A1 Regular and Cartesian Closed Categories A2 Toposes - Basic Theory A3 Allegories A4 Geometric Morphisms - Basic Theory B1 Fibrations and Indexed Categories B2 Internal and Locally Internal Categories B3 Toposes over a base B4 BTop/S as a 2-Category

REVIEWS-Sketches of an elephant: A topos theory compendium

Sentiment analysis is the task of automatically determining from text the attitude, emotion, or some other affectual state of the author. This chapter summarizes the diverse landscape of tasks and applications associated with sentiment analysis. We outline key challenges stemming from the complexity and subtlety of language use, the prevalence of creative and non-standard language, and the lack of paralinguistic information, such as tone and stress markers. We describe automatic systems and datasets commonly used in sentiment analysis. We summarize several manual and automatic approaches to creating valence- and emotion-association lexicons. We also discuss preliminary approaches for sentiment composition (how smaller units of text combine to express sentiment) and approaches for detecting sentiment in figurative and metaphoric language—these are the areas where we expect to see significant work in the near future.

/pdf/sentiment-analysis-detecting-valence-emotions-and-other-424wj1trso.pdf

Sentiment Analysis: Detecting Valence, Emotions, and Other Affectual States from Text

Solving linear systems of equations is a frequently encountered problem in machine learning and optimization. Given a matrix $A$ and a vector $\mathbf{b}$ the task is to find the vector $\mathbf{x}$ such that $A\mathbf{x}=\mathbf{b}$. We describe a quantum algorithm that achieves a sparsity-independent runtime scaling of $\mathcal{O}\mathbf{(}{\ensuremath{\kappa}}^{2}\sqrt{n}\text{polylog}(n)/\ensuremath{\epsilon}\mathbf{)}$ for an $n\ifmmode\times\else\texttimes\fi{}n$ dimensional $A$ with bounded spectral norm, where $\ensuremath{\kappa}$ denotes the condition number of $A$, and $\ensuremath{\epsilon}$ is the desired precision parameter. This amounts to a polynomial improvement over known quantum linear system algorithms when applied to dense matrices, and poses a new state of the art for solving dense linear systems on a quantum computer. Furthermore, an exponential improvement is achievable if the rank of $A$ is polylogarithmic in the matrix dimension. Our algorithm is built upon a singular value estimation subroutine, which makes use of a memory architecture that allows for efficient preparation of quantum states that correspond to the rows of $A$ and the vector of Euclidean norms of the rows of $A$.

Quantum Linear System Algorithm for Dense Matrices.

https://hull-repository.worktribe.com/preview/855359/IJAR-2018.pdf

A review of applications of fuzzy sets to safety and reliability engineering

We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilizers.

Quantum Weakest Preconditions

https://research-information.bris.ac.uk/files/76454741/1_s2.0_S0004370216300492_main.pdf

Hierarchical conceptual spaces for concept combination

Metaphors allow us to convey emotion by connecting physical experiences and abstract concepts. The results of previous research in linguistics and psychology suggest that metaphorical phrases tend to be more emotionally evocative than their literal counterparts. In this paper, we investigate the relationship between metaphor and emotion within a computational framework, by proposing the first joint model of these phenomena. We experiment with several multitask learning architectures for this purpose, involving both hard and soft parameter sharing. Our results demonstrate that metaphor identification and emotion prediction mutually benefit from joint learning and our models advance the state of the art in both of these tasks.

/pdf/modelling-the-interplay-of-metaphor-and-emotion-through-3yadyr45pm.pdf

Modelling the interplay of metaphor and emotion through multitask learning

The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has outperformed other models in mainstream empirical language processing tasks. However, until recently it has lacked the crucial feature of lexical entailment -- as do other distributional models of meaning. 
In this paper we solve the problem of entailment for categorical compositional distributional semantics. Taking advantage of the abstract categorical framework allows us to vary our choice of model. This enables the introduction of a notion of entailment, exploiting ideas from the categorical semantics of partial knowledge in quantum computation. 
The new model of language uses density matrices, on which we introduce a novel robust graded order capturing the entailment strength between concepts. This graded measure emerges from a general framework for approximate entailment, induced by any commutative monoid. Quantum logic embeds in our graded order. 
Our main theorem shows that entailment strength lifts compositionally to the sentence level, giving a lower bound on sentence entailment. We describe the essential properties of graded entailment such as continuity, and provide a procedure for calculating entailment strength.

Graded Entailment for Compositional Distributional Semantics

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.

Interacting Conceptual Spaces I: Grammatical Composition of Concepts

The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of a sentence, given its grammatical structure and the meanings of its words. This approach has outperformed other models in mainstream empirical language processing tasks, but lacks an effective model of lexical entailment. We address this shortcoming by exploiting the freedom in our abstract categorical framework to change our choice of semantic model. This allows us to describe hyponymy as a graded order on meanings, using models of partial information used in quantum computation. Quantum logic embeds in this graded order.

/pdf/graded-hyponymy-for-compositional-distributional-semantics-3ddqrjtkek.pdf

Martha Lewis

Papers

Hierarchical conceptual spaces for concept combination

Modelling the interplay of metaphor and emotion through multitask learning

Graded Entailment for Compositional Distributional Semantics

Interacting Conceptual Spaces I: Grammatical Composition of Concepts

Graded hyponymy for compositional distributional semantics