Group equivariant neural networks seen by a mathematician

Artificial neural networks (ANNs) are incredibly successful at performing certain machine learning tasks, such as classification. In applications such as computer vision or quantum chemistry, we will often seek machine learning algorithms that can handle inputs that are transformed. For example, a cat detector should be able to detect a rotated cat.

Group theory provides the natural formalization of what we mean by transformations and group equivariance is the property we seek in artificial neural networks (ANN) and there is currently a flurry of research activity in group equivariant neural networks. In this talk, I will present the M.Sc. work of my former student Max Hennick, which gives a characterization of (approximate) G-equivariant linear mappings. What is most striking is how effective a bit of functional analysis and algebra can be at answering this question.

I will provide as many examples as possible and conclude with some hopefully interesting questions.

[ recording ]

The AARMS Scientific Machine Learning Seminar takes virtually via WebEx.  If you would like to attend, please email the organizers for connection details.