mlsanityData to 14 Oct 2026

On the Expressive Power of Sparse Geometric MPNNs

arXiv 2407.02025 ↗First posted 2 Jul 2024cs.LG cs.AIcited by 7

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Abstract (arXiv)

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 42 of its 65 references that are in the map. First posted on arXiv 2 Jul 2024.

Builds on

42 of 65 references.

References · 42

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018How Powerful are Graph Neural Networks?cited by 4,393
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,163
  5. 2021E(n) Equivariant Graph Neural Networkscited by 965
  6. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  7. 2022Recipe for a General, Powerful, Scalable Graph Transformercited by 713
  8. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 631
  9. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  10. 2020Directional Message Passing for Molecular Graphscited by 561
  11. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  12. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
30 more
  1. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 343
  2. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  3. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 305
  4. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  5. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 255
  6. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 243
  7. 2021Spherical Message Passing for 3D Graph Networkscited by 168
  8. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 168
  9. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  10. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  11. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  12. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 76
  13. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  14. 2022Message passing all the way upcited by 47
  15. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 47
  16. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  17. 2023Neural Injective Functions for Multisets, Measures and Graphs via a Finite Witness Theoremcited by 34
  18. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  19. 2023Is Distance Matrix Enough for Geometric Deep Learning?cited by 22
  20. 2022Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networkscited by 21
  21. 2021ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Cloudscited by 15
  22. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
  23. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11
  24. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
  25. 2023Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networkscited by 10
  26. 2024Weisfeiler Leman for Euclidean Equivariant Machine Learningcited by 10
  27. 2023Three iterations of (d-1)-WL test distinguish non isometric clouds of d-dimensional pointscited by 9
  28. 2023Learning Over Molecular Conformer Ensembles: Datasets and Benchmarkscited by 9
  29. 2022Polynomial-time algorithms for continuous metrics on atomic clouds of unordered pointscited by 8
  30. 2023Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positivescited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2025Spectral Graph Neural Networks are Incomplete on Graphs with a Simple Spectrumcited by 3
  2. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  3. 2025On the (Non) Injectivity of Piecewise Linear Janossy Poolingcited by 1
  4. 2026Quantitative Approximation Rates for Group Equivariant Learningcited by 1
  5. 2025GoMS: Graph of Molecule Substructure Network for Molecule Property Predictioncited by 0
  6. 2026SymDrift: One-Shot Generative Modeling under Symmetriescited by 0
  7. 2026Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentialscited by 0