ATML: Geometric learning

 

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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 and groups)—can be leveraged in modern machine learning.

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.

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.

Materials

  • Lecture 1. What is geometric learning?
    Slides: link (alternative). Annotated slides: link. Exercises: link. Solutions: link.
  • Lecture 2. Fundamentals: Symmetries
    Slides: link (alternative). 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 (alternative). Annotated slides: link. Exercises: link.  Solutions: link.
  • Lecture 4. Learning on graphs
    Slides: link (alternative). Annotated slides: link. Exercises [including coding]: link. Solutions: link.
  • Lecture 5. Graph convolutional neural networks
    Slides: link (alternative). Annotated slides: link. Exercises [including coding]: link. Solutions: link.
  • Lecture 6. Types of graph neural networks and expressivity
    Slides: link (alternative). Annotated slides: link. Exercises: link. Solutions: link.
  • Lecture 7. More on GNNs: Limitations and transformers
    Slides: link (alternative). Annotated slides: link. Exercises: link. Solutions: link.
    Note: No annotations this time, "Annotated slides" = "Slides".
  • Lecture 8. Graph transformers and group-equivariant networks
    Slides: link (alternative). Annotated slides: link. Exercises [only coding]: link. Solutions: link.
  • Lecture 9. Rotation- and translation-equivariant networks on images 
    Slides: link (alternative). Annotated slides: link. Exercises: link. Solutions: link.
  • Lecture 10. Steerable networks and E(3)-equivariant GNNs 
    Slides: link (alternative). Annotated slides: link. Exercises: link.
  • Revision.
    Annotated slides: link.

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

News

  • 30.03.2026 — Revision slides are published. Sample exam is updated. Pre-exam Q&A will take place April 22, between 14:10-15:00, at room G.02 (access at 19GSq).
  • 28.03.2026 — 10th exercise sheet and solutions to the 8th and 9th exercise sheet have been published. See Materials.
  • 21.03.2026 — 9th exercise sheet and solutions to the 7th exercise sheet have been published. See Materials.
  • 14.03.2026 — 8th exercise sheet and solutions to the 6th exercise sheet have been published. See Materials.
  • 07.03.2026 — 7th exercise sheet and solutions to the 5th 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:
  • 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.
License
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