[2603.23783] Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models

Computer Science > Machine Learning arXiv:2603.23783 (cs) [Submitted on 24 Mar 2026] Title:Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models Authors:Kuepon Aueawatthanaphisut, Kuepon Aueawatthanaphisut View a PDF of the paper titled Probabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models, by Kuepon Aueawatthanaphisut and Kuepon Aueawatthanaphisut View PDF HTML (experimental) Abstract:Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper introduces an uncertainty-aware probabilistic latent transport framework that formulates domain adaptation as a stochastic geometric alignment problem in representation space. A Bayesian transport operator is proposed to redistribute latent probability mass along Wasserstein-type geodesic trajectories, while a PAC-Bayesian regularization mechanism constrains posterior model complexity to mitigate catastrophic overfitting. The proposed formulation yields theoretical guarantees on convergence stability, loss landscape smoothness, and sample efficiency under distributional shift. Empirical analyses demonstrate substantial reduction in latent manifold discrepancy, accelerated transport energy decay, and improved covariance calibration compared with deterministic fine-tuni...