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Found 4 papers, 1 papers with code
Deep Invertible Approximation of Topologically Rich Maps between Manifolds
By exploiting the topological parallels between locally bilipschitz maps, covering spaces, and local homeomorphisms, and by using universal approximation arguments from machine learning, we find that a novel network of the form $\mathcal{T} \circ p \circ \mathcal{E}$, where $\mathcal{E}$ is an injective network, $p$ a fixed coordinate projection, and $\mathcal{T}$ a bijective network, is a universal approximator of local diffeomorphisms between compact smooth submanifolds embedded in $\mathbb{R}^n$.
Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows
We show that in general, injective flows between $\mathbb{R}^n$ and $\mathbb{R}^m$ 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.
Globally Injective ReLU Networks
Injectivity plays an important role in generative models where it enables inference; in inverse problems and compressed sensing with generative priors it is a precursor to well posedness.
Unnormalized Optimal Transport
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier.
Optimization and Control
