Geodesic Calculus on Implicitly Defined Latent Manifolds
Researchers have developed a new framework for analyzing latent manifolds in autoencoders, treating them as implicitly defined submanifolds. This approach enables a discrete Riemannian calculus to approximate geometric operators, offering robustness against representation inaccuracies. The method allows for the computation of geodesic paths and Riemannian exponential maps, and has been evaluated on various autoencoders trained on both synthetic and real data. AI