← 研踪 PaperTrailarXiv:2611.04389 · v1
Spin Spherical Fourier Neural Operators: Efficient Equivariant Learning for Vector and Spin Fields on the Sphere
首次提交 2026-11-03 14:22
版本更新 2026-11-03 14:22
雷达观测 2026-11-04 23:40
摘要
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$^2$FNOs) 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.
作者备注：27 pages, 15 figures
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v1 · 2026-11-03 14:22 · 最新观测版本
Spin Spherical Fourier Neural Operators: Efficient Equivariant Learning for Vector and Spin Fields on the Sphere
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$^2$FNOs) 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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