Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper first proves that inter-class distinctiveness and intra-class compactness among hash codes determine the lower bound of hash codes’ performance. And it shows that promoting these two characteristics could lift the bound and improve hash learning. Then it proposes a surrogate model to fully exploit such objective by estimating posterior of hash codes. Extensive experiments reveal effectiveness of the proposed method.
strengths_and_weaknesses: Strengths:
1. The studied problem is interesting and important because a theoretical analysis on criteria of learning good hash codes remains largely unexplored.
2. The proposed method seems to be reasonable and effective.
3. Experiment seems to be extensive. 

Weaknesses:
1. There exist some typos and grammatical errors in the paper. 
2. The training sets on all datasets are relatively small.

questions: Is the performance improvement still significant when we increase the size of training set? 
limitations: The authors have adequately addressed the limitations and potential negative societal impact of their work.
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The paper on hand addresses the problem if hashing indicating that interclass distinctiveness and intraclass compactness determine the lower bound of hand code performance. Based on these assumptions a model is proposed, showing beneficial properties for different applications.
strengths_and_weaknesses: Strengths:

In general, using hashing could be beneficial for many applications.

The presented results indicate that the approach is beneficial for at least three different applications.


Weaknesses:

There is no clear description of related work. Even though there is a large number of of references, these are quite general and not directly related to the problem on hand.

To fully understand the problem, the preliminary section need to be extended. Neither the overall problem, nor the required technical details are given on an adequate level. 

In general, the reading flow is hampered by inadequate structure and mathematical writing. The (wrong) overuse of definitions, propositions, and corollary prevents a fluently reading the paper. 

In addition, the mathematical writing needs to be improved. This includes the correct embedding of of equations into the text, missing or insufficiently defined mathematical terms, and a proper argumentation flow.

In general, the paper would benefit from a careful proofreading. There are countless typographical and grammatical errors, hampering the reading flow.

The structure of the paper needs to improved. In particular, the introduction, the conclusion, and the discussion need to be structured differently. The argumentation is not straight forward and somehow redundant.

The caption of Fig. 4 needs to be extended. Even though described in the text, from the figure it is not clear what is shown.

The meaning of Fig. 5 is not fully clear. In this case a more thorough discussion in the text is necessarily required.The 
questions: I would argue with benefits in terms of speed but not on "carbon neutrality"

As seen above from the weaknesses, there are several points that would need to be addressed in a revised version to increase the clarity and the reading flow. In particular, the technical contribution needs to discussed in more clear way.

Overall, there are too many flaws for accepting the paper for NeurIPS.
limitations: The paper on hand is a theoretical contribution, thus there are no limitations in this context.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper studies the learn-to-hash problem, where we need to transform images into hash codes for fast retrieval.  The major research highlight of this paper is the lower bound for hash codes' performance. This paper uses inter-class distinctiveness and intra-class compactness to present a lower bound for the average precision, an evaluation metric for learn-to-hash. Moreover, this paper uses this lower bound as an objective for learn-to-hash. As a result, this paper presents a significant increase in average precision and accuracy.
strengths_and_weaknesses: Strengths;

1. The proposed lower bound is useful. It connects the evaluation metric with the current state of the learn-to-hash model. As a result, we can use it as a guide in the model training.

2. The experimental evaluation is extensive. The authors present a comparison with solid baselines. Moreover, the authors study the training efficiency of the proposed objective with Cauchy and BCE.

3.  The paper provides a theoretical analysis of the proposed lower-bound and its gradient when we use it as a loss. In the supplementary material, this paper also includes necessary implementation details.
questions: 1. This paper introduces a lower bound for AP using inter-class distinctiveness and intra-class compactness. Is this lower bound tight? On which situation the lower bound is equal to the AP? Is there any intuition on the edge cases that the lower bound is far way from the AP?

2. This paper introduces the strength of the proposed lower bound as an objective function. Is there any more potential use case for this lower bound other than the objective? For instance, can we use this lower bound in the parameter search of hash code length?

3. This paper presents improvements in both mAP and accuracy using the proposed lower bound as an objective. Since the lower bound is designed for AP. Is there a connection between it and the accuracy so that we observe this improvement. In fact, this leads to a more general question: how does this lower bound connect to other metrics such as recall, and precision? 

limitations: In general, this paper has a nice presentation and organization. Both theoretical analysis and experimental evaluation are presented for better illustration. However, it would be better to provide a deeper analysis of the functionality of the lower bound. I would like to see the answers to the raised questions in the previous section.
review_title: null

Meta-review: metareview: The paper proposed an interesting lower bound in the learning to hash scenarios and builds on that to show a good algorithm that outperforms several learning to hash methods. There were concerns about the size and scale of experiments which was sufficiently addressed in the rebuttal. The reviewers were not in consensus primarily because of the writing. We think that the writing concerns are fixable and the authors will improve the draft using the reviewers comment for the final version. 
confidence: Certain
Decision: Accept