The following peer review was solicited as part of the Distill review process.

The reviewer chose to waive anonymity. Distill offers reviewers a choice between anonymous review and offering reviews under their name. Non-anonymous review allows reviewers to get credit for the service they offer to the community.

Distill is grateful to Ruth Fong for taking the time to review this article.

General Comments

• more examples beyond the 4 that are used throughout would be appreciated (i.e., in the last figure, consider adding more examples; why does the owl example look ""better"" for integrated gradients than for expected gradients)
• how does expected gradients stand up to other desirata for interpretability (i.e., Sanity Checks [Adebayo et al., NeurIPS 2018], Lipton ICML Workshop 2016)
• provide more explanation for sum of cumulative gradients for expected gradients (i.e., why is it desirable that the red line is close to the blue line? what does that mean?)

Small suggestions to improve readability:

1. increase size of labels on diagrams (i.e., slider ticklabels for alpha are unreadable, y-axis ticklabels on eq 4 graph is unreadable)
2. add a bit more explanation around figure of first 4 equations (in particular, explanation of red line [eq 4] -- is this a mean or a sum?; highlight in caption more clearly that red line is sum of cumulative gradient at current alpha over all pixels)
3. provide a brief explanation (i.e., a footnote) for how is a scalar extracted per feature [i.e., pixel] given the 3D RGB vector per feature (i.e., is the max(abs(dy/dx))) taken across color channels, as is done in Simonyan et al., 2014)?

Main weakness regarding ""Scientific Correctness & Integrity"" is a lacking discussion about related works and limitations:

• missing discussion with other highly related literature: SmoothGrad [Smilkov et al., arXiv 2017] and RISE [Petsiuk et al., BMVC 2018]
• should briefly discuss that inputs being presented (interpolation between two images) are outside the training domain
• generally missing citations and mention of other kinds of attribution methods besides path ones
• room to improve discussion on single input choice (what about other typical choices for the baseline value besides a constant color, such as random noise or blurred input [Fong and Vedaldi, 2017])
• to improve reproducibility, having a ""repro in colab notebook"" button for at least one of the figures would be a nice to have

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Any concerns or conflicts of interest that you are aware of?: No known conflicts of interest
What type of contributions does this article make?: Both explanation of existing methods (i.e., integrated gradients) and presentation of novel method (i.e., expected gradients)