[Stipend: ~£20,780/year (tax-free), tuition fees covered at UK rate, co-funded by DAS Ltd and the EPSRC Doctoral Landscape Award, research travel funds, optional paid part-time teaching assistantship.] This fully funded PhD opportunity at the University of Southampton focuses on the mathematics of deep bilevel learning, a cutting-edge area at the intersection of optimization, machine learning, and deep learning. Deep learning has revolutionized artificial intelligence, especially with the advent of large language models and transformer architectures. In parallel, bilevel optimization has become a powerful framework for modeling complex machine learning tasks, leading to the emerging field of deep bilevel learning. The project aims to investigate the mathematical foundations of deep bilevel learning, seeking to uncover structural properties that can be leveraged to design more efficient, robust, and explainable learning algorithms. The research outcomes have the potential to influence the next generation of AI systems and advance theoretical understanding in optimization and machine learning. The successful candidate will join a collaborative research environment, co-funded by DAS Ltd and the EPSRC Doctoral Landscape Award (Collaborative Studentships Scheme). The position offers a tax-free stipend of approximately £20,780 per year, with tuition fees covered at the UK rate. Additional benefits include research travel funds for conferences, possible visits to University College London and the Italian Institute of Technology, and the option for a paid part-time teaching assistantship. The supervisory team consists of Professor Alain Zemkoho (University of Southampton), an expert in bilevel optimization, and Professor Massimiliano Pontil (University College London & Italian Institute of Technology), a leading researcher in machine and deep learning. The project is ideal for candidates with a strong background in optimization, applied mathematics, and/or machine learning, who are motivated to shape the mathematical foundations of future AI technologies. Both UK and international applicants are encouraged to apply, though fees are covered at the UK rate. The PhD will commence on 1 October 2026 and has a duration of four years. The application deadline is 9 January 2026, but rolling interviews may be conducted until the position is filled. For further details and to apply, visit the University of Southampton's postgraduate research application portal for Mathematical Sciences. Enquiries can be directed to Professor Alain Zemkoho at [email protected].

This fully funded PhD position at the University of Southampton offers an exciting opportunity to advance the mathematical foundations of deep bilevel learning—a cutting-edge area at the intersection of optimization and artificial intelligence. The project is co-supervised by Professor Alain Zemkoho (bilevel optimization expert, University of Southampton) and Professor Massimiliano Pontil (machine/deep learning expert, University College London & Italian Institute of Technology), providing a rich collaborative environment and potential for research visits to UCL and IIT. Deep learning has revolutionized AI, especially with the advent of large language models and transformer architectures. Bilevel optimization, meanwhile, has become a powerful framework for modeling complex machine learning tasks, leading to the emergence of deep bilevel learning. This research will focus on uncovering the mathematical structures underlying deep bilevel learning, aiming to design more efficient, robust, and explainable algorithms. The outcomes have the potential to shape future AI systems and contribute to theoretical advances in optimization and machine learning. The position is funded by DAS Ltd and the EPSRC Doctoral Landscape Award (Collaborative Studentships Scheme), offering a tax-free stipend of approximately £20,780 per year for four years, with additional benefits such as research travel funds and optional paid part-time teaching assistantship. Tuition fees are covered at the UK rate, and both UK and international applicants are encouraged to apply. Ideal candidates will have a strong background in optimization, applied mathematics, and/or machine learning, and be motivated to contribute to foundational research in AI. Application requirements include a personal statement (highlighting relevant experience in optimization, operational research, game theory, programming, and mathematical background), a CV, contact details for two academic referees, and all degree transcripts. The application deadline is January 9, 2026, with a start date of October 1, 2026. To apply, visit the University of Southampton's online portal, select the appropriate programme and supervisor, and upload the required documents. For further details, see the official FindAPhD listing and university application page.

This fully funded PhD position at the University of Southampton offers an exciting opportunity to advance the mathematical foundations of deep bilevel learning—a cutting-edge area at the intersection of optimization and artificial intelligence. The project is co-supervised by Professor Alain Zemkoho (bilevel optimization expert, University of Southampton) and Professor Massimiliano Pontil (machine/deep learning expert, University College London & Italian Institute of Technology), providing a rich collaborative environment and potential for research visits to UCL and IIT. Deep learning has revolutionized AI, especially with the advent of large language models and transformer architectures. Bilevel optimization, meanwhile, has become a powerful framework for modeling complex machine learning tasks, leading to the emergence of deep bilevel learning. This project aims to investigate the mathematical underpinnings of deep bilevel learning, uncovering structural properties that can be leveraged to design more efficient, robust, and explainable learning algorithms. The research outcomes have the potential to shape the next generation of AI systems and contribute to theoretical advances in optimization and deep learning. The position is funded by DAS Ltd and the EPSRC Doctoral Landscape Award (Collaborative Studentships Scheme), offering a generous tax-free stipend of approximately £20,780 per year, plus research travel funds for conferences and optional paid part-time teaching assistantship. Both UK and international applicants are welcome, with tuition fees covered at the UK rate. Ideal candidates will have a strong background in optimization, applied mathematics, and/or machine learning, and be motivated to contribute to the mathematical foundations of future AI technologies. Applicants should prepare a personal statement detailing relevant experience (optimization, operational research, game theory, programming, mathematical background, and any industry collaboration), a CV, names and institutional email addresses of two academic referees, and all degree transcripts to date. Applications must be submitted online via the University of Southampton postgraduate research portal. Select 'Research' programme type, 2026/27 entry, Faculty of Social Sciences, and 'PhD Mathematical Sciences (Full time)'. In Section 2 of the application form, insert the name of the supervisor. The deadline for applications is Friday, January 9, 2026. This is a unique opportunity to work at the forefront of mathematical AI research, with strong academic mentorship and excellent funding support. For further details and to apply, visit the official project page or the university application portal.