PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction
Pairwise Distance Distribution;Graph Transformer;Periodic crystal
Yes
No ethics review needed.
See weaknesses.
1. The WPDDFormer model consistently outperforms other state-of-the-art methods across multiple tasks on the JARVIS and Materials Project datasets, demonstrating its effectiveness.
2. The authors provide theoretical guarantees on the continuity and completeness of the WPDD-based graphs, ensuring robust performance under minor structural perturbations.
The paper introduces PDDFormer using the Pairwise Distance Distribution (PDD) as an invariant representation for crystal property prediction and enhances it with atom-specific weights (WPDD) and intra-unit cell structures (UPDD) to better capture atomic interactions and maintain computational efficiency. Experiments on datasets (Materials Project & JARVIS) show that WPDDFormer outperforms existing methods in predictive accuracy and computational efficiency.
I have no major concerns with this paper; however, an ablation study on the effect of varying the radius on WPDDFormer’s performance and efficiency would provide valuable insights into its scalability. Additionally, a time comparison between WPDDFormer and UPDDFormer would strengthen the evidence supporting UPDDFormer’s efficiency claims.
Yes
No ethics concerns.
No ethics review needed.
See Weaknesses part.
Originality:  
This work makes very significant novelty contributions in combining pairwise distance distribution with machine learning based crystal property prediction.

Quality:  
The quality of this work is evidenced by good theoretic analysis and strong experiment results.

Clarity:  
The writing of this work is overall good and clear.

Significance:  
The idea of efficiently integrating pairwise distance distribution into transformer model proposed by this work is insightful and enlightning for researchers in borad AI for science community.
This work proposes PDDFormer, a novel framework for crystal material property prediction. The proposed PDDFormer uses insights about pairwise distance distribution impacts on crystal properties from material science community, designs a novel way to integrate pairwise distance distance distribution into crystal graph representations and a novel transformer model. PDDFormer is shown to achieve state-of-the-art performance on various crystal material property prediction benchmarks.
(1) A remarkable motivation of this work is described in Abstract "However, in reality, atoms in material always vibrate above absolute zero, causing continuous fluctuations in their positions" (line 15-17). But it seems there is no clear discussion why the use of pairwise distance distribution resolves this atom position fluctuation issue? Authors are encouraged to give detailed clarification or discussions to this question.

(2) Generally, two novelty contributions are proposed in this work, including the use of pairwise distance distribution in graph features and a novel transformer architecture. It would make this work more solid if authors could conduct more ablation studies to study which novelty contributes better to good performance, such as applying pairwise distance distribution to other model architecture or removing it from the proposed PDDFormer model.
Yes
No ethics review needed.
As listed above in weaknesses.
1. The proposed crystal representation demonstrates continuity under small distortions and perturbations, which can be advantageous for robustness.
This paper introduces PDDFormer, a model designed to construct geometrically complete and invariant representations of crystals for the task of crystal property prediction. However, the completeness claim of the proposed representation is problematic, as it relies on the assumption that "the PDD is a generally complete invariant" (citing Widdowson & Kurlin, 2022), asserting that distinct crystal structures yield distinct PDD representations. This claim is not accurate. The PDD matrix does not ensure completeness for unstable crystal structures and fails to distinguish between chiral crystal structures. Furthermore, the proposed UPDD crystal graph construction method was previously introduced in "Zeoformer: Coarse-Grained Periodic Graph Transformer for OSDA-Zeolite Affinity Prediction," and the message-passing layers draw inspiration from ComFormer. Given these issues, the paper has limited technical contributions and several potentially misleading claims.
1. Incomplete and Potentially Misleading Claims about Completeness

The completeness proof in the paper relies on the assumption that the PDD matrix acts as a generally complete invariant for distinguishing different crystal structures. However, this is inaccurate. The PDD matrix is not guaranteed to distinguish unstable crystal structures and cannot differentiate between chiral crystal structures, indicating limitations in the claimed theoretical foundation.  Action suggested: reorganize the proof writing section or reorganize the completeness claims.

2. Limited Novelty in Crystal Graph Construction

The proposed UPDD crystal graph construction method is not novel and has been previously introduced in the work "Zeoformer: Coarse-Grained Periodic Graph Transformer for OSDA-Zeolite Affinity Prediction." This overlap with prior work limits the novelty and originality of the proposed approach. Action suggested: check this previous work and discuss similarity and difference with it.

3. Message Passing Layers Largely Derived from ComFormer

The architecture of the message passing layers appears to be inspired by ComFormer, which further limits the technical novelty and contribution of the proposed method. Could you highlight any novel aspects or improvements in your approach compared to ComFormer?

In summary, while this paper proposes a method for generating geometrically complete and invariant crystal representations, its theoretical claims regarding completeness are flawed, and the approach itself relies heavily on prior work, both in graph construction and in network architecture. The combination of these issues limits the paper’s contributions and justifies a rejection at this stage.
Yes
N/A
No ethics review needed.
- UPDD has multiple drawbacks compared to WPDD and shows inferior performance in experiments. What’s its advantage and when is it preferred over WPDD?
- The source of improvement by incorporating PDD is unclear. Is there a way to investigate whether it is because of accounting for periodicity, or because of input being more informative in other ways?
- Would the authors consider evaluating the interpretability of (W/U)PDD crystal graphs and/or the proposed transformer models?
- The proposed (W/U)PDDs incorporate atomic information into PDD and address its high computational cost.
- The paper is overall well-written with nice flow, clarity, and illustrations.
This paper presents atom-Weighted Pairwise Distance Distribution (WPDD) and Unit cell Pairwise Distance Distribution (UPDD) to characterize periodic crystal structure while accounting for atomic information. The continuity and geometrical completeness of these PDDs are theoretically evaluated. It then incorporates them into crystal graphs and develops graph transformer architectures for crystal property prediction. Comparative experiments show their better accuracy and efficiency over previous ML models, and ablation studies validate the importance of (W/U)PDD.
- The experimentation focuses on relatively simple scalar properties, some of which do not physically depend on crystal periodicity.
- Incorporating PDD into crystal graphs makes the data physics-informed, however, the proposed model does not seem to consider interpretability.
- Minor issues
  - In Definition 1, I suggest using boldface or other methods to help distinguish scalar, vector, and matrix.
  - Some languages in Definitions are vague: (1) Line 133, the range of what “crystal graph” refers to in this context should be specified. (2) Line 137, the description of geometrical completeness is unclear.
  - Typos, e.g., Line 129 “and If” and Line 512, “However”.
We introduced the Pairwise Distance Distribution (PDD) and intra-unit cell PDD for characterizing crystal materials, resolving the ambiguity in crystal structure representation.
@inproceedings{
anonymous2024pddformer,
title={{PDDF}ormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=ewjN1MAnJi},
note={under review}
}
The crystal structure can be simplified as a periodic point set repeating across the entire three-dimensional space along an underlying lattice. Traditionally, methods for representing crystals rely on descriptors like lattice parameters, symmetry, and space groups to characterize the structure. However, in reality, atoms in material always vibrate above absolute zero, causing continuous fluctuations in their positions. This dynamic behavior disrupts the underlying periodicity of the lattice, making crystal graphs based on static lattice parameters and conventional descriptors discontinuous under even slight perturbations. To this end, chemists proposed the Pairwise Distance Distribution (PDD) method, which has been used to distinguish all periodic structures in the world's largest real materials collection, the Cambridge Structural Database. However, achieving the completeness of PDD requires defining a large number of neighboring atoms, resulting in high computational costs. Moreover, it does not account for atomic information, making it challenging to directly apply PDD to crystal material property prediction tasks. To address these challenges, we propose the atom-Weighted Pairwise Distance Distribution (WPDD) and Unit cell Pairwise Distance Distribution (UPDD) for the first time, incorporating them into the construction of multi-edge crystal graphs. Based on this, we further developed WPDDFormer and UPDDFormer, graph transformer architecture constructed using WPDD and UPDD crystal graphs. We demonstrate that this method maintains the continuity and completeness of crystal graphs even under slight perturbations in atomic positions. Moreover, by modeling PDD as global information and integrating it into matrix-based message passing, we significantly reduced computational costs. Comprehensive evaluation results show that WPDDFormer achieves state-of-the-art predictive accuracy across tasks on benchmark datasets such as the Materials Project and JARVIS-DFT.
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Pairwise Distance Distribution Graph Transformer Periodic crystal
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PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction
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