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

June 24, 2022, 1:11 a.m. | Brendan Leigh Ross, Gabriel Loaiza-Ganem, Anthony L. Caterini, Jesse C. Cresswell

stat.ML updates on arXiv.org arxiv.org

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

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