Postdoctoral Research Associate

About the Role

The project “An Erlangen Programme for AI” (funded by the UKRI), will broadly involve applying advanced mathematical techniques for understanding training in neural networks, with potential applications in audio and music processing.

Standard neural network training practices largely follow an open-loop paradigm, where the evolving state of the model typically does not influence the training dynamics. This project seeks to establish a mathematical framework for closing this loop by quantitatively measuring and analysing the evolution of neural networks during training. We will explore and compare two distinct mathematical approaches to network metrology: Spectral analysis approach – based on network layer decomposition and spectral measures on singular values to mathematically characterise the internal dynamics of neural networks. Topological approach – based on metrics derived from topological data analysis to capture qualitative structural changes in the neural network configuration.

Both methodologies represent substantial advancements in the theoretical understanding of neural network dynamics and highlight different mathematical aspects of network "trainedness". By rigorously comparing these approaches in terms of computational complexity, implementability, effectiveness, and interpretability, this project aims to establish solid mathematical criteria to inform novel design and architectural choices for neural networks.

This project will be in collaboration with Prof. Mark Sandler from the Centre for Digital Music – a world-leading research centre in the field of AI for Music and Audio.

About You

The successful applicant will have, or soon obtain, a PhD degree in mathematics or related, or equivalent level of professional qualifications and experience, with expertise in at least one of the areas: AI, deep neural networks, machine learning, applied topology, probability, statistics, signal processing.

About the School

The School has an exceptionally strong research presence across the spectrum of Mathematical Sciences. It is part of the Faculty of Science and Engineering, which comprises five schools and two institutes.

This position is based in the Centre for Data Science, Statistics and Probability. Other Centres include the Centre for Combinatorics, Algebra & Number Theory, the Centre for Geometry, Analysis and Gravitation, the Centre for Dynamical Systems, Statistical Physics and Complex Systems, and the Centre for Mathematical Education.

About Queen Mary

At Queen Mary University of London, we believe that a diversity of ideas helps us achieve the previously unthinkable.

Throughout our history, we’ve fostered social justice and improved lives through academic excellence. And we continue to live and breathe this spirit today, not because it’s simply ‘the right thing to do’ but for what it helps us achieve and the intellectual brilliance it delivers.

We continue to embrace diversity of thought and opinion in everything we do, in the belief that when views collide, disciplines interact, and perspectives intersect, truly original thought takes form.

Benefits

We offer competitive salaries, access to a generous pension scheme, 30 days’ leave per annum (pro-rata for part-time/fixed-term), a season ticket loan scheme and access to a comprehensive range of personal and professional development opportunities. In addition, we offer a range of work life balance and family friendly, inclusive employment policies, flexible working arrangements, and campus facilities.

Queen Mary’s commitment to our diverse and inclusive community is embedded in our appointments processes. Reasonable adjustments will be made at each stage of the recruitment process for any candidate with a disability. We are open to considering applications from candidates wishing to work flexibly.

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