__ Summary and Contributions__: The paper proposes to summarize network architectures into a graph generator parameterized by a small number of variables, and to explicitly optimize the generator’s configuration to find better architectures (using Bayesian Optimization). Different from the commonly used cell-based search spaces, the graph generative process is defined over the entire network in a hierarchical manner. Experiments show promising improvements on image classification tasks, both on small datasets (e.g., CIFAR, Flowers) and on ImageNet.

__ Strengths__: * The paper confirms the interesting phenomenon that an architecture’s performance is quite explainable by the graph generator from which it was sampled.
* The idea of optimizing the graph generator is a natural yet meaningful extension of [a]. The fact that the graph generators are of small degrees of freedom enables the usage of well understood optimization tools (e.g., BO) to search for complex architectures.
* The paper is well written and well-motivated. It has also provided convincing ablation studies for several design choices made.
[a] Xie et al. "Exploring randomly wired neural networks for image recognition." ICCV 2019.

__ Weaknesses__: * In experiments the authors fixed \theta_S and \theta_C as constants (Section 4, L185-186), two of the most critical factors that control the global resource allocation of the networks. This makes the search space substantially more restricted than what they were claimed to be in Sections (1-3). I would find the message more appealing if \theta_S and \theta_C are searched, as both are likely going to strongly affect the network’s overall performance. With the current settings, it remains unclear whether BO is able to handle the enlarged search space with reasonable sample efficiency.
* The authors claim the hierarchical graph-based search space as a major contribution, but similar ideas have been studied by quite a few prior works, e.g., [b, c, d], and none of them were mentioned. These need to be discussed to accurately reflect one of the primary contributions of this paper, namely using hierarchical representation for network generators (rather than the hierarchical representation itself).
[b] Liu et al. "Hierarchical representations for efficient architecture search." ICLR 2018.
[c] Liu et al. "Auto-DeepLab: Hierarchical Neural Architecture Search for Semantic Image Segmentation." CVPR 2019.
[d] Tan et al. "MnasNet: Platform-Aware Neural Architecture Search for Mobile" CVPR 2019.
================ update after reading the rebuttal ================
I'd like to thank the authors for providing the additional results with searchable \theta_S and \theta_C. I believe including these results in the main paper can substantially strengthen the work, as it is important to ensure consistency between the method description/claims and the experimental setup.

__ Correctness__: Yes.

__ Clarity__: Yes. The paper is very well written.

__ Relation to Prior Work__: No. Please refer to my comments on hierarchical representations in the "weaknesses" section.

__ Reproducibility__: Yes

__ Additional Feedback__: The paper focused on accuracy-params tradeoff for its main results. It would be interesting to consider FLOPs and/or inference latency, as they are usually more relevant in practice as resource constraints.

__ Summary and Contributions__: This work proposes NAGO, a neural architecture search approach based on neural architecture operator optimization. Similar to the previous work [1], it focuses on searching for an architecture generator instead of a specific architecture. It expands [1] by proposing a hierarchical search space to replace a flat search space proposed in [1], and proposing a Bayesian optimization (BO) based search strategy to replace the random search strategy used in [1]. The authors demonstrated the effectiveness of the proposed approach on six benchmark datasets and show that their approach is able to find extremely lightweight yet highly competitive models.
[1] Exploring Randomly Wired Neural Networks for Image Recognition, ICCV 2019.

__ Strengths__: Casting NAS as a problem of finding the optimal network generator is a natural extension of the pioneer work proposed in [1]. The formulation of optimizing neural network generators with BO is reasonable. Moreover, this work has conducted very solid and comprehensive evaluations on their proposed approach, demonstrating the expressiveness of its proposed search space, and its strong BO-based architecture search results. This paper could raise more awareness of the design of the search space which is important for the community.

__ Weaknesses__: I have two concerns.
The first concern lies at the design of the proposed hierarchical graph-based search space (HNAG). This search space is hand designed with specific types of network generators at different hierarchies (top and bottom levels use WS random network generator and middle level uses ER random network generator). It is not clear to me what are the rationales and insights behind such design. Why the hierarchical search space contains 3 levels? Why WS is selected for top and bottom levels and ER is selected for middle level? Since the proposed HNAG is the key innovation of this work, it is highly desired for the authors to explain its design rationale and insights.
The second concern lies at some of its evaluation methodology and results. For experiments with BO, the authors only sampled 1 architecture to evaluate the performance of a specific generator. Using only one sample for evaluating the performance of the generator is questionable given that the variation in Figure 2 is not that small for many of the network generator configurations. In Table 3, as pinpointed by the authors, most datasets have the optimal solution with a single-node mid-level graph. But I am not fully convinced by the hypothesis provided by the authors. In Figure 5, among 5 datasets, only one dataset (MIT67) shows the superiority of the proposed hierarchical graph-based search space (HNAG). This raises concerns on whether the proposed HNAG is truly effective. It would be more convincing if the authors could also add DropPath and Auxiliary Tower and compare the results again. Another way is to compare the test accuracy given a certain number of epochs.
After reading the rebuttal, my concerns are addressed.

__ Correctness__: This paper is technically correct.

__ Clarity__: The paper is clear and well written.

__ Relation to Prior Work__: Yes. The paper has a clear discussion on its relation to prior work.

__ Reproducibility__: Yes

__ Additional Feedback__: Provide rationales and insights behind the design of the proposed hierarchical graph-based search space (HNAG). Sample more architectures to evaluate the performance of a specific generator during BO experiments. Add DropPath and Auxiliary Tower and compare the results again in Figure 5.

__ Summary and Contributions__: ----------------------- Update after author response ----------------------------------
The authors addressed most of my concerns/questions. The authors showed results on a larger search space (with learnable stage ratios), which worked reasonable well (of course at the cost of much longer training time). While still some other design choices could be optimized, I do think this is an interesting and novel approach that could open up many future research and advance the field of NAS. Thus I think this paper should be accepted and I'm keeping my rating.
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The authors identify a major problem in current neural architecture search (NAS) research: many methods employ over-engineered search spaces, which makes it by design impossible to find truly novel architectures. To overcome this drawback, the authors propose a new perspective to NAS: to search for neural architecture generators rather than searching for a single best architectures within a prespecified search space.
This comes with two major advantages: (i) a much richer space of architectures can be explored and (ii) generators have - in contrast to architectures - a low-dimensional parameterization, allowing for more efficient optimization.
This low-dimensional parameterization allows the authors to use Bayesian Optimization to optimize the generators, not just with respect to high-performing architectures but also with respect to multiple objectives.
The authors furthermore propose a hierarchical search space allowing for a more efficient search in a richer space.
The proposed framework is thoroughly evaluated and ablated on various image recognition tasks (CIFAR10, CIFAR100, ImageNet, Sport8, MIT67, Flowers102).

__ Strengths__: + novel approach to NAS based on neural architecture generator, overcoming major drawbacks of current methods
+ the proposed framework open ups a new research direction, with many potential follow-up work
+ thorough, fair experimental evaluation
+ very well written paper

__ Weaknesses__: I do not have any major concerns, a few nitpicks are:
- there are still a few manual design choices (such as the number of hierarchies, stages, graph generators per hierarchy, how tensors are merged,...)
- from a purely practical/application point of view, the proposed method lacks behind in state-of-the-art performance since methods such as DropPath (which are basically specifically designed for well-known search spaces) do not easily transfer to the architectures generated by this work

__ Correctness__: All claims made are correct, the empirical methodology is fair and correct.

__ Clarity__: The paper is well structured and written, the proposed method is well motivated and introduced.

__ Relation to Prior Work__: Prior work is to a large extent thoroughly discussed and set in contrast to the proposed work.
The authors should add [1], which is also discussing the design search spaces, however in a more manual manner. [2] is also investigating different search spaces. Furthermore, the authors might want to consider mentioning work on multi-objective/constraint NAS such as [3,4], as the authors do also conduct multi-objective optimization.
[1] Designing Network Design Spaces, Radosavovic et al., CVPR 2020
[2] Can weight sharing outperform random architecture search? An investigation with TuNAS, Bender et al., CVPR 2020
[3] Elsken et al., Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution, ICLR 2019
[4] Cai et al., ProxylessNAS, ICLR 2019

__ Reproducibility__: Yes

__ Additional Feedback__: Lines 80-85: Are the number of channels increased to match the highest number? Did the authors experiment with other methods for matching dimensions, e.g., strided convolutions rather than pooling?
Lines 60-63: It would be interesting to explore more options for the models chosen for each hierarchy. Ideally, the choice of model for each hierarchy could also be optimized.
Figure 5 is a little unclear to me. Is there a fixed, underlying search space across all methods from which random samples are drawn, and these samples are then compared to models provided by the methods run on exactly this space? Or is every method run on the space proposed in the original paper? Also, for NAGO, do you compare samples from the optimized generator vs. samples from a not-optimized generator, or what exactly is the baseline here?
Please explain the ad-hoc choice for the generators for different hierarchies (WS for top/bottom, ER for middle).
It would be helpful to have a more detailed explanation on how to combine BOHB and MOBO, this seems not so straightforward to me.
A few more baselines that come to my mind that would be interesting to see: 1) a method not using multi-fidelity optimization (such as vanilla BO) to evaluate the impact of multi-fidelity optimization 2) some evolution-based method since such methods are often used in NAS