Paper:
Machine learning and in particular deep learning approaches have outperformed many traditional techniques in accomplishing complex tasks such as image classfication (Krizhevsky et al., 2012), natural language processing or speech recognition . Most of the state-of-the art deep networks have complex architecture and use a vast number of parameters to reach this superior performance. Though these networks use a large number of learnable parameters, those parameters present significant redundancy (de Freitas, 2013). Therefore, it is possible to compress the network without much affecting its accuracy by eliminating those redundant and unimportant parameters. In this work, we propose a three stage compression pipeline, which consists of pruning, weight sharing and quantization to compress deep neural networks. Our novel pruning technique combines magnitude based ones with dense sparse dense Han et al. (2016) ideas and iteratively finds for each layer its achievable sparsity instead of selecting a single threshold for the whole network. Unlike previous works, where compression is only applied on networks performing classification, we evaluate and perform compression on networks for classification as well as semantic segmentation, which is greatly useful for understanding scenes in autonomous driving. We tested our method on LeNet-5 and FCNs, performing classification and semantic segmentation, respectively. With LeNet-5 on MNIST, pruning reduces the number of parameters by 15.3 times and storage requirement from 1.7 MB to 0.006 MB with accuracy loss of 0.03%. With FCN8 on Cityscapes, we decrease the number of parameters by 8 times and reduce the storage requirement from 537.47 MB to 18.23 MB with class-wise intersection-over-union (IoU) loss of 4.93% on the validation data.

Review:
quality: this paper is of good quality
clarity: this paper is very clear
originality: this paper combines original ideas with existing approaches for pruning to obtain dramatic space reduction in NN parameters.
significance: this paper seems significant.
PROS
- a new approach to sparsifying that considers different thresholds for each layer
- a systematic, empirical method to obtain optimal sparsity levels for a given neural network on a task.
- Very interesting and extensive experiments that validate the reasoning behind the described approach, with a detailed analysis of each step of the algorithm.
CONS
- Pruning time. Although the authors argue that the pruning algorithm is not prohibitive, I would argue that >1 month to prune LeNet-5 for MNIST is certainly daunting in many settings. It would benefit the experimental section to use another dataset than MNIST (e.g. CIFAR-10) for the image recognition experiment.
- It is unclear whether this approach will always work well; for some neural nets, the currently used sparsification method (thresholding) may not perform well, leading to very little final sparsification to maintain good performance.
- The search for the optimal sparsity in each level seems akin to a brute-force search. Although possibly inevitable, it would be valuable to discuss whether or not this approach can be refined.
Main questions
- You mention removing "unimportant and redundant weights" in the pruning step; in this case, do unimportant and redundant have the same meaning (smaller than a given threshold), or does redundancy have another meaning (e.g. (Mariet, Sra, 2016))?
- Algorithm 1 finds the best sparsity for a given layer that maintains a certain accuracy. Have you tried using a binary search for the best sparsity instead of simply decreasing the sparsity by 1% at each step? If there is a simple correlation between sparsity and accuracy, that might be faster; if there isn't (which would be believable given the complexity of neural nets), it would be valuable to confirm this with an experiment.
- Have you tried other pruning methods than thresholding to decide on the optimal sparsity in each layer?
- Could you please report the final accuracy of both models in Table 2?
Nitpicks:
- paragraph break in page 4 would be helpful.