Author

Steffen Dereich

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Preprint Aug 2026

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations

A generalized variant of the MUON optimizer involving an arbitrary number of generalized NS steps with polynomials of possibly arbitrary high degree is proposed and studied and an error analysis for MUON with the generalized NS steps is established that provides convergence rates in terms of the number of gradient step...

Thang Do, Steffen Dereich, Arnulf Jentzen · 4 citations · ⚡1

#machine learning Mar 2026

Uniform a priori bounds and error analysis for the Adam stochastic gradient descent optimization method

This work is the key contribution of this work to establish uniform a priori bounds for Adam and to provide -- for the first time -- an unconditional error analysis for Adam for a large class of strongly convex SOPs.

Steffen Dereich, Thang Do, Arnulf Jentzen · arXiv.org · 4 citations

#machine learning Preprint Aug 2026

Convergence rates for the RMSprop optimizer with full control of the hyperparameters

The key innovative new feature in the proof of the analysis are suitable inverse moment bounds for the second moment process in RMSprop that hold not just for all sufficiently large n but hold for every gradient step $n=1,2,3,...$ with all error constants being explicitly specified.

Steffen Dereich, Arnulf Jentzen · 0 citations