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pro vyhledávání: '"Puthawala, Michael A."'
We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijective neural operators through the lens of diffeomorphisms in infinite dimensions. Framed using ca
Externí odkaz:
http://arxiv.org/abs/2412.03393
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization of the gen
Externí odkaz:
http://arxiv.org/abs/2407.11244
Recently there has been great interest in operator learning, where networks learn operators between function spaces from an essentially infinite-dimensional perspective. In this work we present results for when the operators learned by these networks
Externí odkaz:
http://arxiv.org/abs/2306.03982
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use tools such a
Externí odkaz:
http://arxiv.org/abs/2210.00577
We study approximation of probability measures supported on $n$-dimensional manifolds embedded in $\mathbb{R}^m$ by injective flows -- neural networks composed of invertible flows and injective layers. We show that in general, injective flows between
Externí odkaz:
http://arxiv.org/abs/2110.04227
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. We establish sharp characterizations of injectivity of fully-c
Externí odkaz:
http://arxiv.org/abs/2006.08464
We propose an extension of the computational fluid mechanics approach to the Monge-Kantorovich mass transfer problem, which was developed by Benamou-Brenier. Our extension allows optimal transfer of unnormalized and unequal masses. We obtain a one-pa
Externí odkaz:
http://arxiv.org/abs/1902.03367
We investigate overdetermined linear inverse problems for which the forward operator may not be given accurately. We introduce a new tool called the structure, based on the Wasserstein distance, and propose the use of this to diagnose and remedy forw
Externí odkaz:
http://arxiv.org/abs/1810.12993
Akademický článek
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Autor:
Puthawala, Michael Anthony
Publikováno v:
Puthawala, Michael Anthony. (2019). The Structure of Inverse Problems and Unnormalized Optimal Transport. UCLA: Mathematics 0540. Retrieved from: http://www.escholarship.org/uc/item/16s0m70x
In this thesis we consider the solution of inverse problems, especially the components of a numerical inversion, and detection of forward operator error by the use of an extension optimal transport that accepts unnormalized arguments. We improve the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______325::e6085038517bbf947519ddc822d65c96
http://www.escholarship.org/uc/item/16s0m70x
http://www.escholarship.org/uc/item/16s0m70x