Deep unfolding methods design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence and higher accuracy than the original optimization methods. In this line of research, this paper develops a novel deep recurrent neural network (coined reweighted-RNN) by unfolding a reweighted 1 -1 minimization algorithm and applies it to the task of sequential signal reconstruction. To the best of our knowledge, this is the first deep unfolding method that explores reweighted minimization. Due to the underlying reweighted minimization model, our RNN has a different soft-thresholding function (alias, different activation function) for each hidden unit in each layer. Furthermore, it has higher network expressivity than existing deep unfolding RNN models due to the over-parameterizing weights. Moreover, we establish theoretical generalization error bounds for the proposed reweighted-RNN model by means of Rademacher complexity. The bounds reveal that the parameterization of the proposed reweighted-RNN ensures good generalization. We apply the proposed reweighted-RNN to the problem of video-frame reconstruction from low-dimensional measurements, that is, sequential frame reconstruction. The experimental results on the moving MNIST dataset demonstrate that the proposed deep reweighted-RNN significantly outperforms existing RNN models.
Authors proposed a deep RNN via unfolding reweighted l1-l1 minimization, where reweighted l1-l1 minimization algorithms are applied to a video task. 
Overall, the paper is well explained in a theoretical part and exhibits a good result compared with other conventional RNN methods in the experiment. In Section 3, authors formulate Rademacher complexities for both conventional and proposed method, which shows the generalization performance of the proposed method when d increases. And this is empirically highlighted in Table 3 in Section 4.
Major points:
Section 1:
-	First part of the introduction can be confusing because Eq. (1) sounds like representing dictionary learning framework (plus DNN is immediately described after Eq. (1) instead of RNN) and RNN is not explicitly written. It should be clearly written and flow should be considered.
Section 2:
-	It is hard to get how parameter g in Eq. (3) derives. 
Section 3:
-	How to build network depth d for the network? A figure should be required.
Section 4:
-	Even though previous papers (e.g., Wisdom et al. and Le et al.) just focus on single dataset like moving MNIST, I believe testing on language data is also quite important (this is a full paper and exhaustive experiments should be mandatory). For example, it may be good to use Penn TreeBank dataset to make a comparison. 
-	In Table 3, how did you set LSTM deeper? Is it a stacked LSTM?
-	Existing RNN methods should include other variations of LSTM (in particular, SOTA methods are welcomed) such as bidirectional LSTM and LSTM with attention mechanism. It should be better to compare with these methods.
Appendix:
-	It would be helpful for readers to show interpretabilities of the model additionally. For example, visualizing features from each RNN model would be beneficial.
Minor points:
-	After introduction of unfolding reweighted l1-l1 minimization, how did the computational cost increase compared to previous l1-l1 minimization?
-	In Section3, for easiness to readers, it may be good to briefly summarize how does the predictor’s generalizability and Rademacher complexities relate.