Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The scope of this work falls into image representation learning, and the authors aim to study synthetic images with thresholded polynomial functions (in a generative process). In particular, the authors proposed a sketching algorithm by using locality sensitive hash (LSH). As a result, a succinct sketch is produced from an image, such that the sketch can be used for image reconstruction. The major contribution is that the authors proposed to leverage LSH tables to split an image into regions, then train parameters within each hash bucket, and the resulting parameters can be used to reconstruct image regions. The authors claim potential usage on sketches for image classification and possible extension of using secondary LSH index of sketches for different parts/shapes in the image as well.
strengths_and_weaknesses: Strengths

The overall idea makes sense to me, and the authors provide detailed descriptions of the method, including problem setup, preliminaries, and many additional explanations of the proposed definitions, lemma so on, making the read more smooth (although I have to repeatedly read several times). More details are also provided in the supplementary material.

Weaknesses

The experiments part is somehow limited. The authors only demonstrate the smoothness of the sketch vectors on three functions that can generate simple shapes (ellipses, hyperbolas and rectangles). However, there is no support for the main claim about the usefulness of image classification in the paper title.
questions: I think the authors could provide some possible applications of using the proposed sketching method, where image classification could be one with a very broad impact on the computer vision community.

In addition, is that possible to some visual examples of handling simple and complex images by the proposed method, so that readers can more quickly get the point of what and how the algorithm can do.
limitations: The authors only study synthetic images with basic shapes, while there might be issues when dealing with more complex images or real images.
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 work aims to describe the sketch of a simple image using polynomial functions and hash tables. This is a handcrafted feature technique that has interpretation compared to deep learning.
strengths_and_weaknesses: Overall, I really like the idea of this paper, especially in this era of deep learning run amok.
Not all applications have sufficient samples, and handcrafted features become especially important.

Strengths

[+]  The motivation sounds reasonable and the writing of the paper is good.

[+]  The methodology is also reasonable, considering the trade-off between read efficiency (Hash) and accuracy (Polynomial).

Weaknesses

[-]  My only concern is the experimental part, which is difficult to persuade me that as a feature should be tested by the classification task.
questions: I hope the authors will add a large number of experiments to prove its value as a feature.
limitations: N/A
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper studied the question "Do deep networks learn representations that are isomorphic to the parameters to generate the image?". It provided a sketching algorithm to produce an image sketch that is equivalent to the parameters. The main idea is to use a locality sensitive hash (LSH) table. The authors provided theoretical results on synthetic images that are composed of a union or intersection of several mathematically specified shapes using thresholded polynomial functions (for e.g. ellipses, rectangles).
strengths_and_weaknesses: Strengths:
The methods seems to have theoretical supports. The results seems to be solid.

Weaknesses:
It lacks intuitive explanations behind the theoretical results. Also, it does not tell the potential usage of the proposed method in real applications.
questions: Do the theory proposed in this paper have potential applications on real classification tasks?
limitations: Addressed by the authors.
review_title: null

Meta-review: metareview: All reviewers are positive about this paper. After rebuttal, the authors have well solved the reviewers' concerns, and  improve the quality of this paper. So I suggest accepting this paper.
confidence: Certain
Decision: Accept