Julius Berner
Julius Berner
Faculty of Mathematics, University of Vienna
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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
The Modern Mathematics of Deep Learning
J Berner, P Grohs, G Kutyniok, P Petersen
Mathematical Aspects of Deep Learning, 1-111, 2022
Mathematical Capabilities of ChatGPT
S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ...
arXiv preprint arXiv:2301.13867, 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
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
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
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
An optimal control perspective on diffusion-based generative modeling
J Berner, L Richter, K Ullrich
NeurIPS 2022 Workshop on Score-Based Methods, 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
Learning ReLU networks to high uniform accuracy is intractable
J Berner, P Grohs, F Voigtlaender
International Conference on Learning Representations, 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
Solving stochastic differential equations and Kolmogorov equations by means of deep learning and Multilevel Monte Carlo simulation
J Berner
University of Vienna, 2018
Diskrete Kosinustransformation in der Bildverarbeitung
J Berner
University of Vienna, 2016
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