# DeepSphere: a graph-based spherical CNN

arXiv: https://arxiv.org/abs/2012.15000 · HTML: https://mlsanity.com/paper/2012.15000/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2020.

## Built on by (most cited first, 30 of 66)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future](https://mlsanity.com/paper/2105.13137/) (2021)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Deep Learning for Omnidirectional Vision: A Survey and New Perspectives](https://mlsanity.com/paper/2205.10468/) (2022)
- [Conditional Local Convolution for Spatio-temporal Meteorological Forecasting](https://mlsanity.com/paper/2101.01000/) (2021)
- [SurfGen: Adversarial 3D Shape Synthesis with Explicit Surface Discriminators](https://mlsanity.com/paper/2201.00112/) (2022)
- [Surface Vision Transformers: Attention-Based Modelling applied to Cortical Analysis](https://mlsanity.com/paper/2203.16414/) (2022)
- [A Survey of Representation Learning, Optimization Strategies, and Applications for Omnidirectional Vision](https://mlsanity.com/paper/2502.10444/) (2025)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [HEAL-SWIN: A Vision Transformer On The Sphere](https://mlsanity.com/paper/2307.07313/) (2023)
- [PanoSwin: a Pano-style Swin Transformer for Panorama Understanding](https://mlsanity.com/paper/2308.14726/) (2023)
- [PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNs](https://mlsanity.com/paper/2104.03584/) (2021)
- [A PAC-Bayesian Generalization Bound for Equivariant Networks](https://mlsanity.com/paper/2210.13150/) (2022)
- [Weather2K: A Multivariate Spatio-Temporal Benchmark Dataset for Meteorological Forecasting Based on Real-Time Observation Data from Ground Weather Stations](https://mlsanity.com/paper/2302.10493/) (2023)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Equivariant Networks for Pixelized Spheres](https://mlsanity.com/paper/2106.06662/) (2021)
- [Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning](https://mlsanity.com/paper/2309.04082/) (2023)
- [SphereUFormer: A U-Shaped Transformer for Spherical 360 Perception](https://mlsanity.com/paper/2412.06968/) (2024)
- [Spherical Transformer](https://mlsanity.com/paper/2202.04942/) (2022)
- [Connectivity Optimized Nested Graph Networks for Crystal Structures](https://mlsanity.com/paper/2302.14102/) (2023)
- [360VOT: A New Benchmark Dataset for Omnidirectional Visual Object Tracking](https://mlsanity.com/paper/2307.14630/) (2023)
- [3D Scene Geometry Estimation from 360^circ Imagery: A Survey](https://mlsanity.com/paper/2401.09252/) (2024)
- [Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2306.14064/) (2023)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [360VOTS: Visual Object Tracking and Segmentation in Omnidirectional Videos](https://mlsanity.com/paper/2404.13953/) (2024)
- [Deformation Robust Roto-Scale-Translation Equivariant CNNs](https://mlsanity.com/paper/2111.10978/) (2021)
- [3D reconstruction from spherical images: A review of techniques, applications, and prospects](https://mlsanity.com/paper/2302.04495/) (2023)

## Abstract (arXiv)

Designing a convolution for a spherical neural network requires a delicate tradeoff between efficiency and rotation equivariance. DeepSphere, a method based on a graph representation of the sampled sphere, strikes a controllable balance between these two desiderata. This contribution is twofold. First, we study both theoretically and empirically how equivariance is affected by the underlying graph with respect to the number of vertices and neighbors. Second, we evaluate DeepSphere on relevant problems. Experiments show state-of-the-art performance and demonstrates the efficiency and flexibility of this formulation. Perhaps surprisingly, comparison with previous work suggests that anisotropic filters might be an unnecessary price to pay. Our code is available at https://github.com/deepsphere