Modern artificial intelligence systems achieve remarkable performance, yet the mathematical mechanisms underlying their behavior remain only partially understood. This project seeks to develop a rigorous theory of modern learning algorithms and to explain how their architecture and dynamics determine their performance.
Depending on their background and interests, the candidate will use tools from analysis, probability theory, stochastic processes, statistical physics, dynamical systems, optimization, and optimal transport to prove mathematical results describing the behavior of modern learning algorithms in suitable abstract settings. Possible research directions include training dynamics and signal propagation in deep neural networks, including transformers; generative modeling; high-dimensional learning systems; sampling algorithms; collective phenomena in large-scale models; and quantum algorithms.
The work will be primarily theoretical. Computational experiments may be used to guide conjectures and illustrate theoretical results, depending on the candidate's interests.
You will join an active, supportive, inclusive, and collaborative research environment at the Department of Mathematics and Statistics. You will work on exciting fundamental questions at the interface of mathematics and modern AI and collaborate with national and international researchers. You will also contribute to teaching as a teaching assistant.
Employment conditions and remuneration are in accordance with the standards of the University of Bern, Switzerland.
Applicants should hold, or be close to completing, a Master's degree in pure or applied mathematics, theoretical physics, statistics, or a related field.
We seek motivated candidates with a strong background in mathematics (e.g., in one or more of the following areas: analysis, probability theory, stochastic processes, statistical physics, optimal transport, dynamical systems, optimization, or machine learning theory), an interest in the mathematical principles underlying modern AI (or in related problems), the ability to work both independently and collaboratively, and good written and spoken English. Knowledge of German is not required. Programming experience is beneficial but not required.
