mlsanityData to 7 Oct 2026

An intuitive multi-frequency feature representation for SO(3)-equivariant networks

arXiv 2405.04537 ↗First posted 15 Mar 2024cs.CV cs.AI cs.GRcited by 5

Not on the map. Why?

Abstract (arXiv)

The usage of 3D vision algorithms, such as shape reconstruction, remains limited because they require inputs to be at a fixed canonical rotation. Recently, a simple equivariant network, Vector Neuron (VN) has been proposed that can be easily used with the state-of-the-art 3D neural network (NN) architectures. However, its performance is limited because it is designed to use only three-dimensional features, which is insufficient to capture the details present in 3D data. In this paper, we introduce an equivariant feature representation for mapping a 3D point to a high-dimensional feature space. Our feature can discern multiple frequencies present in 3D data, which is the key to designing an expressive feature for 3D vision tasks. Our representation can be used as an input to VNs, and the results demonstrate that with our feature representation, VN captures more details, overcoming the limitation raised in its original paper.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 27 of its 43 references that are in the map. First posted on arXiv 15 Mar 2024.

Builds on

27 of 43 references.

References · 27

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  3. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  4. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  5. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  6. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  7. 2018PointCNN: Convolution On X-Transformed Pointscited by 764
  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. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  11. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  12. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
15 more
  1. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  2. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  3. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  4. 2022Equivariance with Learned Canonicalization Functionscited by 106
  5. 2019ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statisticscited by 104
  6. 2020DeepGMR: Learning Latent Gaussian Mixture Models for Registrationcited by 91
  7. 2019Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 80
  8. 2020A Rotation-Invariant Framework for Deep Point Cloud Analysiscited by 62
  9. 2020EGAD! an Evolved Grasping Analysis Dataset for diversity and reproducibility in robotic manipulationcited by 61
  10. 2019Effective Rotation-invariant Point CNN with Spherical Harmonics kernelscited by 57
  11. 2020Global Context Aware Convolutions for 3D Point Cloud Understandingcited by 26
  12. 2021Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representationscited by 24
  13. 20223D Equivariant Graph Implicit Functionscited by 18
  14. 2022The Devil is in the Pose: Ambiguity-free 3D Rotation-invariant Learning via Pose-aware Convolutioncited by 18
  15. 2022SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representationcited by 10

Built on by

Cited by year (2026 to 7 Oct)

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

5 papers.

  1. 2025Equivariant Neural Networks for General Linear Symmetries on Lie Algebrascited by 4
  2. 2024DEF-oriCORN: efficient 3D scene understanding for robust language-directed manipulation without demonstrationscited by 1
  3. 2025NeuralSVCD for Efficient Swept Volume Collision Detectioncited by 0
  4. 2025Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learningcited by 0
  5. 2026Rotation-Invariant Multi-IMU Activity Recognition under Independent Per-Location Orientation Shiftscited by 0