Moritz Hehl conducts research on the geometry and topology of discrete structures, with a particular focus on curvature concepts on graphs and the structural insights that can be derived from them. He also investigates what such geometric quantities reveal about the structure of data and the behavior of neural networks.

Along with NeurIPS and ICLR, ICML is one of the three most important conferences in machine learning. It took place from the 6th to the 11th of July 2026 at the COEX Convention & Exhibition Center in Seoul and brought together several thousand researchers from academia and industry. For Moritz Hehl, the conference was above all an opportunity to present his work at the intersection of Riemannian geometry and deep learning to an audience drawn from both fields, and to engage with other groups to see what related questions they are currently working on.

The paper was written during a research stay at Harvard University last summer, in collaboration with Prof. Melanie Weber (Harvard University) and Prof. Dr. Max von Renesse (Leipzig University). The work relates the evolution of the feature geometry of neural networks to the Ricci flow from Riemannian geometry. Since the data manifold itself cannot be directly observed, the authors approximate its geometry using geometric graphs. Experiments involving over 20,000 trained neural networks show that they reshape geometry as predicted by the discrete Ricci flow: positively curved regions contract, while negatively curved regions expand. From this observation, the authors derive two practical design principles: a heuristic for early stopping and a geometric criterion for selecting the network depth.

For further insights into Moritz Hehl’s research and his experience as a researcher, see the interview with Moritz Hehl on page 28 in the Annual Report 2025.