The Riemannian Geometry of Deep Generative Models

@article{Shao2017TheRG,
  title={The Riemannian Geometry of Deep Generative Models},
  author={Hang Shao and Abhishek Kumar and P. Thomas Fletcher},
  journal={2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)},
  year={2017},
  pages={428-4288}
}
Deep generative models learn a mapping from a low-dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation… CONTINUE READING

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