Activation-Space Uncertainty Quantification for Pretrained Networks

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 models uncertainty over activation outputs rather than over network weights. 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 activation-space variances that act as support-based uncertainty estimates. To scale to modern architectures, we use a sparse inducing-point approximation over cached reference pre-activations, combined with local k-nearest-neighbor subset conditioning, enabling deterministic single-pass uncertainty propagation. Across regression, classification, image segmentation, and language modeling, GAPA is competitive with strong post-hoc baselines and often improves calibration or out-of-distribution detection while remaining efficient at test time.