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This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Quantitative investment (``quant'') is an interdisciplinary field combining financial engineering, computer science, mathematics, statistics, etc. Quant has become one of the mainstream investment methodologies over the past decades, and has experienced three generations: Quant 1.0, trading by mathematical modeling to discover mis-priced assets in markets; Quant 2.0, shifting quant research pipeline from small ``strategy workshops'' to large ``alpha factories''; Quant 3.0, applying deep learning techniques to discover complex nonlinear pricing rules. Despite its advantage in prediction, deep learning relies on extremely large data volume and labor-intensive tuning of ``black-box'' neural network models. To address these limitations, in this paper, we introduce Quant 4.0 and provide an engineering perspective for next-generation quant. Quant 4.0 has three key differentiating components. First, automated AI changes quant pipeline from traditional hand-craft modeling to the state-of-the-art automated modeling, practicing the philosophy of ``algorithm produces algorithm, model builds model, and eventually AI creates AI''. Second, explainable AI develops new techniques to better understand and interpret investment decisions made by machine learning black-boxes, and explains complicated and hidden risk exposures. Third, knowledge-driven AI is a supplement to data-driven AI such as deep learning and it incorporates prior knowledge into modeling to improve investment decision, in particular for quantitative value investing. Moreover, we discuss how to build a system that practices the Quant 4.0 concept. Finally, we propose ten challenging research problems for quant technology, and discuss potential solutions, research directions, and future trends.

Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with fewer degrees of freedom, on the dataset. We introduce the frameworks of semiclassical and microlocal analysis to data analysis and develop a novel, yet natural uncertainty principle for extracting fine-scale features of this geometric structure in data, crucially dependent on data-driven approximations to quantum mechanical processes underlying geometric optics. This leads to the first tractable algorithm for approximation of wave dynamics and geodesics on data manifolds with rigorous probabilistic convergence rates under the manifold hypothesis. We demonstrate our algorithm on real-world datasets, including an analysis of population mobility information during the COVID-19 pandemic to achieve four-fold improvement in dimensionality reduction over existing state-of-the-art and reveal anomalous behavior exhibited by less than 1.2% of the entire dataset. Our work initiates the study of data-driven quantum dynamics for analyzing datasets, and we outline several future directions for research.

Metaverse over wireless networks is an emerging use case of the sixth generation (6G) wireless systems, posing unprecedented challenges in terms of its multi-modal data transmissions with stringent latency and reliability requirements. Towards enabling this wireless metaverse, in this article we propose a novel semantic communication (SC) framework by decomposing the metaverse into human/machine agent-specific semantic multiverses (SMs). An SM stored at each agent comprises a semantic encoder and a generator, leveraging recent advances in generative artificial intelligence (AI). To improve communication efficiency, the encoder learns the semantic representations (SRs) of multi-modal data, while the generator learns how to manipulate them for locally rendering scenes and interactions in the metaverse. Since these learned SMs are biased towards local environments, their success hinges on synchronizing heterogeneous SMs in the background while communicating SRs in the foreground, turning the wireless metaverse problem into the problem of semantic multiverse communication (SMC). Based on this SMC architecture, we propose several promising algorithmic and analytic tools for modeling and designing SMC, ranging from distributed learning and multi-agent reinforcement learning (MARL) to signaling games and symbolic AI.

Navigation represents one of the most heavily studied topics in robotics [3]. It is often approached in terms of mapping and planning: constructing a geometric representation of the world from observations, then planning through this model using motion planning algorithms [4-6]. However, such geometric approaches abstract away significant physical and semantic aspects of the navigation problem that in practice leave a range of real-world situations difficult to handle (see Figure 1). These challenges require special handling, resulting in complex systems with many components. Some works have sought to incorporate machine learning techniques to either learn navigational skills from simulation or to learn perception systems for navigation for human-provided labels. In this article, we instead argue that learned navigational models, trained directly on real-world experience rather than human-provided labels or simulators, provide the most promising long-term direction for a general solution to navigation. We refer to such learning approaches as experiential learning, because they learn directly from past experience of performing real-world navigation. As we will discuss in Section 2, such methods relate closely to reinforcement learning.

This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a unified model of syntactic structures in formal grammars. Second, functors compute semantics by turning diagrams into logical, tensor, neural or quantum computation. Third, the resulting functorial models can be composed to form games where equilibria are the solutions of language processing tasks. This framework is implemented as part of DisCoPy, the Python library for computing with string diagrams. We describe the correspondence between categorical, linguistic and computational structures, and demonstrate their applications in compositional natural language processing.

You could start a business that provides AI-powered services, or you could develop AI software that can be used by businesses. If you're interested in making some serious dough from AI, there are a few things you need to do to get started. First and foremost, you need to find an AI business that is willing to invest in your project. Finally, you should also make sure that your AI business can provide good customer service so that your customers feel satisfied with their purchases. Artificial intelligence (AI) is a field of computer science and technology that deals with the development, deployment, and use of intelligent agents.

Welcome to this course on Customising your models with TensorFlow 2! In this course you will deepen your knowledge and skills with TensorFlow, in order to develop fully customised deep learning models and workflows for any application. You will use lower level APIs in TensorFlow to develop complex model architectures, fully customised layers, and a flexible data workflow. You will also expand your knowledge of the TensorFlow APIs to include sequence models. You will put concepts that you learn about into practice straight away in practical, hands-on coding tutorials, which you will be guided through by a graduate teaching assistant. In addition there is a series of automatically graded programming assignments for you to consolidate your skills.