PhD student position at the Department of Mathematics and Mathematical Statistics at Umeå University.
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.