AI and the World's Hard Problems · Astronomy & space · arXiv · 2026-10-19
Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere
Many physics datasets live on the sphere and have no preferred orientation, and methods that ignore this symmetry need far more simulations. The authors propose an SO(3)-equivariant CNN for the HEALPix sphere that builds the symmetry into the architecture, so the network does not have to learn it from data. On benchmarks it gives the most accurate dense gradient regression, and in cosmological lensing simulation-based inference it yields the tightest posteriors at a matched simulation count.