ATML: Geometric learning
Instructor: Viacheslav Borovitskiy
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, manifolds, and groups)—can be leveraged in modern machine learning.
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:
- What is geometric learning?
Key principles, motivating examples, and success stories from recent research. - “Geometric” domains: graphs, groups, manifolds
Mathematical preliminaries, motivation, and formalism behind different geometric domains encountered in machine learning. - Convolution: from images to graphs and beyond
A unified view of convolution in classical domains (images, grids), with extensions to graphs and other geometric objects. - Graph neural networks I
Graph convolutional neural networks (GCNNs): core ideas and practical implementation. - Graph neural networks II
Beyond basic GCNNs: attention mechanisms (relation to Transformers), general message-passing graph neural networks. - Graph neural networks III
Theoretical aspects: expressive power, limitations. - Group equivariant neural networks I
Leveraging symmetries in neural network design. Introduction to equivariant architectures. - Group equivariant neural networks II
A deeper dive into equivariant architectures and their applications. - Geometric learning in the real world: AlphaFold case study
How geometric ideas enabled advances in protein structure prediction. - Geometric probabilistic models
Approaches to uncertainty estimation and probabilistic reasoning on geometric domains. - What’s new in geometric learning?
Recent advances, emerging trends, and open research problems in the field.
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
The above outline is a work in progress; both the ordering and specific topics are likely to evolve as the course is finalized. Further details, materials, and the finalized syllabus will be available before the course starts.