SD
Steffen Dereich
math.PRcs.LGmath.OCcs.NAmath.NAstat.MLmath.STstat.THmath.COcs.AI
On Valency
published · living versionsW_6854d6pd·v1 · currentpublished
Random networks with sublinear preferential attachment: The giant component
with Peter Mörters
1 version
W_ym44nwxm·v1published
W_ftsdgbrz·v1published
Preprints & journals
43 papers in the corpus · 2005–2026Convergence rates for the RMSprop optimizer with full control of the hyperparameters2608.30382v1 · Steffen Dereich, Arnulf Jentzen2026 · 0 citationsarXiv
On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations2608.04607v1 · Thang Do, Steffen Dereich, Arnulf Jentzen2026 · 0 citationsarXiv
Central limit theorem for the averaged Adam optimizer2606.21433v1 · Steffen Dereich, Arnulf Jentzen2026 · 0 citationsarXiv
Uniform a priori bounds and error analysis for the Adam stochastic gradient descent optimization method2603.18899v2 · Steffen Dereich, Thang Do, Arnulf Jentzen2026 · 0 citationsarXiv
ODE approximation for the Adam algorithm: General and overparametrized setting2511.04622v1 · Steffen Dereich, Arnulf Jentzen, Sebastian Kassing2025 · 0 citationsarXiv
Asymptotic stability properties and a priori bounds for Adam and other gradient descent optimization methods2509.10476v1 · Steffen Dereich, Robin Graeber, Arnulf Jentzen et al.2025 · 0 citationsarXiv
SAD Neural Networks: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures2505.09572v3 · Julian Kranz, Davide Gallon, Steffen Dereich et al.2025 · 0 citationsarXiv
Sharp higher order convergence rates for the Adam optimizer2504.19426v1 · Steffen Dereich, Arnulf Jentzen, Adrian Riekert2025 · 0 citationsarXiv
In almost all shallow analytic neural network optimization landscapes, efficient minimizers have strongly convex neighborhoods2504.08867v1 · Felix Benning, Steffen Dereich2025 · 0 citationsarXiv
Mathematical analysis of the gradients in deep learning2501.15646v1 · Steffen Dereich, Thang Do, Arnulf Jentzen et al.2025 · 0 citationsarXiv
Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems2501.06081v1 · Steffen Dereich, Arnulf Jentzen, Adrian Riekert2025 · 0 citationsarXiv
Convergence rates for the Adam optimizer2407.21078v1 · Steffen Dereich, Arnulf Jentzen2024 · 2 citationsarXiv
Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates2407.08100v1 · Steffen Dereich, Robin Graeber, Arnulf Jentzen2024 · 1 citationarXiv
Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses2406.14340v2 · Steffen Dereich, Arnulf Jentzen, Adrian Riekert2024 · 0 citationsarXiv
Traces left by random walks on large random graphs: local limits2403.14787v1 · Steffen Dereich2024 · 0 citationsarXiv
On the existence of optimal shallow feedforward networks with ReLU activation2303.03950v1 · Steffen Dereich, Sebastian Kassing2023 · 5 citationsarXiv
On the existence of minimizers in shallow residual ReLU neural network optimization landscapes2302.14690v2 · Steffen Dereich, Arnulf Jentzen, Sebastian Kassing2023 · 8 citationsarXiv
On minimal representations of shallow ReLU networks.35123261 · Dereich, Steffen, Kassing, Sebastian2022 · 8 citationsNeural networks : the official journal of the International Neural Network Society. 2022;148:121-128
Quasi-processes for branching Markov chains2107.06654v2 · Steffen Dereich, Martin Maiwald2021 · 1 citationarXiv
Cooling down stochastic differential equations: almost sure convergence2106.03510v2 · S. Dereich, S. Kassing2021 · 8 citationsStochastic Processes and their Applications, Volume 152, 2022, Pages 289-311
Central limit theorems for stochastic gradient descent with averaging for stable manifolds1912.09187v1 · Steffen Dereich, Sebastian Kassing2019 · 6 citationsarXiv
The shape of the emerging condensate in effective models of condensation1711.08355v1 · Volker Betz, Steffen Dereich, Peter Morters2017 · 6 citationsarXiv
Local neighbourhoods for first passage percolation on the configuration model1711.06479v1 · Steffen Dereich, Marcel Ortgiese2017 · 2 citationsarXiv
Distances in scale free networks at criticality1604.00779v2 · Steffen Dereich, Christian Monch, Peter Morters2016 · 5 citationsarXiv
Multilevel Monte Carlo for Lévy-driven SDEs: Central limit theorems for adaptive Euler schemes1602.00548v1 · Steffen Dereich, Sangmeng Li2016 · 19 citationsAnnals of Applied Probability 2016, Vol. 26, No. 1, 136-185
Non-extensive condensation in reinforced branching processes1601.08128v2 · Steffen Dereich, Cecile Mailler, Peter Morters2016 · 1 citationarXiv
General multilevel adaptations for stochastic approximation algorithms1506.05482v2 · Steffen Dereich, Thomas Mueller-Gronbach2015 · 9 citationsarXiv
Real Self-Similar Processes Started from the Origin1501.00647v1 · Steffen Dereich, Leif Doering, Andreas E. Kyprianou2015 · 37 citationsarXiv
Random Interlacements via Kuznetsov Measures1501.00649v1 · Steffen Dereich, Leif Doering2015 · 0 citationsarXiv
Robust analysis of preferential attachment models with fitness1302.3385v1 · Steffen Dereich, Marcel Ortgiese2013 · 37 citationsCombinator. Probab. Comp. 23 (2014) 386-411
Emergence of condensation in Kingman's model of selection and mutation1207.6203v1 · Steffen Dereich, Peter Morters2012 · 24 citationsarXiv
Persistence probabilities for an integrated random walk bridge1205.2895v1 · Frank Aurzada, Steffen Dereich, Mikhail Lifshits2012 · 7 citationsProbab. Math. Statist., 2014, 34, 1-22
Constructive quantization: approximation by empirical measures1108.5346v1 · Steffen Dereich, Michael Scheutzow, Reik Schottstedt2011 · 128 citationsarXiv
Typical distances in ultrasmall random networks1102.5680v1 · Steffen Dereich, Christian Monch, Peter Morters2011 · 39 citationsarXiv
Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction1101.1369v1 · Steffen Dereich2011 · 98 citationsAnnals of Applied Probability 2011, Vol. 21, No. 1, 283-311on Valency
The high resolution vector quantization problem with Orlicz norm distortion1010.4248v1 · Steffen Dereich, Christian Vormoor2010 · 10 citationsarXiv
Universality of the asymptotics of the one-sided exit problem for integrated processes1008.0485v1 · Frank Aurzada, Steffen Dereich2010 · 45 citationsarXiv
Random networks with sublinear preferential attachment: The giant component1007.0899v2 · Steffen Dereich, Peter Morters2010 · 69 citationsAnnals of Probability 2013, Vol. 41, No. 1, 329-384on Valency
Random networks with sublinear preferential attachment: Degree evolutions0807.4904v1 · Steffen Dereich, Peter Morters2008 · 88 citationsarXiv
Small deviations of general Lévy processes0805.1330v2 · Frank Aurzada, Steffen Dereich2008 · 18 citationsAnnals of Probability 2009, Vol. 37, No. 5, 2066-2092
High resolution quantization and entropy coding of jump processes0712.0964v1 · Frank Aurzada, Steffen Dereich, Michael Scheutzow et al.2007 · 3 citationsJournal of Complexity 25 (2009), no. 2, 163-187
The coding complexity of Lévy processes0707.3040v1 · Frank Aurzada, Steffen Dereich2007 · 5 citationsFoundations of Computational Mathematics 9 (2009), no. 3, 359-390
The Shannon information of filtrations and the additional logarithmic utility of insidersmath/0503013v2 · Stefan Ankirchner, Steffen Dereich, Peter Imkeller2005 · 72 citationsAnnals of Probability 2006, Vol. 34, No. 2, 743-778on Valency
Career total: 88 works. 43 are in this corpus.
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