mlsanityData to 7 Oct 2026

Equivariant Graph Hierarchy-Based Neural Networks

arXiv 2202.10643 ↗First posted 22 Feb 2022cs.LGcited by 24

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Abstract (arXiv)

Equivariant Graph neural Networks (EGNs) are powerful in characterizing the dynamics of multi-body physical systems. Existing EGNs conduct flat message passing, which, yet, is unable to capture the spatial/dynamical hierarchy for complex systems particularly, limiting substructure discovery and global information fusion. In this paper, we propose Equivariant Hierarchy-based Graph Networks (EGHNs) which consist of the three key components: generalized Equivariant Matrix Message Passing (EMMP) , E-Pool and E-UpPool. In particular, EMMP is able to improve the expressivity of conventional equivariant message passing, E-Pool assigns the quantities of the low-level nodes into high-level clusters, while E-UpPool leverages the high-level information to update the dynamics of the low-level nodes. As their names imply, both E-Pool and E-UpPool are guaranteed to be equivariant to meet physic symmetry. Considerable experimental evaluations verify the effectiveness of our EGHN on several applications including multi-object dynamics simulation, motion capture, and protein dynamics modeling.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 26 of its 46 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

26 of 46 references.

References · 26

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2021E(n) Equivariant Graph Neural Networkscited by 951
  4. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  5. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  6. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2019Hamiltonian Neural Networkscited by 702
  9. 2018PointConv: Deep Convolutional Networks on 3D Point Cloudscited by 656
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  12. 2019Graph U-Netscited by 489
14 more
  1. 2019Self-Attention Graph Poolingcited by 421
  2. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  3. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  4. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  5. 2020Graph Information Bottleneck for Subgraph Recognitioncited by 119
  6. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  7. 2018Towards Sparse Hierarchical Graph Classifierscited by 100
  8. 2020LieTransformer: Equivariant self-attention for Lie Groupscited by 100
  9. 2018Flexible Neural Representation for Physics Predictioncited by 91
  10. 2020Hierarchical Inter-Message Passing for Learning on Molecular Graphscited by 59
  11. 2019GraphZoom: A multi-level spectral approach for accurate and scalable graph embeddingcited by 58
  12. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  13. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  14. 2021Learning Hierarchical Graph Neural Networks for Image Clusteringcited by 18

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 10; 2025: 5; 2026: 3.

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  1. 2023Invariant Slot Attention: Object Discovery with Slot-Centric Reference Framescited by 51
  2. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 37
  3. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  4. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  5. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  6. 2023Approximately Equivariant Graph Networkscited by 16
  7. 2024Geometric Trajectory Diffusion Modelscited by 13
  8. 2024Relaxed Equivariance via Multitask Learningcited by 13
  9. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  10. 2022Finding Diverse and Predictable Subgraphs for Graph Domain Generalizationcited by 9
  11. 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
  12. 2025Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learningcited by 6
12 more
  1. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  2. 2025Geometric Hyena Networks for Large-scale Equivariant Learningcited by 4
  3. 2023Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systemscited by 3
  4. 2025Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systemscited by 3
  5. 2023Molecular Conformation Generation via Shifting Scorescited by 2
  6. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  7. 2024Enhancing Neural Subset Selection: Integrating Background Information into Set Representationscited by 1
  8. 2024Learning System Dynamics without Forgettingcited by 1
  9. 2025Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systemscited by 1
  10. 2026FlowSymm: Physics Aware, Symmetry Preserving Graph Attention for Network Flow Completioncited by 0
  11. 2026Graph Mamba Operator: A Latent Simulator for Interacting Particle Systemscited by 0
  12. 2026NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learningcited by 0