Paper:
Real Time Image Saliency for Black Box Classifiers
In this work we develop a fast saliency detection method that can be applied to any differentiable image classifier. We train a masking model to manipulate the scores of the classifier by masking salient parts of the input image. Our model generalises well to unseen images and requires a single forward pass to perform saliency detection, therefore suitable for use in real-time systems. We test our approach on CIFAR-10 and ImageNet datasets and show that the produced saliency maps are easily interpretable, sharp, and free of artifacts. We suggest a new metric for saliency and test our method on the ImageNet object localisation task. We achieve results outperforming other weakly supervised methods.

Review:
The paper proposes an approach to learn saliency masks. The proposed approach is based on a neural network and can process multiple images per second (i.e. it is fast).
To me the paper is borderline, I would not object rejection or acceptance. I really believe in the concept of learning to explain a model and I think the paper has some good ideas. 
There are no obvious mistakes but there are clear limitations. 
-The saliency is only indirectly measured. Either through weakly supervised localisation or by the proposed saliency metric both these methods have clear limitations and I think these limitations should be discussed in the paper.
The weakly supervised location is not perfect as a measure. If the context in which an object appears is essential to determine its class, the object localisation does not have to correlate with saliency quality. The results on weakly supervised localisation are interesting, but I think there is a big caveat when using them as a quality metric for saliency.
The saliency metric is not perfect because of how it is applied. The estimated salient region is cropped. This crop is then rescaled to the original image size, with the original aspect ratio. This could introduce two artefacts. First, the change of the aspect ratio might impact how well it can be classified. Second in the proposed metric a small salient region is preferred. Since a small region is blown up heavily for re-classification the scale at which the object is now presented to the classifier might not be ideal. (Convnets are generally pretty translation invariant, but the scaling invariance must be learned, and there are  probably limits to this).
What is not discussed here is how much the masking model depends on the architecture for learning the masks? Did the authors at one point experiment with different architectures and how this influenced the result?
Minor comments
Are the results in Table 1 obtained for all classes or only for the correct class?
- Please specify with LRP variant and parameter setting was used for comparison. They have an epsilon, alpha-beta, and more variants with parameters.  
*** Post rebuttal edit ***
The fact that  how well the saliency metric works depends on the quality and the scale invariance of the classifier is strongly limiting the applicability of the proposed method. It can only be applied to networks having this invariance. 
This has important consequences:
-  The method cannot be used for models during the training phase, nor for models that do not exhibit this invariance. 
- This limit the applicability to other domains (e.g. spectrogram analysis with CNN's).
- The method is not generally applicable to black-box classifiers as claimed in the title.
Furthermore, the response hints at a strong dependence on the masking network. 
- As a result, it is not clear to me whether we are visualizing the saliency of the U-network or the masking network.
If these effects are properly discussed in the paper I think it is balanced enough for publication. If not it should not be published