In Search of Projectively Equivariant Networks

Properties
authors	Georg Bokman, Axel Flinth, Fredrik Kahl
year	2022
url	https://arxiv.org/abs/2209.14719

Abstract

Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building a standard equivariant network where the linear group representations acting on each intermediate feature space are"multiplicatively modified lifts"of projective group representations. By theoretically studying the relation of projectively and linearly equivariant linear layers, we show that our approach is the most general possible when building a network out of linear layers. The theory is showcased in two simple experiments.