Course Catalogue

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The course introduces aspects of the underlying mathematics fundamental to deep and machine learning.

34 x 1 hr lectures and 11 x 1 hr tutorials

The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Artificial Intelligence, Mathematics, or Statistics.

None

None

Assessment

90% Examination, 10% Coursework.

Reassessment

In accordance with the University's Code of Assessment reassessments are normally set for all courses which do not contribute to the honours classifications. For non honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students, and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions are listed below in this box.

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

■ To introduce students to fundamental mathematical results in machine learning and deep learning, such as the universal approximation theorem, inner product space methods and the kernel trick, basic spectral theory, and the perceptron convergence theorem.

■ To provide a comprehensive theoretical overview of optimisation of neural networks, including efficient backpropagation methods and the convergence of stochastic gradient descent algorithms.

■ To demonstrate the mathematical foundations of regularisation techniques, such as weight decay and dropout, and their impact on the generalisation performance of neural networks.

■ To introduce core concepts in probabilistic machine learning such as graphical models and variational inference.

■ To demonstrate fundamental mathematical connections between common deep learning architectures such as convolutional neural networks, graph neural networks, and transformers.

■ To provide an introduction to latent variable models, including variational autoencoders and diffusion models, and their applications in generative modelling.

By the end of this course students will be able to:

■ Prove key results in artificial intelligence and machine learning including historical results that contributed to the development of the field.

■ Identify the challenges associated with convex and non-convex optimization in deep learning and the discuss their implications for convergence and generalization.

■ State fundamental approaches to regularization in deep learning and understand the mathematical principles behind them.

■ Derive key results in probabilistic machine learning using Jensen's inequality and the Kullback-Leibler divergence.

■ Describe common deep learning architectures and the connections between them.

■ Compare and relate generative and discriminative models, discussing their relative advantages and disadvantages.

■ State core properties of latent variable models and understand their role in dimensionality reduction and generative modelling.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.