Web: http://arxiv.org/abs/2110.04227

Jan. 31, 2022, 2:11 a.m. | Michael Puthawala, Matti Lassas, Ivan Dokmanić, Maarten de Hoop

cs.LG updates on arXiv.org arxiv.org

We study approximation of probability measures supported on $n$-dimensional
manifolds embedded in R^m by injective flows -- neural networks composed of
invertible flows and injective layers. We show that in general, injective flows
between R^n and R^m universally approximate measures supported on images of
extendable embeddings, which are a subset of standard embeddings: when the
embedding dimension m is small, topological obstructions may preclude certain
manifolds as admissible targets. When the embedding dimension is sufficiently
large, m \geq 3n+1, we …

arxiv

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