X-GradCAM

Axiom-based GradCAM

Axiom-based GradCAM or X-GradCAM is an enhanced version of GradCAM that satisfies two explainability axioms—sensitivity and conservation.

Let's assume that $\mathcal{F}_l \in \R^{h \times w}$ is the $l^{th}$ feature map obtained from the penultimate convolutional layer ($h$ and $w$ are the height and width of the feature map) and $\mathcal{F}_l(i,j)$ represents the activation of the $(i,j)^{th}$ neuron in the $l^{th}$ feature map (total $L$ feature maps in $\mathcal{F}$).

The X-GradCAM algorithm optimizes for linear combination weights $\alpha_l$ such that the resulting CAM $C^{\ \text{x-grad}}(i,j) = \sum_{l} \alpha_l \cdot \mathcal{F}_l(i,j)$ satisfies both axioms as follows.

Sensitivity is a property in which each feature’s contribution to the explanation should equal the change in the network prediction caused by removing that feature from the input. In other words, given the network prediction $f^{k^*}(X)$,