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-Ãmery curvature, providing a discrete an…
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…
Ollivier-Ricci curvature of regular graphs
Moritz Hehl
We derive explicit formulas for the Lin-Lu-Yau curvature and the Ollivier-Ricci curvature in terms of graph parameters and an optimal assignment. Utilizing these precise expression…