Paper:
Various methods of measuring unit selectivity have been developed with the aim of better understanding how neural networks work. But the different measures provide divergent estimates of selectivity, and this has led to different conclusions regarding the conditions in which selective object representations are learned and the functional relevance of these representations. In an attempt to better characterize object selectivity, we undertake a comparison of various selectivity measures on a large set of units in AlexNet, including localist selectivity (Bowers et al., 2014), precision (Zhou et al., 2015, class-conditional mean activity selectivity (CCMAS) (Morcos et al., 2018), network dissection (Zhou et al., 2018a), the human interpretation of activation maximization (AM) images, and standard signaldetection measures. We find that the different measures provide different estimates of object selectivity, with precision and CCMAS measures providing misleadingly high estimates. Indeed, the most selective units had a poor hit-rate or a high falsealarm rate (or both) in object classification, making them poor object detectors. We fail to find any units that are even remotely as selective as the 'grandmother cell' units reported in recurrent neural networks. In order to generalize these results, we compared selectivity measures on a few units in VGG-16 and GoogLeNet trained on the ImageNet or Places-365 datasets that have been described as 'object detectors'. Again, we find poor hit-rates and high false-alarm rates for object classification.

Review:
The paper empirically studies the category selectivity of individual cells in hidden units of CNNs. It is a sort of "meta-study" and comparison of different metrics proposed to identify cells with a preference for a specific target category. The claimed finding is that there are no cells that are "sufficiently" selective to be called object detectors.
The paper is seemingly motivated by the authors' perceiving a contradiction: it is assumed that the power of neural networks is (among others) due to the distributed representation; whereas the presence of object detectors would, in the extreme case, mean that the representation is disentangled into a separate unit per category. It may be a matter of terminology, but this is where my disagreement with the authors start. I do not see a simplistic dichotomy, where one could or should determine which of the two interpretations is "right" or "wrong". In my view, which I believe is the mainstream interpretation, a distributed representation does not contradict the presence of specialised units. Some categories probably are easily identified by few distinctive features, so there will be more detector-like units; others are complex and hence more diffusely spread through the network; and of course there is no guarantee that the learned "object detectors" are tuned to exactly the target categories, after all it is the purpose of the network to gradually translate the data distribution to the label distribution - if the categories were directly apparent in the data, nearest-neighbour would be enough. So it is not only possible, but rather likely that the learned "object detectors" are to some degree driven by the statistics of the data, not the labels - e.g., there could be a highly selective "bird" unit which nevertheless has high false positive rate for any of the more specific bird species categories in the imageNet nomenclature. And vice versa, there could be a highly specific "Ferrari" detector that is so specialised that it has low recall for the "sports car" class (this case includes, among others, the case of viewpoint-specific detectors for certain categories). In the words of the paper, the "selective units are sensitive to some feature that is frequently, but not exclusively associated with the class" - I thought this is the standard majority view, not a surprising finding. In this context terminology matters: the study effectively tries to disprove that the network learns "near-perfect single output-category detectors", but who claims that it would do that?
I agree with the authors that there is by now a zoo of selectivity metrics that are not always highly correlated. But is that a problem? We have a zoo of quality metrics for many machine learning problems - that is not necessarily a weakness, but simply reflects the obvious fact that a single number is not enough to characterise performance in a complex cognitive task. It is the job of the researcher/user to chose the metric that s most suitable for their specific question, and to correctly interpret its numerical value.
Regarding the methodology, the paper did a lot of work to systematically crunch the numbers and analyse network units. It is a laudable effort that someone took on that job. A few technical decisions are unclear to me. Why analyse only some of the units? If one collects statistics over >2000 units of a fully connected layer, one might as well do the complete job and use all 4096 units. Similarly, why analyse only the correctly classified images? While it is clear that one must separately look at them, also the activations on incorrectly classified ones could provide valuable insights. E.g., do false positives of class X on average activate a certain "class X detector"? Why chose only the class with highest mean activation for CCMAS? That might be unrepresentative, e.g., a neuron might, for that particular class, always have high activation due to some very common background context, and still be not selective at all.
Regarding the results, I find them much less clear-cut than the paper claims. For example, I find it quite remarkable that some unit has 8% recall at perfect precision. After all, only approximately 0.1% of the images are in the correct category, so a unit that flags 8% of them without making a mistake is a pretty good detector for (part of) the target class, cf Fig. 3. Also regarding Fig. 2 / maximum informedness, the statistics actually do not look bad. Of course false alarm proportion remains high - but the chance level here is 99.9%, so even a 99% false alarm rate means that your unit can, on its own, reject 90% of the true negatives. I find the proposed "minimum condition" for an object detector (>50% recall at >50% precision) unrealistic: the top-1 accuracy of AlexNet is, to my knowledge, <63%. Even the complete network probably never reaches 50% recall for most classes.
Especially the user study - which is again a commendable effort - in my view does not confirm the claims. According to that study, almost 60% 0f all fc8 units are "object detectors", with very high conherence between humans and selectivity metrics.
Overall, while it is an interesting study, it remains unclear to me what I should learn from it. I don't see why different measures provide "misleading conclusions" that need to be rectified. Conclusions are the responsibility of the researcher interpreting the numbers, not of the formula to calculate some statistical performance metric. I am in a difficult situation here: the study is one of those things (like determining human performance on ImageNet, or re-coding some baseline where the original code is not available) where I find it valuable that someone did them in the community, but still I don't think they need a reviewed paper.  A note on the blog, or on arXiv, is enough.