I am a researcher in mathematics at RiskLab, ETH Zurich, from which I obtained my doctoral degree in March 2023. My doctoral advisors were Patrick Cheridito and Arnulf Jentzen. Prior to that, I conducted my bachelor and master studies also at ETH Zurich.

ETH Zurich, RĂ¤mistrasse 101, 8092 Zurich, (office HG G32.2)

florian.rossmannek@math.ethz.ch

Here is my official page at ETH Zurich.

My BSc and MSc studies focussed on dynamical systems theory and geometry. For my PhD, I turned my attention to the mathematical theory of neural networks, tackling approximation and optimization problems. Looking forward, I am interested in applications of machine learning grounded in geometry and physics.

Expand the tabs below for a complete list of my publications and preprints. See also my Google Scholar profile here and my ORCID records here .

- Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions (with P. Cheridito and A. Jentzen),
*J. Nonlinear Sci.*, vol 32, 64 (2022) [journal version (open access), arXiv] - A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions (with P. Cheridito, A. Jentzen, and A. Riekert),
*J. Complexity*, vol 72 (2022) [journal version, arXiv] - Non-convergence of stochastic gradient descent in the training of deep neural networks (with P. Cheridito and A. Jentzen),
*J. Complexity*, vol 64 (2021) [journal version (open access), arXiv] - Efficient approximation of high-dimensional functions with neural networks (with P. Cheridito and A. Jentzen),
*IEEE Trans. Neural Netw. Learn. Syst.*, vol 33, no. 7 (2022) [journal version (open access), arXiv]

- Gradient descent provably escapes saddle points in the training of shallow ReLU networks (with P. Cheridito and A. Jentzen) (2022) [arXiv]

- PhD thesis: The curse of dimensionality and gradient-based training of neural networks: shrinking the gap between theory and applications (2023) [link]
- MSc thesis: Magnetic and Exotic Anosov Hamiltonian Structures (2019) [link]
- MSc project: Currents in Geometry and Analysis (2019) [link]
- MSc project: The Moduli Space of Hyperbolic Surfaces, Analytic Teichmüller Theory, and the Pants Graph (2018) [link]
- BSc thesis: An Introduction to Complex Dynamics and the Mandelbrot Set (2017) [link]

- On gradient-based training of neural networks, Stochastic Finance Group Seminar, ETH Zurich (2023)
- Approximation Capacities of ReLU Neural Networks, Post/Doctoral Seminar in Mathematical Finance, ETH Zurich (2021)

Over the past years, I was involved with various courses as a teaching assistant or coordinator. Expand the tab below for a complete list of courses.

- Fall 2022: coordinator for Mathematics I (D-BIOL/CHAB/HEST)
- Spring 2022: coordinator for Probability and Statistics (D-MATH)
- Spring 2021: coordinator for Mathematics II (D-BIOL/CHAB/HEST)
- Fall 2019: co-organizer of an undergraduate seminar on machine learning (D-MATH)
- Fall 2018: teaching assistant for Analysis I (D-MATH)
- Fall 2017: teaching assistant for Algorithms and Complexity (D-INFK)
- Spring 2017: teaching assistant for Topology (D-MATH)
- Fall 2016: teaching assistant for Algorithms and Complexity (D-INFK)

At the mathematics department of ETH Zurich, I served as a board member of the association of the mid-level academic faculty (VMM) and as a member of the teaching commission (UK) and of the commission of the mathematics library (MathBib).

Here is some combinatorics exercise for fun.