<p>After thinking about it for a while, I noticed that distance matrices are rotation and translation <strong>invariant</strong> rather than <strong>equivariant</strong>.</p>
<p>For equivariant representation, you'd want that a rotation will produce a rotated output.</p>

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2022-07-19T06:50:04.863Z
2022-07-19T06:50:04.863Z
Protostome
<p>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:</p>
<p>Is there a reason one can't use distance matrix representation, e.g.:
<span class="math-container">$$
 M[i,j]=d(i,j),  \forall i &gt; j
$$</span>
as a valid rotation translation equivarient representation for point cloud data? Why is there a need for a neural network to encode such representation?</p>
<p>(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)</p>

<neural-networks><transformer><graph-neural-networks>
Rationalle behind SE3 Transformer?
Protostome
# Rationalle behind SE3 Transformer?

(Asked by: username_0 on 2022-07-17)

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)

**Tags:** neural-networks, transformer, graph-neural-networks


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## 1 answers

### Answer by username_0 on 2022-07-19. Score: 1 | Accepted answer

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.


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