4 papers
Neural Feature Geometry Evolves as Discrete Ricci Flow
Moritz Hehl, Max von Renesse, Melanie Weber
Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our under…
Betti number estimates for non-negatively curved graphs
Moritz Hehl, Florentin Münch
In this paper, we establish Betti number estimates for graphs with non-negative Ollivier curvature, and for graphs with non-negative Bakry-Émery curvature, providing a discrete ana…
A condition for non-negative Lin-Lu-Yau curvature
Moritz Hehl
We investigate the Ollivier-Ricci curvature and its modification introduced by Lin, Lu, and Yau on locally finite graphs. The main contribution of this work is a lower bound on the…
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs
Moritz Hehl
We study the Ollivier-Ricci curvature and its modification introduced by Lin, Lu, and Yau on graphs. We provide a complete characterization of all graphs with Lin-Lu-Yau curvature…