2 citations · 3 across the 14 of their papers we have counts for
8 papers · 1 filter
On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations
Thang Do, Steffen Dereich, Arnulf Jentzen
Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs). In many relevant artificial intelligence (AI) s…
ODE approximation for the Adam algorithm: General and overparametrized setting
Steffen Dereich, Arnulf Jentzen, Sebastian Kassing
The Adam optimizer is currently presumably the most popular optimization method in deep learning. In this article we develop an ODE based method to study the Adam optimizer in a fa…
Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer
Steffen Dereich, Thang Do, Arnulf Jentzen +1
Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training…
Asymptotic stability properties and a priori bounds for Adam and other gradient descent optimization methods
Steffen Dereich, Robin Graeber, Arnulf Jentzen +1
Gradient descent (GD) based optimization methods are these days the standard tools to train deep neural networks in artificial intelligence systems. In optimization procedures in d…
Sharp higher order convergence rates for the Adam optimizer
Steffen Dereich, Arnulf Jentzen, Adrian Riekert
Gradient descent based optimization methods are the methods of choice to train deep neural networks in machine learning. Beyond the standard gradient descent method, also suitable…
Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems
Steffen Dereich, Arnulf Jentzen, Adrian Riekert
Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent i…
Convergence rates for the Adam optimizer
Steffen Dereich, Arnulf Jentzen
Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In prac…
Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses
Steffen Dereich, Arnulf Jentzen, Adrian Riekert
The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to…