Elias Nyholm

Reach me at eliasny@chalmers.se!

My work lies at the intersection between geometric deep learning and mathematics. I am particularly interested in the role of symmetries and equivariance/invariance in machine learning models, both in the analysis of existing architectures and the design of novel ones. I have a background in theoretical physics where symmetries have a prominent role, and I would like to bring this perspective into machine learning. Symmetries in machine learning and physics are closely linked to group theory and representation theory in mathematics, and the study of invariant and equivariant spaces and functions has a long tradition in pure mathematics.

You can find a complete list of my publications at Google Scholar. You can also click here for my CV (pdf).

My research is supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP). Are you a WASP PhD student interested in what geometric deep learning can do for you and what you can do for geometric deep learning? I am organising the Geometric Deep Learning WASP Cluster where we discuss articles and exchange ideas related to geometric deep learning. If you’re interested, contact me!

news

Jan 15, 2026	From January to July 2026 I will be visiting Boston to work with Maurice Weiler at MIT and Robin Walters at Northeastern If you are working on (mathematics of) geometric deep learning in Boston/NY area, reach out!
Nov 18, 2025	I gave a talk at the Applied CATS seminar at KTH Royal Institute of Technology in Stockholm
Nov 13, 2025	I gave a lightning talk at the Workshop on Geometry, Topology and Machine Learning Workshop at the Max Planck Institute for Mathematics in the Sciences in Leipzig
Feb 11, 2025	I was one of the organisers of the Learning on Graphs and Geometry Sweden Workshop in Uppsala, which was also the offical swedish meetup of the virtual LoG Conference

selected publications

Equivariant non-linear maps for neural networks on homogeneous spaces

Elias Nyholm, Oscar Carlsson, Maurice Weiler, and Daniel Persson

2025

Bib

@misc{nyholm2025equivariantnonlinearmapsneural,
  title = {Equivariant non-linear maps for neural networks on homogeneous spaces},
  author = {Nyholm, Elias and Carlsson, Oscar and Weiler, Maurice and Persson, Daniel},
  year = {2025},
  eprint = {2504.20974},
  archiveprefix = {arXiv},
  primaryclass = {cs.LG},
  url = {https://arxiv.org/abs/2504.20974}
}