Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere

Joshua Williamson, Niall Jeffrey, Lorne Whiteway|October 16, 2026arXiv

Key Takeaway

Encoding physical symmetries directly into neural network architecture—rather than letting the model learn them—dramatically improves data efficiency and accuracy for scientific problems with inherent geometric structure.

Summary

This paper presents a spherical convolutional neural network designed for data naturally living on spheres (like cosmic microwave background maps). By building in rotational symmetry mathematically rather than learning it, the network uses training data more efficiently and achieves better results on cosmology tasks with fewer simulations needed.

architecture efficiency reasoning

Key Terms

equivariant-architecture steerable-filters spin-weighted-features healpix simulation-based-inference