1 citations · 1 across the 8 of their papers we have counts for
11 papers
SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
Viktor Stein, Levin Maier, Wuchen Li +1
The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood. Recent perspectives interpret attention blocks as interacting p…
SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics
Gregor Kornhardt, Moritz Piening, Jannis Chemseddine +1
Evaluating text generation requires measuring how well the generated distribution matches the data distribution. For autoregressive models, this is done by the perplexity. Diffusio…
Generalized Wasserstein Flow Matching: Nested Couplings for Point Cloud Generation
Moritz Piening, Richard Duong, Gabriele Steidl
We formulate flow matching on probability measures over probability measures. Directly from the Wasserstein-on-Wasserstein (WoW) continuity equation, we show that admissible nested…
Spherical Flows for Sampling Categorical Data
Jannis Chemseddine, Gregor Kornhardt, Gabriele Steidl
We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the p…
Adapting Noise to Data: Generative Flows from 1D Processes
Jannis Chemseddine, Gregor Kornhardt, Richard Duong +1
The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for lea…
Telegrapher's Generative Model via Kac Flows
Richard Duong, Jannis Chemseddine, Peter K. Friz +1
We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equat…
Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flows
Nicolaj Rux, Michael Quellmalz, Gabriele Steidl
Negative distance kernels were used in the definition of maximum mean discrepancies (MMDs) in statistics and lead to favorable numerical results in various ap…
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 and…
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 measu…
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…
Morphing of Manifold-Valued Images inspired by Discrete Geodesics in Image Spaces
Sebastian Neumayer, Johannes Persch, Gabriele Steidl
This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued set…