arXiv AI
Jul 7
Wasserstein Residuals: Learning Gradient Flows from Population Dynamics
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
Neural Wasserstein Splines: Representation-Invariant Second-Order Priors for Trajectory Inference
Related stories
Hugging Face Trending Papers
Jul 6
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.
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.
arXiv Machine Learning
Sep 23
Penalized Nonreversible Langevin for Constrained Sampling
The paper introduces penalized nonreversible Langevin algorithms for sampling from a target distribution constrained to a compact convex set. It combines a squared distance penalty with skew-symmetric perturbations that preserve the penalized Gibbs distribution, and provides nonasymptotic total variation and Wasserstein bounds under various smoothness and contraction assumptions. Numerical experiments demonstrate the methods on constrained Bayesian regression, classification, neural networks, and truncated sampling, highlighting acceleration in a stochastic quadratic model.
arXiv Statistics ML
1d ago
Synthetic Data Augmentation for Functional Data: Wasserstein Risk Bounds and Diffusion-Based Conditional Generation
arXiv:2610.34120v1 Announce Type: cross Abstract: Functional data are costly to collect; samples of tens to hundreds of curves are common. Synthetic data augmentation can help, but its theory is deve...
arXiv Machine Learning
Oct 5
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.
arXiv Machine Learning
Oct 9
Barron Optimal Transport I: Generative Modeling
The paper introduces a new optimal transport framework that uses the Barron energy—an intrinsic neural network complexity measure—instead of the traditional kinetic energy. By modeling transport as deep residual networks that map a reference distribution to a target distribution, the authors define a new metric on probability measures and analyze its properties for generative modeling. They demonstrate that diffusion generative models are suboptimal in this Barron geometry and explore how adaptivity can improve alternative generative approaches.
arXiv AI
Aug 24
TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics
arXiv:2608.21070v1 Announce Type: cross Abstract: Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal T...
arXiv Machine Learning
Jul 10
Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
arXiv:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
arXiv Machine Learning
Jun 29
Deep Residual Networks Learn the Geodesic Curve in the Wasserstein Space
arXiv:2102. 09235v3 Announce Type: replace Abstract: Recent studies revealed the mathematical connection between deep neural networks (DNNs) and dynamic systems.
arXiv Machine Learning
Aug 7
The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
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.