Uncertainty Quantification

Reliable camera input is essential for safety-critical ADAS perception, but most monitoring approaches detect sensor failures only after downstream performance has degraded. We propose a proactive camera reliability monitoring framework that estimates perception risk from degradation-induced uncertainty patterns before downstream failure becomes observable. The method introduces a Global Sensor Health Index (GSHI), a continuous reliability score that aggregates per-degradation severities using a risk-aware multiplicative formulation, allowing severe single-mode failures such as lens occlusion or motion blur to dominate the health estimate. A lightweight multi-task network predicts degradation type, severity, GSHI, and spatial uncertainty maps from a single RGB image without downstream task feedback. Training uses physics- and geometry-aware synthetic supervision over twelve camera degradation modes. Experiments on KITTI-derived degradations show that GSHI decreases monotonically with severity, achieves a health-estimation MAE of 0.064, and provides positive early-warning lead time of 0.47 $\pm$ 0.25 severity units before YOLOv8 detection failure. GSHI also outperforms IQA, detector-confidence, and clean-feature OOD baselines, and transfers zero-shot to real adverse-weather driving data. These results support degradation-aware uncertainty analysis as a practical direction for proactive camera reliability monitoring in intelligent vehicles.

Self-consistency detects hallucinations by generating multiple sampled answers to a question and measuring agreement, but this requires repeated decoding and can be sensitive to lexical variation. Semantic self-consistency improves this by clustering sampled answers by meaning using natural language inference, but it adds both sampling cost and external inference overhead. We show that first-token confidence, phi_first, computed from the normalized entropy of the top-K logits at the first content-bearing answer token of a single greedy decode, matches or modestly exceeds semantic self-consistency on closed-book short-answer factual question answering. Across three 7-8B instruction-tuned models and two benchmarks, phi_first achieves a mean AUROC of 0.820, compared with 0.793 for semantic agreement and 0.791 for standard surface-form self-consistency. A subsumption test shows that phi_first is moderately to strongly correlated with semantic agreement, and combining the two signals yields only a small AUROC improvement over phi_first alone. These results suggest that much of the uncertainty information captured by multi-sample agreement is already available in the model's initial token distribution. We argue that phi_first should be reported as a default low-cost baseline before invoking sampling-based uncertainty estimation.

Automated mental health prediction using textual data has shown promising results with deep learning and large language models. However, deploying these models in high-stakes real-world settings remains challenging, as existing approaches largely rely on semantic representations and often produce overconfident predictions under ambiguous, noisy, or shifted data. Moreover, most methods lack reliable uncertainty estimation, undermining trust in risk-sensitive mental health applications. To address these limitations, we formulate the task as a multi-view learning problem that integrates semantic information from encoder-only models with higher-level reasoning information from decoder-only models, where reasoning-aware representations and uncertainty modeling are obtained in a trustworthy manner. To ensure reliable fusion, we adopt an evidential learning framework based on Subjective Logic to explicitly model uncertainty and introduce an evidential fusion strategy that balances complementary views while discounting unreliable evidence. Benchmarking on three real-world datasets, Dreaddit, SDCNL, and DepSeverity, reports accuracies of 0.835, 0.731, and 0.751, respectively, demonstrating its potential for reliable mental health prediction. Additional experiments on robustness to noise and case studies for interpretability confirm that our proposed framework not only improves predictive performance but also provides trustworthy uncertainty estimates and human-understandable reasoning signals, making it suitable for risk-sensitive applications in mental health assessment.

Uncertainty quantification (UQ) in graph neural networks (GNNs) is crucial in high-stakes domains but remains a significant challenge. In graph settings, message passing often relies on strong assumptions such as exchangeability, which are rarely satisfied in practice, and achieving reliable UQ typically requires costly resampling or post-hoc calibration. To address these issues, we introduce Quantile-free Prediction Interval GNN (QpiGNN), a framework that builds on quantile regression (QR) to enable GNN-based UQ by directly optimizing coverage and interval width without requiring quantile inputs or post-processing. QpiGNN employs a dual-head architecture that decouples prediction and uncertainty, and is trained with label-only supervision through a quantile-free joint loss. This design allows efficient training and yields robust prediction intervals, with theoretical guarantees of asymptotic coverage and near-optimal width under mild assumptions. Experiments on 19 synthetic and real-world benchmarks show QpiGNN achieves average 22% higher coverage and 50% narrower intervals than baselines, while ensuring efficiency and robustness to noise and structural shifts.

Uncertainty quantification (UQ) is an important technique for ensuring the trustworthiness of LLMs, given their tendency to hallucinate. Existing state-of-the-art UQ approaches for free-form generation rely heavily on sampling, which incurs high computational cost and variance. In this work, we propose the first gradient-based UQ method for free-form generation, SemGrad, which is sampling-free and computationally efficient. Unlike prior gradient-based methods developed for classification tasks that operates in parameter space, we propose to consider gradients in semantic space. Our method builds on the key intuition that a confident LLM should maintain stable output distributions under semantically equivalent input perturbations. We interpret the stability as the gradients in semantic space and introduce a Semantic Preservation Score (SPS) to identify embeddings that best capture semantics, with respect to which gradients are computed. We further propose HybridGrad, which combines the strengths of SemGrad and parameter gradients. Experiments demonstrate that both of our methods provide efficient and effective uncertainty estimates, achieving superior performance than state-of-the-art methods, particularly in settings with multiple valid responses.

Climate classification plays a vital role in agricultural planning, hydrological studies, and climate science. One of the most widely used systems for classifying global climate zones is the Köppen-Trewartha (KT) classification. However, the KT classification is fundamentally deterministic, offering discrete labels to spatial locations without accounting for uncertainties in classification. In this paper, we provide a framework for probabilistic modeling of climatic zones. We implement a feedforward artificial neural network (ANN) for classification, allowing for efficient, uncertainty-aware categorization of climatic regions, thereby offering a more nuanced understanding of transitional climate zones compared to traditional deterministic methods. We apply this method to the Sahara Desert region over the 30-year period of 1960 - 1989, using data at more than 400,000 space-time locations from the first 11 years to train our model. We assess the model's short- and long-term classification capabilities to evaluate its stability and accuracy over time. We also compare the probabilistic classification from our model with the traditional KT classification. In addition, we use fluctuation analysis methods to highlight the temporal evolution of climatic zones across the Sahara region and identify areas undergoing significant flux of probabilities of their climate classes, providing insights into broader trends in desertification.

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior distribution of model parameters, and then propagating posterior samples through the predictive model via Monte Carlo simulation. This sequential workflow can be computationally demanding, particularly for high-fidelity models such as those governed by partial differential equations. We propose a variational Bayesian framework that directly targets the posterior-predictive distribution and jointly learns variational approximations of both the posterior and the corresponding predictive distribution. The formulation introduces a variational upper bound on the Kullback--Leibler divergence together with moment-based regularization terms. The variational distributions are trained in an amortized manner, shifting computational effort to an offline stage and enabling efficient online inference. Numerical experiments ranging from analytical benchmarks to a finite-element solid mechanics problem demonstrate that the proposed method achieves more accurate predictive distributions than conventional two-stage variational inference, while substantially reducing the cost of online predictive inference.

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection-diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Reliable wildfire spread prediction is vital for risk-aware emergency planning, yet most deep learning models lack principled uncertainty quantification (UQ). Further, for boundary-sensitive cases like wildfire spread, evaluating models with global metrics alone is often insufficient. To shift the focus of UQ evaluation toward a more operationally relevant approach, the Fire-Centered Evaluation Region (FCER) framework is introduced as a spatially conditioned protocol to characterize UQ within critical fire zones. Using FCER, an Ensemble is compared against an distilled single-pass student model on the WildfireSpreadTS dataset. The student model demonstrates comparable calibration and complementary uncertainty ranking in boundary-relevant regimes. Code is available at https://github.com/jonasvilhofunk/WildfireUQ-FCER

Vision-Language Models (VLMs) have enabled autonomous GUI agents that translate natural language instructions into executable screen coordinates. However, grounding performance degrades in high-resolution interfaces, where dense layouts and small interactive elements expose a resolution gap between modern displays and model input constraints. Existing zoom-in strategies rely on fixed anchors, heuristic grids, or reinforcement learning, lacking a principled mechanism to adaptively determine where refinement is needed and how much spatial uncertainty should be explored. We propose AutoFocus, a training-free, uncertainty-aware active visual search framework for GUI grounding. Our key insight is that token-level perplexity in coordinate generation naturally reflects spatial uncertainty. Rather than committing to a single prediction, AutoFocus samples multiple coordinate hypotheses and converts their axial perplexities into an anisotropic gaussian spatial probability field, explicitly modeling directional uncertainty. Based on this field, we generate global and local region proposals and introduce Shape-Aware Zooming to balance tight localization with contextual preservation. A visual prompt-based aggregation step then selects the most consistent prediction via structured comparison. Extensive experiments on ScreenSpot-Pro and ScreenSpot-V2 demonstrate consistent improvements across both general-purpose and GUI-specialized VLMs.

Missing data imputation remains a fundamental challenge in modern data science, especially when uncertainty quantification is essential. In this work, we propose MissBGM, an AI-powered missing data imputation method via Bayesian generative modeling that bridges the expressive flexibility of neural networks with the statistical rigor of Bayesian inference. Unlike existing methods that often focus on point estimates or treat the missingness mechanism implicitly, MissBGM explicitly and jointly models the data-generating and missingness mechanisms, providing principled posterior uncertainty over imputations rather than a single point estimate. We develop a stochastic optimization framework with alternating updates among missing values, model parameters, and latent variables until convergence. Our theoretical analysis shows that estimates of missing values from MissBGM converge consistently under mild assumptions. Empirically, we demonstrate that MissBGM achieves superior performance over traditional imputers and recent neural network-based methods across extensive experimental settings. These results establish MissBGM as a principled and scalable solution for modern missing data imputation. The code for MissBGM is open sourced at https://github.com/liuq-lab/MissBGM.

Epistemic uncertainty estimation is essential for identifying regions where deep learning system outputs may be unreliable. However, existing approaches require computationally expensive ensemble methods or multiple stochastic forward passes, limiting their scalability to dense prediction tasks like segmentation. We propose Resolution-Aggregated Decoder Mutual Information (RADMI), a single-pass method that estimates prediction uncertainty by measuring mutual information (MI) between consecutive decoder layers in segmentation networks. We observe that elevated inter-layer MI correlates with prediction uncertainty, as the network must integrate conflicting contextual information at ambiguous regions such as class boundaries. Evaluating on a seismic facies segmentation benchmark, RADMI achieves the highest correlation with deep ensemble uncertainty among all single-pass methods, outperforming the next-best baselines by 5.5% in Pearson and 10.7% in Spearman correlation coefficients. Compared to baselines that either lack spatial precision or demand significant computational overhead, RADMI yields sharp, boundary-localized uncertainty maps without architectural modifications. Our results suggest that linear aggregation of normalized information flow provides a principled and efficient proxy for prediction uncertainty in encoder-decoder architectures.

Libraries of Low-Rank Adaptation (LoRA) adapters are becoming a practical by-product of parameter-efficient adaptation. Once such adapters accumulate, a natural question is no longer how to train one adapter for one task, but how to reuse an open pool of adapters for a new task given only a small support set. Prior work has shown that LoRA modules can be composed at the task level and dynamically selected at the instance level. However, open-pool LoRA reuse is not automatic: retrieving relevant adapters does not guarantee that their parameter updates are compatible, and composing adapters does not guarantee reliable outputs. We introduce the Sparse-Composition Agreement Layer (SCALE), a post-retrieval audit and composition framework for open-pool LoRA reuse. SCALE contains a deployable 1.0* merge path, Layer-Adaptive Sparse Residual Composition (LASRC), and a higher-cost reliability-analysis layer for multi-view disagreement. LASRC addresses merge interference by preserving a linear anchor while residualizing block-wise adapter update directions. The reliability layer treats disagreement among sparse composition views as an observable uncertainty signal and compares agreement, support-loss proxy selection, and oracle headroom under explicit path cost. In matched FLAN-T5-Large, BIG-Bench Hard (BBH), and 97-LoRA experiments, LASRC gives a directional single-view gain under fixed retrieval, while SCALE-support is reported as a query-label-free 3.0* reliability-analysis variant rather than as a calibrated or throughput-equivalent selector. Protocol-distinct BBH-8 validation shows the same qualitative trend on three decoder-only backbones. Detailed scores, paired audits, and path-cost records are reported in the experimental section.

Learning-based approaches to verifying unknown Markov decision processes (MDPs) often employ uncertain MDPs. These models use, for example, confidence intervals to capture transition uncertainty and allow synthesis of policies that are robust to this uncertainty. However, this approach typically quantifies uncertainty independently for individual transition probabilities, ignoring dependencies due to shared latent quantities. We propose to learn such models using parametric MDPs (pMDPs), where transition probabilities are expressions over a set of parameters. We project statistical uncertainty from empirical transition frequencies onto the pMDP's parameter space, yielding a probably approximately correct (PAC) uncertainty model for the underlying MDP that respects the algebraic dependencies between transitions. The resulting models are algorithmically challenging to solve, so we propose a hierarchy of sound polytopic outer approximations of the induced confidence set. We implement and evaluate our approach, demonstrating substantially tighter uncertainty estimates than classical interval-based uncertain MDP learning techniques.

Large-scale GPS trajectory data offer rich observations of human mobility, yet assigning trip purposes to detected stops remains challenging due to the absence of individual-level ground truth, spatial uncertainty from GPS noise and incomplete points of interest (POIs) coverage, and fundamental behavioral differences across trip purposes. We propose a weakly supervised framework integrating neighborhood-level POI semantic zones with distance-weighted spatial likelihoods, differentiated inference strategies for mandatory and non-mandatory activities, and a multi-phase Pareto optimization that jointly minimizes distributional divergence from household travel survey statistics and maximizes inference reliability without requiring annotated labels. Evaluated on over 81 million staypoints in Los Angeles, the framework reduces activity type frequency Jensen-Shannon distance (JSD) by 23%, start time JSD by 48%, and duration JSD by 12% respectively relative to a comparable baseline. The proposed approach provides a scalable and uncertainty-aware path from raw GPS trajectories to semantically annotated mobility data for travel demand modeling and transportation policy analysis.

Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty in the presence of noisy and limited data. Deep Symbolic Regression (DSR) uses a neural network to generate symbolic expressions, but it is designed to identify a single best-fitting expression rather than infer a posterior distribution over models. We introduce Deep Variational Inference Symbolic Regression (DVISR), a variational Bayesian extension of DSR. DVISR replaces the original reward with the integrand of the evidence lower bound. It also extends the network architecture to output distributions over constants within expressions, enabling posterior inference over both expression trees and their associated constants. We show that DVISR can recover the true posterior in simple settings, both with and without constant tokens, and we examine how its performance changes as the size of the expression space increases. These results position DVISR as a step toward scalable Bayesian symbolic regression with uncertainty over full symbolic models.

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency. Code is available at https://github.com/MaxwellYaoNi/DAPPr.

Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or propagate approximate covariance through many integration steps, trading off training cost, inference cost, or accuracy. We show that none of these trade-offs is necessary. By extending Tweedie's formula from the denoising setting to the flow matching interpolant, we derive an exact, closed-form expression for the posterior covariance at every point along the generative trajectory. The result depends on a single quantity, namely the divergence of the learned velocity field, which can be computed post-hoc on any pre-trained flow matching model, requiring no retraining and no architectural modification. For one-step generators such as MeanFlow, the same formula yields the end-to-end generation uncertainty in a single forward pass, eliminating the multi-step variance propagation required by all prior methods. Experiments on MNIST confirm that the resulting per-pixel uncertainty maps are semantically meaningful, concentrating on digit boundaries where inter-sample variation is highest, and that the scalar uncertainty score tracks actual prediction error, all at roughly $10^4 \times$ less total compute than ensembling or Monte Carlo dropout.

Operator learning enables fast surrogate modelling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: the quadratic cost of dense neural layers and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously. Using Quantum Orthogonal Neural Networks (QOrthoNNs), we characterize the resource regime in which their established $\widetilde{\mathcal{O}}(n)$ hidden-layer running-time scaling improves on the $\mathcal{O}(n^2)$ cost of a classical dense layer. To quantify uncertainty, we combine ensemble predictions with split conformal calibration. For a new input-output function pair jointly exchangeable with the calibration pairs, we prove a finite-sample, distribution-free lower bound on the expected fraction of covered query locations. As a secondary proof-of-concept, we explore hybrid classical-quantum architectures and superposed execution to manage ensemble runtime and hardware requirements. Experiments on synthetic operator benchmarks and real-world power-system dynamics show accurate predictions under ideal simulation and empirical coverage near the target under both ideal conditions and selected compact-circuit simulations with depolarizing or device-calibrated composite noise. Together, these results connect resource-aware scalability analysis with finite-sample uncertainty guarantees for quantum operator learning.

Egocentric pose estimation for Augmented Reality (AR) and assistive devices requires not just accurate predictions but guaranteed uncertainty regions. Conformal prediction (CP) provides such guarantees without retraining, but we show that standard CP with a single fixed threshold achieves nominal 90% overall coverage while covering only ~60% of the hardest 25% of frames (Q4) -- a ~30 percentage-point conditional coverage gap consistent across 12 participants, 3 predictors, and 3 horizons (108 evaluations) on EPIC-Fields. We further show that a geodesic SE(3) nonconformity score identifies physically harder frames than Euclidean scoring, with only 15-26% Q4 overlap and 2-3x higher ground-truth camera displacement for geodesic Q4 frames. To close the coverage gap, we propose DINOv2-Bridge adaptive CP: a two-stage difficulty estimator trained on a single source participant that transfers cross-participant without any images at test time, improving Q4 coverage from ~0.75 to ~0.93 while maintaining overall coverage at the 90% target.

Automatic Short Answer Grading (ASAG) with generative large language models (LLMs) has recently demonstrated strong performance without task-specific fine-tuning, while also enabling the generation of synthetic feedback for educational assessment. Despite these advances, LLM-based grading remains imperfect, making reliable confidence estimates essential for safe and effective human-AI collaboration in educational decision-making. In this work, we investigate confidence estimation for ASAG with LLMs by jointly considering model-based confidence signals and dataset-derived uncertainty. We systematically compare three model-based confidence estimation strategies, namely verbalizing, latent, and consistency-based confidence estimation, and show that model-based confidence alone is insufficient to reliably capture uncertainty in ASAG. To address this limitation, we propose a hybrid confidence framework that integrates model-based confidence signals with an explicit estimate of dataset-derived aleatoric uncertainty. Aleatoric uncertainty is operationalized by clustering semantically embedded student responses and quantifying within-cluster heterogeneity. Our results demonstrate that the proposed hybrid confidence measure yields more reliable confidence estimates and improves selective grading performance compared to single-source approaches. Overall, this work advances confidence-aware LLM-based grading for human-in-the-loop assessment, supporting more trustworthy AI-assisted educational assessment systems.

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.

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.

The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools create new opportunities for semi-supervised inference, in which labeled data are limited and expensive to obtain, whereas unlabeled data are abundant and widely available. Given a collection of predictors, we treat them as a mixture of experts (MOE) and introduce an MOE-powered semi-supervised inference framework built upon prediction-powered inference (PPI). Motivated by the variance reduction principle underlying PPI, the proposed framework seeks the mixture of experts that achieves the smallest possible variance. Compared with standard PPI, the MOE-powered inference framework adapts to the unknown performance of individual predictors, benefits from their collective predictive power, and enjoys a best-expert guarantee. The framework is flexible and applies to mean estimation, linear regression, quantile estimation, and general M-estimation. We develop non-asymptotic theory for the MOE-powered inference framework and establish upper bounds on the coverage error of the resulting confidence intervals. Numerical experiments demonstrate the practical effectiveness of MOE-powered inference and corroborate our theoretical findings.

Automatic Emergency Braking (AEB) systems represent a safety-critical national interest, with the National Highway Traffic Safety Administration (NHTSA) Federal Motor Vehicle Safety Standard (FMVSS No. 127) requiring AEB in all new light vehicles sold in the United States by September 2029. However, production implementations frequently rely on deterministic stopping-distance or Time-to-Collision (TTC) thresholds that fail to capture uncertainty in sensing, road conditions, and vehicle dynamics. This paper presents a GPU-accelerated Monte Carlo framework for stochastic evaluation of emergency braking performance using a high-fidelity longitudinal vehicle model incorporating aerodynamic drag, road grade, brake actuator dynamics, and weight transfer effects. A one-thread-per-sample execution strategy exploits the independence of Monte Carlo rollouts, while deterministic CPU-generated sampling ensures bit-exact numerical consistency between CPU and GPU implementations. The framework is evaluated across four hardware platforms spanning development and deployment environments: two laptop GPUs (GTX 1650, RTX 5070) and two automotive-grade embedded platforms (Jetson Orin Nano, Jetson AGX Orin). Peak speedups of 54.57x are achieved while maintaining exact numerical agreement. Real-time feasibility analysis with a complete AEB timing budget (700 ms human reaction time minus 120 ms perception and 50 ms decision overhead) demonstrates that the Jetson AGX Orin can execute approximately 25,000 Monte Carlo samples within a 530 ms budget, enabling real-time probabilistic AEB evaluation as part of a complete embedded pipeline. These results establish Monte Carlo-based uncertainty evaluation as a deployable runtime component rather than an offline validation tool and provide quantitative guidance for risk-aware AEB threshold selection under the NHTSA final rule.

Conformal Prediction provides distribution-free prediction intervals with guaranteed coverage, but its reliance on a single global calibration threshold obscures the sources of uncertainty at the instance level. In particular, it conflates irreducible noise with uncertainty induced by heterogeneous training data (aleatoric), model limitations, or calibration mismatch (epistemic), offering little insight into why an interval is wide or whether it could be reduced. We introduce an uncertainty-aware explainability framework that analyses the reducibility of calibration-induced epistemic conformal uncertainty via progressive calibration localisation for regression tasks. The approach is diagnostic rather than causal: it does not estimate true aleatoric or epistemic uncertainty, but explains how conformal intervals contract and stabilise as calibration support is localised around a test instance. Across benchmarks and real-world data, absolute reducible uncertainty aligns with epistemic proxies, while its relative contribution varies by task, revealing regimes hidden by interval width. This instance-level view complements conformal uncertainty, enhancing interpretability without altering the predictor or coverage.

Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability. Meanwhile, model-based RL (MBRL) methods routinely employ probabilistic ensemble (PE) neural networks to capture complex, high-dimensional dynamics from data with minimal prior knowledge. However, existing attempts to integrate PEs into PSFs lack rigorous uncertainty quantification. We introduce the Uncertainty-Aware Predictive Safety Filter (UPSi), a PSF that provides rigorous safety predictions using PE dynamics models by formulating future outcomes as reachable sets. UPSi introduces an explicit certainty constraint that prevents model exploitation and integrates seamlessly into common MBRL frameworks. We evaluate UPSi within Dyna-style MBRL on standard safe RL benchmarks and report substantial improvements in exploration safety over prior neural network PSFs while maintaining performance on par with standard MBRL. UPSi bridges the gap between the scalability and generality of modern MBRL and the safety guarantees of predictive safety filters.

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and perform well on small- to medium-scale datasets. Alternatively, formulating the weight space learning problem under tensor network assumptions yields scalable tensor network kernel machines. However, these assumptions break Gaussianity, complicating standard probabilistic inference. This raises a fundamental question: how can tensor network kernel machines provide principled uncertainty estimates? We propose a novel Bayesian Tensor Network Kernel Machine (LA-TNKM) that employs a (linearized) Laplace approximation for Bayesian inference. A comprehensive set of numerical experiments shows that the proposed method consistently matches or surpasses Gaussian Processes and Bayesian Neural Networks (BNNs) across diverse UCI regression benchmarks, highlighting both its effectiveness and practical relevance.