Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation

2026-07-27 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Data Science & Analytics · Depth: Expert, extended

Summary

A new framework for computing Wasserstein barycenters, based on Wasserstein Gradient Flows (WGFs), addresses the scalability limitations of existing discrete methods. Developed by Eduardo Fernandes Montesuma, Yassir Bendou, and Mike Gartrell from Sigma Nova, this approach enables mini-batch sampling from input measures and scales effectively with the number of input measures. It also allows for regularization through internal, potential, and interaction energy functionals. The authors present two algorithms for empirical and Gaussian mixture measures, providing convergence guarantees under the Polyak-Łojasiewicz inequality. Experimental validation on toy datasets and multi-source domain adaptation benchmarks demonstrates that WGF methods outperform previous discrete and neural network-based techniques, particularly when incorporating label information.

Key takeaway

For Machine Learning Engineers working on multi-source domain adaptation, consider adopting Wasserstein Gradient Flows for barycenter computation. This method offers superior scalability and accuracy, especially when integrating label information into the Optimal Transport objective. You should experiment with the proposed regularization functionals, like entropy and repulsion terms, to improve class separation and overall performance on benchmarks such as Office 31 and ISRUC.

Key insights

Wasserstein Gradient Flows offer a scalable, regularized approach to computing Wasserstein barycenters.

Principles

• Mini-batch sampling improves barycenter scalability.
• Regularization via energy functionals enhances barycenter quality.
• Label information is crucial for domain adaptation performance.

Method

The method recasts barycenter computation as a gradient flow, using block-coordinate descent with mini-batches and incorporating internal, potential, and interaction energy functionals for regularization.

In practice

• Apply WGFs for scalable barycenter computation.
• Integrate label information into Optimal Transport objectives.
• Use entropy and repulsion functionals to regularize barycenters.

Topics

• Wasserstein Barycenters
• Gradient Flows
• Optimal Transport
• Multi-Source Domain Adaptation
• Gaussian Mixture Models
• Scalability

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.