Question about partial transformations on the input

[SumeetBatra]

Hey folks,

I'm somewhat new to equivariant neural networks so this question might be naive. I wanted to see if it's possible to maintain equivariance if only part of the input is transformed i.e. a transformation of a fraction of the feature outputs of the network occurs from a partial transformation of the input. Is there some notion of locality and maintaining equivariance?

I'm asking because I have a model that produces factorized feature vectors for input images, so I had this intuition that a transformation on part of the image that only effects one feature vector might maintain equivariance given a transformation from a symmetry group and an equivariant NN. Hope the question makes sense!