Visualizing Uncertainty: Spatial Maps of Missing and Conflicting Evidence in Deep Learning

Uncertainty Quantification (UQ) aims to measure the reliability of model predictions, serving as a critical safeguard for deploying Vision-Language Models (VLMs) in safety-critical scenarios. Post-hoc approaches are widely adopted due to their lightweight nature, mapping the outputs of VLMs to uncertainty measures through learnable modules or inductive summarization. However, Post-hoc approaches remain inherently confined to fitting the failure patterns of the source domain, ignoring the dynamic nature of test distributions. To address this challenge, we propose a Dynamic Distribution-Aware Uncertainty Quantification framework (DDA-UQ) that shifts the paradigm from static mapping to a dynamic distribution-aware process. During training, we leverage a Gaussian Mixture Model to model the VVLMs'embedding space and extract distributional evidence, thereby dynamically deriving uncertainty estimates. During inference, the design dynamically responds to changes in the data distribution. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art methods.

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional assumptions, we propose Hyperspherical Confidence Mapping (HCM), a simple yet principled framework for sampling-free and distribution-free uncertainty estimation. HCM decomposes outputs into a magnitude and a normalized direction vector constrained to lie on the unit hypersphere, enabling a novel interpretation of uncertainty as the degree of violation of this geometric constraint. This yields deterministic and interpretable estimates applicable to both regression and classification. Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment. Our results highlight the power of geometric structure in uncertainty estimation and position HCM as a versatile alternative to conventional techniques.

The deployment of deep neural networks in safety-critical domains demands reliable estimates of predictive confidence, yet conventional architectures lack principled uncertainty quantification. This survey provides a structured, critical review of methods for Uncertainty Quantification (UQ) in deep learning, scoped to ensemble-based and approximate Bayesian approaches and the measures used to summarize their outputs. Relative to existing UQ surveys, our contribution is depth on efficient ensemble approximations and single-pass methods, and a unified treatment that separates the method producing a predictive distribution from the measure that summarizes its uncertainty. We organize methods into five families: Bayesian neural networks, Monte Carlo Dropout, deep ensembles, efficient ensemble approximations, and last-layer or single-pass approaches. We situate adjacent work on evidential and prior networks, conformal prediction, and post-hoc calibration, together with the decision-time tasks of out-of-distribution detection and selective prediction. For each, we examine theoretical motivation, implementation, empirical performance, and limitations. We then review ensemble diversity theory and uncertainty measures and their decompositions, contrasting the entropy decomposition with pairwise divergence measures, and consolidate evaluation methodology so that our qualitative comparisons share a common basis. We close with a brief treatment of uncertainty in large language models and open research directions, including efficient epistemic measures for classification, last-layer diversity, diversity and calibration under shift, and hybrid architectures.