I have just finished reading the SE3 transformer paper (SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks) by Fuchs et-al and although I'm sure I understand less than 50% of the math involved, I have a lingering question:
Is there a reason one can't use distance matrix representation, e.g.: $$ M[i,j]=d(i,j), \forall i > j $$ as a valid rotation translation equivarient representation for point cloud data? Why is there a need for a neural network to encode such representation?
(of course, it is not a one - to - one representation, inverted/flipped point clouds can still map to the same distance matrix, but in most practical applications this distinction carry little significance)