ATML: Geometric learning

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.

General Information

Instructor: Viacheslav (Slava) Borovitskiy.
Tutors: Viacheslav (Slava) Borovitskiy and Sahel Torkamani.
Teaching Assistant: Rajit Rajpal.

Lectures: Thursdays 17:10-18:00, 40 George Square, Lecture Theatre B.

Tutorials: Wednesdays 13:10-14:00, Appleton Tower M2. Starting Week 3.

Optional resources: https://geometricdeeplearning.com/, also https://uvagedl.github.io/.

Sample exam [for this track only]: link. Solutions: link.

News

• 31.01.2026 — 3rd exercise sheet has been published. See Materials.
• 31.01.2026 — Lecture notes for Lecture 2 have been published (see Materials). Note: Due to the missing audio track, we are making an exception to provide notes for this session. We do not plan to release notes for other lectures.
• 27.01.2026 — It's been reported that the recording of Lecture 2 is inaudible. We're investigating into this.
• 23.01.2026 — 2nd exercise sheet has been published. See Materials.
• 23.01.2026 — Here are some optional resources on groups:

  • Section 1.2 in https://arxiv.org/abs/2508.02723

  • Section 1.1 in https://pure.uva.nl/ws/files/60770359/Thesis.pdf

  • Section 1.1 in https://people.cs.uchicago.edu/~risi/papers/KondorThesis.pdf

  • 20min video by 3Blue1Brown: https://www.youtube.com/watch?v=mH0oCDa74tE

• 22.01.2026 — Small update of the sample exam paper and solutions. Affected items: 2a and 2c. Links are the same.
• 19.01.2026 — Sample exam paper for the track has been published. The paper and the solutions can be found in General Information.
• 19.01.2026 — First exercise sheet has been published. See Materials.

Materials

• Lecture 1. What is geometric learning?
  Slides: link. Annotated slides: link. Exercises: link.
• Lecture 2. Fundamentals: Symmetries
  Slides: link. Annotated slides: link. Exercises: link. Lecture notes: link.
  Note: Due to the missing audio track, we are making an exception to provide notes for this session. We do not plan to release notes for other lectures.
• Lecture 3. Fundamentals: Convolutions
  Slides: link. Annotated slides: link. Exercises: link.
• Lecture 4. Learning on graphs

Legend. "Annotated slides" are slides with ink notes added during the lecture.

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.