Answers.Body: <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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Answers.CreationDate: 2022-07-19T06:50:04.863Z
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Body: <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>
  
Tags: <neural-networks><transformer><graph-neural-networks>
Title: Rationalle behind SE3 Transformer?
UserDisplayName: Protostome
ThreadText: # 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
  
  ---
  
  ## 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.
  
  
  ---
  
  