5 papers
Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions
Richard Duong, Viktor Stein, Robert Beinert +2
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals towards given target mea…
SympFormer: Accelerated attention blocks via Inertial Dynamics on Density Manifolds
Viktor Stein, Wuchen Li, Gabriele Steidl
Transformers owe much of their empirical success in natural language processing to the self-attention blocks. Recent perspectives interpret attention blocks as interacting particle…
Interpolating between Optimal Transport and KL regularized Optimal Transport using Rényi Divergences
Jonas Bresch, Viktor Stein
Regularized optimal transport (OT) has received much attention in recent years starting from Cuturi's introduction of Kullback-Leibler (KL) divergence regularized OT. In this paper…
Wasserstein Gradient Flows of MMD Functionals with Distance Kernels under Sobolev Regularization
Richard Duong, Nicolaj Rux, Viktor Stein +1
We consider Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals for positive and negative distance kernels an…
Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces
Viktor Stein, Sebastian Neumayer, Nicolaj Rux +1
Commonly used -divergences of measures, e.g., the Kullback-Leibler divergence, are subject to limitations regarding the support of the involved measures. A remedy is regularizin…