PhD Opportunity : The Mathematics of Deep Bilevel Learning

Deep learning has been a driving force behind the rapid progress of AI for more than a decade, culminating recently in the success of large language models powered by transformer architectures—a class of deep neural networks. In parallel, bilevel optimization has emerged as a powerful framework for modeling complex machine learning tasks, giving rise to what we refer to as deep bilevel learning. This PhD project will investigate the mathematical foundations of deep bilevel learning, with the goal of uncovering structural properties that can be exploited to design more efficient, robust, and explainable learning algorithms. The results have the potential to influence the next generation of AI systems and advance theory at the intersection of optimization, machine learning, and deep learning.

Project Details

• Start Date: 1 October 2026
• Duration: 4 years
• Funding: Co-funded by DAS Ltd and the EPSRC Doctoral Landscape Award (Collaborative Studentships Scheme)
• Stipend: ~£20,780/year (i.e., £1,730/month, tax-free)
• Additional benefits:
  • Research travel funds for conferences, and possible visits to UCL & Italian Institute of Technology
  • Optional paid part-time teaching assistantship

Ideal Candidate

• Strong background in optimization, applied mathematics, and/or machine learning
• UK or international applicants welcome (fees covered at UK rate)
• Motivated to shape the mathematical foundations of future AI technologies

Supervisory Team

• Professor Alain Zemkoho (University of Southampton) – project lead, bilevel optimization expert
• Professor Massimiliano Pontil (University College London & Italian Institute of Technology) – machine/deep learning expert

Key Dates

• Application Deadline: 9 January 2026
  (Rolling interviews may be conducted until position filled)
• How to apply: Mathematical sciences | Postgraduate Research | University of Southampton
• Enquiries: to Professor Alain Zemkoho ( a.b.zemkoho@soton.ac.uk)

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