where ri denotes the relative rate

where ri denotes the relative rate of change of the ith feature element value of the top conv layer. We randomly se- lect N images from the CASIA-WebFace [40] and add oc- clusions on the faces, then calculate the ris for every face pair. The metric MED to approximately represents the al- tered degree of the ith feature element under occlusions is obtained by calculating the median value of these ris. If the MED of a feature element is high when an area of the input face is occluded, then it will likely bring unreasonable noise into the final feature.In Figure 3 we show the MED values of feature elementsin 8 channels of the top conv feature maps under three types of occlusions. Obviously, the feature values are altered in a different way for different channels, elements of some channels change very little while elements of some chan- nels change drastically in the same spatial locations. This is interesting because in view of the receptive field, the same spatial location of different conv channels gather informa- tion from the same region of the input image, but they ac- tually react quite differently to occlusions. Therefore, webelieve the output dimension of Mθ should be the same as the top conv feature maps, which is C × W × H.