# Scaling Spherical CNNs

arXiv: https://arxiv.org/abs/2306.05420 · HTML: https://mlsanity.com/paper/2306.05420/

## 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 (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Spherical CNNs on Unstructured Grids](https://mlsanity.com/paper/1901.02039/) (2019)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)

## Built on by (most cited first, 21 of 21)

- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups](https://mlsanity.com/paper/2410.02698/) (2024)
- [U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster](https://mlsanity.com/paper/2604.09041/) (2026)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [EqNIO: Subequivariant Neural Inertial Odometry](https://mlsanity.com/paper/2408.06321/) (2024)
- [Unitary convolutions for learning on graphs and groups](https://mlsanity.com/paper/2410.05499/) (2024)
- [ArchesWeather: An efficient AI weather forecasting model at 1.5deg resolution](https://mlsanity.com/paper/2405.14527/) (2024)
- [SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimation](https://mlsanity.com/paper/2411.07326/) (2024)
- [SciVid: Cross-Domain Evaluation of Video Models in Scientific Applications](https://mlsanity.com/paper/2507.03578/) (2025)
- [Reconstructing Historical Climate Fields With Deep Learning](https://mlsanity.com/paper/2311.18348/) (2023)
- [Equivariant Neural Tangent Kernels](https://mlsanity.com/paper/2406.06504/) (2024)
- [3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction](https://mlsanity.com/paper/2411.00543/) (2024)
- [SO(3)-Equivariant Neural Networks for Learning from Scalar and Vector Fields on Spheres](https://mlsanity.com/paper/2503.09456/) (2025)
- [Correspondence-Free Fast and Robust Spherical Point Pattern Registration](https://mlsanity.com/paper/2508.02339/) (2025)
- [SAFE: A Novel Approach to AI Weather Evaluation through Stratified Assessments of Forecasts over Earth](https://mlsanity.com/paper/2510.26099/) (2025)
- [Unified Spherical Frontend: Learning Rotation-Equivariant Representations of Spherical Images from Any Camera](https://mlsanity.com/paper/2511.18174/) (2025)
- [An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making](https://mlsanity.com/paper/2601.00142/) (2026)
- [Potential Paradigm Shift in Hazard Risk Management: AI-Based Weather Forecast for Tropical Cyclone Hazards](https://mlsanity.com/paper/2404.18440/) (2024)
- [Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment](https://mlsanity.com/paper/2512.00659/) (2025)
- [Neural Operators for Biomedical Spherical Heterogeneity](https://mlsanity.com/paper/2601.03561/) (2026)
- [A library for differentiable signal processing and machine learning on the sphere](https://mlsanity.com/paper/2609.39737/) (2026)

## 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.