23 citations · 72 across the 17 of their papers we have counts for
20 papers
Jumping up and down: Denoiser diffusion models for discrete ordinal data
Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti
Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data,…
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…
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…
A dynamical formulation of multi-marginal optimal transport
Brendan Pass, Yair Shenfeld
We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation…
Sectional curvature and matrix displacement convexity
Gautam Aishwarya, Liran Rotem, Yair Shenfeld
We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy tensor is matrix displacement convex. As an application, under the assumpt…
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…
Improvement of Wu's logarithmic Sobolev inequality via the Poisson-Föllmer process
Shrey Aryan, Pablo López-Rivera, Yair Shenfeld
We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show…
The Poisson transport map
Pablo López-Rivera, Yair Shenfeld
We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes…
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…
Transportation onto log-Lipschitz perturbations
Max Fathi, Dan Mikulincer, Yair Shenfeld
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bo…
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…
The extremals of Stanley's inequalities for partially ordered sets
Zhao Yu Ma, Yair Shenfeld
Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality…
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-Émery criterion, to Lipschitz transport…
On the Lipschitz properties of transportation along heat flows
Dan Mikulincer, Yair Shenfeld
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several…
The Brownian transport map
Dan Mikulincer, Yair Shenfeld
Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however…
The Extremals of the Alexandrov-Fenchel Inequality for Convex Polytopes
Yair Shenfeld, Ramon van Handel
The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The cha…
Stability of the logarithmic Sobolev inequality via the Föllmer Process
Ronen Eldan, Joseph Lehec, Yair Shenfeld
We study the stability and instability of the Gaussian logarithmic Sobolev inequality, in terms of covariance, Wasserstein distance and Fisher information, addressing several open…
The Extremals of Minkowski's Quadratic Inequality
Yair Shenfeld, Ramon van Handel
In a seminal paper "Volumen und Oberfläche" (1903), Minkowski introduced the basic notion of mixed volumes and the corresponding inequalities that lie at the heart of convex geomet…
Mixed volumes and the Bochner method
Yair Shenfeld, Ramon van Handel
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coeffici…
The equality cases of the Ehrhard-Borell inequality
Yair Shenfeld, Ramon van Handel
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian me…