Activation-Space Uncertainty Quantification for Pretrained Networks

• URL: http://arxiv.org/abs/2602.14934v2
• Date: Mon, 23 Feb 2026 10:54:32 GMT
• Title: Activation-Space Uncertainty Quantification for Pretrained Networks
• Authors: Richard Bergna, Stefan Depeweg, Sergio Calvo-Ordoñez, Jonathan Plenk, Alvaro Cartea, Jose Miguel Hernández-Lobato,
• Abstract summary: We introduce Gaussian Process Activations (GAPA), a post-hoc method that shifts Bayesian modeling from weights to activations.<n>GAPA replaces standard nonlinearities with activations whose posterior mean exactly matches the original activation, preserving the backbone's point predictions by construction.<n>To scale to modern architectures, we use a sparse variational inducing-point approximation over cached training activations, combined with local k-nearest-neighbor conditioning.
• Score: 2.001149416674759
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reliable uncertainty estimates are crucial for deploying pretrained models; yet, many strong methods for quantifying uncertainty require retraining, Monte Carlo sampling, or expensive second-order computations and may alter a frozen backbone's predictions. To address this, we introduce Gaussian Process Activations (GAPA), a post-hoc method that shifts Bayesian modeling from weights to activations. GAPA replaces standard nonlinearities with Gaussian-process activations whose posterior mean exactly matches the original activation, preserving the backbone's point predictions by construction while providing closed-form epistemic variances in activation space. To scale to modern architectures, we use a sparse variational inducing-point approximation over cached training activations, combined with local k-nearest-neighbor subset conditioning, enabling deterministic single-pass uncertainty propagation without sampling, backpropagation, or second-order information. Across regression, classification, image segmentation, and language modeling, GAPA matches or outperforms strong post-hoc baselines in calibration and out-of-distribution detection while remaining efficient at test time.

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