Learning Directional Randers Geometry for Latent-Space Exploration

arXiv:2611.03675v1 Announce Type: new Abstract: Deep neural networks extract powerful latent representations from images, enabling fast and efficient downstream analysis. However, these latent spaces lack explicit geometric structure, leading to possibly poor interpolation fidelity and misleading extrapolation. Latent interpolation techniques assume symmetric transition costs which are often not the case for real world data. Their symmetric nature cannot capture directional processes, such as disease progression, where certain transitions are impossible (e.g. tumor growth dynamics or cognitive improvement in Alzheimer's disease). Although Riemannian metrics extend Euclidean geometry by incorporating curvature, they remain symmetric.