Kati8/ICLR_2023_2025 huggingface dataset:
authors: Shih-Hsin Wang
authors: Yuhao Huang
authors: Justin M. Baker
authors: Yuan-En Sun
authors: Qi Tang
authors: Bao Wang
reviews: 
Comments: The paper presents a hyperparameter-free graph construction method for molecular modeling that ensures sparsity, connectivity, and rigidity. It addresses the limitations of traditional methods, like radial cutoff graphs, which lack guarantees for both connectivity and sparsity and fail to leverage spatial arrangements effectively. The proposed method consistently generates connected, sparse graphs with an edge-to-node ratio capped at 3, and ensures rigidity, making spatial arrangements uniquely determinable. The approach is proven effective and efficient in various molecular modeling benchmarks.
Strengths: 1.The proposed SCHull method is quite innovative. I appreciate the author's idea of introducing unit spherical mapping, which makes the graph construction more reasonable and reliable. The implementation is also very clever.

2.The paper provides thorough validation of the proposed method in well-justified experimental settings.

3.The paper conducts comprehensive theoretical validation to demonstrate the effectiveness of the method.
Weaknesses: 1.The discussion primarily focuses on molecular analysis, which may make the paper lean somewhat towards chemistry and biology. However, this does not detract from it being a strong paper. It may be worth considering whether this method could be applied to other types of graph data analysis.

2.Could consider conducting some visualization experiments, if the level of difficulty permits.
Recommendation: 6
Reviewer confidence: 4
Soundness/correctness: 3
Clarity: 3
reviews: 
Comments: This paper proposes a novel method for constructing sparse yet connected geometric graphs: Project the points onto a sphere, construct a polyhedron, and construct a graph from its edge structure. This aims to mitigate earlier costly approaches of taking the power graph of the original graph. The authors first prove theoretical properties of their construction and show that maximally expressive MPNNs with particular initializations for node and edge features can distinguish among generic graphs, essentially proving that via a sparse graph structure (degree bounded by 3) 1-WL can distinguish all generic point cloud configurations (i.e. not assuming a fully connected point cloud as in earlier works). The authors then empirically show the construction's efficacy and value of the SCHull face angles that allow for universality on sparse configurations, by obtaining consistently better results on synthetic, classification, and regression tasks.
Strengths: 1. Novel technique relying on a fast (n*log(n)) algorithm is scalable and empirically also negligible computational overhead
2. Introduces a novel technique to a paradigm not challenged much in research: the distance cutoff construction for geometric graphs. Theoretical and empirical proof this approach is sound.
3. An architecture-agnostic method that can be applied to a large variety of MPNN-like models
Weaknesses: 1. Proofs mainly rely on previous work and the construction of the graph is also backed by a known algorithm, thus there is a notion of an incremental advance. Although, I believe that tying these two areas together constitutes a strong advancement for ML.

2. The empirical results are consistent yet are not pushing the boundary on SOTA, but rather give a `boost' to low expressive models. It would be nice to see the performance of working on SCHull graphs with the initial edge and node features for more expressive architecture, for instance, MACE or SEGNN ("Geometric and physical quantities improve equivariant message passing", Brandstetter et al.) I suspect it would make less of a difference but please prove me wrong. Anyway, only having a comparable result to these architectures (when they process distance-restricted graphs) with faster inference is still a great achievement. If this is performed I may increase my score.

3. The background for geometric deep learning is insufficient in my opinion. For instance, there is no discussion on research on expressivity when point clouds are not necessarily generic and a comparison of your approach with models that are universal (or complete) on **all** point clouds. For a couple of papers on this topic please note:

Hordan, S., Amir, T. and Dym, N., 2024. Weisfeiler Leman for Euclidean Equivariant Machine Learning. ICML 2024

Li, Zian, et al. "Is distance matrix enough for geometric deep learning?." Advances in Neural Information Processing Systems 36 (2024).

Overall this paper has strong potential, addressing these weaknesses will likely increase the rating.
Recommendation: 10
Reviewer confidence: 5
Soundness/correctness: 4
Clarity: 3
reviews: 
Comments: This work introduces an innovative approach for generating sparse yet interconnected geometric graphs by projecting points onto a sphere, constructing a polyhedron, and deriving graph structure from polyhedron edges. This strategy circumvents the computational expense of earlier power graph methodologies. The paper establishes theoretical guarantees regarding their construction and demonstrates that highly expressive message-passing neural networks with appropriate node and edge feature initialization can differentiate among generic graphs. Notably, this shows that 1-WL expressiveness for distinguishing all generic point cloud configurations can be achieved through sparse graph structures with bounded degree (≤3), removing the assumption of full connectivity required in prior work. Empirical validation confirms the method's utility and the significance of SCHull face angles for enabling universality on sparse settings, with consistently improved performance across synthetic data, classification, and regression benchmarks.
Strengths: 1. Presents an innovative technique leveraging a computationally efficient O(n log n) algorithm with negligible practical computational cost and strong scalability properties. 2. Introduces a fresh perspective to an underexplored area within graph construction for geometric learning: challenging conventional distance-based cutoff approaches through both theoretical validation and empirical demonstration of soundness. 3. Provides a model-independent solution applicable across diverse message-passing neural network architectures and variants.
Weaknesses: 1. The theoretical contributions substantially build upon established prior work, and the graph construction itself utilizes well-known algorithmic techniques. While this represents incremental progress in methodology, the integration of these distinct research areas delivers meaningful value to the machine learning community. 2. Experimental outcomes demonstrate consistent improvements but do not establish new state-of-the-art benchmarks; rather, they provide meaningful enhancements to models with limited expressivity. Further investigation comparing SCHull graphs with fully specified node and edge attributes on more expressive models (such as MACE or SEGNN with equivariant designs) would strengthen the contribution. While maintaining performance parity with these advanced architectures while achieving faster inference is valuable, empirical evidence of the method's impact across expressiveness levels would be beneficial. 3. The presentation of geometric deep learning fundamentals appears incomplete. Notably absent are discussions regarding expressivity constraints when point clouds deviate from generic configurations and comparative analysis with approaches achieving universality across all point cloud types. Engagement with recent relevant literature would enhance contextual understanding.
Recommendation: 10
Reviewer confidence: 5
Soundness/correctness: 4
Clarity: 3