> More general mathematical definition of tensor is that tensors are multilinear maps from vector spaces to scalars. That's how TensorFlow and HPTT see these tensors.

Oof, you have to squint very hard to see things that way.

Just because an image is physically a two-dimensional array of pixels doesn't suddenly make it a rank-2 multilinear map, and just because you have N planes of images doesn't mean you suddenly have a rank-3 tensor!