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We introduce Stiefel-Bayes Adapters (SBA), a Bayesian PEFT framework that places a Matrix Langevin prior over orthonormal adapter factors on the Stiefel manifold $\\St$ and performs approximate posterior inference via tangent space Laplace approximation with geodesic retraction. Unlike Gaussian priors in flat space projected onto orthogonality constraints, our prior on the manifold naturally encodes the inductive bias that adapter subspaces should be well conditioned and orthogonal, while the posterior provides calibrated predictive uncertainty without recalibration. 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