Venue: ICLR 2017 conference

Reviews:

final_score: rating: null
review_content: I am trying to understand the necessity of the appendix in light of modern technologies.  Can you please clarify: with the pervasive availability and ease of automatic differentiation, are there additional insights to be gained from this appendix and this detailed computation, and if so, what?  I appreciate the genuine effort to calculate this derivative, and I'm simply trying to understand if there is a more subtle point here. 
review_title: appendix a

final_score: rating: 3: Clear rejection
review_content: The authors have put forward a sincere effort to investigate the "fundamental nature of learning representations in neural networks", a topic of great interest and importance to our field.  They propose to do this via a few simplistic pruning algorithms, to essentially monitor performance decay as a function of unit pruning.  This is an interesting idea and one that could potentially be instructive, though in total I don't think that has been achieved here.  

First, I find the introduction of pruning lengthy and not particularly novel or surprising.  For example, Fig 1 is not necessary, nor is most of the preamble section 3.3.0.  The pruning algorithms themselves are sensible (though overly simplistic) approaches, which of course would not matter if they were effective in addressing the question.  However, in looking for contributions this paper makes, an interesting, pithy, or novel take on pruning is not one of them, in my opinion.

Second, and most relevant to my overall rating, Section 4 does not get deeper than scratching the surface.  The figures do not offer much beyond the expected decay in performance as a percentage of neurons removed or gain value.  The experiments themselves are not particularly deep, covering a toy problem and MNIST, which does not convince me that I can draw lessons to the broader story of neural networks more generally.  

Third, there is no essential algorithmic, architectural, or mathematical insight, which I expect out of all but the most heavily experimental papers.
review_title: a good effort at understanding representations via pruning, but unclear overall contribution, with less than necessary results and methodological novelty 

final_score: rating: null
review_content: The page limit are 8 pages, you have 23.
review_title: Page limit

final_score: rating: null
review_content: The paper describes and analyses a more advanced method for pruning neural networks. The analysis seems quite solid but after a first read I am left with the following three comments that I hope the authors can address:

1) I find the writing and the figures excessively long and fairly repetitive. E.g. all figures show the gain from 0 to 10, but I am not sure what I should learn from gains > 1 (other then sanity checks)? At least that part of the figure, which takes up 90% of the space, should be thoroughly reduced. Plus, the take-away gist of the paper is quite bounded, in my opinion not justifying a paper of more then eight pages.

2) Your title includes “new perspectives on learning representations through the lens on pruning”, and it is indeed an interesting observation that large parts of the neurons can be pruned and the representation is thus not evenly spread. However, this has been observed earlier (e.g. by brute-force pruning), so I am not sure how your methods expands on this. In the conclusions you argue that your results suggest that Mozer was right in his dualist view, in particular that many neurons simply cancel each other. You seem to base this conclusion on the “bumpy” error landscape you get for successive pruning with your method, but if at all the “smooth” results from the brute-force pruning suggests that this is rather an artefact of your method then any insight into the neural representations.

3) Currently I feel your paper is not so much about representations but about a more efficient method for pruning. However, all results you show are “toy examples” in the sense that they can be solved with brute-force pruning; no applications on realistically sized networks (e.g. VGG) are shown.
review_title: What are the new insights regarding representations?

final_score: rating: 3: Clear rejection
review_content: I did enjoy reading some of the introductions and background, in particular that of reminding readers of popular papers from the late 1980s and early 1990s. The idea of the proposal is straight forward: remove neurons based on the estimated change in the loss function from the packpropagation estimate with either first or second order backpropagation. The results are as expected that the first order method is worse then the second order method which in turn is worse than the brute force method.

However, there are many reasons why I think that this work is not appropriate for ICLR. For one, there is now a much stronger comprehension of weight decay algorithms and their relation to Bayesian priors which has not been mentioned at all. I would think that any work in this regime would require at least some comments about this. Furthermore, there are many statements in the text that are not necessarily true, in particular in light of deep networks with modern regularization methods. For example, the authors state that the most accurate method is what they call brute-force. However, this assumes that the effects of each neurons are independent which might not be the case. So the serial order of removal is not necessarily the best. 

I also still think that this paper is unnecessarily long and the idea and the results could have been delivered in a much compressed way. I also don’t think just writing a Q&A section is not enough, and the points should be included in the paper.

review_title: null

final_score: rating: 3: Clear rejection
review_content: 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.
review_title: Looking at feature representations from the point of pruning is an interesting topic, but the conclusions nor the focus of this paper are clear

Meta-review: The paper does not seem to have enough novelty, and the contribution is not clear enough due to presentation issues.
Decision: Reject