PhD position in mathematics or mathematical statistics, with focus on geometric deep learning

Project description

and tasks

Machine learning (‘artificial intelligence’) is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many machine learning tasks. Mathematicians have taken huge steps towards theoretically understanding their empirical success, but many open questions remain.

A subfield within neural network theory is geometric deep learning. It concerns symmetries in the data or the learning task and constructing neural networks that react properly to them (equivariant networks). Examples of such symmetries are symmetries towards rotations of point clouds, translations of images or permutations of nodes in graphs. Combining the geometric / algebraic theory of (group) symmetries with the more analytical / statistical theory of machine learning allows for mathematically multifaceted research.

The project aims at deepening the mathematical theory of geometric deep learning. Exciting research questions include the development of new ways of constructing equivariant networks, describing the resulting models mathematically, and directly analyzing how symmetries affect the training of neural networks.

The project is affiliated with the AI / Math track within Wallenberg AI, Autonomous Systems and Software Program (WASP), and the PhD student will take part in the WASP graduate school.

Qualifications

The doctoral student will be admitted to study one of the two third-cycle programmes : Mathematics or Mathematical Statistics. To fulfil the general entry requirements, the applicant must have qualifications equivalent to a completed degree at second-cycle level or completed course requirements of at least 240 ECTS credits, including at least 60 ECTS credits at second-cycle level.

To fulfil the specific entry requirements to be admitted for studies in either mathematics or mathematical statistics, the applicant is required to have completed at least 60 ECTS credits within mathematics or mathematical statistics, of which at least 15 ECTS credits shall have been acquired at second-cycle level. Applicants who have acquired largely equivalent skills in some other system, either within Sweden or abroad, are also eligible.

Good programming skills (preferably Matlab or Python) and good written and spoken English knowledge are required. Documented knowledge and experience in machine learning, image analysis, probability theory, differential geometry, algebra, optimization, representation theory and functional analysis are merits. Note that you are not expected to have specialist knowledge in all of the above-listed fields. You will acquire knowledge as a part of your doctoral studies and be able to collaborate with others to complement your specific skill set.

You are expected to take an active role in this project and institutional work. You have a scientific mindset and are determined to continuously develop your skills and contribute to mathematical machine learning research.

The assessment of applicants is based on their qualifications and ability to benefit from the doctoral study they will receive.

About the employment

The employment is a full-time paid position, for a fixed term of four years full-time or up to five years when teaching part-time. The position is intended to result in a doctoral degree. The position is intended to result in a doctoral degree. The main task of doctoral students is to pursue their third-cycle studies, including active participation in research and third-cycle courses and activities and courses at the WASP graduate school. The duties may include teaching or other departmental work, although duties of this kind may not comprise more than 20 per cent of a full-time post. Salary is set according to the salary ladder for PhD positions at Umeå University. Employment commences in the winter of 2024 / 2025 or by agreement.