Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

תקציר מקורי באנגליתarXiv: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. Existing discrete methods are not because as they assume access to the complete set of samples from the input measures. Meanwhile, neural network approaches do scale well, but rely on complex optimization problems and cannot easily incorporate label information. We address these limitations through gradient flows in the space of probability measures. Through time discretization, we achieve a scalable algorithm that i) relies on mini-batch optimal transport, ii) accepts modular regularization through task-aware functions, and iii) seamlessly integrates supervised information into the ground