arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.
arXiv:2608. 12111v1 Announce Type: cross Abstract: A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation.
arXiv:2605. 30253v2 Announce Type: replace-cross Abstract: We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm.
arXiv:2511.07414v2 Announce Type: replace-cross Abstract: The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainmen...
arXiv:2511.18060v3 Announce Type: replace-cross Abstract: Wasserstein-Fisher-Rao (WFR) gradient flows have been recently proposed as a powerful sampling tool that combines the advantages of pure Wass...
The paper studies the finite‑sample approximation of a Hessian‑guided perturbed Wasserstein gradient flow (PWGF), which adds Gaussian perturbations to Wasserstein gradient descent to escape saddle points in nonconvex problems. It analyzes when an interacting‑particle approximation remains accurate over growing time horizons, showing that accumulated negative curvature can amplify errors while subsequent positive curvature can damp them. Under regularity assumptions and a fixed perturbation schedule, the authors prove high‑probability tracking bounds for both particles and objective values, construct a population‑first coupling to handle state‑dependent jumps, and verify the theory in a variance‑plus‑cosine model and a regularized matrix‑factorization setting.
arXiv:2608. 03967v1 Announce Type: cross Abstract: Generative Flow Networks (GFlowNets) have emerged as a flexible framework for amortised inference over discrete and mixed discrete-continuous objects, requiring only an unnormalised target density specified through a reward.
The paper investigates a natural gradient method based on the Fisher information matrix of state-action distributions, which follows a Fisher‑Rao gradient flow within the state-action polytope under a linear potential. It establishes linear convergence rates for Fisher‑Rao gradient flows of linear programs, with the rate tied to the program’s geometry, and provides improved error bounds for entropic regularization. Additionally, the authors extend their analysis to perturbed flows, proving sublinear convergence for both perturbed Fisher‑Rao and natural gradient flows, thereby encompassing state‑action natural policy gradients.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
arXiv:2610.10278v1 Announce Type: cross Abstract: We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kin...
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 distributions driven by an energy functional.