about the implement of sort error

[FL77N]

according the paper, I can compute the $L_{ij}$ as following defined in Eq. 9:

I notice that the implement of sort error in your code is as following:

# Compute sorting error on example ii
sorting_error[ii] = current_sorting_error - target_sorting_error

why not multiply the sort pmf? as following

sorting_error[ii] = (current_sorting_error - target_sorting_error)*missorted_examples/sorting_pmf_denom

[kemaloksuz]

Your expression seems correct. In terms of our implementation.

• We first compute the sorting error (\ell_S(i)- \ell_S^*(i) in Eq. 9 in the paper - https://arxiv.org/pdf/2107.11669.pdf) in line 66:

  RankSortLoss/mmdet/models/losses/ranking_losses.py

  Line 66 in b41f64d

  sorting_error[ii] = current_sorting_error - target_sorting_error

• Then, this sorting error is distributed over positive examples using sorting pmf in this line:

  RankSortLoss/mmdet/models/losses/ranking_losses.py

  Line 87 in b41f64d

  fg_grad += (missorted_examples*(sorting_error[ii]/sorting_pmf_denom))

  . In otherwords, sorting pmf is taken into account in line 87.
  Please feel free to ask further questions if you have.

[FL77N]

Thank you for the detailly reply! I notice that in the RankSortLoss/mmdet/models/losses/ranking_losses.py Line 87 in b41f64d sorting pmf is used to compute the gradient caused by the sort loss, however, (\ell_S(i)- \ell_S^*(i) should mutiply the sort pmf like the rank error. I clear that for the gradient of sort error is calculated correctly, the BP will be fine. Actually, Our final goal is the gradient.

[FL77N]

Sry! I got it! We will compute the integral of (current_sorting_error - target_sorting_error)*sorting_pmf for sorting_error[ii], then sorting_error[ii] should equal (current_sorting_error - target_sorting_error) as same as in the paper.