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07/03/2023
Improved sampling via learned diffusions
Recently, a series of papers proposed deep learning-based approaches to ...
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01/31/2023
Mathematical Capabilities of ChatGPT
We investigate the mathematical capabilities of ChatGPT by testing it on...
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11/02/2022
An optimal control perspective on diffusion-based generative modeling
We establish a connection between stochastic optimal control and generat...
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06/21/2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning
The combination of Monte Carlo methods and deep learning has recently le...
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05/26/2022
Training ReLU networks to high uniform accuracy is intractable
Statistical learning theory provides bounds on the necessary number of t...
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05/09/2021
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning. Thi...
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11/09/2020
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
We present a deep learning algorithm for the numerical solution of param...
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05/23/2019
How degenerate is the parametrization of neural networks with the ReLU activation function?
Neural network training is usually accomplished by solving a non-convex ...
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05/13/2019
Towards a regularity theory for ReLU networks -- chain rule and global error estimates
Although for neural networks with locally Lipschitz continuous activatio...
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09/09/2018
