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This paper proposes BaryFM, a flow matching model that learns to approximate the entire Wasserstein simplex — the full family of Wasserstein barycenters over the simplex of weight vectors — rather than a fixed-weight barycenter. BaryFM achieves the best average rank among 15 methods across 10 domain adaptation benchmarks and is validated on tasks including generalization, Bayesian posterior aggregation, and algorithmic fairness.
This paper introduces a method using Wasserstein barycenters to reconstruct language model embedding fields for predicting peer-misalignment penalties in spatial factor models, outperforming conventional weighting schemes.