# Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network

arXiv: https://arxiv.org/abs/1806.09231 · HTML: https://mlsanity.com/paper/1806.09231/

## Key facts

- Cited by 171 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2018.

## Built on by (most cited first, 30 of 171)

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- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
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- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
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- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
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- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximations](https://mlsanity.com/paper/2202.10638/) (2022)
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- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
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- [Equivariance versus Augmentation for Spherical Images](https://mlsanity.com/paper/2202.03990/) (2022)

## Abstract (arXiv)

Recent work by Cohen et al. has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler. An unusual feature of the proposed architecture is that it uses the Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding repeated forward and backward Fourier transforms. The underlying ideas of the paper generalize to constructing neural networks that are invariant to the action of other compact groups.