Julius Berner

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philipp grohsUniversity of ViennaVerified email at univie.ac.at
Philipp PetersenUniversity of ViennaVerified email at univie.ac.at
Gitta KutyniokBavarian AI Chair for Mathematical Foundations of Artificial Intelligence, LMU MunichVerified email at math.lmu.de
Arnulf JentzenThe Chinese University of Hong Kong, Shenzhen & University of MünsterVerified email at uni-muenster.de
Dennis ElbrächterUniversity of ViennaVerified email at univie.ac.at
Ryan-Rhys GriffithsMeta ResearchVerified email at cam.ac.uk
Tommaso SalvatoriVERSES, Inc.Verified email at verses.io
Luca PinchettiDphil Computer Science, Oxford UniversityVerified email at cs.ox.ac.uk
Thomas LukasiewiczVienna University of Technology, Austria; University of Oxford, UKVerified email at tuwien.ac.at
Pavol HararPostDoc @ University of Vienna, Faculty of MathematicsVerified email at univie.ac.at
David Sebastian FischerBroad Institute of MIT and HarvardVerified email at broadinstitute.org
Fabian J TheisHelmholtz Munich, Technical University of MunichVerified email at helmholtz-muenchen.de
Claudio M. VerdunTechnical University of MunichVerified email at ma.tum.de
Felix KrahmerAssociate Professor for Optimization and Data Analysis, Technische Universität MünchenVerified email at ma.tum.de
Tim FuchsTechnical University of MunichVerified email at tum.de
Markus DablanderDPhil (= PhD) Researcher, University of OxfordVerified email at maths.ox.ac.uk
Lorenz Richterdida, Zuse Institute BerlinVerified email at zib.de
Karen UllrichFAIRVerified email at fb.com
Felix VoigtlaenderProfessor for Mathematics, Catholic University Eichstätt-IngolstadtVerified email at ku.de

Julius Berner

Faculty of Mathematics, University of Vienna

Verified email at univie.ac.at - Homepage

Deep Learning Applied Mathematics


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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of … J Berner, P Grohs, A Jentzen SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020	161	2020
The Modern Mathematics of Deep Learning J Berner, P Grohs, G Kutyniok, P Petersen Mathematical Aspects of Deep Learning, 1-111, 2022	86*	2022
Mathematical Capabilities of ChatGPT S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ... arXiv preprint arXiv:2301.13867, 2023	59	2023
Group testing for SARS-CoV-2 allows for up to 10-fold efficiency increase across realistic scenarios and testing strategies CM Verdun, T Fuchs, P Harar, D Elbrächter, DS Fischer, J Berner, ... Frontiers in Public Health 9, 583377, 2021	49	2021
How degenerate is the parametrization of neural networks with the ReLU activation function? J Berner, D Elbrächter, P Grohs Advances in Neural Information Processing Systems, 7790-7801, 2019	30*	2019
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning J Berner, M Dablander, P Grohs Advances in Neural Information Processing Systems 33, 2020	29	2020
Towards a regularity theory for ReLU networks–chain rule and global error estimates J Berner, D Elbrächter, P Grohs, A Jentzen 2019 13th International conference on Sampling Theory and Applications …, 2019	13	2019
An optimal control perspective on diffusion-based generative modeling J Berner, L Richter, K Ullrich NeurIPS 2022 Workshop on Score-Based Methods, 2022	3	2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning L Richter, J Berner International Conference on Machine Learning, 18649-18666, 2022	2	2022
Learning ReLU networks to high uniform accuracy is intractable J Berner, P Grohs, F Voigtlaender International Conference on Learning Representations, 2023	1	2023
Die moderne Mathematik des tiefen Lernens J Berner, P Grohs, G Kutyniok, P Petersen Mitteilungen der Deutschen Mathematiker-Vereinigung 29 (4), 191-197, 2021	1	2021
Solving stochastic differential equations and Kolmogorov equations by means of deep learning and Multilevel Monte Carlo simulation J Berner University of Vienna, 2018		2018
Diskrete Kosinustransformation in der Bildverarbeitung J Berner University of Vienna, 2016		2016

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