Error in the implementation of the LRP Alpha1_Beta0_Rule

[romain-xu-darme]

❓ Questions and Help

I am currently attempting to use LRP to propagate relevance through a ResNet50 and I noticed that the implementation of the $LRP_{\alpha,\beta}$ rule for $\alpha=1$ and $\beta=0$ seems incorrect.
Indeed, if I look at the formula given in https://iphome.hhi.de/samek/pdf/MonXAI19.pdf, the rule is $$R_j=\sum_k \dfrac{(a_jw_{jk})^+}{\sum_j (a_jw_{jk})^+}R_k$$
However, by only removing the negative weights in the implementation of the class Alpha1_Beta0_Rule, the resulting rule in Captum seems to be
$$R_j=\sum_k \dfrac{a_j(w_{jk})^+}{\sum_j a_j(w_{jk})^+}R_k$$
In practice, and similar to the implementation proposed here, I believe that both positive AND negative weights should be split in order to compute the value $(a_jw_{jk})^+$ as $$(a_jw_{jk})^+ = a_j^+w_{jk}^+ + a_j^-w_{jk}^-$$
However, I'm not sure that the current Captum class PropagationRule really allows this sort of shenanigans as it rely mostly on forward and backward hooks.
Anyway, I would love to have the opinion of the developers on this subject. Have a nice day :)