Prof. Dr. Steffen Dereich

Topics in Mathematics Münster

Research Interests

$\bullet$ Complex networks and non-standard growth models.
$\bullet$ Stochastic algorithms, numerical analysis and complexity.
$\bullet$ Stochastic analysis.

Recent Publications of Prof. Dr. Steffen Dereich

$\bullet$ Steffen Dereich, Arnulf Jentzen, and Adrian Riekert. Averaged Adam accelerates stochastic optimization in the training of deep neural network approximations for partial differential equation and optimal control problems. arXiv e-prints, January 2025.

$\bullet$ Steffen Dereich and Arnulf Jentzen. Convergence rates for the Adam optimizer. arXiv e-prints, July 2024. arXiv:2407.21078.

$\bullet$ Steffen Dereich, Robin Graeber, and Arnulf Jentzen. Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates. arXiv e-prints, July 2024. arXiv:2407.08100.

$\bullet$ Steffen Dereich and Sebastian Kassing. Convergence of stochastic gradient descent schemes for Łojasiewicz-landscapes. Journal of Machine Learning, 3(3):245–281, June 2024. doi:10.4208/jml.240109.

$\bullet$ Steffen Dereich, Arnulf Jentzen, and Adrian Riekert. Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses. arXiv e-prints, June 2024. arXiv:2406.14340.

$\bullet$ Steffen Dereich and Sebastian Kassing. On the existence of optimal shallow feedforward networks with ReLU activation. Journal of Machine Learning, 3(1):1–22, January 2024. doi:10.4208/jml.230903.

$\bullet$ Steffen Dereich and Sebastian Kassing. On the existence of optimal shallow feedforward networks with ReLU activation. arXiv e-prints, March 2023. arXiv:2303.03950.

$\bullet$ Steffen Dereich, Arnulf Jentzen, and Sebastian Kassing. On the existence of minimizers in shallow residual ReLU neural network optimization landscapes. arXiv e-prints, February 2023. arXiv:2302.14690.

$\bullet$ Steffen Dereich and Sebastian Kassing. Central limit theorems for stochastic gradient descent with averaging for stable manifolds. Electronic Journal of Probability, 28:1–48, January 2023. doi:10.1214/23-EJP947.

$\bullet$ Steffen Dereich and Sebastian Kassing. Cooling down stochastic differential equations: Almost sure convergence. Stoch. Process. their Appl., 152:289–311, October 2022. doi:10.1016/j.spa.2022.06.020.

$\bullet$ Steffen Dereich and Sebastian Kassing. On minimal representations of shallow ReLU networks. Neural Networks, 148:121–128, April 2022. doi:10.1016/j.neunet.2022.01.006.

$\bullet$ Steffen Dereich and Martin Maiwald. Quasi-processes for branching Markov chains. arXiv e-prints, July 2021. arXiv:2107.06654.

$\bullet$ Steffen Dereich and Sebastian Kassing. Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes. arXiv e-prints, February 2021. arXiv:2102.09385.

$\bullet$ Steffen Dereich. General multilevel adaptations for stochastic approximation algorithms II: CLTs. Stochastic Process. Appl., 132:226–260, February 2021. doi:10.1016/j.spa.2020.11.001.

$\bullet$ Steffen Dereich and Sebastian Kassing. Central limit theorems for stochastic gradient descent with averaging for stable manifolds. arXiv e-prints, December 2019. arXiv:1912.09187.

$\bullet$ Steffen Dereich. The rank-one and the preferential attachment paradigm. In Network Science, pages 43–58. November 2019. doi:10.1007/978-3-030-26814-5_4.

$\bullet$ Steffen Dereich and Thomas Müller-Gronbach. General multilevel adaptations for stochastic approximation algorithms of Robbins–Monro and Polyak–Ruppert type. Numer. Math., 142(2):279–328, June 2019. doi:10.1007/s00211-019-01024-y.