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06/29/2023
Efficient Sobolev approximation of linear parabolic PDEs in high dimensions
In this paper, we study the error in first order Sobolev norm in the app...
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08/03/2022
Gradient descent provably escapes saddle points in the training of shallow ReLU networks
Dynamical systems theory has recently been applied in optimization to pr...
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03/19/2021
Landscape analysis for shallow ReLU neural networks: complete classification of critical points for affine target functions
In this paper, we analyze the landscape of the true loss of a ReLU neura...
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02/19/2021
A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
Gradient descent optimization algorithms are the standard ingredients th...
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06/12/2020
Non-convergence of stochastic gradient descent in the training of deep neural networks
Deep neural networks have successfully been trained in various applicati...
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12/09/2019