The Department of Mathematical Sciences at the University of Bath is inviting applications from excellent candidates for a PhD studentship in the EPSRC Programme Grant EP/V026259/1 on the “Mathematics of Deep Learning” (Maths4DL). Maths4DL is a joint programme run by the University of Bath, the University of Cambridge and University College London.
Start date: 2 October 2023.
This is an exceptional opportunity to conduct ambitious research at the forefront of mathematics, statistics, and machine learning. The Vision and Ambition of Maths4DL is to develop a comprehensive mathematical, statistical and computational framework that addresses i) the foundational challenges on interpretability of the trained Deep Neural Networks (DNN), ii) robustness and generalisation of DNN on test data, iii) statistical confidence in DNN-outputs and iv) computational challenges with large-scale models and high-dimensional training data.
Project Overview:
In recent years, machine learning has seen tremendous progress, with several breakthroughs directly connected to the theory of Stochastic Differential Equations (SDEs). This increasingly fruitful relationship between machine learning and SDEs has produced a variety of state-of-the-art techniques, ranging from diffusion models in computer vision to Langevin algorithms for Bayesian learning.
At the same time, SDEs are themselves classical models from mathematics and commonly used to describe random phenomena such as molecular dynamics, biological systems and financial markets. Consequently, there is significant interest in applying the computational tools from machine learning to enhance traditional SDE modelling.
This project will sit at the intersection of SDE theory and data science, with the aim of generating innovative research across the two domains. For example, the project may investigate whether recently developed SDE solvers [1] can improve popular learning algorithms, such as Stochastic Gradient Langevin Dynamics [2] – which is based on Euler’s method.
Project keywords: machine learning, stochastic algorithms, data science, mathematics.
Candidate Requirements:
Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree (or the equivalent) in mathematics or statistics, or a closely-related discipline. A master’s level qualification would also be advantageous.
The ideal candidate will have experience in one or more of the following areas: machine learning, stochastic processes, mathematical or computational analysis, optimisation and/or data science. Experience in programming is desirable (e.g. Python / MATLAB, PyTorch / TensorFlow).
Non-UK applicants must meet our English language entry requirement.
Enquiries and Applications:
Informal enquiries are encouraged and should be directed to Dr James Foster on email address [Email Address Removed].
Formal applications should be submitted via the University of Bath’s online application form for a PhD in Mathematics.
More information about applying for a PhD at Bath may be found on our website.
Note: Applications may close earlier than the advertised deadline if a suitable candidate is found. We recommend, therefore, that you contact Dr Foster prior to applying and submit your formal application as early as possible.
Funding Eligibility:
To be eligible for funding, you must qualify as a Home student. The eligibility criteria for Home fee status are detailed and too complex to be summarised here in full; however, as a general guide, the following applicants will normally qualify subject to meeting residency requirements: UK and Irish nationals (living in the UK or EEA/Switzerland), those with Indefinite Leave to Remain and EU nationals with pre-settled or settled status in the UK under the EU Settlement Scheme. This is not intended to be an exhaustive list. Additional information may be found on our fee status guidance webpage, on the GOV.UK website and on the UKCISA website.
Equality, Diversity and Inclusion:
We value a diverse research environment and aim to be an inclusive university, where difference is celebrated and respected. We welcome and encourage applications from under-represented groups.
If you have circumstances that you feel we should be aware of that have affected your educational attainment, then please feel free to tell us about it in your application form. The best way to do this is a short paragraph at the end of your personal statement.