Scaling Spherical CNNs
Not on the map. Why?
Abstract (arXiv)
Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.
Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 43 of its 66 references that are in the map. First posted on arXiv 8 Jun 2023.
Builds on
43 of 66 references.
References · 43
- 2017Attention Is All You Needcited by 60,361
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
- 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
- 2017Deep Setscited by 1,421
- 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
- 2021E(n) Equivariant Graph Neural Networkscited by 965
- 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
- 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
- 2020Directional Message Passing for Molecular Graphscited by 561
31 more
- 2018Spherical CNNscited by 456
- 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
- 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
- 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 311
- 2020WeatherBench: A benchmark dataset for data-driven weather forecastingcited by 275
- 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
- 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
- 2019Cormorant: Covariant Molecular Neural Networkscited by 263
- 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 255
- 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 248
- 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
- 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 182
- 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
- 2022Forecasting Global Weather with Graph Neural Networkscited by 168
- 2020Improving data-driven global weather prediction using deep convolutional neural networks on a cubed spherecited by 96
- 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 92
- 2019Spherical CNNs on Unstructured Gridscited by 79
- 2018DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applicationscited by 62
- 2018Kernel Transformer Networks for Compact Spherical Convolutioncited by 56
- 2019Machine Learning for Precipitation Nowcasting from Radar Imagescited by 56
- 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 56
- 2020Spin-Weighted Spherical CNNscited by 50
- 2017Machine Learning Molecular Dynamics for the Simulation of Infrared Spectracited by 30
- 2020Efficient Generalized Spherical CNNscited by 29
- 2022Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutionscited by 24
- 2022Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spacescited by 20
- 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
- 2021Equivariant Networks for Pixelized Spherescited by 16
- 2022M"obius Convolutions for Spherical CNNscited by 13
- 2022Global Extreme Heat Forecasting Using Neural Weather Modelscited by 13
- 2021Phase Collapse in Neural Networkscited by 5
Built on by
Citing papers per year: 2023: 2; 2024: 8; 2025: 7; 2026: 4.
21 papers.
Sort:
By area:
- 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 236
- 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
- 2026U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecastercited by 12
- 2025Attention on the Spherecited by 10
- 2024EqNIO: Subequivariant Neural Inertial Odometrycited by 8
- 2024Unitary convolutions for learning on graphs and groupscited by 8
- 2024ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolutioncited by 6
- 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
- 2025SciVid: Cross-Domain Evaluation of Video Models in Scientific Applicationscited by 6
- 2023Reconstructing Historical Climate Fields With Deep Learningcited by 4
- 2024Equivariant Neural Tangent Kernelscited by 4
- 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Predictioncited by 4
9 more
- 2025SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spherescited by 2
- 2025Correspondence-Free Fast and Robust Spherical Point Pattern Registrationcited by 1
- 2025SAFE: A Novel Approach to AI Weather Evaluation through Stratified Assessments of Forecasts over Earthcited by 1
- 2025Unified Spherical Frontend: Learning Rotation-Equivariant Representations of Spherical Images from Any Cameracited by 1
- 2026An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Makingcited by 1
- 2024Potential Paradigm Shift in Hazard Risk Management: AI-Based Weather Forecast for Tropical Cyclone Hazardscited by 0
- 2025Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignmentcited by 0
- 2026Neural Operators for Biomedical Spherical Heterogeneitycited by 0
- 2026A library for differentiable signal processing and machine learning on the spherecited by 0
- 2026A library for differentiable signal processing and machine learning on the sphere30 Sep 2026
- 2026U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster10 Apr 2026
- 2026Neural Operators for Biomedical Spherical Heterogeneity7 Jan 2026
- 2026An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making1 Jan 2026
- 2025Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment29 Nov 2025
- 2025Unified Spherical Frontend: Learning Rotation-Equivariant Representations of Spherical Images from Any Camera22 Nov 2025
- 2025SAFE: A Novel Approach to AI Weather Evaluation through Stratified Assessments of Forecasts over Earth30 Oct 2025
- 2025Correspondence-Free Fast and Robust Spherical Point Pattern Registration4 Aug 2025
- 2025SciVid: Cross-Domain Evaluation of Video Models in Scientific Applications4 Jul 2025
- 2025Attention on the Sphere16 May 2025
- 2025SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres12 Mar 2025
- 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimation11 Nov 2024
9 more
- 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction1 Nov 2024
- 2024Unitary convolutions for learning on graphs and groups7 Oct 2024
- 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups3 Oct 2024
- 2024EqNIO: Subequivariant Neural Inertial Odometry12 Aug 2024
- 2024Equivariant Neural Tangent Kernels10 Jun 2024
- 2024ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolution23 May 2024
- 2024Potential Paradigm Shift in Hazard Risk Management: AI-Based Weather Forecast for Tropical Cyclone Hazards29 Apr 2024
- 2023Reconstructing Historical Climate Fields With Deep Learning30 Nov 2023
- 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather models29 Aug 2023
- 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 236
- 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 24
- 2026U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecastercited by 12
- 2025Attention on the Spherecited by 10
- 2024EqNIO: Subequivariant Neural Inertial Odometrycited by 8
- 2024Unitary convolutions for learning on graphs and groupscited by 8
- 2024ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolutioncited by 6
- 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimationcited by 6
- 2025SciVid: Cross-Domain Evaluation of Video Models in Scientific Applicationscited by 6
- 2023Reconstructing Historical Climate Fields With Deep Learningcited by 4
- 2024Equivariant Neural Tangent Kernelscited by 4
- 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Predictioncited by 4
12 most cited of 20 All 20 (JSON)
- 2026A library for differentiable signal processing and machine learning on the sphere30 Sep 2026
- 2026U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster10 Apr 2026
- 2026Neural Operators for Biomedical Spherical Heterogeneity7 Jan 2026
- 2025Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment29 Nov 2025
- 2025Unified Spherical Frontend: Learning Rotation-Equivariant Representations of Spherical Images from Any Camera22 Nov 2025
- 2025SAFE: A Novel Approach to AI Weather Evaluation through Stratified Assessments of Forecasts over Earth30 Oct 2025
- 2025Correspondence-Free Fast and Robust Spherical Point Pattern Registration4 Aug 2025
- 2025SciVid: Cross-Domain Evaluation of Video Models in Scientific Applications4 Jul 2025
- 2025Attention on the Sphere16 May 2025
- 2025SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres12 Mar 2025
- 2024SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimation11 Nov 2024
- 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction1 Nov 2024
12 newest of 20 All 20 (JSON)