mlsanityData to 7 Oct 2026

A Simple and Universal Rotation Equivariant Point-cloud Network

arXiv 2203.01216 ↗First posted 2 Mar 2022cs.LG cs.CVcited by 11

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Abstract (arXiv)

Equivariance to permutations and rigid motions is an important inductive bias for various 3D learning problems. Recently it has been shown that the equivariant Tensor Field Network architecture is universal -- it can approximate any equivariant function. In this paper we suggest a much simpler architecture, prove that it enjoys the same universality guarantees and evaluate its performance on Modelnet40. The code to reproduce our experiments is available at urlhttps://github.com/simpleinvariance/UniversalNetwork

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 29 of its 40 references that are in the map. First posted on arXiv 2 Mar 2022.

Builds on

29 of 40 references.

References · 29

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  5. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  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. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  10. 2019Provably Powerful Graph Networkscited by 385
  11. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  12. 2018Invariant and Equivariant Graph Networkscited by 339
17 more
  1. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  2. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  3. 2019On the Universality of Invariant Networkscited by 151
  4. 2018Universal approximations of invariant maps by neural networkscited by 127
  5. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  6. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  7. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  8. 2020On Learning Sets of Symmetric Elementscited by 97
  9. 2019Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 80
  10. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  11. 2020A Rotation-Invariant Framework for Deep Point Cloud Analysiscited by 62
  12. 2019Effective Rotation-invariant Point CNN with Spherical Harmonics kernelscited by 57
  13. 2018Covariant Compositional Networks For Learning Graphscited by 54
  14. 2020Universal Equivariant Multilayer Perceptronscited by 49
  15. 2020Global Context Aware Convolutions for 3D Point Cloud Understandingcited by 26
  16. 2021ZZ-Net: A Universal Rotation Equivariant Architecture for 2D Point Cloudscited by 15
  17. 2016Exact Recovery with Symmetries for Procrustes Matchingcited by 10

Built on by

Cited by year

Citing papers per year: 2022: 3; 2023: 4; 2024: 3; 2025: 1.

11 papers.

  1. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  2. 2022Equivariant Networks for Crystal Structurescited by 24
  3. 2022Brauer's Group Equivariant Neural Networkscited by 17
  4. 2025Equivariance Everywhere All At Once: A Recipe for Graph Foundation Modelscited by 17
  5. 2023Approximately Equivariant Graph Networkscited by 16
  6. 2023Complete Neural Networks for Complete Euclidean Graphscited by 10
  7. 2023Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networkscited by 10
  8. 2024A Characterization Theorem for Equivariant Networks with Point-wise Activationscited by 9
  9. 2024On the Expressive Power of Sparse Geometric MPNNscited by 7
  10. 2024Towards Stable, Globally Expressive Graph Representations with Laplacian Eigenvectorscited by 2
  11. 2023Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbitscited by 1