Paper:
The large memory requirements of deep neural networks limit their deployment and adoption on many devices. Model compression methods effectively reduce the memory requirements of these models, usually through applying transformations such as weight pruning or quantization. In this paper, we present a novel scheme for lossy weight encoding which complements conventional compression techniques. The encoding is based on the Bloomier filter, a probabilistic data structure that can save space at the cost of introducing random errors. Leveraging the ability of neural networks to tolerate these imperfections and by re-training around the errors, the proposed technique, Weightless, can compress DNN weights by up to 496× with the same model accuracy. This results in up to a 1.51× improvement over the state-of-the-art.

Review:
This paper proposes an interesting approach to compress the weights of a network for storage or transmission purposes. My understanding is, at inference, the network is 'recovered' therefore there is no difference in processing time (slight differences in accuracy due to the approximation in recovering the weights).
- The idea is nice although it's applicability is limited as it is only for distribution of the model and storing (is storage really a problem?). 
Method:
- the idea of using the Bloomier filter is new to me. However, the paper is miss-leading as the filtering is a minor part of the complete process. The paper introduces a complete pipeline including quantization, and pruning to maximize the benefits of the filter and an additional (optional) step to achieve further compression. 
- The method / idea seems simply and easy to reproduce (except the subsequent steps that are not clearly detailed).
Clarity
- The paper could improve its clarity. At the moment, the Bloomier is the core but needs many other components to make it effective. Those components are not detailed to the level of being reproducible.
- One interesting point is the self-implementation of the Deep compression algorithm. The paper claims this is a competitive representation as it achieves better compression than the original one. However, those numbers are not clear in tables (only in table 3 numbers seem to be equivalent to the ones in the text). This needs clarification, CSR achieves 81.8% according to Table 2 and 119 according to the text.
Results:
- Current results are interesting. However I have several concerns:
1) it is not clear to me why assuming similar performance. While Bloomier is weightless the complete process involves many retraining steps involving performance loss. Analysis on this would be nice to see (I doubt it ends exactly at the same number). Section 3 explicitly suggest there is the need of retraining to mitigate the effect of false positives which is then increased with pruning and quantization. Therefore, would be nice to see the impact in accuracy (even it is not the main focus of the work). 
2) Resutls are focused on fully connected layers which carry (for the given models) the larger number of weights (and therefore it is easy to get large compression numbers). What would happen in newer models where the fully connected layer is minimal compared to conv. layers? What about the accuracy impact there? Let's say in a Resnet-34.
3) I would like to see further analysis on why Bloomier filter encoding improves accuracy (or is a typo and meant to be error?) by 2%. This is a large improvement without training from scractch.
4) It is interesting to me how the retraining process is 'hidden' all over the paper. At the beginning it is claimed that it takes about one hour for VGG-16 to compute the Bloomier filters. Howerver, that is only a minimal portion of the entire pipeline. Later in the experimental section it is mentioned that 'tens of epochs' are needed for retraining (assuming to compensate for errors) after retraining for compensating l1 pruning?.... tens of epochs is a significant portion of the entire training process assuming VGG is trained for 90epochs max.
5) Interestingly, as mentioned in the paper, this is 'static compression'. That is, the model needs to be completely 'restored' before inference. This is miss-leading as an embedded device will need the same requirements as any other at inferece time(or maybe I am missing something). That is, the benefit is mainly for storing and transmission.
6) I would like to see the sensibility analysis with respect to t and the number of clusters. 
7) As mentioned before, LeNet is great but would be nice to see more complicated models (even resnet on CIFAR). These models are not only large in terms of parameters but also quite sensitive to modifications in the weight structure.
8) Results are focused on a single layer. What happens if all the layers are considered at the same time? Here I am also concerned about the retraining process (fixing one layer and retraining the deeper ones). How is this done using only fully connected layers? What is the impact of doing it all over the network (let's say VGG-16 from the first convolutional layer to the very last).
Summary:
All in all, the idea has potential but there are many missing details. I would like to see clearer and more comprehensive results in terms of modern models and in the complete model, not only in the FC layer, including accuracy impact.