Subject areas:
Mathematics.
Funding type:
Tuition fee.
Stipend.
Bench Fees / Research Training & Support Grant.
Fully-funded PhD studentship available to start in the 2025/26 academic year.
Award details
The proliferation of generative models, combined with pretraining on web-scale data, raises a crucial question: what happens when these models are trained on their own generated outputs? Recent investigations have hinted that such models would create loops that would lead to a phenomenon called model collapse, under which the performance progressively degrades with each model-data feedback iteration until fitted models become useless. Goal of this project is to rigorously define at the mathematic level these systems and phenomena, and to study them by means of tools from probability theory (e.g. Markov chains), stochastic calculus (SDEs theory) and functional analysis. The theoretical study will be corroborated by extensive numerical experiments geared towards potential applications in e.g. image-generation and finance.
Award value
The studentship covers full Home or Overseas tuition fees, Stipend, and Bench fees for up to 3.5 years.
Eligibility criteria
This position is open to both Home and Overseas students.
Applicants should have a 2:1 or first-class undergraduate degree, or an MMath, MSci or Master’s degree with Merit and high grades in modules relating to the research area.
Application process
To be considered for the position, candidates must apply via King’s Apply online application system. Details are available on the Department of Mathematics website.
Please apply for Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability MPhil/PhD, indicate Dr Luca Galimberti as the supervisor and quote the project title in your application and all correspondence.
Please ensure to add the following code “StartUpGalimberti” in the Funding section of the application form. Please select option 5: ‘I am applying for a funding award or scholarship administered by King’s College London’ and type the code into the ‘Award Scheme Code or Name’ box. Please copy and paste the code exactly.
The selection process will involve a pre-selection on documents and, if selected, will be followed by an invitation to an interview. If successful at the interview, an offer will be provided in due course.
Contact Details
Dr Luca Galimberti, luca.galimberti@kcl.ac.uk
If you require support with the administrative side of the application process, please contact mathematics-pgr@kcl.ac.uk.