Neural Implicit Manifold Learning for Topology-Aware Generative Modelling. (arXiv:2206.11267v1 [stat.ML])

Web: http://arxiv.org/abs/2206.11267

Natural data observed in $\mathbb{R}^n$ is often constrained to an
$m$-dimensional manifold $\mathcal{M}$, where $m < n$. Current generative
models represent this manifold by mapping an $m$-dimensional latent variable
through a neural network $f_\theta: \mathbb{R}^m \to \mathbb{R}^n$. Such
procedures, which we call pushforward models, incur a straightforward
limitation: manifolds cannot in general be represented with a single
parameterization, meaning that attempts to do so will incur either
computational instability or the inability to learn probability densities
within the manifold. To …

arxiv learning manifold ml modelling neural topology