text: The authors analyze show theoretical shortcomings in previous methods of explaining neural networks and propose an elegant way to remove these shortcomings in their methods PatternNet and PatternAttribution. The quest of visualizing neural network decision is now a very active field with many contributions. The contribution made by the authors stands out due to its elegant combination of theoretical insights and improved performance in application. The work is very detailed and reads very well. I am missing at least one figure with comparison with more state-of-the-art methods (e.g. I would love to see results from the method by Zintgraf et al. 2017 which unlike all included prior methods seems to produce much crisper visualizations and also is very related because it learns from the data, too). Minor questions and comments:* Fig 3: Why is the random method so good at removing correlation from fc6? And the S_w even better? Something seems special about fc6. * Fig 4: Why is the identical estimator better than the weights estimator and that one better than S_a? * It would be nice to compare the image degradation experiment with using the ranking provided by the work from Zintgraf which should by definition function as a kind of gold standard * Figure 5, 4th row (mailbox): It looks like the umbrella significantly contributes to the network decision to classify the image as "mailbox" which doesn't make too much sense. Is is a problem of the visualization  (maybe there is next to no weight on the umbrella), of PatternAttribution or a strange but interesting a artifact of the analyzed network? * page 8 "... closed form solutions (Eq (4) and Eq. (7))" The first reference seems to be wrong. I guess Eq 4. should instead reference the unnumbered equation after Eq. 3.