Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation

A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions

(2022) Patrick Cheridito et al.   JOURNAL OF COMPLEXITY

Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions

(2022) Patrick Cheridito et al.   JOURNAL OF NONLINEAR SCIENCE

A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions

(2022) Arnulf Jentzen et al.   ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

Solving the Kolmogorov PDE by Means of Deep Learning

(2021) Christian Beck et al.   JOURNAL OF SCIENTIFIC COMPUTING

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

(2020) Weinan E et al.   Science China-Mathematics

Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size

(2020) Philipp Petersen et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning

(2020) Jérôme Bolte et al.   MATHEMATICAL PROGRAMMING

{Euclidean, metric, and Wasserstein} gradient flows: an overview

(2017) Filippo Santambrogio   Bulletin of Mathematical Sciences