__ Summary and Contributions__: This paper raises the problem that previous DARTS-based methods have some gaps between the trained supernet and the derived architecture, due to the sparsity constraints are not satisfied with the architecture parameters. Instead of projecting the supernet onto the sparsity constraint, this paper directly optimizes in the equalized parameters space, where the architecture parameters satisfy the constraint at each step.

__ Strengths__: 1. The idea is novel and efficient.
2. By performing the differentiable search on a compressed space, which is then recovered using sparse coding, the sparsity constraint is enforced at each step, which improves the correlation between the supernet and the derived architecture.
3. Also, the convergence speed is faster than previous methods.
4. The paper is well-organized and easy to understand.

__ Weaknesses__: 1. Itâ€™s not clear to me that as the sparse constraint is enforced at the beginning, is it sufficient to explore the entire search space? Could the authors specify the proportion of the explored architectures?
2. The results on ImageNet are not very impressive as it is comparable but not surpass previous methods.

__ Correctness__: Yes.

__ Clarity__: Yes.

__ Relation to Prior Work__: The following one-stage NAS should be cited and discussed:
[1] Mei et al., AtomNAS: Fine-Grained End-to-End Neural Architecture Search, ICLR 2019.
[2] Gao et al., MTL-NAS: Task-Agnostic Neural Architecture Search towards General-Purpose Multi-Task Learning. arXiv:2003.14058.

__ Reproducibility__: Yes

__ Additional Feedback__: I have read the authors' rebuttal and remain my initial recommendation.

__ Summary and Contributions__: This work proposes to explicitly enforce sparsity on the architecture parameters during search process in NAS. This is achieved by sampling a dictionary matrix A and map the sparse architecture parameters to a low-dimensional space B, and perform the search on B. Both supernet weight W, architecture B, and the sparse constraint are jointly optimized.

__ Strengths__: 1. The sparsity of architecture parameters is explicitly enforced via sparse coding. The gap between supernet and derived architecture is minimized since the redundant edges are inactive.
2. The authors further propose a one-stage search, where the network weight is being updated based on converged architecture parameters, thus returning both the derived architecture and optimized weights.

__ Weaknesses__: 1. I could not see a strong motivation for explicitly enforcing sparsity on architecture parameters. This is because there are already many works trying to decouple the dependency of evaluating sub-networks on the training of supernet (i.e., making the correlation higher). This means that we have ways to explicitly decouple the network evaluation with supernet training without adding a sparsity regularizaiton.
2. Properly understanding Table 2 requires more experiment details. As far as I know, weight-sharing methods require the BN to be re-calculated [1] to properly measure the Kendall correlation. Other works that can reduce the gap between supernet and sub-networks (e.g. [3]) or can make the edges activated to be sparse like GDAS [2] are not compared. Moreover, there seems no explanation in main content regarding Table 2.
3. The one-stage method proposed basically focusing on training network weights W after the training of architecture parameters is converged. However, similar idea can also be achieved in other differentiable NAS framework, where one can continue training the supernet weights after the architecture remains little change. For example, in GDAS, after the entropy of edges is well minimized, the sampled architecture will be close to determnistic, and one can keep training W to obtain the optimal weights. Moreover, other one-stage methods like [4] are not compared nor discussed.
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After reading the author's response, most of my concerns have been addressed. I choose to accept this submission.
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[1] Guo, Zichao, et al. "Single path one-shot neural architecture search with uniform sampling." ICLR 2020.
[2] X. Dong and Y. Yang. Searching for a robust neural architecture in four gpu hours. CVPR 2019.
[3] Bender, Gabriel, et al. "Understanding and simplifying one-shot architecture search." ICML2018.
[4] Cai, Han, Chuang Gan, and Song Han. "Once for all: Train one network and specialize it for efficient deployment." ICLR 2020.

__ Correctness__: The overall formualation and pipeline makes sense to me.

__ Clarity__: The overall written is good.

__ Relation to Prior Work__: Some of the existing one-stage NAS work is not discussed, as mentioned above.

__ Reproducibility__: No

__ Additional Feedback__:

__ Summary and Contributions__: -----post rebuttal---------
First of all, I appreciate the feedback from the authors. In the rebuttal, the authors claimed that "Aj (1 < j _x0014_ n) are sampled as fixed matrices". To me, it is really weird. For a sparse coding method, the base matrices should also be optimized. I did not see the reason to just sample and fixed the basis in this paper. Thus, I suspect the correctness of this method. I will lower my score to suggest to reject.
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This paper proposed to formulate differentiable NAS as a sparse coding optimization problem. Specifically, the basic idea of this work is that the differentiable search is performed on a compressed space, thus, by introducing sparse coding technique, the sparsity constraint could be satisfied. The paper reports competitive performance on both CIFAR10 and ImageNet dataset with one-stage and two-stage pipelines.

__ Strengths__: 1. The idea of this paper is nice. It is really natural to utilize sparse coding techniques to resolve the decoding problem of differentiable NAS problem.
2. The experimental results are also quite competitive.

__ Weaknesses__: 1. The details of the model are not that clear. For example, the authors should clarify the meaning of the "arrow" symbol in Equation 8. And it also need to clarify how is A optimized (or derived) for each iteration in equation 9.
2. Reproducibility. Since a sparse coding part is involved in the optimization, the model cannot be optimized directly by a differential manner and mosek is used for the sparse coding part. Moreover, the paper did not mention how the model is implemented (PyTorch, TensorFlow or other framework). The code of the paper should be provided for reproducibility.

__ Correctness__: Might be correct. The details of the proof for Proposition 1 should be provided. So far the proof for Proposition 1 is too short.

__ Clarity__: Satisfied.

__ Relation to Prior Work__: good

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: This paper proposes to use sparse coding to bridge the gap between search and evaluation, with the help of sparsity constraint. It further proposes a one-stage framework, which avoids the original architecture-level hyper-parameters gaps.
The efficiency and effectiveness have been validated in experiments.

__ Strengths__: 1. Using sparse coding to solve the gap issue in NAS is novel and promising. I like this idea. The formulation and notations are neat.
2. The one-stage framework makes the overall method unified. There are also a performance improvement in the one-stage framework.
3. The correlation analysis in Table 2 is very important for the overall idea. It successfully validate the previous motivation.

__ Weaknesses__: This paper is good, but some aspects are still required improvements.
1. [Structure of this paper]
The major contribution of this paper is sparse coding formulation, but not the one-stage framework. I suggest that the authors shorten the words on two-stage and one-stage ISTA-NAS. Moreover, as the one-stage method performs consistently better, the two-stage one seems less necessary.
2. [Experiments]
It is a bit disappointing to find the authors only conduct experiments on NASNet search space. We all know that many constraints, e.g., fixed depth and width, and drawbacks exist in this cell-based search space, e.g., inference time. This idea is promising and deserves more comprehensive results on other search space. I strongly suggest the authors apply it in at least one chain-based search space, like ProxyLess search space.
3. There are NEW hyper-parameters introduced by the proposed method, e.g., \epsilon in Algorithm 2. The authors should show ablations on how to choose it.

__ Correctness__: Yes.

__ Clarity__: Yes. It is clear for me to understand the idea.

__ Relation to Prior Work__: For the first contribution, it has clearly discussed.
For the second contribution, i.e., one-stage NAS, differences from DSNAS should be clarified. In addition, to my best knowledge, the first one-stage NAS method is not DSNAS, but ONCE-FOR-ALL (Han et al.). The authors miss it.

__ Reproducibility__: Yes

__ Additional Feedback__: The major idea in this paper is promising and novel. But some aspects can still be improved. I will give a better rate if my above concerns well explained.