Preprints

  • Polyak's Heavy Ball Method Achieves Accelerated Local Rate of Convergence under Polyak-Lojasiewicz Inequality,
    joint work with Simon Weissmann
    (Preprint)

  • Exponential convergence rates for momentum stochastic gradient descent in the overparametrized setting,
    joint work with Benjamin Gess
    (Preprint)

Publications

  • Stochastic Modified Flows for Riemannian Stochastic Gradient Descent,
    joint work with Benjamin Gess and Nimit Rana
    SIAM J. Control Optim. 62(6): 3288-3314 (arXiv, PDF)

  • On the existence of minimizers in shallow residual ReLU neural network optimization landscapes,
    joint work with Steffen Dereich and Arnulf Jentzen
    SIAM J. Numer. Anal. 62(6): 2640-2666 (2024) (arXiv, PDF)

  • Convergence of Stochastic Gradient Descent Schemes for Lojasiewicz-Landscapes,
    joint work with Steffen Dereich
    J. Mach. Learn. 3(3): 245-281 (2024) (arXiv,
    PDF)

  • On the Existence of Optimal Shallow Feedforward Networks with ReLU Activation,
    joint work with Steffen Dereich
    J. Mach. Learn. 3(1): 1-22 (2024) (arXiv, PDF)

  • Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent,
    joint work with Benjamin Gess and Vitalii Konarovskyi
    J. Mach. Learn. Res. 25(30):1-27 (2024) (arXiv, PDF)

  • Central limit theorems for stochastic gradient descent with averaging for stable manifolds,
    joint work with Steffen Dereich
    Electron. J. Probab. 28, 1-48 (2023) (arXiv, PDF)

  • Cooling down stochastic differential equations: almost sure convergence,
    joint work with Steffen Dereich
    Stochastic Process. Appl. 152, 289-311 (2022) (arXiv, PDF)

  • On minimal representations of shallow ReLU networks,
    joint work with Steffen Dereich
    Neural Networks 148, 121-128 (2022) (arXiv, PDF)