Deep neural networks trained on a wide range of datasets demonstrate impressive transferability. Deep features appear general in that they are applicable to many datasets and tasks. Such property is in prevalent use in real-world applications. A neural network pretrained on large datasets, such as ImageNet, can significantly boost generalization and accelerate training if fine-tuned to a smaller target dataset. Despite its pervasiveness, few effort has been devoted to uncovering the reason of transferability in deep feature representations. This paper tries to understand transferability from the perspectives of improved generalization, optimization and the feasibility of transferability. We demonstrate that 1) Transferred models tend to find flatter minima, since their weight matrices stay close to the original flat region of pretrained parameters when transferred to a similar target dataset; 2) Transferred representations make the loss landscape more favorable with improved Lipschitzness, which accelerates and stabilizes training substantially. The improvement largely attributes to the fact that the principal component of gradient is suppressed in the pretrained parameters, thus stabilizing the magnitude of gradient in backpropagation.
3) The feasibility of transferability is related to the similarity of both input and label. And a surprising discovery is that the feasibility is also impacted by the training stages in that the transferability first increases during training, and then declines. We further provide a theoretical analysis to verify our observations.
I thank the authors for the clarifications and the modifications to the paper. However, I still lean towards rejection. While the authors provided detailed explanations on some of my points here, most of these are still not in the paper, so the reader would still probably be confused. There are new figures in the appendix, but they are not referred to from the text. The paper feels like a hastily compiled collection of weakly related, somewhat anecdotal and not necessarily clearly explained and motivated experiments. While I believe there is interesting content, with the current presentation style it is really difficult to digest. As an advice, I think it may be better to not squeeze in all the results into one paper, but rather focus on some aspects and analyze them really well, with clear explanation, motivation, and preferably with demonstrating practical gains that result from the analysis - not just hypothetical, but supported by experiments.
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The paper studies transfer of representations learned by deep networks across datasets and tasks. Namely, the paper analzes the standard setup with pre-training on one dataset and further fine-tuning on a different  dataset. Results include both experiments and theory. On the experimental side, the focus is mainly on TODO. On the theory side, an analysis of transfer in two-layer fully connected networks, based on the ICML-2019 work of Arora et al., is proposed. 
I lean towards rejecting the paper, since the presentation and the technical quality are somewhat substandard. This is mainly based on evaluation of the experimental results, since I am not an expert in this subfield of theory and was therefore not able to check the statements and the proofs thoroughly. On the presentation side, many details are missing, which often makes understanding difficult and will likely lead to the results not being reproducible. On the experiments side, the issue is that they are quite anecdotal and have multiple confusing or questionable details, as specified below.
Pros:
1) An interesting topic of trying to understand generalization and transfer in deep learning
2) Multiple types of experiments, including visualizations of loss landscapes at convregence and at initialization, plots of Hessian eigenvalues, measuring the deviation of the weights from their initial values, measuring the variance of the gradients of the weights, measuring the transfer between different datasets, measuring the transfer performance depending on the durarion of pre-training.
3) Theoretical analysis. As mentioned, I cannot really judge about the quality of the results.
Cons:
1) The presentation is quite confusing. 
1a) The paper includes many different experiments as well as theory, and it is not very clear how these all come together and what message do they give to the reader. The paper states at one point that it "may stimulate further algorithmic advances", and it would be great if there was a bit more elaboration on this. 
1b) Experimental methodology is not presented in the main paper and not referred to. Some of it is described in the appendix, but also not too detailed, for instance the duration of ResNet training is not clear, the details of loss landscape visualization are confusing (for instance, the phrase "... i.e. 0.1× gradient and a total of 200 × 200 grids"), 
1c) The paper is over 9 pages, which is more than the recommended length of 8 pages.
1d) Scaling in Figure 8(b) is quite suboptimal, it is impossible to read the test accuracy results.
1e) Minor issues:
 - No color-code in Figure 3 (unclear what values do the colors correspond to) and it does not seem to be referred to in the text. 
 - Page 5: "predictive" -> "predictable"?
 - Page 6 "While pretraining on sufficiently large datasets..." - I do not think the experiments tell anything about the dependence of the effect on the size of the dataset, so this phrasing is not justified
2) I found many of the experiments confusing or unconvincing. This is partially affected by the aforementioned issues with presentation.
2a) In Table 1 and Figure 2, it is unclear if difference in generalization between the dataesets is due to similarity to ImageNet (by the way, ImageNet is only mentioned in the caption of Table 1, but not in the text) or due to the inherent properties of the datasets (perhaps some are naturally more difficult or prone to overfitting). I think numbers for training from scratch would be helpful for disambiguating the two cases.
2b) It is unclear why is the norm difference normalized by the square root of the number of target examples. This choice is not justified and it seems it can very noticeably affect the results in counter-intuitive way. For instance, if I understand right, if one duplicates each example in the training set, these values will change, which seems somewhat counter-intuitive. Would it make more sense to normalize by the initial norm of the weights?
2c) In Figure 4, it is unclear if the permutations of the weights are accounted for. The output of a deep network is invariant under a wide variety of weight permutations, and it is natural that networks trained from different random initializations may converge to weights permuted in different ways. In order to meaningfully compare the weight vectors of these networks, one would have to first "align" them, which is a non-trivial task. Another issue I have with the results on Figure 4 is that I don't find them all that counter-intuitive: it seems natural that the weights stay relatively close to the pre-trained network when fine-tuned for that (paritally because the aforementioned permutation symmetry is already largely broken during pre-trianing).
2d) It is unclear which downstream task is analyzed in Figure 6. Moreover, the plot seems to mix two factors: magnitue of the gradient and the smoothness of the loss landscape. Would it not make more sense to make fixed-size steps in the direction of the gradient? Moreover, I am wondering if the difference between the loss values is simply because the overall loss magnitude is larger for the randomly initialized network?
2e) A few parts of subsection 5.1 are confusing. It is not clear where does the interpretation of Figure 8 follow from (perhaps partially because figure 8(b) is partially difficult to read). \psi and W are not defined. What does it move that the weight matrices "show no improvement"? Where are the results on Caltech-101 and Webcam? Why is Food-101 mentioned in the text, but CUB-200 shown in the plots?