The Riemannian Geometry of Deep Generative Models

@article{Shao2018TheRG,
  title={The Riemannian Geometry of Deep Generative Models},
  author={Hang Shao and Abhishek Kumar and P. Fletcher},
  journal={2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)},
  year={2018},
  pages={428-4288}
}
Deep generative models learn a mapping from a low-dimensional latent space to a high-dimensional data space. [...] Key Method 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 of a tangent vector along a path on the manifold.Expand
Atlas Generative Models and Geodesic Interpolation
Only Bayes should learn a manifold
Geometry of Deep Generative Models for Disentangled Representations
Only Bayes should learn a manifold (on the estimation of differential geometric structure from data)
PACE OF G ENERATIVE M ODELS
Geometry-Aware Hamiltonian Variational Auto-Encoder
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 25 REFERENCES
Mapping a Manifold of Perceptual Observations
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold
Algorithms for manifold learning
The Manifold Tangent Classifier
Semi-Supervised Learning on Riemannian Manifolds
Testing the Manifold Hypothesis
Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples
A global geometric framework for nonlinear dimensionality reduction.
Nonlinear dimensionality reduction by locally linear embedding.
Auto-Encoding Variational Bayes
...
1
2
3
...