Question regarding circle loss

[Bloos]

Hi!

I've got a question regarding the implementation of the circle loss. It is implemented like this:

new_mat[pos_mask_bool] = (
    -self.gamma
    * torch.relu(self.op - anchor_positive.detach())
    * (anchor_positive - self.delta_p)
)
new_mat[neg_mask_bool] = (
    self.gamma
    * torch.relu(anchor_negative.detach() - self.on)
    * (anchor_negative - self.delta_n)
)

logsumexp_pos = lmu.logsumexp(
    new_mat, keep_mask=pos_mask_bool, add_one=False, dim=1
)
logsumexp_neg = lmu.logsumexp(
    new_mat, keep_mask=neg_mask_bool, add_one=False, dim=1
)

losses = self.soft_plus(logsumexp_pos + logsumexp_neg)

or rewritten in mathematical Notation:

This is not according to the paper wich defines the loss as

When looking at how the formula was derived we can see that the brackets should be like this

(multiplication of the term inside of the sum instead of adding positive and negative parts up.

Am I missing something?

[Bloos]

I think I've found a mistake in my formulas.

is not correct. Actually it is:

Which is equivalent to

and therefore equivalent to the paper. I'll close the discussion.

Sometimes posing a questions helps :D