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Hugging Face Trending Papers

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

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.

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arXiv Machine Learning
5d ago

Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals

The paper introduces Double‑Stitch, a simulation‑free method for learning population dynamics in Wasserstein space. It penalizes the residual of the equation of motion along a learned path, derived from a Clebsch variational principle that avoids gradient velocities. Experiments on synthetic, single‑cell, and ocean vortex data show that Double‑Stitch matches or surpasses gradient‑flow and simulation‑based methods while training 4–14 times faster.

By Fedor Sergeev, Markus Heinonen, Daniel Waxman, Tim Cooijmans, Ricardo Baptista, Dmitry Batenkov, Eli Bingham
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arXiv Machine Learning
Jun 30

Learning from samples: inverse problems over measures

arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon
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arXiv AI
Oct 2

Discrete Wasserstein Flows for One-Step Generative Modeling

The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.

By Alessandro Micheli, Andrea Zerio, Samir Bhatt
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arXiv AI
Sep 7

Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty

The paper introduces SUDO, a simulation‑free framework for unbalanced dynamic optimal transport (UDOT) that supports general convex growth penalties beyond the quadratic Wasserstein‑Fisher‑Rao case. By showing that concave penalties lead to degenerate solutions, the authors focus on convex penalties, learning conditional paths and transport costs to solve a semi‑coupling problem and then applying unbalanced flow matching. On benchmark datasets, SUDO matches the accuracy of analytical WFR solvers while being faster than simulation‑based methods, and it also handles asymmetric penalties that better reflect proliferation‑dominant biological priors.

By Junda Ying, Yuxuan Wang, Bowen Yang, Peijie Zhou, Lei Zhang
diffusionbenchmarks
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arXiv Machine Learning
2d ago

Finite-Sample Approximation of Hessian-Guided Perturbed Wasserstein Gradient Flows

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.

By Ryotaro Kawata, Atsushi Nitanda, Taiji Suzuki
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arXiv Machine Learning
Oct 2

RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.

By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung
diffusionbenchmarks
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arXiv Machine Learning
Aug 13

Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.

By Thejani Gamage, Hyemin Gu, Zhizhen Zhang, Ziyu Chen, Markos Katsoulakis, Luc Rey-Bellet
fine-tuning
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