# DeepSphere: towards an equivariant graph-based spherical CNN

arXiv: https://arxiv.org/abs/1904.05146 · HTML: https://mlsanity.com/paper/1904.05146/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

## Built on by (most cited first, 13 of 13)

- [GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations](https://mlsanity.com/paper/2202.08956/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [Curvature Graph Generative Adversarial Networks](https://mlsanity.com/paper/2203.01604/) (2022)
- [Single-Shot Cuboids: Geodesics-based End-to-end Manhattan Aligned Layout Estimation from Spherical Panoramas](https://mlsanity.com/paper/2102.03939/) (2021)
- [Graph-Based Deep Learning for Sea Surface Temperature Forecasts](https://mlsanity.com/paper/2305.09468/) (2023)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Hermitian Symmetric Spaces for Graph Embeddings](https://mlsanity.com/paper/2105.05275/) (2021)
- [Gaussian map predictions for 3D surface feature localisation and counting](https://mlsanity.com/paper/2112.03736/) (2021)
- [Advancing Marine Heatwave Forecasts: An Integrated Deep Learning Approach](https://mlsanity.com/paper/2412.04475/) (2024)
- [PR-CapsNet: Pseudo-Riemannian Capsule Network with Adaptive Curvature Routing for Graph Learning](https://mlsanity.com/paper/2512.08218/) (2025)
- [Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples](https://mlsanity.com/paper/2608.06687/) (2026)

## Abstract (arXiv)

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than spherical convolutions. As equivariance is desired to exploit rotational symmetries, we discuss how to approach rotation equivariance using the graph neural network introduced in Defferrard et al. (2016). Experiments show good performance on rotation-invariant learning problems. Code and examples are available at https://github.com/SwissDataScienceCenter/DeepSphere