4 citations · 8 across the 12 of their papers we have counts for
14 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…
Strong error analysis for the stochastic momentum optimizer
Davide Gallon, Arnulf Jentzen
Stochastic gradient descent (SGD) optimization schemes are the methods of choice for the optimization of deep neural networks (DNNs) in artificial intelligence (AI) systems. Often…
Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks
Shokhrukh Ibragimov, Arnulf Jentzen
Gradient based optimization methods are nowadays the methods of choice for training deep neural networks (DNNs) in artificial intelligence (AI) systems. In practically relevant DNN…
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…
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…
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…