What is an equivariant neural network?

Abstract

We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of equivariance or neural networks. The basic mathematical ideas are simple but are often obscured by engineering complications that come with practical realizations. We extract and focus on the mathematical aspects, and limit ourselves to a cursory treatment of the engineering issues at the end.