Paper:
Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations
We present a new approach to learn compressible representations in deep architectures with an end-to-end training strategy. Our method is based on a soft (continuous) relaxation of quantization and entropy, which we anneal to their discrete counterparts throughout training. We showcase this method for two challenging applications: Image compression and neural network compression. While these tasks have typically been approached with different methods, our soft-to-hard quantization approach gives results competitive with the state-of-the-art for both.

Review:
This paper proposed a unified end-to-end framework for training neural networks to get compressible representations or weights.
The proposed method encourages compressibility by minimizing the entropy of representation or weight.  Because the original entropy-based objective cannot be minimized directly, the authors instead relax the objective and use discretized approximations.
The proposed method also use an annealing schedule to start from a soft discretization to gradually transform to a hard discretization. 
My main concerns with this paper are on experiments and comparisons. The authors performed two sets of experiments, one on compressing representations of image and the other on compressing classifier weights.
For the image compression experiment, the proposed method offers visually appealing results but it is only compared to BPG and JPEG. I suggest the authors also include comparisons against other neural network based approaches [1].
In the weight compression experiment, the proposed method does not show advantage over previous state-of-the-art. The authors also noted this but argued that the proposed method is trained end-to-end while the previous methods have many hand designed steps. However, I would expect integrated end-to-end training to improve performance instead of hindering it. I suggest the authors investigate more and improve their method to fully realize the benefit of end-to-end training.
[1] Full Resolution Image Compression with Recurrent Neural Networks