2.3.2. Grad-CAM++

Grad-CAM++ is a generalization to Grad-CAM and provides better visualizations of the network decisions [48]. In Grad-CAM++, the weights *w<sup>k</sup> c* are computed as follows [51]:

$$w\_c^k = \sum\_i \sum\_j \alpha\_{ij}^{k\varepsilon}.ReLU\left(\frac{\partial y^\varepsilon}{\partial A\_{ij}^k}\right) \tag{3}$$

where *αkcij* are weighting coefficients for the pixel-wise gradients for class *c* and feature map *A<sup>k</sup>* and are defined as follows:

$$\alpha\_{ij}^{kc} = \frac{\frac{\overline{\partial^2 y^c}}{\left(\overline{\partial A\_{ij}^k}\right)^2}}{2\frac{\overline{\partial^2 y^c}}{\left(\overline{\partial A\_{ij}^k}\right)^2} + \sum\_{a} \sum\_{b} A\_{ab}^k \left\{ \frac{\overline{\partial^3 y^c}}{\left(\overline{\partial A\_{ij}^k}\right)^3} \right\}}\tag{4}$$
