledge base space is prepared by collecting random walks from a graph enhanced with textual features, which act as a set of semantic bridges between text and knowledge base entities. The ideas of this work are demonstrated on large-scale text-to-entity mapping and entity classification tasks, with state of the art results., Comment: Accepted for presentation at EMNLP 2018 (main conference)

We propose a methodology that adapts graph embedding techniques (DeepWalk (Perozzi et al., 2014) and node2vec (Grover and Leskovec, 2016)) as well as cross-lingual vector space mapping approaches (Least Squares and Canonical Correlation Analysis) in order to merge the corpus and ontological sources of lexical knowledge. We also perform comparative analysis of the used algorithms in order to identify the best combination for the proposed system. We then apply this to the task of enhancing the coverage of an existing word embedding's vocabulary with rare and unseen words. We show that our technique can provide considerable extra coverage (over 99%), leading to consistent performance gain (around 10% absolute gain is achieved with w2v-gn-500K cf.\S 3.3) on the Rare Word Similarity dataset.

According to the distributional inclusion hypothesis, entailment between words can be measured via the feature inclusions of their distributional vectors. In recent work, we showed how this hypothesis can be extended from words to phrases and sentences in the setting of compositional distributional semantics. This paper focuses on inclusion properties of tensors; its main contribution is a theoretical and experimental analysis of how feature inclusion works in different concrete models of verb tensors. We present results for relational, Frobenius, projective, and holistic methods and compare them to the simple vector addition, multiplication, min, and max models. The degrees of entailment thus obtained are evaluated via a variety of existing word-based measures, such as Weed's and Clarke's, KL-divergence, APinc, balAPinc, and two of our previously proposed metrics at the phrase/sentence level. We perform experiments on three entailment datasets, investigating which version of tensor-based composition achieves the highest performance when combined with the sentence-level measures., Comment: To appear in COLING 2016

An open problem with categorical compositional distributional semantics is the representation of words that are considered semantically vacuous from a distributional perspective, such as determiners, prepositions, relative pronouns or coordinators. This paper deals with the topic of coordination between identical syntactic types, which accounts for the majority of coordination cases in language. By exploiting the compact closed structure of the underlying category and Frobenius operators canonically induced over the fixed basis of finite-dimensional vector spaces, we provide a morphism as representation of a coordinator tensor, and we show how it lifts from atomic types to compound types. Linguistic intuitions are provided, and the importance of the Frobenius operators as an addition to the compact closed setting with regard to language is discussed., Comment: In Proceedings SLPCS 2016, arXiv:1608.01018

Distributional semantic models provide vector representations for words by gathering co-occurrence frequencies from corpora of text. Compositional distributional models extend these from words to phrases and sentences. In categorical compositional distributional semantics, phrase and sentence representations are functions of their grammatical structure and representations of the words therein. In this setting, grammatical structures are formalised by morphisms of a compact closed category and meanings of words are formalised by objects of the same category. These can be instantiated in the form of vectors or density matrices. This paper concerns the applications of this model to phrase and sentence level entailment. We argue that entropy-based distances of vectors and density matrices provide a good candidate to measure word-level entailment, show the advantage of density matrices over vectors for word level entailments, and prove that these distances extend compositionally from words to phrases and sentences. We exemplify our theoretical constructions on real data and a toy entailment dataset and provide preliminary experimental evidence., Comment: 8 pages, 1 figure, 2 tables, short version presented in the International Symposium on Artificial Intelligence and Mathematics (ISAIM), 2016

Deep compositional models of meaning acting on distributional representations of words in order to produce vectors of larger text constituents are evolving to a popular area of NLP research. We detail a compositional distributional framework based on a rich form of word embeddings that aims at facilitating the interactions between words in the context of a sentence. Embeddings and composition layers are jointly learned against a generic objective that enhances the vectors with syntactic information from the surrounding context. Furthermore, each word is associated with a number of senses, the most plausible of which is selected dynamically during the composition process. We evaluate the produced vectors qualitatively and quantitatively with positive results. At the sentence level, the effectiveness of the framework is demonstrated on the MSRPar task, for which we report results within the state-of-the-art range., Comment: Accepted for presentation at EMNLP 2015

The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The theoretical framework allows for reasoning about compositional aspects of language and offers structural ways of studying the underlying relationships. While the model so far has been applied on the level of syntactic structures, a sentence can bring extra information conveyed in utterances via intonational means. In the current paper we extend the framework in order to accommodate this additional information, using Frobenius algebraic structures canonically induced over the basis of finite-dimensional vector spaces. We detail the theory, provide truth-theoretic and distributional semantics for meanings of intonationally-marked utterances, and present justifications and extensive examples., Comment: Accepted for presentation in the 14th Meeting on Mathematics of Language (2015)

This thesis contributes to ongoing research related to the categorical compositional model for natural language of Coecke, Sadrzadeh and Clark in three ways: Firstly, I propose a concrete instantiation of the abstract framework based on Frobenius algebras (joint work with Sadrzadeh). The theory improves shortcomings of previous proposals, extends the coverage of the language, and is supported by experimental work that improves existing results. The proposed framework describes a new class of compositional models that find intuitive interpretations for a number of linguistic phenomena. Secondly, I propose and evaluate in practice a new compositional methodology which explicitly deals with the different levels of lexical ambiguity (joint work with Pulman). A concrete algorithm is presented, based on the separation of vector disambiguation from composition in an explicit prior step. Extensive experimental work shows that the proposed methodology indeed results in more accurate composite representations for the framework of Coecke et al. in particular and every other class of compositional models in general. As a last contribution, I formalize the explicit treatment of lexical ambiguity in the context of the categorical framework by resorting to categorical quantum mechanics (joint work with Coecke). In the proposed extension, the concept of a distributional vector is replaced with that of a density matrix, which compactly represents a probability distribution over the potential different meanings of the specific word. Composition takes the form of quantum measurements, leading to interesting analogies between quantum physics and linguistics., Comment: Ph.D. Dissertation, University of Oxford

In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the categorical framework of Coecke, Sadrzadeh and Clark (2010) for natural language, from an entanglement perspective. Specifically, our goal is to better understand in what way the level of entanglement of the relational tensors (or the lack of it) affects the compositional structures in practical situations. Our findings reveal that a number of proposals for verb construction lead to almost separable tensors, a fact that considerably simplifies the interactions between the words. We examine the ramifications of this fact, and we show that the use of Frobenius algebras mitigates the potential problems to a great extent. Finally, we briefly examine a machine learning method that creates verb tensors exhibiting a sufficient level of entanglement., Comment: In Proceedings QPL 2014, arXiv:1412.8102

Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural language, and are implicit in a distributional model of word meaning based on vector spaces. Specifically, in previous work Coecke-Clark-Sadrzadeh used the product category of pregroups with vector spaces and provided a distributional model of meaning for sentences. We recast this theory in terms of strongly monoidal functors and advance it via Frobenius algebras over vector spaces. The former are used to formalize topological quantum field theories by Atiyah and Baez-Dolan, and the latter are used to model classical data in quantum protocols by Coecke-Pavlovic-Vicary. The Frobenius algebras enable us to work in a single space in which meanings of words, phrases, and sentences of any structure live. Hence we can compare meanings of different language constructs and enhance the applicability of the theory. We report on experimental results on a number of language tasks and verify the theoretical predictions.

This survey presents in some detail the main advances that have been recently taking place in Computational Linguistics towards the unification of the two prominent semantic paradigms: the compositional formal semantics view and the distributional models of meaning based on vector spaces. After an introduction to these two approaches, I review the most important models that aim to provide compositionality in distributional semantics. Then I proceed and present in more detail a particular framework by Coecke, Sadrzadeh and Clark (2010) based on the abstract mathematical setting of category theory, as a more complete example capable to demonstrate the diversity of techniques and scientific disciplines that this kind of research can draw from. This paper concludes with a discussion about important open issues that need to be addressed by the researchers in the future.