# Convolutional Networks for Spherical Signals

arXiv: https://arxiv.org/abs/1709.04893 · HTML: https://mlsanity.com/paper/1709.04893/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2017.

## Built on by (most cited first, 18 of 18)

- [ACDNet: Adaptively Combined Dilated Convolution for Monocular Panorama Depth Estimation](https://mlsanity.com/paper/2112.14440/) (2021)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Spherical Space Feature Decomposition for Guided Depth Map Super-Resolution](https://mlsanity.com/paper/2303.08942/) (2023)
- [Rotation-Equivariant Deep Learning for Diffusion MRI](https://mlsanity.com/paper/2102.06942/) (2021)
- [Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs](https://mlsanity.com/paper/2102.02828/) (2021)
- [Diffusion Earth Mover's Distance and Distribution Embeddings](https://mlsanity.com/paper/2102.12833/) (2021)
- [E2PN: Efficient SE(3)-Equivariant Point Network](https://mlsanity.com/paper/2206.05398/) (2022)
- [VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds](https://mlsanity.com/paper/2106.15301/) (2021)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [Differentiable and accelerated spherical harmonic and Wigner transforms](https://mlsanity.com/paper/2311.14670/) (2023)
- [Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU(d) Symmetry](https://mlsanity.com/paper/2207.07250/) (2022)
- [ChaRRNets: Channel Robust Representation Networks for RF Fingerprinting](https://mlsanity.com/paper/2105.03568/) (2021)
- [Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications](https://mlsanity.com/paper/2305.16657/) (2023)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)
- [Applying VertexShuffle Toward 360-Degree Video Super-Resolution on Focused-Icosahedral-Mesh](https://mlsanity.com/paper/2106.11253/) (2021)
- [Application of Spherical Convolutional Neural Networks to Image Reconstruction and Denoising in Nuclear Medicine](https://mlsanity.com/paper/2307.03298/) (2023)
- [Neural Operators for Biomedical Spherical Heterogeneity](https://mlsanity.com/paper/2601.03561/) (2026)
- [eCP: Equivariant Conformal Prediction with pre-trained models](https://mlsanity.com/paper/2602.03986/) (2026)

## Abstract (arXiv)

The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing. Many areas of science and egineering deal with signals with other symmetries, such as rotation invariant data on the sphere. Examples include climate and weather science, astrophysics, and chemistry. In this paper we present spherical convolutional networks. These networks use convolutions on the sphere and rotation group, which results in rotational weight sharing and rotation equivariance. Using a synthetic spherical MNIST dataset, we show that spherical convolutional networks are very effective at dealing with rotationally invariant classification problems.