Topological and Geometric Deep Learning: Theory, Methods, and Applications
This page is dedicated to the course Topological and Geometric Deep Learning: Theory, Methods and Applications, taught in May, 2026 at the Universidad Complutense of Madrid.
The course was intended as an introduction to the use of topological and geometric tools in deep learning, starting from the very basics and building up until arriving to current research. This includes deep learning architectures that are able to learn from topological and combinatorial domains, such as graphs or simplicial complexes, but also the development of methodologies that allow us to better understand how AI systems learn.
This is a non-exhaustive course, focused on persistent homology as the main tool. There are many other tools that could be used with the same purpose (Euler transforms, curvature, magnitude) that are not mentioned in the course.
I have tried to add the most relevant references for each topic to the slides, but of course, I might have missed something! Feel free to reach out if I have neglected something important in this regard.