6 papers
Dynamical Optimal Transport with -Invariance: From Theory to Computation
Kevine Meugang Toukam, Max von Renesse, Johannes Storn
We introduce a modified Benamou--Brenier (MBB) formulation of optimal transport that incorporates Euclidean invariance at the dynamical level. We establish existence of minimizers…
Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusion
Vitalii Konarovskyi, Victor Marx, Max von Renesse
Introducing an interpolation method we derive lower bounds for the spectral gap for Brownian motion on general domains with sticky-reflecting boundary diffusion associated to the f…
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…
A gradient flow that is none: Heat flow with Wentzell boundary condition
Marie Bormann, Léonard Monsaingeon, D. R. Michiel Renger +1
We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold…
Dual Block Gradient Ascent for Entropically Regularised Quantum Optimal Transport
Marvin Randig, Max von Renesse
We present a block gradient ascent method for solving the quantum optimal transport problem with entropic regularisation similar to the algorithm proposed in [D. Feliciangeli, A. G…
Adiabatic Approximation of Coarse Grained Second Order Response
Fenna Müller, Max von Renesse
We propose estimators for dynamic second order response theory in coarse grained variables for driven out-of-equilibrium subsystems. The error is controlled through the the notion…