On translation and rotation equivariance

[JLuij]

This may be a naive question but I'd like a clear answer as this claim is not discussed in the paper whereas it is in other pointcloud literature.

The questions is, is PTv3 a rotation and translation equivariant architecture?

Perhaps it's not that trivial due to the space-filling curve neighbours search, but nothing suggests that the architecture by default relies on absolute point location.

[Gofinge]

Hi, in my opinion, model-wise rotation and translation equivariant are not necessary. As long as we add rotation augmentation or translation augmentation to the training pipeline, you will find that the model output is relatively consistent, no matter the orientation of the point cloud. Open for discussion :).

[JLuij]

Sure, that's valid however not the point of my question. My question is, is PTv3 a rotation and translation equivariant architecture, or is that property limited to particular layers or is no part of PTv3 rotation/translation equivariant?

[adithyamurali]

I believe the architecture is not rotation and translation equivariant by design

[Gofinge]

I believe the architecture is not rotation and translation equivariant by design

I agree, it is not designed to be rotation- and translation-equivariant, because I don’t think it matters much. For example, consider the Image Transformer: when we rotate or translate an image, the positional encoding changes, which means that attention on the image is also not rotation- or translation-equivariant, unlike convolution.