riemannian-manifold

Introduces Energy Manifold Natural Gradient Descent (EMNGD), a manifold optimization framework for neural PDE solvers that aligns parameter updates with function-space energy curvature while respecting parameter constraints. Theoretical guarantees and empirical results show improved accuracy and convergence.

This paper proposes Geodesic Flow Matching, a Riemannian transport method for denoising Spatial Semantic Pointers (SSPs) on toroidal manifolds, and demonstrates a 72% reduction in tracking error and 40% efficiency gain in a spiking neural SLAM system.