Theoretical Aspects of Group Equivariant Neural Networks

Understand

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints.

• They leverage concepts from group representation theory, non-commutative harmonic analysis and differential geometry that do not often appear in machine learning.
• In practice, they have been shown to reduce sample and model complexity, notably in challenging tasks where input transformations such as arbitrary rotations are present.
• We begin this work with an exposition of group representation theory and the machinery necessary to define and evaluate integrals and convolutions on groups.