mlsanityData to 7 Oct 2026

Clifford Group Equivariant Simplicial Message Passing Networks

arXiv 2402.10011 ↗First posted 15 Feb 2024cs.AIcited by 22

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Abstract (arXiv)

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 37 of its 52 references that are in the map. First posted on arXiv 15 Feb 2024.

Builds on

37 of 52 references.

References · 37

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018How Powerful are Graph Neural Networks?cited by 4,355
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  4. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  6. 2021E(n) Equivariant Graph Neural Networkscited by 951
  7. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  9. 2019Graph Neural Networks for Social Recommendationcited by 711
  10. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  11. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  12. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
25 more
  1. 2018Neural Relational Inference for Interacting Systemscited by 339
  2. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  3. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  4. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  5. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  6. 2020Can Graph Neural Networks Count Substructures?cited by 235
  7. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  8. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  9. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
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  11. 2022GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoningcited by 128
  12. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  13. 2022Clifford Neural Layers for PDE Modelingcited by 91
  14. 2019Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANscited by 78
  15. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  16. 2022Expressiveness and Approximation Properties of Graph Neural Networkscited by 63
  17. 2020Collaborative Motion Prediction via Neural Motion Message Passingcited by 55
  18. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  19. 2023Clifford Group Equivariant Neural Networkscited by 54
  20. 2018Generating Multi-Agent Trajectories using Programmatic Weak Supervisioncited by 46
  21. 2023Geometric Clifford Algebra Networkscited by 37
  22. 2020DAG-Net: Double Attentive Graph Neural Network for Trajectory Forecastingcited by 30
  23. 2023E(n) Equivariant Message Passing Simplicial Networkscited by 23
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  25. 2021Geometric Algebra Attention Networks for Small Point Cloudscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 8; 2026: 5.

22 papers.

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  1. 2024Does equivariance matter at scale?cited by 49
  2. 2024Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physicscited by 36
  3. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  4. 2024E(n) Equivariant Topological Neural Networkscited by 22
  5. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  6. 2025Probing Equivariance and Symmetry Breaking in Convolutional Networkscited by 12
  7. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  8. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  9. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  10. 2024Multivector Neurons: Better and Faster O(n)-Equivariant Clifford Graph Neural Networkscited by 4
  11. 2025Equivariant Neural Networks for General Linear Symmetries on Lie Algebrascited by 4
  12. 2024ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3Dcited by 3
10 more
  1. 2024E(n) Equivariant Message Passing Cellular Networkscited by 3
  2. 2025Clifford Group Equivariant Diffusion Models for 3D Molecular Generationcited by 3
  3. 2025AdS-GNN -- a Conformally Equivariant Graph Neural Networkcited by 2
  4. 2025GLGENN: A Novel Parameter-Light Equivariant Neural Networks Architecture Based on Clifford Geometric Algebrascited by 2
  5. 2025Resolving Oversmoothing with Opinion Dissensuscited by 1
  6. 2026Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentialscited by 1
  7. 2026ART: Adaptive Reasoning Trees for Explainable Claim Verificationcited by 0
  8. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0
  9. 2026Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianccited by 0
  10. 2026Clifford Sheaf Neural Networkscited by 0