Spin Spherical Fourier Neural Operators: Efficient Equivariant Learning for Vector and Spin Fields on the Sphere
Abstract
Many fields of physical interest on the sphere, such as wind, the polarisation of the cosmic microwave background and the shear of weak gravitational lensing, are spin fields, whose values change phase when the local frame rotates. We extend spherical Fourier neural operators (SFNOs) to fields of any spin, through lifted spherical convolutions that are exactly rotationally equivariant. Lifting spin fields to Mackey functions on the rotation group provides the conceptual framework, while computation is performed exactly and efficiently through their harmonic representation and by appealing to sampling theorems on the sphere and rotation group. We construct spin SFNOs (S2FNOs) from these building blocks. We demonstrate empirically that rotational equivariance holds to machine precision for these layers. We achieve state-of-the-art performance on existing benchmarks, and introduce new benchmarks on which spin-aware models outperform their scalar counterparts.
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BibTeX
@misc{mulder2026spin,
title = {{Spin Spherical Fourier Neural Operators: Efficient Equivariant Learning for Vector and Spin Fields on the Sphere}},
author = {Kevin Mulder and Matthew A. Price and Eirini Leftaki and Jason D. McEwen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04389},
eprint = {2611.04389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04389},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin Spherical Fourier Neural Operators: Efficient Equivariant Learning for Vector and Spin Fields on the Sphere
AU - Kevin Mulder
AU - Matthew A. Price
AU - Eirini Leftaki
AU - Jason D. McEwen
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04389
UR - https://arxiv.org/abs/2611.04389
AB - Many fields of physical interest on the sphere, such as wind, the polarisation of the cosmic microwave background and the shear of weak gravitational lensing, are spin fields, whose values change phase when the local frame rotates. We extend spherical Fourier neural operators (SFNOs) to fields of any spin, through lifted spherical convolutions that are exactly rotationally equivariant. Lifting spin fields to Mackey functions on the rotation group provides the conceptual framework, while computation is performed exactly and efficiently through their harmonic representation and by appealing to sampling theorems on the sphere and rotation group. We construct spin SFNOs (S^2FNOs) from these building blocks. We demonstrate empirically that rotational equivariance holds to machine precision for these layers. We achieve state-of-the-art performance on existing benchmarks, and introduce new benchmarks on which spin-aware models outperform their scalar counterparts.
ER -