Scalable AI Uncertainty Quantification via Generalized Laplace Active Subspaces

The paper introduces a scalable method for uncertainty quantification in neural networks by applying a low‑rank generalized Laplace approximation within a data‑informed active subspace. It constructs a local Gaussian posterior around pretrained weights, calibrates the prior variance via empirical Bayes, and compares two posterior scalings: standard Bayesian and mean‑loss scaling. The study finds that mean‑loss scaling yields a more stable, lower‑dimensional subspace and produces calibrated, coherent predictive confidence intervals, whereas standard scaling can cause posterior variance contraction and degrade predictive coherence.

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