mlsanityData to 7 Oct 2026

Spherical CNNs

arXiv 1801.10130 ↗First posted 30 Jan 2018cs.LG stat.MLcited by 452

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Abstract (arXiv)

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.

Key facts. Cited by 452 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jan 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 95; 2022: 104; 2023: 87; 2024: 60; 2025: 56; 2026: 50.

452 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  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. 2021How to Train Your Energy-Based Modelscited by 271
  5. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  6. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  7. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  8. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  9. 2022From data to functa: Your data point is a function and you can treat it like onecited by 183
  10. 2022e3nn: Euclidean Neural Networkscited by 171
  11. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  12. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
38 more
  1. 2023Spherical Transformer for LiDAR-based 3D Recognitioncited by 124
  2. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  3. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  4. 2021DualPoseNet: Category-level 6D Object Pose and Size Estimation Using Dual Pose Network with Refined Learning of Pose Consistencycited by 103
  5. 2022PanoFormer: Panorama Transformer for Indoor 360 Depth Estimationcited by 94
  6. 2022Learning to Generate Realistic LiDAR Point Cloudscited by 91
  7. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  8. 2021Generative Models as Distributions of Functionscited by 89
  9. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  10. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  11. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  12. 2022PAC-Bayes Compression Bounds So Tight That They Can Explain Generalizationcited by 75
  13. 2021Aligning Latent and Image Spaces to Connect the Unconnectablecited by 70
  14. 2023Permutation Equivariant Neural Functionalscited by 69
  15. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  16. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  17. 2023CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representationscited by 67
  18. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  19. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  20. 2021360MonoDepth: High-Resolution 360deg Monocular Depth Estimationcited by 60
  21. 2022OmniFusion: 360 Monocular Depth Estimation via Geometry-Aware Fusioncited by 60
  22. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  23. 2023Clifford Group Equivariant Neural Networkscited by 54
  24. 2023Towards Stability of Autoregressive Neural Operatorscited by 54
  25. 2022Transformation-Equivariant 3D Object Detection for Autonomous Drivingcited by 52
  26. 2023Equivariant Similarity for Vision-Language Foundation Modelscited by 51
  27. 2021Wide-Baseline Relative Camera Pose Estimation with Directional Learningcited by 49
  28. 2022DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detectioncited by 48
  29. 2021Self-Supervised Learning Disentangled Group Representation as Featurecited by 47
  30. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  31. 2021Learning Partial Equivariances from Datacited by 44
  32. 2021LED2-Net: Monocular 360 Layout Estimation via Differentiable Depth Renderingcited by 42
  33. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  34. 2023EGformer: Equirectangular Geometry-biased Transformer for 360 Depth Estimationcited by 42
  35. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  36. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  37. 2023Self-supervised learning of Split Invariant Equivariant representationscited by 41
  38. 2021ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generatorscited by 40

50 most cited of 452 All 452 (JSON)