Comparison of the perturbation loss between eq. (6) and (14)

[tgoncalv]

Hello @shivangi-aneja, I have a question about the perturbation loss used for the single VS multiple manipulation methods.

In eq.14, you try to minimize $||\delta_i^{all}||_2$ but in eq.6, you try to minimize $||X_i^p-X_i||_2 + ||X_i^{Gp}-X_i||_2$. I understand that both formula are approximately the same since we approximately have $$||X_i^p-X_i||_2=||Clamp_{\epsilon}(X_i+\delta_i)-X_i||_2\approx||\delta_i||_2$$
If my above supposition is correct, why would you use $||\delta_i^{all}||_2$ in eq.14 instead of $||X_i^{all}-X_i||_2$ ?

I suppose that this is not a really important question since there wouldn't be much difference in the result, but still I'd want to know if there is a particular reason for doing that.

In any cases, thank you for this great work. I've learned a lot thanks to your paper.