Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 3: Weak Reject
review_content: Paper extends LISTA by introducing learned re-weighting for the problem of sparse signal recovery. Paper combines the insights from RW-ISTA (a re-weighted iterative algorithm with fixed parameters and LISTA, a learned iterative algorithm without re-weighting. 

Results show that: 
(a) On synthetic data, performance of Rw-LISTA is superior to many variants of LISTA for various SNRs
(b) On synthetic data, Rw-LIST is better than classical approaches when SNR, Sparsity and other factors are varied. Why is LISTA not compared under all these different variations? 
(c) On MNIST, Rw-LISTA is much better than non-learned approaches, but seems very close to LISTA. 

It strikes me that authors make all evaluations based on NMSE. However, motivation for CSS is that there is structure in the recovered signal — however no comparison of the recovered structure is made. While it is true, that is the signal is perfectly recovered, it would follow the structure from this data was obtained, however no such guarantees can be made for non-zero errors. 

I would also like to see what happens whens a pure learning based approach (such as denoting auto-encoders) is used to recover the signal. Do they perform worse than Rw-LISTA? 

At present, I think the paper doesnot meet the standard of ICLR submissions. However, if authors address my concerns, I am happy to change the rating. 

Minor Comments:
“considered as unsupervised approaches since all the paramters are fixed instead of learning from data.” — this is incorrect. A significant human intuition went into design of these systems. While one can argue that even NNet architecture design requires human intuition, the trend is towards using less domain-specific architectures. 
review_title: Official Blind Review #2

final_score: rating: 6: Weak Accept
review_content: An approach is proposed to learn sparse representations while preserving some structures in the data.

The idea seems quite nice where we want to learn the structure that induces sparsity instead of simply sparse representations. The idea is to extend a recent algorithm RwISTA by adding reweighting block. The reweighing block changes weights to encode whether coefficients in the model learned by the network are similar or dissimilar to each other. To build the reweighing block convolutional layers are used.

The paper is slightly hard to read due to many typos, and hard-to-read sentences. Also, I think a more intuitive explanation of how the reweighting helps preserve structure is needed. Right now it is very difficult to understand (except maybe for experts working on similar problems?) Regarding the experiments, most of them are run with synthetic cases. It seems like the approach is compared with several recent approaches though showing good results. On the MNIST data, results are shown where the images are recovered from the sparse representation. I did not really see any substantial improvements in performance as compared to say LISTA. Maybe I am misunderstanding what is being evaluated in Figure 7. Also I am not sure how it shows that the sparse representation is learning the underlying structure? Maybe some re-writing is needed to make this clearer.

I think the paper is interesting but needs some polishing to make it easier to read and perhaps some improved experiments in real datasets.

review_title: Official Blind Review #1

final_score: rating: 1: Reject
review_content: The paper combines deep learning and compressed sensing. Specifically the RW-LISTA algorithm is proposed for cluster-structured sparse recovery, building upon two existing methods: the Reweighted Iterative Shrinkage Algorithm and the LISTA algorithm. The reweighing process is employed to infer the dependencies between coefficients and encourage cluster structure. Strategies for local and global dependence are presented. The approach is evaluated on synthetic and real datasets.

The paper considers and important topic. However the proposed approach is too incremental and the empirical evaluation could also be improved. In addition the presentation needs more work.  Specifically:
- the use of unsupervised vs supervised is misleading. Traditional CS approaches are in fact supervised as they map to a regression problem when both input sensing matrix and response vector are available. The distinction has more to do with the ability (or lack of ability) to learn representations.
- the proposed approach is a straightforward combination of LISTA and RwISTA and the section of global/local dependence regarding cluster-sparse structures is unsurprising.
- Even though signals may exhibit cluster-sparsity, the size of such cluster might vary widely and it is therefore questionable if such patterns can be best captured via connections in the proposed reweighing blocks. Indeed for some blocks wider or lower neighborhoods might be needed to capture various radii of dependence.  
- As an alternative to adopting RwISTA it might be pertinent to compare against a counterpart using fused lasso penalty (Tibshirani et al 2005).
- Experiments are limited: a wider variety of block structure with more or less variability in block size etc should be considered. In addition it would be important to compare against vanilla  Rw-ISTA, as one of the classical CSS solvers.
- It is somewhat disappointing that the proposed approach should be better the higher the SNR, where other approaches can do well enough. Ideally we are looking to improve in less favorable conditions of low SNR.

review_title: Official Blind Review #3

Meta-review: The paper is proposed a rejection based on majority reviews.
Decision: Reject