Summary
This paper presents a novel protocol for general symmetrization that adds rotational equivariance to any given 3D point-cloud processing model while preserving symmetries with respect to translations and permutations.
Applying the protocol to a model a-posteriori (i.e., at inference) makes the model rigorously rotation-equivariant.
To demonstrate the potential use of the protocol, the authors present Point Edge Transformer (PET).
Albeit not intrinsically equivariant, it achieves state-of-the-art performance on several benchmarks of molecules and solids.
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POST REBUTTAL
Given the clarification the authors provided by the rebuttal, as well as the additional demonstration of the robustness of their proposed method wrt. noise, I have raised my score to 5.
Strengths
S1. The proposed idea of training a model that is intrinsically non-SO(3)-equivariant and making it equivariant during inference is novel, and its mathematical presentation appears correct.
S2. The proposed experimental evaluation is extensive and substantial.
Weaknesses
W1. Contributions: The main contribution the authors claim is the equivariance scheme.
Unfortunately, there is not much in the article to support this. Instead, the bulk of the improvement appears to come from the PET model, which is already sufficiently equivariant across multiple tasks.
It is unclear what benefits smoothness gave in practice (I might have missed something in the experiment part).
W2. Presentation: The presentation is a bit convoluted and seems too verbose; the provided Appendix contains many important details, e.g., about the PET architecture, that should instead be in the main paper. Furthermore, I had a hard time finding a precise definition of the problem in the paper. The paper addresses an important question of rotational equi- and invariance, but its vague presentation makes it difficult to appreciate the contributions.
W3. Related work: Somewhat lacking related work on geometric deep learning. There is a detailed overview of related work on GNNs, but almost no discussion about group equivariant CNNs (G-CNNs). It is unclear how different the proposed model is and if the proposed protocol could be applied to such models.
Questions
Q1. In the abstract, it says (line 11), "We propose a general symmetrization protocol that adds rotational equivariance to any given model". However, the symmetrization seems to assume a base model based on the atom-centric local coordinate system. How common is this? Does this assumption cover the related work, or are there methods that do not use this?
Q2. In the analysis (F.8), it is said that one can improve performance further by introducing extra rotations at inference (not on input but on extracted coordinate systems, so the model is still technically invariant/equivariant). I would like to know why this improves performance.
If I understood correctly from the training description, it is done in a non-equivariant way with rotational augmentation. Is this the reason for the improvement?
Q3. Given that the most common metric is MAE, have the authors tried using MAE as training loss?
Q4. Figure 2: $\bar{x}$ seems to refer to edges between atoms in $A_i$, but as far as I can see, $x$ has not been introduced before. The same applies to $E$ and $M$ and $H$. These terms should be clearly introduced in the text before the figure, not in the Appendix.
Q5. It appears that **r**$_i$ is the 3D position per atom, and $A_i$ is a group of atoms centered around **r**$_i$. However, it was unclear how features per atom are extracted from the beginning. Are different atoms treated as one-hot embeddings?
Rating
5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Limitations
The authors adequately address the limitations and broader impact.