I have a question About the eq.7 in paper

[divided7]

Eq7:
$\left.\Delta s=\left{\begin{array}{cc}\Delta i_c\cdot\Delta i&\quad\text{if}|\Delta i_c\cdot\Delta i|\geq\beta\0&\quad\text{otherwise}\end{array}\right.\right.$
In my mind, the $\Delta i_c$ is $\Delta i[c]$, that's right?
So the $\Delta i_c$ is a number, and the $\Delta i$ is a vector?
So the $\Delta i_c$，c=1,2,...,512 ?
So$\Delta s$ have 512 vector？

[orpatashnik]

Hi @divided7 ,
$\Delta i_c$ is the direction in CLIP image space implied by perturbing the $c$ channel in StyleGAN's $\mathcal{S}$ space.
Please refer to our video https://www.youtube.com/watch?v=PhR1gpXDu0w&t=470s for more details.