arXiv：cs.LG（机器学习，全量分类）· Eduardo Fernandes Montesuma·· 5 小时前AI 评分33
BaryFM：用流匹配实现通用 Wasserstein 重心
Towards Universal Wasserstein Barycenters through Flow Matching
AI 导读
研究者提出 BaryFM，一个流匹配模型，可将边缘测度输运到 Wasserstein 单纯形中的任意重心，训练后通过常微分方程从该单纯形内的测度采样。该方法在域适应、泛化、贝叶斯后验聚合与算法公平性 4 项下游任务上验证，在 10 个域适应基准、15 种对比方法中取得最佳平均排名，匹配或超越非通用求解器。
正文
Abstract:Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called \emph{Wasserstein barycenters}. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the \emph{Wasserstein simplex}, remains underexplored. We refer to this problem as \emph{Universal Barycenter Approximation}, and propose \texttt{BaryFM}, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. \texttt{BaryFM} achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.
| Comments: | Under review |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2609.38547 [cs.LG] |
| (or arXiv:2609.38547v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38547 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Eduardo Fernandes Montesuma [view email]
[v1]
Tue, 29 Sep 2026 21:06:29 UTC (15,582 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org