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It is often said that a deep learning model is "invariant" to some specifictype of transformation. However, what is meant by this statement stronglydepends on the context in which it is made. In this paper we explore the natureof invariance and equivariance of deep learning models with the goal of betterunderstanding the ways in which they actually capture these concepts on aformal level. We introduce a family of invariance and equivariance metrics thatallows us to quantify these properties in a way that disentangles them fromother metrics such as loss or accuracy. We use our metrics to better understandthe two most popular methods used to build invariance into networks: dataaugmentation and equivariant layers. We draw a range of conclusions aboutinvariance and equivariance in deep learning models, ranging from whetherinitializing a model with pretrained weights has an effect on a trained model'sinvariance, to the extent to which invariance learned via training cangeneralize to out-of-distribution data.

In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?