AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-20
Integrable building blocks for symplectic neural networks: learned-type layers, fiber-preserving layers, and what a single layer can do
The authors propose three families of single explicit symplectic layers: learned-type, moving-plane shear, and fiber-preserving layers. In experiments on sixteen systems, layers built on nonlinear integrals were much more accurate than the compared symplectic networks. On nonlinear Schrödinger lattices, twist layers alternating with linear maps were over a hundred times more accurate than shear-based networks.