Summer 2025
This is a learning seminar on geometry and topology in machine learning in Summer 2025. The seminar runs from the week of June 9th - June 13th and to the week of August 18th - August 22nd. For more details, please see the (original) syllabus. Note that the contents listed in the syllabus is out-dated, please see the section below for the accurate contents covered.
From June 9th to June 30th 2025, we ran a 6-lecture minicourse on geometric deep learning focusing on two themes - (A) Groups and Representations, and (B) Manifolds. We followed the schedule below:
- Lecture 1 (June 9th, By Mattie) | Soft introduction to machine learning, neural networks, convolutional and graph neural networks, with an eye towards geometry and topology.
- Lecture 2 (June 13rd, By Daiyuan) | Introduction to groups, representations, vector bundles, principle G-bundles, gauge theory.
- Lecture 3 (June 16th, By Mattie) | Equivariant and convolutional neural networks on homogeneous spaces and examples.
- Lecture 4 (June 20th, By Matthew and Mattie) | Introduction to differentiable manifolds. Tangent and cotangent spaces/bundles, normal bundles, smooth maps, regular value theorem, Lie groups and Lie algebras, boundary and orientations.
- Lecture 5 (June 23rd, By Mattie) | Introduction to Riemannian manifolds, constructing feature spaces in Coordinate-Independent CNNs, gauge theory and G-structures, Mobius Band CNN as an example. (Annotated version)
- Lecture 6 (June 30th, By Daiyuan and Mattie) | More on Coordinate-Independent CNNs: Convolutions and Isometry. 1x1 GM-convolutions, Kernel Field Transformations, and GM-convolutions, Isometry Equivariance.
The main reference for Part A is
Taco Cohen, Mario Geiger, Maurice Weiler. A general theory of equivariant CNNs on homogeneous spaces.
The main reference for Part B is
Maurice Weiler, Patrick Forré, Erik Verlinde, Max Welling. Equivariant and Coordinate Independent Convolutional Networks: A Gauge Field Theory of Neural Networks
Note that much of Part A is also discussed in the main reference for Part B.
The remaining weeks of the seminar will be paper presentations. Volunteered participants from the seminar would give presentations on a research paper (or an academic topic in general) of their choice related to this seminar.
| Date | Title | Abstract | Presenter |
|---|---|---|---|
| July 14th | Polyhedral decomposition of Feed-Forward ReLU Neural Networks | Link | Vicente Bosca |
| July 21st | Geometric and Topological Methods for Machine Learning in Molecular Dynamics: A Historical and Practical Perspective | Link | Matthew Meeker |
| July 28th | Hyperbolic Geometry and Neural Networks | Link | Riley Guyett |
| August 4th | The Reeb Transform | Link | Shankha Mukherjee |
| August 11th | Network sheaves and laplacians in neural networks | Link | Daiyuan Li |
| August 18th | Gauge Theory for Convolutional Neural Networks | Link | Mats Hansen |