1
$\begingroup$

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)

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

After thinking about it for a while, I noticed that distance matrices are rotation and translation invariant rather than equivariant.

For equivariant representation, you'd want that a rotation will produce a rotated output.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .