Model is SO(3) equivariant only for the first 12 testing elements about escnn HOT 2 CLOSED

Hi @JacobHelwig

The reason why the test works for the first 12 elements is that rot3donR3.testing_elements contains the 60 rotations of the Icosahedral group but, among these, only the first 12 are also symmetries of the cube, i.e. they only involve 90 or 180 deg rotations.

That means that the first 12 elements are also symmetries of the voxel grid containing your data.
However, the other 48 are not and will introduce some kind of interpolation artefacts when you rotate your input/outputs.

Testing for equivariance to rotations which don't preserve the grid should be done with some care to avoid (or at least reduce) these artefacts (e.g. work with higher resolution images such that you can rotate them at higher resolution and then downsample them. This should also be done for the outputs).
Moreover, remember that perfect equivariance to these rotations is impossible so you always need to account for some equivariance error (up to 1e-2 or 1e-1 relative error)

Let me know if this answers your question!
Gabriele

from escnn.

Thank you, @Gabri95. This answers my question

from escnn.