resources

Geometric Deep Learning (GDL)

Overview

Geometric Deep Learning (GDL) is a subfield of machine learning that combines deep learning with geometric data. It is a powerful tool for learning from geometric data, such as graphs, meshes, and point clouds.

Resources from geometricdeeplearning.com

• https://geometricdeeplearning.com/
• https://geometricdeeplearning.com/book/
• https://geometricdeeplearning.com/blogs/

• https://geometricdeeplearning.com/keynotes/

• The proto-book: Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges (Bronstein et al, 2021) - https://arxiv.org/abs/2104.13478
• Mathematical Foundations of Geometric Deep Learning (Bronstein et al, 2025) - https://arxiv.org/abs/2508.02723

People

• Michael M Bronstein - https://www.cs.ox.ac.uk/people/michael.bronstein/
• Petar Veličković - https://petar-v.com/

Blogs

• https://thegradient.pub/towards-geometric-deep-learning/

Podcasts / Videos

• https://geometricdeeplearning.com/lectures/
• Petar Veličković - https://www.youtube.com/@petarvelickovic6033
  • Into the Realm Categorical - https://www.youtube.com/watch?v=yUxiDOTj_zc
  • ^ Geometric Deep Learning: GNNs Beyond Permutation Equivariance - https://www.youtube.com/watch?v=aCUOAkOqNoU
• AMMI 2022 Course “Geometric Deep Learning” Playlist: https://www.youtube.com/watch?v=5c_-KX1sRDQ&list=PLn2-dEmQeTfSLXW8yXP4q_Ii58wFdxb3C
• GDL on MLST: https://www.youtube.com/watch?v=bIZB1hIJ4u8 / https://open.spotify.com/episode/6g58GSZ4cZuot8rEBr46XH
• ICLR 2021 Keynote - “Geometric Deep Learning: The Erlangen Programme of ML” - M Bronstein - https://www.youtube.com/watch?v=w6Pw4MOzMuo
• Beyond the Patterns 28 - Petar Veličković - Geometric Deep Learning - https://www.youtube.com/watch?v=9cxhvQK9ALQ

Courses

• First Italian School on Geometric Deep Learning held in Pescara in July 2022: https://www.youtube.com/playlist?list=PLn2-dEmQeTfRQXLKf9Fmlk3HmReGg3YZZ (Includes prerequisites lectures)

  1. Prerequisites I: Groups, Representations & Equivariance – Maurice Weiler
  2. Prerequisites II: Topology – Cristian Bodnar
  3. Prerequisites III: Manifolds & Fiber Bundles – Maurice Weiler
  4. Prerequisites IV: Category Theory – Pim de Haan
  5. Lecture 1: A Brief History of Geometric Deep Learning – Michael Bronstein
  6. Lecture 2: Topological Message Passing – Cristian Bodnar
  7. Lecture 3: Sheaf Neural Networks – Cristian Bodnar
  8. Lecture 4: Equivariant CNNs I (Euclidean Spaces) – Maurice Weiler
  9. Lecture 5: Equivariant CNNs II (Riemannian Manifolds) – Maurice Weiler
  10. Lecture 6: Gauge-equivariant Mesh CNN – Pim de Haan
  11. Lecture 7: From Equivariance to Naturality – Pim de Haan
  12. Lecture 8: Curvature & Oversquashing in GNNs – Francesco Di Giovanni
  13. Lecture 9: GNNs as Dynamic Systems – Francesco Di Giovanni
  14. Lecture 10: What’s Next? – Michael Bronstein

• Second Edition of the course “Geometric Deep Learning” taught in the African Master in Machine Intelligence in July 2022: https://www.youtube.com/playlist?list=PLn2-dEmQeTfSLXW8yXP4q_Ii58wFdxb3C

1. Introduction (Michael)
2. Basics of ML in high dimension (Joan)
3. Geometric priors I (Taco)
4. Geometric priors II (Joan)
5. Graphs & Sets I (Petar)
6. Graphs & Sets II (Petar)
7. Grids (Joan)
8. Groups (Taco)
9. Manifolds & Meshes (Michael)
10. Gauges & Bundles (Taco)
11. Beyond groups (Petar)
12. Applications & Conclusions (Michael)

• First Edition of the course “Geometric Deep Learning” taught in the African Master in Machine Intelligence in July-August 2021: https://www.youtube.com/playlist?list=PLn2-dEmQeTfQ8YVuHBOvAhUlnIPYxkeu3

Erlangen Program

• https://en.wikipedia.org/wiki/Erlangen_program
• https://ncatlab.org/nlab/show/Erlangen+program
• A comparative review of recent researches in geometry (1872) - https://arxiv.org/abs/0807.3161

Graph Neural Networks

• https://www.youtube.com/watch?v=A-yKQamf2Fc

Categorical Deep Learning

• https://categoricaldeeplearning.com/
• https://cats.for.ai/
• Position: Categorical Deep Learning is an Algebraic Theory of All Architectures - https://arxiv.org/abs/2402.15332
• https://www.youtube.com/playlist?list=PLxbiIYgRO7kbH1IBrBl59GTDMaksb3mJ6
• Categories for AI (cats.for.ai) - https://www.youtube.com/playlist?list=PLSdFiFTAI4sQ0Rg4BIZcNnU-45I9DI-VB
• https://github.com/bgavran/Category_Theory_Machine_Learning