
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning. Thi...
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Numerically Solving Parametric Families of HighDimensional Kolmogorov Partial Differential Equations via Deep Learning
We present a deep learning algorithm for the numerical solution of param...
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How degenerate is the parametrization of neural networks with the ReLU activation function?
Neural network training is usually accomplished by solving a nonconvex ...
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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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Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of B
The development of new classification and regression algorithms based on...
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Julius Berner
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