Shearlet approximation of functions with discontinuous derivatives. - Philipp Petersen (J. Approx. Theory, 2016)

Equivalence of approximation by convolutional neural networks and fully-connected networks. - Philipp Petersen; Felix Voigtländer (CoRR, 2018)

Optimal approximation of piecewise smooth functions using deep ReLU neural networks. - Philipp Petersen; Felix Voigtländer (Neural Networks, 2018)

Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces. - Philipp Petersen; Mones Raslan (Adv. Comput. Math., 2019)

The Oracle of DLphi. - Dominik Alfke; Weston Baines; Jan Blechschmidt; Mauricio J. del Razo Sarmina; Amnon Drory; Dennis Elbrächter; Nando Farchmin; Matteo Gambara; Silke Glas; Philipp Grohs; Peter Hinz; Danijel Kivaranovic; et al. (CoRR, 2019)

Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms. - Ingo Gühring; Gitta Kutyniok; Philipp Petersen (CoRR, 2019)

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs. - Gitta Kutyniok; Philipp Petersen; Mones Raslan; Reinhold Schneider (CoRR, 2019)

Approximation in Lp(μ) with deep ReLU neural networks. - Felix Voigtländer; Philipp Petersen (CoRR, 2019)

Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks. - Héctor Andrade-Loarca; Gitta Kutyniok; Ozan Öktem; Philipp Petersen (SIAM J. Imaging Sci., 2019)

Optimal Approximation with Sparsely Connected Deep Neural Networks. - Helmut Bölcskei; Philipp Grohs; Gitta Kutyniok; Philipp Petersen (SIAM J. Math. Data Sci., 2019)

Anisotropic multiscale systems on bounded domains. - Philipp Grohs; Gitta Kutyniok; Jackie Ma; Philipp Petersen; Mones Raslan (Adv. Comput. Math., 2020)

Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs. - Fabian Laakmann; Philipp Petersen (Adv. Comput. Math., 2021)

The Modern Mathematics of Deep Learning. - Julius Berner; Philipp Grohs; Gitta Kutyniok; Philipp Petersen (CoRR, 2021)

Deep Microlocal Reconstruction for Limited-Angle Tomography. - Héctor Andrade-Loarca; Gitta Kutyniok; Ozan Öktem; Philipp Petersen (CoRR, 2021)

Optimal learning of high-dimensional classification problems using deep neural networks. - Philipp Petersen; Felix Voigtländer (CoRR, 2021)

Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size. - Philipp Petersen; Mones Raslan; Felix Voigtländer (Found. Comput. Math., 2021)

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. - Moritz Geist; Philipp Petersen; Mones Raslan; Reinhold Schneider; Gitta Kutyniok (J. Sci. Comput., 2021)

Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems. - Andrés Felipe Lerma Pineda; Philipp Christian Petersen (CoRR, 2022)

Mathematical Capabilities of ChatGPT. - Simon Frieder; Luca Pinchetti; Alexis Chevalier; Ryan-Rhys Griffiths; Tommaso Salvatori; Thomas Lukasiewicz; Philipp Petersen; Julius Berner (NeurIPS, 2023)

Large Language Models for Mathematicians. - Simon Frieder; Julius Berner; Philipp Petersen; Thomas Lukasiewicz (CoRR, 2023)

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. - Carlo Marcati; Joost A. A. Opschoor; Philipp Christian Petersen; Christoph Schwab (Found. Comput. Math., 2023)

Efficient Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders. - A. Martina Neuman; Philipp Christian Petersen (CoRR, 2024)

Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks. - Adeyemi D. Adeoye; Philipp Christian Petersen; Alberto Bemporad (CoRR, 2024)

Mathematical theory of deep learning. - Philipp Petersen; Jakob Zech (CoRR, 2024)

Dimension-independent learning rates for high-dimensional classification problems. - Andrés Felipe Lerma Pineda; Philipp Petersen; Simon Frieder; Thomas Lukasiewicz (CoRR, 2024)

First Order System Least Squares Neural Networks. - Joost A. A. Opschoor; Philipp Christian Petersen; Christoph Schwab (CoRR, 2024)

The sampling complexity of learning invertible residual neural networks. - Yuanyuan Li; Philipp Grohs; Philipp Petersen (CoRR, 2024)

VC dimensions of group convolutional neural networks. - Philipp Christian Petersen; Anna Sepliarskaia (Neural Networks, 2024)

Limitations of neural network training due to numerical instability of backpropagation. - Clemens Karner; Vladimir A. Kazeev; Philipp Christian Petersen (Adv. Comput. Math., 2024)

High-dimensional classification problems with Barron regular boundaries under margin conditions. - Jonathan García 001; Philipp Petersen (Neural Networks, 2025)

Sustainable AI: Mathematical Foundations of Spiking Neural Networks. - Adalbert Fono; Manjot Singh; Ernesto Araya; Philipp Christian Petersen; Holger Boche; Gitta Kutyniok (CoRR, 2025)

Numerical Error Analysis of Large Language Models. - Stanislav Budzinskiy; Wenyi Fang; Longbin Zeng; Philipp Petersen (CoRR, 2025)

Causal pieces: analysing and improving spiking neural networks piece by piece. - Dominik Dold; Philipp Christian Petersen (CoRR, 2025)

Minimax learning rates for estimating binary classifiers under margin conditions. - Jonathan García 001; Philipp Petersen (CoRR, 2025)