c622c085c04eadc473f08541b255320e-Supplemental.pdf

The positive with the lowest rankx1 has a gradient in the good direction, since it leads to increasex1'sscore because the correct ordering is not reached (the negativeinstance WecanseeinFig.2bthatthis change enables tohavegradients inthecorrect directions forthetwopositiveinstancesx1 and x2 (tending to increase their scores), and for the negative instancex3 (tending to decrease its score). However there is still vanishing gradients. Overall, LSupAP has all the desired properties: i) A correct gradient flow during training, ii) No vanishing gradients while the correct ranking isnot reached, iii)Being anupper bound onthe AP lossLAP. We now write that each positive instance that respects the constraint ofLcalibr. A.3 Choiceofδ In the main paper we introduceδ in Eq. (4) to defineH .