Thank you for the insightful work presented in the paper. I have a question which might seem trivial but is important for my understanding.
In the paper, it is mentioned that L⊤L, in equation (6), exhibits O(3) invariance, and ψFT(fj − fi) is described as having periodic translation invariance. Referring to Proposition 3, the paper asserts that the score εˆF, as defined in Equation (9), is periodic translation invariant. However, I am curious about the underlying assumptions for this claim. Specifically, is it necessary to prove that L⊤L is also periodic translation invariant to ensure εˆF?
Thank you for the insightful work presented in the paper. I have a question which might seem trivial but is important for my understanding.
In the paper, it is mentioned that L⊤L, in equation (6), exhibits O(3) invariance, and ψFT(fj − fi) is described as having periodic translation invariance. Referring to Proposition 3, the paper asserts that the score εˆF, as defined in Equation (9), is periodic translation invariant. However, I am curious about the underlying assumptions for this claim. Specifically, is it necessary to prove that L⊤L is also periodic translation invariant to ensure εˆF?
Thank you in advance for your answer.