Some questions on ViMON

[SeanNobel]

Hello, I'm somewhat new to this field and having questions on ViMON implementation (I'm sorry if this is not the right place to have questions).

1. About the calculation of KL divergence between prior and posterior, I don't think that "KL between product of Normals and Standard Normal" equals to "Sum of KLs between each Normal and Standard Normal".

However in the implementation it is calculated simply as sum over k.

def kl_div(mu, logvar):
    return - 0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp(), dim=3).mean(dim=(0, 1)).sum()

Should I assume that some approximation is happening here?

2. Why isn't the scope calculated like in the paper here? From the paper it should be:

log_s_k = log_s_k + F.logsigmoid(1 - alpha_k)

I'm guessing that it is because it doesn't really matter if we add 1 to -alpha_k in log-space (it just slides in the negative area after logsigmoid), but is there a reason to positively omit 1?

Sorry for taking your time and thanks in advance!