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

• 07.03.2026 — 7th exercise sheet and solutions to the 5nd exercise sheet have been published. See Materials.
• 28.02.2026 — 6th exercise sheet has been published. See Materials.
• 27.02.2026 — Solutions to the 4th exercise sheet have been published. See Materials.
• 20.02.2026 — Solutions to the 3rd exercise sheet have been published. See Materials.
• 14.02.2026 — 5th exercise sheet and solutions to the 2nd exercise sheet have been published. See Materials.
• 07.02.2026 — 4th exercise sheet and solutions to the 1st exercise sheet have been published. See Materials.
• 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. Solutions: link.
• Lecture 2. Fundamentals: Symmetries
  Slides: link. Annotated slides: link. Exercises: link. Lecture notes: link. Solutions: 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.  Solutions: link.
• Lecture 4. Learning on graphs
  Slides: link. Annotated slides: link. Exercises [including coding]: link. Solutions: link.
• Lecture 5. Graph convolutional neural networks
  Slides: link. Annotated slides: link. Exercises [including coding]: link. Solutions: link.
• Lecture 6. Types of graph neural networks and expressivity
  Slides: link. Annotated slides: link. Exercises: link. Solutions: link.
• Lecture 7. More on GNNs: Limitations and Transformers
  Slides: link. Annotated slides: link. Exercises: link.
  Note: No annotations this time, "Annotated slides" = "Slides".
• Lecture 8. Graph Transformers and Group-equivariant Networks
  Slides: link. Annotated slides: link. Exercises [only coding]: link.

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 4-8. 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 9-10. Group equivariant neural networks.
  Group Equivariant Convolutional Networks. Steerable Neural Networks. Geometric graph neural networks.
• 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.