Uncertainty quantification for trustworthy deep learning: Methods and measures

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.

Covariance Last-Layer Ensembles: Function-Space Diversity for Efficient Uncertainty Quantification

A Last-Layer Ensemble (LLE), $K$ linear units on one shared frozen feature map, is an efficient single-pass approach to the disagreement-based epistemic uncertainty for out-of-distribution (OOD) detection. Its weakness is that members share the backbone gradient and can converge toward the same function, collapsing the inter-member diversity the signal depends on. Whether last-layer diversity can be restored, and what mitigates the collapse, is an open question. The weight-orthonormality defining Orthonormal Certificates (OC), the weight-orthonormal special case of the LLE, is only an indirect correction; it decorrelates the weights of the members, not their predictions. Here, we instead target the collapse directly in function space, with a Covariance Last-Layer Ensemble (cov-LLE) that places a direct covariance penalty on member activations. Cov-LLE restores the function-space diversity that weight-orthonormality cannot, and at matched $K$ recovers much of the diversity and calibration of a deep ensemble at $1\times$ backbone cost (in-distribution prediction variance $0.05\!\to\!9.3$ vs.\ $22.1$ ($\times10^{-3}$), and ECE $0.135\!\to\!0.090$ vs.\ $0.035$, for a $K\times$-cost deep ensemble), at no cost to accuracy. Viewing OC as a last-layer ensemble also organizes detectors into a two-axis taxonomy (by how their units are trained and how their outputs are scored) and exposes the OC score as a magnitude, motivating a scale-invariant, label-free direction score that repairs its near-OOD failure, adding $+0.16$ to $+0.18$ ROC AUC on every backbone.

Variance-Gated Ensembles: An Epistemic-Aware Framework for Uncertainty Estimation

Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric (i.e., data-related) and epistemic (i.e., model-related) components. However, additive decomposition has recently been questioned, with evidence that it breaks down when using finite-ensemble sampling and/or mismatched predictive distributions. This paper introduces Variance-Gated Ensembles (VGE), an intuitive, differentiable framework that injects epistemic sensitivity via a signal-to-noise gate computed from ensemble statistics. VGE provides: (i) a Variance-Gated Margin Uncertainty (VGMU) score that couples decision margins with ensemble predictive variance; and (ii) a Variance-Gated Normalization (VGN) layer that generalizes the variance-gated uncertainty mechanism to training via per-class, learnable normalization of ensemble member probabilities. We derive closed-form vector-Jacobian products enabling end-to-end training through ensemble sample mean and variance. VGE matches or exceeds state-of-the-art information-theoretic baselines while remaining computationally efficient. As a result, VGE provides a practical and scalable approach to epistemic-aware uncertainty estimation in ensemble models. An open-source implementation is available at: https://github.com/nextdevai/vge.

Platelet enumeration in dense aggregates

Identifying and counting blood components such as red blood cells, various types of white blood cells, and platelets is a critical task for healthcare practitioners. Deep learning approaches, particularly convolutional neural networks (CNNs) using supervised learning strategies, have shown considerable success for such tasks. However, CNN based architectures such as U-Net, often struggles to accurately identify platelets due to their sizes and high variability of features. To address these challenges, researchers have commonly employed strategies such as class weighted loss functions, which have demonstrated some success. However, this does not address the more significant challenge of platelet variability in size and tendency to form aggregates and associations with other blood components. In this study, we explored an alternative approach by investigating the role of convolutional kernels in mitigating these issues. We also assigned separate classes to singular platelets and platelet aggregates and performed semantic segmentation using various U-Net architectures for identifying platelets. We then evaluated and compared two common methods (pixel area method and connected component analysis) for counting platelets and proposed an alternative approach specialized for single platelets and platelet aggregates. Our experiments provided results that showed significant improvements in the identification of platelets, highlighting the importance of optimizing convolutional operations and class designations. We show that the common practice of pixel area-based counting often over estimate platelet counts, whereas the proposed method presented in this work offers significant improvements. We discuss in detail about these methods from segmentation masks.

Masked strategies for images with small objects

The hematology analytics used for detection and classification of small blood components is a significant challenge. In particular, when objects exists as small pixel-sized entities in a large context of similar objects. Deep learning approaches using supervised models with pre-trained weights, such as residual networks and vision transformers have demonstrated success for many applications. Unfortunately, when applied to images outside the domain of learned representations, these methods often result with less than acceptable performance. A strategy to overcome this can be achieved by using self-supervised models, where representations are learned and weights are then applied for downstream applications. Recently, masked autoencoders have proven to be effective to obtain representations that captures global context information. By masking regions of an image and having the model learn to reconstruct both the masked and non-masked regions, weights can be used for various applications. However, if the sizes of the objects in images are less than the size of the mask, the global context information is lost, making it almost impossible to reconstruct the image. In this study, we investigated the effect of mask ratios and patch sizes for blood components using a MAE to obtain learned ViT encoder representations. We then applied the encoder weights to train a U-Net Transformer for semantic segmentation to obtain both local and global contextual information. Our experimental results demonstrates that both smaller mask ratios and patch sizes improve the reconstruction of images using a MAE. We also show the results of semantic segmentation with and without pre-trained weights, where smaller-sized blood components benefited with pre-training. Overall, our proposed method offers an efficient and effective strategy for the segmentation and classification of small objects.