Philipp Petersen

According to our database, Philipp Petersen authored at least 34 papers between 2016 and 2025.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of four.

2025

Minimax learning rates for estimating binary classifiers under margin conditions.

Jonathan García, Philipp Petersen

CoRR, May, 2025

Causal pieces: analysing and improving spiking neural networks piece by piece.

Dominik Dold, Philipp Christian Petersen

CoRR, April, 2025

Numerical Error Analysis of Large Language Models.

Stanislav Budzinskiy, Wenyi Fang, Longbin Zeng, Philipp Petersen

CoRR, March, 2025

Sustainable AI: Mathematical Foundations of Spiking Neural Networks.

Adalbert Fono, Manjot Singh, Ernesto Araya, Philipp Christian Petersen, Holger Boche, Gitta Kutyniok

CoRR, March, 2025

High-dimensional classification problems with Barron regular boundaries under margin conditions.

Jonathan García, Philipp Petersen

Neural Networks, 2025

2024

Limitations of neural network training due to numerical instability of backpropagation.

Clemens Karner, Vladimir A. Kazeev, Philipp Christian Petersen

Adv. Comput. Math., February, 2024

VC dimensions of group convolutional neural networks.

Philipp Christian Petersen, Anna Sepliarskaia

Neural Networks, January, 2024

The sampling complexity of learning invertible residual neural networks.

Yuanyuan Li, Philipp Grohs, Philipp Petersen

CoRR, 2024

First Order System Least Squares Neural Networks.

Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab

CoRR, 2024

Dimension-independent learning rates for high-dimensional classification problems.

Andrés Felipe Lerma Pineda, Philipp Petersen, Simon Frieder, Thomas Lukasiewicz

CoRR, 2024

Mathematical theory of deep learning.

Philipp Petersen, Jakob Zech

CoRR, 2024

Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks.

Adeyemi D. Adeoye, Philipp Christian Petersen, Alberto Bemporad

CoRR, 2024

Efficient Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders.

A. Martina Neuman, Philipp Christian Petersen

CoRR, 2024

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., June, 2023

Large Language Models for Mathematicians.

Simon Frieder, Julius Berner, Philipp Petersen, Thomas Lukasiewicz

CoRR, 2023

Mathematical Capabilities of ChatGPT.

Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, Julius Berner

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.

Andrés Felipe Lerma Pineda, Philipp Christian Petersen

CoRR, 2022

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

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

Philipp Petersen, Mones Raslan, Felix Voigtländer

Found. Comput. Math., 2021

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

Philipp Petersen, Felix Voigtländer

CoRR, 2021

Deep Microlocal Reconstruction for Limited-Angle Tomography.

Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen

CoRR, 2021

The Modern Mathematics of Deep Learning.

Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

CoRR, 2021

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

Fabian Laakmann, Philipp Petersen

Adv. Comput. Math., 2021

2020

Anisotropic multiscale systems on bounded domains.

Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, Mones Raslan

Adv. Comput. Math., 2020

2019

Optimal Approximation with Sparsely Connected Deep Neural Networks.

Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

SIAM J. Math. Data Sci., 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

Approximation in L^p(μ) with deep ReLU neural networks.

Felix Voigtländer, Philipp Petersen

CoRR, 2019

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs.

Gitta Kutyniok, Philipp Petersen, Mones Raslan, Reinhold Schneider

CoRR, 2019

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

Ingo Gühring, Gitta Kutyniok, Philipp Petersen

CoRR, 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, Christian Kümmerle, Gitta Kutyniok, Sebastian Lunz, Jan MacDonald, Ryan Malthaner, Gregory Naisat, Ariel Neufeld, Philipp Christian Petersen, Rafael Reisenhofer, Jun-Da Sheng, Laura Thesing, Philipp Trunschke, Johannes von Lindheim, David Weber, Melanie Weber

CoRR, 2019

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

Philipp Petersen, Mones Raslan

Adv. Comput. Math., 2019

2018

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

Philipp Petersen, Felix Voigtländer

Neural Networks, 2018

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

Philipp Petersen, Felix Voigtländer

CoRR, 2018

2016

Shearlet approximation of functions with discontinuous derivatives.

Philipp Petersen

J. Approx. Theory, 2016