Paper:
We describe an explainable AI saliency map method for use with deep convolutional neural networks (CNN) that is much more efficient than popular gradient methods. It is also quantitatively similar and better in accuracy. Our technique works by measuring information at the end of each network scale which is then combined into a single saliency map. We describe how saliency measures can be made more efficient by exploiting Saliency Map Order Equivalence. Finally, we visualize individual scale/layer contributions by using a Layer Ordered Visualization of Information. This provides an interesting comparison of scale information contributions within the network not provided by other saliency map methods. Since our method only requires a single forward pass through a few of the layers in a network, it is at least 97x faster than Guided Backprop and much more accurate. Using our method instead of Guided Backprop, class activation methods such as Grad-CAM, Grad-CAM++ and Smooth Grad-CAM++ will run several orders of magnitude faster, have a significantly smaller memory footprint and be more accurate. This will make such methods feasible on resource limited platforms such as robots, cell phones and low cost industrial devices. This will also significantly help them work in extremely data intensive applications such as satellite image processing. All without sacrificing accuracy. Our method is generally straight forward and should be applicable to the most commonly used CNNs 1 .

Review:
The paper presents a new approach, SMOE scale, to extract saliency maps from a neural network. The approach is deemed as efficient, because it does not require one or multiple backward passes, as opposed to other approaches based on gradients. The main idea is to process the output activation tensors of a few selected layers in a deep network using an operator combining mean and std.dev. called SMOE scale. The result of this operator can be combined through different scales to obtain a global saliency map, or visualized in such a way that shows the consistency of saliency maps at different scales. Experiments show some improvement against traditional gradient-based approaches.
This paper is interesting in that it provides a different way to extract saliency maps from a network. The visualization at multiple scales is also nice and while I do not perfectly agree with the HSV encoding in Fig.2, I do see the potential. Being efficient is also a nice to have. There are three issues, however, which limits the novelty of the paper. First, the SMOE metric does not seem to bring much improvement compared to simple metrics. Second, the few comparisons made against other methods do not reveal a significant improvement. Third, at core, the paper suggests that the "high efficiency" of this approach is one of its main advantages, a statement I do not forcibly agree with. More details follow.
For the first element, we have to consider the paper as the combination of two things. 1) the use of activation maps as source of salient information, and 2) the way we should process these activation maps. 1) is relatively straightforward, so the core of the contribution should lie in 2). However, while the SMOE scale method definition (eq.2) is sound, it does not bring valuable improvement compared to other "trivial" metrics, like standard deviation. For instance, Fig.4 caption tells that "SMOE Scale differentiates itself the most early on in the network", but it is actually only for the very first scale layer. At every other scale, standard deviation (for instance) is at least as good. Same thing can be said about Table 4 in appendix, and also about Table 2 (and the scores of Trunc. Normal Entropy). Overall, while SMOE is indeed novel, it is not highly convincing.
On a side note about the SMOE description, I did not find the list of "conditions and assumptions" at the beginning of Sec. 2.1. It looks more like an after-thought over which the proposed method coincidentally fits. Moreover, point 3 is kind of conflicting in its formulation.
For the second element, the improvements in KAR and ROAR scores are quite minimal. It does seem to have an edge on KAR score, but not by a huge amount. Additionally, the methods compared are relatively old. To give just two examples of missing new techniques, Smooth Grad-CAM++ (Omeiza et al.) or even Grad-CAM++ (Chattopadhay et al.) would presumably obtain better performances. Moreover, Smooth Grad-CAM++ allows to target a particular feature map or even a specific neuron, which makes it even more relevant to this work.
Finally, a note about efficiency. Generally speaking, I agree that it is always good to be more efficient. However, I fail to see the high importance given to efficiency for this particular problem. Sure, gradient-based approaches are probably not suitable to online, in-network applications, but is it an important requisite? Computing saliency maps on a subset of the dataset once a few epochs already gives a good idea of what the network is doing. In any case, since these saliancy maps are intended for human use, I am not convinced about the importance of computing them for each training example at each epoch. Overall, in my opinion, being efficient at generating saliency maps is a nice to have, but not much more.
Some general comments:
- In Sec. 2.2, the last "con" seems a bit out of place. This could be applied to pretty much anything.
- Sec. 2.3 is interesting, but the explanations are convoluted. In essence, what should be said is 1) value encompasses the importance of a pixel, 2) saturation presents the max-min of the distribution and 3) hue shows the position in the network. Also, superimposing these HSV maps over gray scale version of the image like is Fig.2 is difficult to analyze because the "gray" of the image can be confused with the saturation channel. 
- On p.2, "this is proceeded" -> "this is preceded"?
In summary, this paper presents a nice way of generating saliency maps from activations inside a network. However, the comparison to other approaches does not show a clear advantage, and the related work (and experiments) lacks recent techniques. I would thus ask this general question: what is the "selling point" of this method? The current focus on efficiency does not convince me. That being said, there are no clear flaws in the paper, so I am open to reconsider my assessment if improvements are made to the paper (better descriptions, comparison with more recent techniques, experimental justification for SMOE instead of simpler approaches, etc.).
On a final note, there is also the Score-CAM approach (Wang et al.) that looks similar (in the idea of using activation maps). I did not consider it in this review since it was published a few weeks ago on Arxiv, but it could be interesting to discuss it nevertheless.