Deep Convolutional Neural Networks (CNNs) have been repeatedly shown to perform well on image classification tasks, successfully recognizing a broad array of objects when given sufficient training data. Methods for object localization, however, are still in need of substantial improvement. In this paper, we offer a fundamentally different approach to the localization of recognized objects in images. Our method is predicated on the idea that a deep CNN capable of recognizing an object must implicitly contain knowledge about object location in its connection weights. We provide a simple method to interpret classifier weights in the context of individual classified images. This method involves the calculation of the derivative of network generated activation patterns, such as the activation of output class label units, with regard to each input pixel, performing a sensitivity analysis that identifies the pixels that, in a local sense, have the greatest influence on internal representations and object recognition. These derivatives can be efficiently computed using a single backward pass through the deep CNN classifier, producing a sensitivity map of the image. We demonstrate that a simple linear mapping can be learned from sensitivity maps to bounding box coordinates, localizing the recognized object. Our experimental results, using real-world data sets for which ground truth localization information is known, reveal competitive accuracy from our fast technique.
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SUMMARY
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The paper proposes a method to extend the output of a network trained for visual object recognition (i.e. image classification) with bounding box coordinates that can serve to localize the recognized object. 
This process is referred to as "object localization", and it resembles to some extent the object detection task.
Object localization is achieved by analyzing the absolute values of the gradients in the last convolutional layer (referred to as "attention map" in the paper) with regard to the pixel locations of the input image.
Then, a linear model is trained in order to predict the bounding box coordinates that serve to localize the recognized object instance. This is different from traditional object detection methods, which learn how to predict bounding boxes directly from image pixels. The paper claims that by learning how to predict bounding boxes from sensitivity maps the amount of needed training data is reduced.
Experiments on the PASCAL VOC'07 and a subset of the ImageNet'12 dataset show the performance of the proposed method.
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REVIEW
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The content of the paper is clear, has a good flow. Moreover, the proposed method is sound and relatively easy to follow. The reported experiments show good performance of the proposed method. In addition, there seems to be hints that the proposed method has a computation speed that makes it suitable for on-the-fly computations.
My main concerns with the manuscript are the following:
The manuscript proposes to analyze the internal spatial activations/gradients of a network trained for object recognition with the goal of exploiting internally encoded cues that can serve for object localization. At the high level, as recognized in the manuscript, this is very similar to the work from Zhou et al.,CVPR'16 with some differences regarding how the attention maps are defined, and if additional components are added to the network.
In addition, the way in which the proposed object localization problem is formulated bears resemblance to work on weakly-supervised object detection where object detectors are trained by using only image-level annotations (no bounding box annotations are used). 
Keeping these two groups of work in mind, I find the contribution of the proposed method limited. 
Perhaps a explicit positioning with respect to this work is required.
Section 2.3 states that there two possibilities, i.e. max or average. to aggregate the sensitivity maps obtained for each of the RGB channels from images. However, in Section 3.2, it is stated that the max operation is used for the Pascal VOC'07 dataset while the average operation was used for ImageNet data. This inconsistency in the way these maps are aggregated makes it hard to observe if there is a difference or trend across these two operations. Is there a reason why different operations were applied to different datasets? I recommend applying both operations on both datasets and discuss observations from the results.
While the proposed method have been evaluated on two datasets, and compared with respect to standard classic baselines, a deeper evaluation analyzing the inner workings of the method is not conducted.
In this regard, in addition to evaluating the effect of the method to aggregate sensitivity maps accross color channels (previously mentioned), I suggest reporting results by changing the threshold used in intersection over union (IoU) measure used to verify matching (Section 3,1). In addition, I am curious about the performance of the method in the two following scenarios: i) when multiple instances of the recognized object are present in the image, and ii) when instances of other distractor classes are present in the image.
In several parts of the manuscript, e.g. Sec. 1, 3.4, and 4, claims regarding the speed of the proposed method are made. However, there is no evaluation focusing on this aspect that could be used to support this claims. In this regard, either a evaluation focusing on the computation speed of the proposed method should be conducted or claims regarding to computation speed should be toned down.
  
Finally, the first title of the manuscript, i.e. "Interpreting Deep Neural Networks", suggests that the manuscript will cover topics regarding model interpretation of DNNs. However, model interpretation as such is never touched wich makes this title somewhat misleading. In fact the main theme of the manuscript is about object localization/detection, hence the second part of its title: "Fast Object Localization via Sensitivity Analysis". 
If this manuscript is to be accepted, the first part of the title should be removed.
I would appreciate if my main concerns are addressed in the rebuttal.