The paper introduces a new pruning method for neural networks based on the second-order Taylor expansion and compares the results against a first-order method and brute-force pruning. It performs experiments of the three methods on several toy examples - including a two-layer network on MNIST - and shows that the second-order method behaves much worse then the brute-force baseline. In addition, from the success of the brute-force pruning the authors conclude that the hypothesis of Mozer et al - that neurons either contribute to performance or cancel out the effect of other neurons - is probably correct.  The authors put in considerable effort to explain all details of the paper clearly and at length, so the content of the paper is accessible even to people novel to pruning methods. Additionally, the authors have very carefully answered all questions that were coming up through the pre-review and have been very responsive.  My major criticism is that the paper lacks focus, does not have a concrete conclusion and does not explain what it adds to the literature. To make this apparent, I here summarise each paragraph of the conclusion section:  Paragraph 1: We do not benchmark / Pruning methods do not fare well against brute-force baseline / Some evidence for hypothesis of Mozer & Smolensky, but further investigation needed  Paragraph 2: Introduced 2nd order Taylor method / Does not fare well against baseline  Paragraph 3: Re-training may help but is not fair  Paragraph 4: Brute-force can prune 40-70% in shallow networks  Paragraph 5: Brute-force less effective in deep networks  Paragraph 6: Not all neurons contribute equally to performance of network  The title of the paper and answers of the authors to the pre-review questions seemed to strongly suggest that the paper is not about the new second-order method, is not about benchmarking pruning algorithms but is instead about the learnt representations. But only two or three sentences in the conclusion, and no sentence in the part on results in the abstract, even refers to neural representations. In an answer to the pre-review questions the authors stated:  > Furthermore, we do not have to accept the conclusion that re-training is a necessary part of pruning because a brute force search reveals that neurons can in fact be  > pruned from trained networks in a piecemeal fashion with no retraining and minimal adverse effect on the overall performance of the network. This would be  > impossible if neurons did not belong to the distinct classes we describe."  But this can already be concluded from the 2nd order method, which has a similar characteristic and is based on other 2nd order methods (not shown here). What is the motivation to introduce a new 2nd order method here?  In addition, some other minor conclusions about representations - in particular the cancellation effect - might be based on side-effects of the greedy serial pruning method. Optimally, one would need to consider all the different ways of pruning (which, of course, scales exponentially with the number of neurons and is computationally infeasible). Notably, the authors do consider this limitation in the context of conventional pruning methods in the conclusions: "Third, we assumed that pruning could be done in a serial fashion [...]. We found that all of these assumptions are deeply flawed in the sense that the true relevance of a neuron can only be partially approximated [...] at certain stages of the pruning process". But the brute-force pruning process is also serial - why is that not a problem?  All in all it is unclear to me what the paper adds: there are little conclusions regarding the learnt representations nor is there sufficient benchmarking against state-of-the-art pruning methods. I would suggest to focus the paper in the following way: first, use a state-of-the-art pruning method from the literature (that works without re-training) or do not use any other pruning methods besides brute-force (depending on whether you want to compare pruning methods against brute-force, or want to learn something about the learnt representations). In this way you need to write little about this second-order tuning methods, and readers are not so easily confused about the purpose of this paper (plus it will be considerably shorter!). Then concentrate on 2-layer MNIST and a deeper CIFAR10 network. Further focus the paper by adding an itemised list of the exact contributions that you make, and streamline the paper accordingly. These measures could strongly boost the impact of your work but will require a major revision.  PS: I think the confusion starts with the following sentence in the abstract: "In this work we set out to test several long-held hypothesis about neural network learning representations and numerical approaches to pruning." Both aspects are pretty orthogonal, but are completely mixed up in the paper.
Output: en