About Me
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.
Contact
ETH Zurich, Rämistrasse 101, 8092 Zurich, (office HG G32.2)
florian.rossmannek@math.ethz.ch
Here is my official page at ETH Zurich.
Research Interest
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.
Research Articles
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 .
Publications
- 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]
Preprints
- Gradient descent provably escapes saddle points in the training of shallow ReLU networks (with P. Cheridito and A. Jentzen) (2022) [arXiv]
Theses
- 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]
Talks
Seminar Talks
- 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)
Teaching
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.
Courses at ETH
- 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)
Miscellaneous
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.