Hidden Axis of Uncertainty: Latent-Posterior Alignment in Graph Neural Networks with Bayesian Output Layers

Bayesian Neural Networks (BNNs) with Bayesian output layers provide a principled and tractable framework for quantifying predictive uncertainty, yet the mechanisms shaping that uncertainty remain unclear. While conventional theory attributes uncertainty reduction to posterior contraction, the corresponding assumptions need not hold for deep models. In the Graph Neural Networks (GNNs) with Bayesian output layers studied here, we observe that predictive uncertainty decreases as latent representations shift toward lower-variance posterior directions, even though the posterior variance does not contract. We term this behavior Latent-Posterior Alignment (LPA) and conduct interventional experiments that support its functional role in shaping predictive uncertainty. Building on this insight, we propose Alignment-Guided Learning (AGL), which explicitly promotes this alignment during training. AGL effectively reduces predictive uncertainty while preserving accuracy and improves structural calibration, ensuring that the model confidence faithfully mirrors underlying data density. These findings provide a new perspective on uncertainty dynamics in GNNs with mean-field Bayesian output layers, shifting the focus from the magnitude of the posterior to the geometric interplay between latent and parameter spaces.

Uncertainty-Aware Deep Learning for Genomics Applications: Insights from an Empirical Study

Deep learning models have emerged as the standard computational tool for a wide range of applications in genomics. Yet, uncertainty quantification (UQ) -- and more specifically, the reliability of different uncertainty estimates in this domain -- has received little systematic attention. This work presents an empirical analysis of UQ in deep learning models, focusing on genomics applications. In a series of experiments, we contrast Deep Ensembles, Bayesian Neural Networks, and Monte Carlo-dropout methods. We assess their ability to quantify uncertainty in different scenarios, accounting for common dataset characteristics in two genomic application areas and modalities: sequence-to-activity models, and single-cell expression analysis. Our systematic comparison framework provides guidelines for the applicability and reliability of UQ methods in genomics, highlighting their strengths and limitations in different scenarios. We show that Bayesian Neural Networks are better at capturing uncertainty caused by strong class imbalance and out-of-distribution data in genomics, despite their computational disadvantages. Moreover, we show how uncertainty scores can be used to select high-quality predictions in protein-RNA interactions.

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.

TreeGRNG: Binary Tree Gaussian Random Number Generator for Efficient Probabilistic AI Hardware

Bayesian Neural Networks (BNNs) offer opportunities for greatly enhancing the trustworthiness of conventional neural networks by monitoring the uncertainties in decision-making. A significant drawback for BNN inference at the extreme edge, however, is the imperative need to incorporate Gaussian Random Number Generators (GRNG) within each neuron. State-of-the-art GRNG algorithms heavily depend on multiple arithmetic operations and the use of extensive look-up tables, posing significant implementation challenges for ultra-low power hardware implementations. To overcome this, this paper presents an innovative binary tree random number generator (TreeGRNG) allowing the use of ultra-low-cost constant comparators instead of arithmetic units. We further enhance the TreeGRNG proposal with a set of hardware-aware optimizations exploiting the Gaussian properties. The optimized TreeGRNG surpasses the State-of-the-Art (SoTA) in terms of distribution accuracy while achieving a 3.7$\times$ reduction in energy per sample and boosting the throughput per unit area by 5.8$\times$. Moreover, our TreeGRNG proposal possesses a distinct advantage over the current SoTA in terms of flexibility, as it easily enables designers to adjust the shape of the sampled probability distribution, extending beyond the capabilities of traditional GRNGs, opening the horizon towards future probabilistic AI designs. The TreeGRNG design is available open-source in the link

Neural Aided Kalman Filtering for UAV State Estimation in Degraded Sensing Environments

Accurate state estimation of nonlinear dynamical systems is fundamental to modern aerospace operations across air, sea, and space domains. Online tracking of adversarial unmanned aerial vehicles (UAVs) is especially challenging due to agile nonlinear motion, noisy and sparse sensor measurements, and unknown control inputs; conditions that violate key assumptions of classical Kalman filter variants and degrade estimation performance. Neural networks (NNs) can learn complex nonlinear relationships from data, but lack principled uncertainty quantification, which is critical for state estimation tasks where confidence bounds drive downstream decisions. We address this with Bayesian Neural Networks (BNNs), which model uncertainty through distributions over network weights and produce predictive means and uncertainties via Monte Carlo sampling. Building on this, we propose the Bayesian Neural Kalman Filter (BNKF): a hybrid framework coupling a trained BNN with a Kalman correction step for robust online UAV state estimation. Unlike related neural Kalman approaches, BNKF produces full state predictions and incorporates Bayesian uncertainty directly into covariance propagation, improving robustness under high noise conditions. We evaluate BNKF under varying radar noise levels and sampling rates using synthetic nonlinear UAV flight data. Five fold cross validation demonstrates that BNKF outperforms Extended and Unscented Kalman Filters in accuracy, precision, and truth containment under degraded sensing. An ensemble variant (BNKFe) further improves precision in high-noise edge cases at a slight accuracy tradeoff. Runtime analysis confirms minimal inference overhead, supporting real-time deployment feasibility.