Geometric regularization of autoencoders via observed stochastic dynamics

ArXi:2604.16282v1 Announce Type: new Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a long-standing problem: local-chart methods like ATLAS suffer from exponential landmark scaling and per-step reprojection, while autoencoder alternatives leave tangent-bundle geometry poorly constrained, and the errors propagate into the learned drift and diffusion.