Philipp Petersen

Adv. Comput. Math., February, 2024

VC dimensions of group convolutional neural networks.

[BibT_eX]

[DOI]

Anna Sepliarskaia

Neural Networks, January, 2024

2023

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities.

[BibT_eX]

[DOI]

Carlo Marcati

Joost A. A. Opschoor

Andrés Felipe Lerma Pineda

Christoph Schwab

Found. Comput. Math., June, 2023

Large Language Models for Mathematicians.

[BibT_eX]

[DOI]

CoRR, 2023

Mathematical Capabilities of ChatGPT.

[BibT_eX]

[DOI]

Proceedings of the Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, 2023

2022

Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems.

[BibT_eX]

[DOI]

CoRR, 2022

2021

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks.

[BibT_eX]

[DOI]

J. Sci. Comput., 2021

Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size.

[BibT_eX]

[DOI]

Mones Raslan

Found. Comput. Math., 2021

Optimal learning of high-dimensional classification problems using deep neural networks.

[BibT_eX]

[DOI]

CoRR, 2021

Deep Microlocal Reconstruction for Limited-Angle Tomography.

[BibT_eX]

[DOI]

Héctor Andrade-Loarca

Gitta Kutyniok

Ozan Öktem

CoRR, 2021

The Modern Mathematics of Deep Learning.

[BibT_eX]

[DOI]

CoRR, 2021

Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs.

[BibT_eX]

[DOI]

Fabian Laakmann

Adv. Comput. Math., 2021

2020

Anisotropic multiscale systems on bounded domains.

[BibT_eX]

[DOI]

Adv. Comput. Math., 2020

2019

Optimal Approximation with Sparsely Connected Deep Neural Networks.

[BibT_eX]

[DOI]

SIAM J. Math. Data Sci., 2019

Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks.

[BibT_eX]

[DOI]

Héctor Andrade-Loarca

Gitta Kutyniok

Ozan Öktem

SIAM J. Imaging Sci., 2019

Approximation in L<sup>p</sup>(μ) with deep ReLU neural networks.

[BibT_eX]

[DOI]

CoRR, 2019

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs.

[BibT_eX]

[DOI]

CoRR, 2019

Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms.

[BibT_eX]

[DOI]

Ingo Gühring

Gitta Kutyniok

CoRR, 2019

The Oracle of DLphi.

[BibT_eX]

[DOI]

CoRR, 2019

Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces.

[BibT_eX]

[DOI]

Mones Raslan

Adv. Comput. Math., 2019

2018

Optimal approximation of piecewise smooth functions using deep ReLU neural networks.

[BibT_eX]

[DOI]

Neural Networks, 2018

Equivalence of approximation by convolutional neural networks and fully-connected networks.

[BibT_eX]

[DOI]

CoRR, 2018

2016

Shearlet approximation of functions with discontinuous derivatives.

[BibT_eX]

[DOI]