mlsanityData to 7 Oct 2026

E(n) Equivariant Message Passing Simplicial Networks

arXiv 2305.07100 ↗First posted 11 May 2023cs.LG cs.AIcited by 23

Not on the map. Why?

Abstract (arXiv)

This paper presents E(n) Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an E(n) equivariant fashion. EMPSNs simultaneously generalize E(n) Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method. Furthermore, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures. Last, we show that EMPSNs are on par with state-of-the-art approaches for learning on geometric graphs.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 21 of its 25 references that are in the map. First posted on arXiv 11 May 2023.

Builds on

21 of 25 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  7. 2021E(n) Equivariant Graph Neural Networkscited by 951
  8. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  11. 2020Directional Message Passing for Molecular Graphscited by 556
  12. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
9 more
  1. 2018Neural Relational Inference for Interacting Systemscited by 339
  2. 2018Modeling polypharmacy side effects with graph convolutional networkscited by 237
  3. 2020Can Graph Neural Networks Count Substructures?cited by 235
  4. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  5. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  6. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  7. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  8. 2020Latent-Graph Learning for Disease Predictioncited by 39
  9. 2021Iterative SE(3)-Transformerscited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 12; 2025: 3; 2026: 7.

23 papers.

Sort:

By area:

  1. 2023Generalized Simplicial Attention Neural Networkscited by 27
  2. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  3. 2024E(n) Equivariant Topological Neural Networkscited by 22
  4. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  5. 2024Grounding Continuous Representations in Geometry: Equivariant Neural Fieldscited by 19
  6. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  7. 2024Graph Neural PDE Solvers with Conservation and Similarity-Equivariancecited by 15
  8. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  9. 2024E(3)-Equivariant Mesh Neural Networkscited by 9
  10. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  11. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  12. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
11 more
  1. 2024E(n) Equivariant Message Passing Cellular Networkscited by 3
  2. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  3. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  4. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  5. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0
  6. 2026Geometry-Aware Simplicial Message Passingcited by 0
  7. 2026Augmented Equivariant Mesh Networks for Anatomical Segmentationcited by 0
  8. 2026Hypergraph Pattern Machine: Compositional Tokenization for Higher-Order Interactionscited by 0
  9. 2026A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of O(2)cited by 0
  10. 2026Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operatorscited by 0
  11. 2026Clifford Sheaf Neural Networkscited by 0