PhD in Mathematics – Dissecting Neural Networks

Start date: 01 October 2025

Deep learning has shown promising applicability to real-world problems. However, our understanding of deep learning is currently still limited. There are many open questions on the generalization performance of neural networks, the role played by individual layers and substructures, the success of optimizers like sharpness-aware minimization, and other aspects of training. Neural network optimization landscapes may offer insights, but their high-dimensionality and non-convexity makes them difficult to study. This project, that lies in the area of mathematics of deep learning, aims to address some of these open questions, while redesigning how these models are trained to enhance efficiency, explainability, and robustness. Application areas can range from computer vision to natural language processing. The group has various ongoing ecology and climate change AI research collaborations, so applications can focus on this area, depending on the applicant’s interest.  

As a PhD student in this group, you will be supported in working towards building international collaborations with researchers across different disciplines. Further, you will be supported in gaining science communication skills that will allow you to effectively communicate your research to diverse audiences.  

Applicant’s profile: A degree or higher qualification in a relevant field with a strong element of mathematics (such as Physics, Computing Science, Machine Learning, Mathematics/Statistics, or related fields) and some prior programming experience is desirable. An interest in machine learning is expected, but as relevant machine learning background will be attained during the project, prior knowledge in this area is not a requirement.  

Reach out to the supervisor (with motivation for applying and CV attached) to discuss PhD options at the University of Glasgow.  

Supervisor contact: Tiffany.Vlaar@glasgow.ac.uk  

Websites: https://www.gla.ac.uk/schools/mathematicsstatistics/staff/tiffanyvlaar/ and https://tiffanyvlaar.github.io  

Applicants from all backgrounds, identities, and experiences are actively encouraged to apply. 

How to Apply: Please refer to the following website for details on how to apply: 

http://www.gla.ac.uk/research/opportunities/howtoapplyforaresearchdegree/  

Early application is encouraged. Shortlisting starts early January, and continues until all funded places are awarded.