Introduction to Geometric Deep Learning


Content

The lecture focuses on concepts of differential geometry that are relevant for the mathematics of data science and machine learning in the context of geometric deep learning. Topics include: tensor-based analysis of affine layer mappings and associative memories; fiber bundles for data representation and learning; generalized Laplacian-based learning of data manifolds; basic manifolds, curvature and data embeddings; outlook: research into symmetry and advanced models for data science and machine learning.

Previous knowledge expected

Undergraduate studies of mathematics; basic concepts of Riemannian geometry (manifolds, charts and local coordinates, tangent bundle, k-forms, metrics, Lie groups); the essence of such basic concepts will be explained but in a telegraphic manner only, in order to devote the time to the topics listed above.

Objectives

Understanding of mathematical theory required for understanding and conducting research in a highly active field of data science and machine learning. In addition, students should learn that data science and machine learning also stimulates in the reverse direction mathematical research through problems raised by discretization and network design. Throughout, mathematical principles are emphasized that help the student to classify the field and to recognize common and distinguishing aspects that may arise in concrete applications. The course sets the stage for master thesis projects in the field of data science and geometric deep learning.

Detailed Course Type

Master programme: Mathematical Methods of Machine Learning and Data Science. The course is creditable also for master students of mathematics and scientific computing.

Further information