Florian Rossmannek

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.


ETH Zurich, Rämistrasse 101, 8092 Zurich, (office HG G32.2)


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 .

  • 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.