no code implementations • 2 Oct 2022 • Michael Puthawala, Matti Lassas, Ivan Dokmanic, Pekka Pankka, Maarten de Hoop
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 $\mathbb{R}^n$.
no code implementations • 8 Oct 2021 • Michael Puthawala, Matti Lassas, Ivan Dokmanić, Maarten de Hoop
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.
no code implementations • 15 Jun 2020 • Michael Puthawala, Konik Kothari, Matti Lassas, Ivan Dokmanić, Maarten de Hoop
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.
1 code implementation • 9 Feb 2019 • Wilfrid Gangbo, Wuchen Li, Stanley Osher, Michael Puthawala
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