SO(3)-equivariant CNN targets HEALPix data on the sphere
Original title: Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere
In cosmology lensing inference it produced the tightest posteriors when simulation count was held fixed.
The paper presents a gauge-equivariant mesh CNN for Hierarchical Equal Area isoLatitude Pixelization of the sphere. Convolutions use steerable filters, parallel transport, and spin-weighted features, and are constructed for exact SO(3) equivariance given a band-limit. Full networks reach per-cent-level or lower invariance error. On benchmarks, the authors report the most accurate dense gradient regression and competitive cosmic microwave background foreground removal and denoising.
Unconfirmed: Accuracy and posterior claims are reported by the authors on their benchmarks and are not independently confirmed.
- The network is not trained to rediscover rotational symmetry already built into the architecture.
- Invariance error is controlled through stated hyperparameters.
- Results include competitive CMB foreground removal and denoising.
- The method is aimed at generative and inference tasks for spherical scientific data.
From the original article
1 min read at arxiv.orgMany 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).
By Joshua Williamson · arxiv.org
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