1 citations · 1 across the 6 of their papers we have counts for
7 papers
Mathematical analysis of the gradients in deep learning
Steffen Dereich, Thang Do, Arnulf Jentzen +1
Deep learning algorithms -- typically consisting of a class of deep artificial neural networks (ANNs) trained by a stochastic gradient descent (SGD) optimization method -- are nowa…
Li-Yau and Harnack inequalities via curvature-dimension conditions for discrete long-range jump operators including the fractional discrete Laplacian
Sebastian Kräss, Frederic Weber, Rico Zacher
We consider operators of the form on the one-dimensional lattice with symmetric, integrable kernel . We prove se…
Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel
Frederic Weber, Rico Zacher
We establish a reduction principle to derive Li-Yau inequalities for non-local diffusion problems in a very general framework, which covers both the discrete and continuous setting…
Entropy-information inequalities under curvature-dimension conditions for continuous-time Markov chains
Frederic Weber
In the setting of reversible continuous-time Markov chains, the condition has been shown recently to be a consistent analogue to the Bakry-Émery condition in the diffusive s…
The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains
Frederic Weber, Rico Zacher
We consider continuous-time (not necessarily finite) Markov chains on discrete spaces and identify a curvature-dimension inequality, the condition , which serves as…
The Fractional Laplacian has Infinite Dimension
Adrian Spener, Frederic Weber, Rico Zacher
We show that the fractional Laplacian on fails to satisfy the Bakry-Émery curvature-dimension inequality for all curvature bounds and all…