ATML: Geometric learning

Instructor: Viacheslav Borovitskiy

Geometric Learning is a track within the Advanced Topics in Machine Learning (ATML) course. In this track, we will explore how geometric concepts—such as symmetries, invariances, and the structure of non-Euclidean domains (e.g., graphs, groups, and manifolds)—can be leveraged in modern machine learning.

What to expect?

The curriculum outlined below is tentative and subject to change as the course is developed. It is meant to give a rough notion of what the Geometric Learning track will cover:

• Lecture 1. What is geometric learning?
  Introduction to the course. Key principles. Success stories.
• Lectures 2-3. Fundamentals.
  Formalism behind "geometric" domains. Symmetries and elements of group theory. Abstract convolutions.
• Lectures 4-6. Graph neural networks.
  Graph convolutional neural networks (GCNNs). Beyond GCNNs: attention (relation to Transformers), general message-passing graph neural networks. Graph Transformers. Theoretical aspects: expressive power, limitations.
• Lectures 7-8. Group equivariant neural networks.
  Group Equivariant Convolutional Networks. Steerable Neural Networks. Geometric graph neural networks.
• Lectures 9-10. More.
  Geometric probabilistic models: approaches to uncertainty estimation and probabilistic reasoning on geometric domains. Recent advances, emerging trends, and open research problems in the field.
• Lecture 11. Review.

Who should take this track?

If you are keen to understand how machine learning models can exploit symmetries in data (and why this is beneficial), or if you want to know how to apply machine learning to graphs, point clouds, and other structured data (representing, for example, molecules, spatial data, or social networks), this track is for you.

Prerequisites: You should have a basic understanding of machine learning, and (almost as important) you should not dislike mathematics. You don’t need to be an expert or have advanced math background—essential concepts will be introduced as needed—but an open and positive attitude toward mathematical ideas is very important.

Disclaimer

This curriculum guides the course’s intended trajectory. It is kept intentionally broad, allowing for adjustments to the flow and pacing as the semester proceeds.