PhD student position in the research project “Mathematics for AI: geometric deep learning and equivariant transformers” at the Department of Mathematical Sciences at Chalmers University of Technology.
Despite the overwhelming success of deep neural networks we are still at a loss for explaining exactly why deep learning works so well. One way to address this is to explore the underlying mathematical framework. A promising direction is to consider symmetries as a fundamental design principle for network architectures. This can be implemented by constructing deep neural networks that are compatible with a symmetry group G that acts transitively on the input data. This is directly relevant for instance in the case of spherical signals where G is a rotation group. In practical applications, it was found that equivariance improves per-sample efficiency, reducing the need for data augmentation. Group equivariance has successfully been implemented in convolutional neural networks.
Recently, transformer networks have increased in popularity, in particular with impressive results both in natural language processing and computer vision. The goal of the present project is to explore equivariance in the context of transformers. This entails developing the underlying mathematical theory of equivariant transformers, as well as to consider applications in image processing, such as for example in cosmology, medical imaging or autonomous driving (e.g. fisheye camera images).