What is the usage of geocross loss?

[yvoonne06]

I wonder how the geocross loss works to find the direction of updating the latent vector.

def _loss_geocross(self, latent, **kwargs):
    if(latent.shape[1] == 1):
        return 0
    else:
        X = latent.view(-1, 1, 18, 512)
        Y = latent.view(-1, 18, 1, 512)
        A = ((X-Y).pow(2).sum(-1)+1e-9).sqrt()
        B = ((X+Y).pow(2).sum(-1)+1e-9).sqrt()
        D = 2*torch.atan2(A, B)
        D = ((D.pow(2)*512).mean((1, 2))/8.).sum()
        return D

[MikeLasz]

You can check out Appendix B of the paper to learn more about the Cross Loss.

In short: StyleGAN uses a style vector $w \in \mathbb{R}^{512}$, which is then tiled, i.e. copied 18 times. This is used as the input of the synthesis network.
PULSE's optimization problem is seeking vectors $v_1, \dots, v_{18}\in \mathbb{R}^{512}$ that minimizes the loss given in eq (9). To enforce $v_1, \dots , v_{18}$ to be more similar, they add the Cross Loss to regularize towards that similarity condition. Since they optimize $v_1, \dots, v_{18}$ on the unit sphere (see the discussion in Section 3.2.), they define that loss as the geodesic distance, which is why they coin it Geo Cross Loss.