275 citations · 1.7k across the 132 of their papers we have counts for
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Globally injective and bijective neural operators
Takashi Furuya, Michael Puthawala, Matti Lassas +1
Recently there has been great interest in operator learning, where networks learn operators between function spaces from an essentially infinite-dimensional perspective. In this wo…
An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning
Anastasis Kratsios, Chong Liu, Matti Lassas +2
Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces and $\m…
Deep Invertible Approximation of Topologically Rich Maps between Manifolds
Michael Puthawala, Matti Lassas, Ivan Dokmanic +2
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. Neu…
Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows
Michael Puthawala, Matti Lassas, Ivan Dokmanić +1
We study approximation of probability measures supported on -dimensional manifolds embedded in by injective flows -- neural networks composed of invertible flows…
Globally Injective ReLU Networks
Michael Puthawala, Konik Kothari, Matti Lassas +2
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 pos…