Our group frequently supervises master's theses on topics related to our research. This page lists past and ongoing master's projects as well as thesis opportunities if available.
The goal of this project is to explore different ways of constructing invariant and equivariant machine learning models, which are models that adhere to particular symmetry-related constraints. This family of models is especially well-suited for processing geometric data such as images and molecules, and has been used with success for tasks like molecular simulations, robotics and computer vision.
There exist several different ways of constructing invariant/equivariant models in practice, where the two most popular methods either rely on regular representations or irreducible representations. In this project, you will learn about these different representations and run experiments to test which representation performs better on what type of task. We will also investigate the difference between choices of representation when scaling up the model.
Prerequisites: Linear algebra, groups and representations. Python and PyTorch on the programming side.
Contact Elias Nyholm for more information.
The goal of this project is to use mathematical tools to design new machine learning models. More specifically, we are interested in constructing new invariant and equivariant machine learning models that are particularly well-suited for specific types of data such as 2D data (images) and 3D data (molecules).
To design new models with these properties, we will use tools from computational invariant theory, the field of mathematics concerned with generating invariant and equivariant polynomials using computational tools. In practice, software like SageMath includes algorithms from computational invariant theory which we can make use of. The project will include learning about mathematical basics such as Hilbert’s finiteness theorem and Gröbner bases, alongside hands-on use of SageMath to build new equivariant machine learning models.
Prerequisites: Linear algebra, groups and representations, abstract algebra. Python and PyTorch on the programming side.
Contact Elias Nyholm for more information.
