Log In Sign Up

Geometry-Aware Hamiltonian Variational Auto-Encoder

by   Clément Chadebec, et al.

Variational auto-encoders (VAEs) have proven to be a well suited tool for performing dimensionality reduction by extracting latent variables lying in a potentially much smaller dimensional space than the data. Their ability to capture meaningful information from the data can be easily apprehended when considering their capability to generate new realistic samples or perform potentially meaningful interpolations in a much smaller space. However, such generative models may perform poorly when trained on small data sets which are abundant in many real-life fields such as medicine. This may, among others, come from the lack of structure of the latent space, the geometry of which is often under-considered. We thus propose in this paper to see the latent space as a Riemannian manifold endowed with a parametrized metric learned at the same time as the encoder and decoder networks. This metric is then used in what we called the Riemannian Hamiltonian VAE which extends the Hamiltonian VAE introduced by arXiv:1805.11328 to better exploit the underlying geometry of the latent space. We argue that such latent space modelling provides useful information about its underlying structure leading to far more meaningful interpolations, more realistic data-generation and more reliable clustering.


page 18

page 22

page 24

page 25

page 27

page 34

page 36

page 37


Chart Auto-Encoders for Manifold Structured Data

Auto-encoding and generative models have made tremendous successes in im...

Pulling back information geometry

Latent space geometry has shown itself to provide a rich and rigorous fr...

Data Generation in Low Sample Size Setting Using Manifold Sampling and a Geometry-Aware VAE

While much efforts have been focused on improving Variational Autoencode...

Learning Flat Latent Manifolds with VAEs

Measuring the similarity between data points often requires domain knowl...

Identifying latent distances with Finslerian geometry

Riemannian geometry provides powerful tools to explore the latent space ...

Discovering latent topology and geometry in data: a law of large dimension

Complex topological and geometric patterns often appear embedded in high...

Latent linear dynamics in spatiotemporal medical data

Spatiotemporal imaging is common in medical imaging, with applications i...