PhD student position in mathematical statistics at the Department of Mathematics and Mathematical Statistics, Umeå University.
Project description and tasks
Machine learning, especially deep neural networks, has, during the early 21st century, had an immense impact on both research and society at large. This rapid development has made great progress possible and caused significant challenges. A subfield within machine learning is so-called geometric deep learning. This concept can mean many things, but at its core, the field is dealing with situations in which the in-data is of non-standard type. One can, for instance, consider 3D models, point clouds, or spherical images. To deal with such data poses special requirements on the network architectures.
One of the more interesting questions is the one of so-called equivariance. An essential property of the popular convolutional neural networks is translation equivariance; a translation of the in-data causes a translation of the out-data. With in-data of different types comes the need for equivariance with respect to other groups of transformations, both of discrete and continuous type. Examples of exciting research questions are how such networks can be constructed, how they can be trained, and their mathematical properties.
This project aims to develop new methods and new theories within geometric deep learning. This can, for instance, consist of the design of new network architectures, analysis of universality properties, explorations of a new class of transformations, and applications to simulated and real data. The PhD candidate is also expected to cooperate with our other ongoing AI-related projects.