procrustes-rotation-invariant-scaling-sensitive

Summary

Procrustes similarity ignores how data is rotated or flipped, so orientation never changes the score, but it will flag a representation if it has been stretched more in one direction than another. This matters because if you're comparing neural network representations and one has been directionally distorted, Procrustes will treat it as different while CKA (which shrugs off uniform stretching) might not, so the choice of metric changes what you consider "the same."