Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere
Many of the most important datasets in the physical sciences live natively on the sphere, and these data often carry no preferred position or orientation. Using methods that do not reflect this symmetry leads to far higher simulation requirements, which can be catastrophic for scientific analyses (forcing reliance on cheap, imperfect models that bias results). We present a novel spherical implementation of a gauge equivariant mesh architecture that is specifically designed for the Hierarchical Equal Area isoLatitude Pixelization (\healpix{}) of the sphere. The $\mathrm{SO}(3)$-equivariant convolution is built from steerable filters, parallel transport and spin-weighted features. The archi...
| Authors | Joshua Williamson, Niall Jeffrey, Lorne Whiteway |
|---|---|
| Primary category | stat.ML |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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