Question about equivariant regularization in classification task

Dear All,
Recently, I met with a question, that is, whether I can introduce equivariant regularization (ER) in classification task? even I don’t make it clear why ER can be boldly used in segmentation task?
Can anybody give some explainations, thanks.

As above, assumed i have an image X, and its affine transformed version t(X), here affine transformation is denoted as A. After some conv. layers, the new features are Fx and Ftx, respectively, now can i compute the loss among A(Fx) and Ftx in classification task?
help explain whether this possibility or not, be grateful!