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Learning SO(3) Equivariant Representations with Spherical CNNs

arXiv 1711.06721 ↗First posted 17 Nov 2017cs.CVcited by 244

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Abstract (arXiv)

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

Key facts. Cited by 244 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Nov 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 61; 2022: 57; 2023: 48; 2024: 28; 2025: 26; 2026: 24.

244 papers.

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  1. 2021Perceiver: General Perception with Iterative Attentioncited by 1,089
  2. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  3. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  4. 2021Self-Supervised Pretraining of 3D Features on any Point-Cloudcited by 217
  5. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  6. 2021Equivariant Subgraph Aggregation Networkscited by 154
  7. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  8. 2022Equivariance with Learned Canonicalization Functionscited by 106
  9. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  10. 2021Model-Based Domain Generalizationcited by 103
  11. 2021DualPoseNet: Category-level 6D Object Pose and Size Estimation Using Dual Pose Network with Refined Learning of Pose Consistencycited by 103
  12. 20213D AffordanceNet: A Benchmark for Visual Object Affordance Understandingcited by 100
38 more
  1. 2022PanoFormer: Panorama Transformer for Indoor 360 Depth Estimationcited by 94
  2. 2021Generative Models as Distributions of Functionscited by 89
  3. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  4. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  5. 2023CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representationscited by 67
  6. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  7. 2021360MonoDepth: High-Resolution 360deg Monocular Depth Estimationcited by 60
  8. 2023Towards Stability of Autoregressive Neural Operatorscited by 54
  9. 2021Wide-Baseline Relative Camera Pose Estimation with Directional Learningcited by 49
  10. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  11. 2021LED2-Net: Monocular 360 Layout Estimation via Differentiable Depth Renderingcited by 42
  12. 2023VI-Net: Boosting Category-level 6D Object Pose Estimation via Learning Decoupled Rotations on the Spherical Representationscited by 40
  13. 2023Equivariant Adaptation of Large Pretrained Modelscited by 40
  14. 2022Deep Learning for Omnidirectional Vision: A Survey and New Perspectivescited by 38
  15. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  16. 2022BiFuse++: Self-supervised and Efficient Bi-projection Fusion for 360 Depth Estimationcited by 35
  17. 2022Robust (Controlled) Table-to-Text Generation with Structure-Aware Equivariance Learningcited by 32
  18. 2021Deep Learning on Monocular Object Pose Detection and Tracking: A Comprehensive Overviewcited by 31
  19. 2021Geometry-Aware Self-Training for Unsupervised Domain Adaptationon Object Point Cloudscited by 31
  20. 2022ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapescited by 31
  21. 2021Conditional Local Convolution for Spatio-temporal Meteorological Forecastingcited by 30
  22. 2022RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learningcited by 29
  23. 2022PointConvFormer: Revenge of the Point-based Convolutioncited by 29
  24. 2023E(2)-Equivariant Vision Transformercited by 27
  25. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 26
  26. 2021Correspondence-Free Point Cloud Registration with SO(3)-Equivariant Implicit Shape Representationscited by 24
  27. 2023Deep Learning-based 3D Point Cloud Classification: A Systematic Survey and Outlookcited by 24
  28. 2022Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutionscited by 23
  29. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22
  30. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  31. 2021Homogeneous vector bundles and G-equivariant convolutional neural networkscited by 21
  32. 2022Rotationally Equivariant 3D Object Detectioncited by 21
  33. 2022Towards General-Purpose Representation Learning of Polygonal Geometriescited by 21
  34. 2023Scaling Spherical CNNscited by 21
  35. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
  36. 2022Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spacescited by 20
  37. 2021PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNscited by 19
  38. 2022Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysiscited by 19

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