UvA Mini-Course Introduces Group Equivariant Deep Learning with Practical Tutorials and Libraries

The University of Amsterdam (UvA) has launched a mini-course on Group Equivariant Deep Learning (GEDL), aimed at researchers and practitioners interested in geometric data processing. The course, developed by Erik Bekkers from the Amsterdam Machine Learning Lab (AMLab), is still under development but already offers valuable lecture notes and practical tutorials.

What Changed Technically

Group equivariant deep learning extends traditional convolutional neural networks (CNNs) to handle symmetries in data more effectively. This is particularly useful for geometric data, such as images, point clouds, and 3D structures. By designing models that are equivariant to specific transformations (e.g., rotations, translations), GEDL can improve model performance and reduce the amount of training data required.

Why It Matters

For practitioners working with geometric data, understanding and implementing group equivariant deep learning can lead to more robust and efficient models. This is especially relevant in fields like computer vision, robotics, and scientific machine learning where data often has inherent symmetries.

Key Resources and Libraries

Lecture Notes

The most important resource for the course are the lecture notes, which cover:

• Introduction: Motivation and overview of group equivariant deep learning.
• Group Theory Basics: Concepts like groups, group products, inverses, actions, representations, and affine groups (G = Rd ⋊ H).

Autumn School on Scientific Machine Learning

For participants in the Autumn School on Scientific Machine Learning and Dynamical Systems, a tutorial on group convolutions with vector field data is available:

• Tutorial: Group Convolutions with Vector Field Data

Useful Libraries

Several libraries are recommended for implementing group equivariant deep learning:

• escnn: A comprehensive library for E(n) equivariant networks on 2D and 3D grids.
• e3nn: Focuses on steerable/tensor field methods for 3D point clouds, utilizing the Clebsch-Gordan tensor product.
• e2cnn: A streamlined version of regular group convolutions with support for SO(2) Fourier transforms.
• ponita: Offers fast and expressive methods for 3D point clouds using regular group convolutions over position-orientation space. It has been benchmarked on tasks such as interatomic energy and force prediction, n-body interacting particle systems, and denoising diffusion models for generating 3D molecular representations.

Additional Resources

Deep Learning 2 Course Website

The Deep Learning 2 Course Website provides GEDL tutorials along with materials on other advanced topics:

• Bayesian Deep Learning
• Deep Probabilistic Models
• Causality
• Dynamical Systems

Video Lectures

A series of video lectures is available on YouTube, covering the fundamentals of group equivariant deep learning:

• Lecture 1.1: Introduction to GEDL.
• Lecture 1.2: Group theory basics.

Conclusion

The UvA mini-course on Group Equivariant Deep Learning offers a comprehensive introduction to this advanced topic, complete with practical tutorials and useful libraries. Whether you're working on computer vision, robotics, or scientific machine learning, understanding GEDL can significantly enhance your models' performance and efficiency.