Hi!
According to this 33 and this 7, backward and forward transformations are tensor/matrices that learn move back and forth between different coordinate system. This simply means, given two vector space, it’s possible to:

Build a vector for the new basis from the old basis using backward (B) transformation matrix
Build a vector for the old basis from the new basis using Forward (F)  transformation matrix

With the product of F.B = Identity matrix. also B = Inv(F)

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The above images show B and F transformation matrix for 2-dimensional vector space. For n-dim vector space, we have something like that

Since the feature of an image can be thought as belonging to an n-dimensional feature space, is it possible to make pytorch learn the transformation matrices through a machine learning procedure? The two input images belong to two different views/feature space as shown below