12 papers
Wasserstein Residuals: Learning Gradient Flows from Population Dynamics
Markus Heinonen, Yair Shenfeld, Ricardo Baptista +4
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distribu…
Matrix displacement convexity along density flows
Yair Shenfeld
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and sem…
Exact renormalization groups and transportation of measures
Yair Shenfeld
This note provides a new perspective on Polchinski's exact renormalization group, by explaining how it gives rise, via the multiscale Bakry-Ãmery criterion, to Lipschitz transport…
Optimal transport maps, majorization, and log-subharmonic measures
Guido De Philippis, Yair Shenfeld
Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous pheno…
Intrinsic dimensional functional inequalities on model spaces
Alexandros Eskenazis, Yair Shenfeld
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model…
Binomial flows: Denoising and flow matching for discrete ordinal data
Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, thi…