Venue: NeurIPS 2022 Conference

Reviews:

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 provides a method based on the Point-wise Distance Distribution PDD(S; k) to describe/characterize periodic crystal arrangements, i.e. atomic/molecular configurations. 
This can be used to efficiently identify instances of similar periodic crystal patterns in large datasets.
Essentially, to find a function I on all periodic sets of unlabeled points in Rn such that invariance, completeness, metricity, continuity, computability and inverse design criteria hold.
Proofs are shown.
Various experiments demnostrate the system on atomic crystal configurations from the Cambridge Crystallographic Data Centre (CCDC).
strengths_and_weaknesses: Strengths: the method apparently works well for indexing crystals, proofs are shown as to the method here, based on distance distributions.

Weakness: predicting periodic crystal structures is a niche domain, it is unclear how this is relevant to general DL.
   Lack of citation to directly relevant research.
questions: Is this method relevant to general volumetric AI, where geometric structure is generally not be periodic?

Other approaches such as the Hough transform can be used to identify and classify non-periodic 3D atom-like structures with high accuracy, which invariance to scale, translation, rotation. It seems such a method work well in predicting the periodic structures shown here, also in a manner invariant to scaling. Is this the case?
Chauvin, L., et al. 2022. Registering Image Volumes using 3D SIFT and Discrete SP-Symmetry. arXiv preprint arXiv:2205.15456.



limitations: Limited to periodic atomic crystal structures.

Alternative methods based on non-periodic atomic 3D image structures may outperform this method.
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: The authors provide a periodic-invariant feature called Pointwise Distance Distributions (PDD). The feature is constructed by distances to the first k nearest neighbors of every point in a periodic set with near-linear complexity. The authors also prove that this feature can remove ambiguity due to different representations of a crystal cell, is invariant that different basis of the same material won’t change output, and is continuous that small perturbation won’t largely change the output. The authors use this feature to remove duplicate materials and perform their experiments on the Cambridge Structural Database. The effectiveness of the method is shown by less time and fewer failures.
strengths_and_weaknesses: Strength:
The authors give many examples to show problems of periodic representation and the proof of continuity and completeness of PDD is well-stated.

Weakness:
Using the k-nearest distances to build the features is not novel enough. It’s easy to build a crystal graph with k-nearest neighbors. The experiment is only done in one database and the task is not significant enough. 

questions: Figure 3 Left: Why can’t we distinguish between these two graphs? The distance matrices of them are different.
limitations: The method is not novel enough. I think other methods such as the radius graph or the combination of radius graph and k-NN graph also suffice to distinguish materials.

For experiments, I recommend using PDD for other material databases to remove variance of your experiments; and also using PDD as features of other important tasks such as material energy prediction.
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 focuses on the problem of geometric isomorphism for periodic structures of materials. They propose a new crystal descriptor without false negatives, which means if two periodic structures are the same, the output of this PDD descriptor will be the same. This PDD descriptor has a near-linear time complexity. They achieve this by formulating a PDD matrix using k-nearest pairwise distances for all atoms in a unit cell.
strengths_and_weaknesses: ## Strengths
* This proposed descriptor has near-linear time-complexity without false negative when only the positions of points considered.
* The illustration of different unit cell representations for the same material is insightful and easy to understand.
* This proposed method can deal with a larger unit cell representation as shown in Fig.2 in the main paper.

## Weaknesses
* Originality: The idea of using k-nearest pairwise distances is not new. CGCNN proposed by Xie et al. actually uses k-nearest pairwise distances to form the crystal graph representation to make the graph input invariant to different unit cell representations. 
* The false positive, which is defined in 1.1b, can not be satisfied when the k is given (large enough k can not be achieved during usage of this PDD descriptor). The increase of k will  increase the time-complexity at least linearly. 
* The false negative, which is defined in 1.1a, can not be satisfied when you consider atomic numbers of points. Two different materials with the same geometric structure and a bit different atomic numbers will result in the same output of PDD descriptor. 
questions: My main concerns are the weaknesses 2 and 3 mentioned above, could you please give some clarifications about them? 
limitations: Yes.
review_title: null

Meta-review: metareview: While the paper is not rated too high by the reviewers, and overall the endorsement for it is a bit less strong that what we would have liked to see, it seems that the paper might have results that are of interest to those working on materials science applications of ML. 

One common complaint the authors had was the limited experimentation, but given the authors' response regarding the validation (which in particular goes through an important dataset), the concern was overcome. However, to improve the impact of the paper, and to offer stronger motivation for followup works, it would be a valuable addition to the final version of the paper to have more experiments, especially those that more elaborately outline suitable ablation studies, to illustrate the theory in action, and importantly, to add in some comparisons against some of the generic methods (which will be understandably, not respecting all desired invariances, still, it is good to see how much of a big deal that is, notwithstanding the comments on Platon et al).

One minor but potentially useful technical point to note is that what the authors call "continuity" (Theorem 4.3) is a type of Lipschitz continuity, which can be further exploited for algorithm design and analysis.


confidence: Less certain
Decision: Accept