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20172022
most citedProof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces

6 citations · 9 across the 8 of their papers we have counts for

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7 papers · 1 filter

math.FA2021

Sobolev-type embeddings for neural network approximation spaces

Philipp Grohs, Felix Voigtlaender

We consider neural network approximation spaces that classify functions according to the rate at which they can be approximated (with error measured in ) by ReLU neural networ…

math.FA20211 cited

-stability analysis for Gabor phase retrieval

Philipp Grohs, Martin Rathmair

We consider the problem of reconstructing the missing phase information from spectrogram data with $$ \mathcal{G}f(x,y)=\int_\mathbb{R} f(t) e^{-π(t-x)^2}e^{-2πi…

math.FA2020

Phase Transitions in Rate Distortion Theory and Deep Learning

Philipp Grohs, Andreas Klotz, Felix Voigtlaender

Rate distortion theory is concerned with optimally encoding a given signal class using a budget of bits, as . We say that can be compres…

math.FA2019

Stable Gabor phase retrieval for multivariate functions

Philipp Grohs, Martin Rathmair

In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabo…

math.FA2019

Phase Retrieval: Uniqueness and Stability

Philipp Grohs, Sarah Koppensteiner, Martin Rathmair

The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astr…

math.FA2018

Gabor phase retrieval is severely ill-posed

Rima Alaifari, Philipp Grohs

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This…