Stochastic Nonlinearities Improve Uncertainty Estimation

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.

In this study, we explore in depth a few under-studied topics at the intersection of uncertainty estimation and segmentation. Prior work has shown that the quality of uncertainty estimates can be very sensitive to a range of variables. As one of the main uses of uncertainty estimation is to help identify and deal with prediction errors in practical scenarios, any factors that affect this must be clearly identified. For example, do more challenging domains or different datasets and architectures result in worse performance when using uncertainty estimates? Can prior frames in a video sequence in fact provide useful uncertainty estimates comparable to other approaches? Is it possible to combine uncertainty estimation approaches, taking advantage of sample diversity, to get better estimates? Finally, when might it make sense to use an ensemble-based uncertainty estimate over a deterministic network? We address these questions by creating a framework for and executing a large scale study across many variables such as datasets, backbones, and downstream tasks, for both semantic and panoptic segmentation. We find that a) the more challenging task of panoptic segmentation usually results in worse performance while high performance variance between datasets and backbones indicates that generalization is not guaranteed, b) time series samples can be useful for specific configurations, but in many cases are not worth the cost, c) sample diversity shows the most promise in the downstream task of calibration, but otherwise fails to beat simpler alternatives, d) a deterministic approach is adequate for some downstream tasks, but ensembles allow for significant improvements if the right conditions can be achieved in deployment.

Neural activation coverage (NAC) is a recently-proposed technique for out-of-distribution detection and generalization. We build upon this promising foundation and extend the method to work as an uncertainty estimation technique for already-trained artificial neural networks in the domain of regression. Our experiments confirm NAC uncertainty scores to be more meaningful than other techniques, e.g. Monte-Carlo Dropout.