Is the word "pose" used correctly in the paper "Matrix Capsules with EM Routing"? In traditional computer vision and computer graphics, the pose matrix is a $4 \times 4$ matrix of the form 

$$
\begin{bmatrix}
r_{11}  &amp; r_{12}  &amp;  r_{12}   &amp; t_{1} \\
r_{21}  &amp;  r_{22}   &amp; r_{22} &amp;   t_{2} \\
r_{31}   &amp; r_{32}  &amp;  r_{32}  &amp;  t_{3} \\ 
0   &amp;   0    &amp;  0   &amp;   1
\end{bmatrix}
$$

and is a transformation to change viewpoints from one frame to another.

In the Matrix Capsules with EM Routing paper, they say that the "pose" of various sub-objects of an object are encoded by each capsule lower layer. But from the procedure described in the paper, I understand that the pose matrix they talk about doesn't conform to the definition of the pose matrix. There isn't any restriction on keeping the form of the pose matrix shown above. 


So, is it right to use the word "pose" to describe the $4 \times 4$ matrix of each capsule?
Moreover, since the claim is that the capsules learn the pose matrices of the sub-objects of an object, does it mean they learn the viewpoint transformations of the sub-objects, since the pose matrix is actually a transformation?
Great question, and one that I think we could have done a better job of answering in the paper. 

Essentially, the pose matrix of each capsule is set up so that it could learn to represent the affine transformation between the object and the viewer, but we are not restricting it to necessarily do that. So we talk about the output of a capsule as though it is an affine transformation matrix, but we can't ensure that it will be. We do things explicitly that make it more like such a matrix — like adding in the coordinates to the right-hand column — but we can't be sure. This somewhat embodies a large part of the capsule network theory — we set up scaffolding so that the network can learn to be equivalent to transformations that we think it ought to be invariant to, but we don't ensure that it is.