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.
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
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.
arXiv Machine Learning
Jul 7
Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics
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.
arXiv Machine Learning
6d ago
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
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
Jul 27
Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation
arXiv:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
Hugging Face Trending Papers
Jul 29
Equilibrium Training of Energy-Based Models with Parallel Trajectory Tempering
Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning.
Hugging Face Trending Papers
Jun 24
Variational Inference via Entropic Transport Descent
Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.
arXiv Machine Learning
Jun 19
Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
arXiv:2604. 21097v2 Announce Type: replace-cross Abstract: Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model with data-driven methods such as machine learning emulators.
arXiv Machine Learning
Jun 30
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
arXiv AI
Jun 18
Correcting Sensor-Induced Distribution Drift with Wasserstein Adversarial Learning
arXiv:2606. 18561v1 Announce Type: cross Abstract: The quality of recorded data depends on the stability of the sensor system that acquires it.
arXiv Machine Learning
22h ago
Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields
arXiv:2608. 18004v1 Announce Type: new Abstract: Probabilistic modeling of physical fields benefits from both a data-driven prior and known physical structure such as the governing equations.