Uncertainty Quantification

Also known as UQ

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44 papers in the last four weeks, up 110% on the four weeks before. 0.4% of all new papers.

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Latest papers 431

May 23, 2026cs.AI

Proper Scoring Rules for Agentic Uncertainty Quantification

Language-model agents increasingly emit uncertainty signals throughout a trajectory, but existing agentic UQ evaluations often conflate ranking usefulness with probabilistic truthfulness. AUROC, AUPRC, risk-coverage, Trajectory ECE, and scalarized trajectory scores evaluate discrimination, binwise calibration, or collapsed summaries, but do not strictly elicit the full prefix-conditioned success-probability trace

q_t = P^π(Y=1 | H_t)

. Building on prequential proper scoring, we introduce the Trajectory Proper Score (TPS), a predictor-agnostic family of strictly proper trajectory-level scoring rules for any per-step uncertainty signal calibrated into a probability of eventual success. We prove that TPS strictly elicits the success-probability process under complete observation, within the chosen score family and weight schedule. We extend the construction to administratively censored trajectories by projecting the complete-data score onto the observable stopped prefix, yielding an exact

q_Z

-weighted reduced score and a tractable approximation when

q_Z

is unestimated. We further show that common trajectory evaluators target weaker objects than the full prefix-conditioned probability process: Trajectory ECE is resolution-blind, while scalarized Trajectory Brier elicits only the collapsed scalar, not the full trace. Experiments on StrategyQA, Tau2-Bench, HotpotQA, and WebShop show that these theoretical distinctions are operationally visible: probability recalibration can substantially change TPS while leaving rank metrics nearly unchanged, and the tractable censored approximation can change the verdict relative to complete-only evaluation.

Suresh Raghu, Satwik Pandey, Shashwat Pandey

Independent Researcher

Uncertainty Quantification Agent Evaluation Proper Scoring Rules Uncertainty Calibration

May 23, 2026cs.LG

Position: AI for Science Should Treat Measurement-to-Dataset Pipelines as Inference Components

AI for Science (AI4Science) workflows often treat the released dataset as a fixed interface to the underlying system. However, in domains relying on \emph{indirect observation}, the learner observes a derivative representation produced by multi-stage measurement, reconstruction, and preprocessing pipelines. \textbf{We argue that these measurement-to-dataset pipelines are inference components: treating their outputs as

given data'' freezes an observation model and obscures uncertainty over feasible pipeline choices.} We identify three failure modes arising from this

frozen lens'': \textbf{(C1) hidden hypothesis space}, where the released dataset does not specify the pipeline configuration or its validity conditions; \textbf{(C2) uncertified transportability}, where a pipeline may be documented but its regime of validity is untested, so failures under distribution shift cannot be adjudicated; \textbf{(C3) ungoverned multiplicity}, where many defensible pipelines exist and dispersion is real but not propagated into uncertainty-aware evidence. We stress-test these claims with a large-scale neuroscience empirical audit, finding a survival rate of

\approx 0.0004\%

under a cross-dataset stability criterion. We call on the AI4Science community to make pipelines \emph{computable} inference objects via domain-specific Computable Observation Frameworks. This shift enables quantifying pipeline adequacy and stability, converting implicit implementation choices into auditable, reproducible, and cumulative scientific evidence.

Ling Zhan, Xiaoyao Yu, Tao Jia

College of Computer and Information Science, Southwest University, Chongqing, China · Chongqing Key Laboratory of Brain-Inspired Cognitive Computing and Educational Rehabilitation for Children with Special Needs, Chongqing Normal University, Chongqing, China · College of Computer and Information Science, Chongqing Normal University, Chongqing, China

AI for Science Uncertainty Quantification Scientific Reproducibility Cross-Dataset Generalization

May 23, 2026cs.CV

Robust Fuzzy Multi-view Learning under View Conflict

Trusted multi-view classification aims to deliver reliable fusion for accurate predictions and has recently attracted substantial attention in both academia and industry. However, existing TMVC methods typically assume strict alignment across different views during both training and testing phases, which is often impractical in real-world scenarios. This limitation motivates us to revisit TMVC and extend it to a more challenging setting: how to mitigate the impact of view conflict (VC) during both training and inference. To tackle this setting, existing TMVC methods suffer from three critical limitations: underestimated uncertainty, misleading decisions, and overfitting to VC. To address these issues, this paper proposes a novel Robust Fuzzy Multi-View Learning (R-FUML) framework grounded in Fuzzy Set Theory. Specifically, R-FUML models network outputs as fuzzy memberships to quantify category credibility and uses an entropy-based method for reliable multi-view fusion. To this end, we present a Robust Multi-view Fusion (RMF) strategy that accounts for both view-specific uncertainty and inter-view conflicts, thereby alleviating the adverse impacts of VC on decision-making. To identify and conquer VC during training, we further design a Robust Learning Against VC (RLVC) framework. RLVC isolates conflicting samples by leveraging neural networks' memory effects and then retrains the model by applying a penalty to these conflicting views. Extensive experiments across eight public datasets demonstrate that R-FUML consistently outperforms 15 state-of-the-art baselines in robustness and uncertainty estimation. The code will be released upon acceptance.

Siyuan Duan, Yuan Sun, Dezhong Peng +3

College of Computer Science, Sichuan University, Chengdu 610065, China · College of Computer Science, Sichuan University, Chengdu 610065, China, and also with the Tianfu Jincheng Laboratory, Chengdu 611130, China · Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, UK +1

Uncertainty Quantification Multi-View Learning

May 22, 2026cs.LG

Neural Bayesian Sequential Routing

Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

Yongchao Huang

Uncertainty Quantification Adaptive Model Routing Cost-Aware Inference Bayesian Decision Theory

May 22, 2026cs.LG

Overcoming "Physics Shock" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference

Rapid and accurate flood extent mapping from Remote Sensing data, such as Synthetic Aperture Radar (SAR), is critical for operational disaster response, but standard Deep Learning models often produce physically impossible predictions due to a lack of hydrological constraints. While PhysicsInformed Neural Networks (PINNs) attempt to address this by embedding governing laws directly into the loss function, their application to real-world remote sensing data frequently fails. Enforcing rigid spatial derivatives (e.g., the 2D Shallow Water Equations) onto unconditioned latent spaces attempting to fit noisy SAR speckle causes catastrophic gradient divergence, a phenomenon we term Physics Shock. In this paper, we propose a novel Uncertainty-Aware PINN framework tailored specifically for applied Earth Observation that addresses this instability. By integrating a dynamic Warm-Start protocol and modeling heteroscedastic aleatoric uncertainty via a negative log-likelihood objective, the network learns to dynamically relax physical constraints in regions of high sensor noise while strictly enforcing them in high-confidence areas. Evaluated on the Sen1Floods11 dataset, our probabilistic Attention-Gated FNO-UNet successfully stabilizes multi-objective optimization, achieving a +25% relative improvement in Intersection over Union (IoU) compared to deterministic baselines. Furthermore, through Deep Ensembles, we successfully disentangle intrinsic sensor noise from out-of-distribution terrain ignorance, providing operational agencies with highly calibrated, physically consistent confidence bounds for robust disaster mitigation and real-time decision-making.

Tewodros Syum Gebre, Jagrati Talreja, Matilda Anokye +1

Built Environment Department, College of Science and Technology, North Carolina A&T State University, Greensboro, NC 27405 USA · United Nations University Institute for Water, Environment and Health, Richmond Hill, ON, Canada

Remote Sensing Image Segmentation Uncertainty Quantification Flood Inundation Mapping Remote Sensing Physics-Informed ML Uncertainty Calibration

May 22, 2026stat.ML

Dirichlet-Based Monte Carlo Dropout for Uncertainty Estimation in Neural Networks

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits scalability. Monte Carlo (MC) Dropout, initially introduced as a regularization technique, has been shown to approximate Bayesian inference by enabling probabilistic modeling through multiple stochastic forward passes. In this work, we enhance uncertainty estimation in deep learning by integrating a Dirichlet-based framework within MC Dropout. Specifically, we leverage the formulation proposed by Sensoy et al. (2018), where class probabilities are modeled using a Dirichlet distribution, allowing for a more informative uncertainty representation. The proposed approach maintains the computational efficiency of MC Dropout while improving the quality of uncertainty estimates. We discuss the theoretical foundations of our method and compare it with existing uncertainty quantification techniques. The results highlight the effectiveness of the proposed method in producing well-calibrated uncertainty estimates, offering a practical solution for uncertainty-aware deep learning models.

Rouaa Hoblos, Noura Dridi, Noureddine Zerhouni +1

FEMTO-ST · Universit´e Marie et Louis Pasteur, SUPMICROTECH, CNRS, Institut FEMTO-ST, F-25000 Besan¸con, France

Evidential Deep Learning Uncertainty Quantification Uncertainty Calibration

May 21, 2026cs.RO

UfM: Uncertainty from Motion for DNN Depth Estimation Using Gaussians

Reliable uncertainty estimation is critical for deploying monocular depth deep neural networks (DNNs) in safety-critical robotic systems. Conventional uncertainty methods such as ensembles and sampling-based approaches require multiple inferences per image, incurring substantial compute and memory overhead. Moreover, uncertainty predicted from a single image misses out on measuring disagreement between predictions across views of the same region. We propose Uncertainty from Motion* (UfM*), an uncertainty estimation algorithm that measures multiview disagreement efficiently by comparing previous and current views using a compact Gaussian mixture, requiring only a single DNN inference per image. Using Gaussians to compute multiview disagreement is not only more compute- and memory-efficient than a prior approach using a point cloud, but also improves uncertainty by measuring disagreement across regions of 3D space. UfM* paired with aleatoric uncertainty improves expected calibration error by 24-28% compared to an ensemble, while requiring only 3% of the energy and 0.02% of the memory on 100 out-of-distribution ScanNet sequences. We demonstrate UfM* consumes only 63 mJ per 224x224 image while running real-time at 30 FPS on an Arm Cortex-A76 CPU onboard a miniature energy-constrained robot, highlighting that measuring multiview disagreement using Gaussians enables efficient uncertainty for resource-constrained robotic systems.

Soumya Sudhakar, Sertac Karaman, Vivienne Sze

Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Uncertainty Quantification Depth Estimation Monocular Depth Estimation Uncertainty Calibration

May 21, 2026q-bio.QM

Uncertainty-aware classification and triage of structural heart disease using electrocardiography and echocardiography metrics

Machine learning methods provide a methodological innovation that can help screen for cardiovascular disease through noninvasive and readily available measurement modalities. Recent investments in using electrocardiogram (ECG) data to screen for structural heart disease (SHD) are one example, where ECGs provide a low-cost, available modality for screening. This has led to the EchoNext dataset, a paired ECG-echocardiogram data repository for testing new methods of SHD detection. However, relatively few studies have investigated how more probabilistic classification through Bayesian inference may improve uncertainty quantification in this setting. Moreover, few studies have considered how triage systems can be developed to alleviate healthcare bottlenecks, such as the review of data from underserved, rural clinics by expert sonographers for SHD assessment. In this study, we leverage existing ECG-echocardiogram data to compare frequentist and Bayesian neural network classifiers. We show that the Bayesian approach is comparable or better than frequentist methods in SHD classification, and that they have a more robust uncertainty quantification attached to them. We provide an example of how this uncertainty-aware classification scheme can be used for screening SHD, providing a proof-of-concept for how machine learning can help with triage in getting individuals expert sonographer input when SHD is highly likely or measurements are highly uncertain.

Mitchel J. Colebank

Department of Mathematics, University of South Carolina,, Columbia, 29208, South Carolina, USA

Bayesian Neural Networks Uncertainty Quantification Healthcare Clinical Triage Clinical Decision Support Bayesian Inference+2

May 21, 2026cs.LG

Ternary Decision Trees with Locally-Adaptive Uncertainty Zones

Decision trees assign identical confidence to instances near and far from each split threshold. We introduce ternary decision trees, which augment each split node with an uncertainty zone of half-width delta. A decision-theoretic framework characterises the optimal zone width delta* as the solution to a node-local cost-minimisation problem; four formal properties are established: accuracy decomposition, a sufficiency condition for decided accuracy improvement, an exact efficiency characterisation (eta = Dec-Acc minus Acc_u, the accuracy gap between decided and boundary-uncertain predictions), and asymptotic consistency of the margin method. Instances within the zone receive predictions by weighted blending of both child subtrees and are flagged as boundary-uncertain. We propose and evaluate five delta-estimation methods: quality-plateau (plateau width of the split criterion curve), class-overlap (empirical class-distribution overlap), gain-ratio (split quality relative to split entropy), node-bootstrap (threshold variance under node-level resampling), and margin (SVM-inspired distance to the nearest cross-class training example). All methods reuse statistics already computed during standard CART split finding, requiring no external noise specification. Evaluated across 71 of the 72 OpenML-CC18 datasets with 5-fold cross-validation, all five methods with probabilistic routing significantly outperform standard CART on decided accuracy (Wilcoxon signed-rank, p < 0.001). The margin method achieves the best efficiency (0.104 accuracy gain per unit flagging rate), wins on 42 of 72 datasets, and requires zero hyperparameters. Analysis on Breiman synthetic benchmarks confirms margin is self-calibrating on clean data. On mammography, node-bootstrap achieves +0.71% decided accuracy by flagging 10.8% of cases as boundary-uncertain.

William Smits

Avathon, Austin, TX, USA

Uncertainty Quantification Selective Prediction Decision Tree Learning Classification

May 21, 2026cs.LG

A Posterior-Predictive Variance Decomposition for Epistemic and Aleatoric Uncertainty in Wind Power Forecasting

Accurate wind power forecasting requires reliable uncertainty quantification, yet most existing methods report a single predictive uncertainty that conflates epistemic and aleatoric sources. This paper applies the law of total variance to the joint setting of heteroscedastic neural network regression and Bayesian posterior approximation, deriving an explicit decomposition of total uncertainty (TU) into aleatoric (AU) and epistemic (EU) components. The resulting estimators are compatible with standard posterior-approximation methods and with

β

-NLL training to regulate the mean--variance learning trade-off. A wind power--specific evaluation framework is proposed to validate disentanglement without access to ground-truth uncertainty labels, comprising three modules: controlled synthetic experiments to verify responses to heteroscedastic noise and distribution shift; data-property--driven validation on a real-world wind turbine SCADA dataset; and dataset-size scaling experiments to examine the predicted asymptotic behavior of EU. Across synthetic and real-world experiments, the decomposed AU and EU components respond in theoretically consistent directions to noise structure, distributional shift, and training-scale variation, supporting the theoretical consistency and operational utility of the proposed decomposition and evaluation protocol.

Yinsong Chen, Samson S. Yu, Kashem M. Muttaqi

School of Engineering, Deakin University, Melbourne, VIC 3216, Australia · ARC Training Centre in Energy Technologies for Future Grids, School of Engineering, University of Wollongong, Wollongong, NSW 2522, Australia

Uncertainty Quantification Time Series Forecasting Probabilistic Forecasting Aleatoric Uncertainty Wind Power Forecasting Uncertainty Decomposition+1

May 21, 2026cs.LG

Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale Lorenz 1996 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel Bayesian and flow-based approaches. Our results show that ensemble perturbations do not increase the system's long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.

Birgit Kühbacher, Daan Crommelin, Niki Kilbertus

Technical University of Munich, Munich, Germany · Helmholtz Munich, Munich, Germany · Munich Center for Machine Learning (MCML), Munich, Germany +2

Uncertainty Quantification Chaotic Dynamical Systems Uncertainty Propagation Uncertainty Calibration Uncertainty Decomposition

May 21, 2026cs.AI

Towards a compositional semantics for quantitative confidence assessment in assurance arguments

Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational semantics for deriving assurance confidence. Existing approaches address structure and soundness but largely reason over truth values, not over confidence in the justification of claims. Subjective Logic (SL) offers a calculus of belief, disbelief, and uncertainty with operators for combining opinions, enabling confidence propagation under incomplete, conflicting, or subjective evidence. However, existing SL-based approaches do not provide a uniform, compositional semantics that covers all argument elements and relations to enable overall confidence assessment. We propose a confidence semantics that represents argument elements as SL opinions and maps relations between elements to SL operators modelling how confidence flows, effectively turning the argument into an analyzable confidence network. The approach provides explicit warrants, principled handling of context, preserved provenance, and compatibility with GSN, along with practical guidance using an exemplary assurance confidence assessment.

Benjamin Herd, Jessica Kelly, Jan Sabsch +1

Fraunhofer IKS · Munich, Germany · Luxoft GmbH +2

AI Assurance Uncertainty Quantification Computational Argumentation

May 20, 2026cs.LG

Calibration, Uncertainty Communication, and Deployment Readiness in CKD Risk Prediction: A Framework Evaluation Study

Machine learning models for chronic kidney disease (CKD) risk prediction often post strong discrimination scores on internal test sets. Calibration and uncertainty quantification get far less attention, leaving clinicians without reliable information about whether the probability outputs are accurate. We trained five classifiers on the UCI CKD dataset (400 patients, 62.5% CKD prevalence): logistic regression, random forest, XGBoost, SVM with Platt scaling, and Gaussian naive Bayes. We evaluated each across calibration quality, conformal prediction coverage, and an eight-criterion deployment readiness framework. A distributional stress-test applied the best-calibrated variant of each model to the open-access MIMIC-IV demo cohort (97 patients, 23.7% CKD) to assess behaviour under prevalence shift and feature missingness. We measured calibration before and after Platt scaling and isotonic regression using Expected Calibration Error and Brier Score, and quantified uncertainty through split conformal prediction targeting 90% marginal coverage. All five models reached AUROC 1.00 on the UCI test set. Isotonic recalibration reduced internal ECE to 0.000-0.022. On MIMIC-IV, AUROC fell to 0.48-0.58, ECE rose to 0.68-0.76, and conformal coverage dropped from 0.80-0.98 to 0.21-0.25 against a 90% target. No model scored above 4 out of 16 on the deployment readiness checklist. Near-perfect internal performance did not transfer. Calibration stability and conformal coverage should be evaluated on external data before any clinical prediction model moves toward deployment.

Michael O. Eniolade

University of the Cumberlands

Uncertainty Quantification Conformal Prediction Model Calibration Clinical Risk Prediction Cross-Dataset Generalization

May 20, 2026cs.LG

A Unified Framework for Uncertainty-Aware Explainable Artificial Intelligence: A Case Study in Power Quality Disturbance Classification

Post-hoc explainable AI (XAI) methods typically produce deterministic attribution maps, whereas Bayesian neural networks (BNNs) induce a distribution over explanations. Capturing the variability of this distribution is important for uncertainty-aware decision-making. This paper formalises the \emph{explanation distribution} as the push-forward measure of the BNN posterior through any Lipschitz-continuous attribution operator. It further proposes the uncertainty-aware relevance attribution operator (UA-RAO), a general family of operators that summarises the explanation distribution using the mean, variance, coefficient of variation, quantiles, and set-theoretic aggregation measures. Theoretical support is provided through Monte Carlo accessibility and Wasserstein approximation bounds. The framework is evaluated on a 15-class power quality disturbance (PQD) classification benchmark, comparing three BNN approximations paired with three attribution operators using relevance mass accuracy and intersection-over-union as localisation metrics. Results show that deep ensembles with the mean UA-RAO improve localisation over the deterministic baseline, while other UA-RAO summaries reveal uncertainty patterns absent from point-estimate attributions. Qualitative results on measured signals further suggest that these patterns generalise beyond the synthetic training distribution. The framework is domain-agnostic and can be applied to any BNN paired with a Lipschitz-continuous attribution operator.

Yinsong Chen, Samson S. Yu, Zhong Li +1

School of Engineering, Deakin University, Melbourne, 3216, VIC, Australia · Faculty of Mathematics and Computer Science, FernUniversität in Hagen, 58084, Germany · Department of Computing Technologies, Swinburne University of Technology, Hawthorn, 3122, VIC, Australia

Bayesian Neural Networks Feature Attribution Explainable Artificial Intelligence Uncertainty Quantification

May 19, 2026cs.AI

ECUAS $_n$ : A family of metrics for principled evaluation of uncertainty-augmented systems

In high-stakes automated decision-making, access to predictive uncertainty is essential for enabling users -- human or downstream systems -- to accept or reject predictions based on application-specific cost trade-offs. Such uncertainty-augmented (UA) systems -- i.e., systems that output both predictions and uncertainty scores -- are currently being assessed in the literature in a variety of ways, using separate metrics to evaluate the predictions and the uncertainty scores, setting a cost function with a fixed rejection cost or integrating over a coverage-risk curve. We argue that these evaluation approaches are inadequate for assessing overall performance of the UA system for decision making under uncertainty and propose a novel family of metrics, ECUAS

_n

, formulated as proper scoring rules for the task of interest. The parameter

n

controls the trade-off between the cost of incorrect predictions and imperfect uncertainties depending on the needs of the use-case. We demonstrate the advantages of the ECUAS

_n

metrics both theoretically and empirically, through experiments on diverse classification and generation datasets, including a manually annotated subset of TriviaQA.

Lautaro Estienne, Erik Ernst, Matías Vera +2

School of Engineering, UBA, Argentina · ICC, CONICET-Universidad de Buenos Aires, Argentina · LISN, CNRS, Université Paris-Saclay, France +4

Uncertainty Quantification Proper Scoring Rules Decision-Making under Uncertainty

May 19, 2026cs.AI

Distribution-Free Uncertainty Quantification for Continuous AI Agent Evaluation

We adapt split conformal prediction and adaptive conformal inference (ACI) to continuous AI agent evaluation, providing distribution-free coverage guarantees for forecasted quality scores. Conformal intervals achieve calibration error below 0.02 across all nominal levels at the 24h horizon, while ACI correctly widens intervals by 35% following agent releases then reconverges. We further develop compositional uncertainty bounds for multi-agent pipelines (validated via simulation across inter-stage correlations rho in [-0.5, 0.9]), a conformal abstention rule for pairwise rankings with controlled false-ranking rate, and FDR-corrected abstention for leaderboard-scale multiple testing. Evaluating 50 agents via 18 real-time signals collected hourly, we show that per-agent conditional coverage is well-concentrated around the nominal level (mean 80.4%, 90% of agents within [72%, 90%]), and that cross-source sentiment divergence predicts ranking instability (r=0.64, p<0.01). A circularity-controlled validation confirms the framework captures signal beyond benchmarks (rho_s=0.52, p<0.01, n=35). Code and data are released under CC BY 4.0.

Yuxuan Gao, Megan Wang, Yi Ling Yu

OpenMesh · University of Pennsylvania · Columbia Univer

Uncertainty Quantification AI Agent Evaluation Conformal Prediction Adaptive Conformal Inference

May 19, 2026cs.CL

Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution

Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a diagnostic signal, yet existing methods are restricted to final answers or require internal model access. In this paper, we introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5% over answer-level feedback.

Xiaoou Liu, Tiejin Chen, Dengjia Zhang +3

1Arizona State University · 2Johns Hopkins University · 3Purdue +1

Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation LLM Reasoning

May 19, 2026cs.CL

Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Tiejin Chen, Longchao Da, Xiaoou Liu +1

School of Computing and Augmented Intelligence, Arizona State University

LLM Evaluation Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

May 18, 2026stat.ML

Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either impose a single low-rank structure, which can miss localized signal, or treat the tensor as a long vector, which discards its multiway geometry. We propose a Dual-Channel Tensor Neural Network (DC-TNN) that decomposes each tensor input into a low-rank core and a sparse refinement, and processes the two components through coupled neural channels. The framework is structure-agnostic and accommodates CP, Tucker, and tensor-train cores within a single architecture. For estimation, we establish non-asymptotic risk bounds for the DC-TNN estimator that decompose into network approximation, core estimation, and refinement-selection terms, and show that the effective dimension is determined jointly by the core rank and refinement sparsity rather than by the ambient tensor size. For inference, we develop a structure-aware conformal ROC procedure that calibrates within the core-refinement latent space and produces ROC and AUC confidence bands with finite-sample, distribution-free coverage. Building on this, we propose a conformal structure selector that, to our knowledge, is the first distribution-free procedure for choosing among candidate tensor decompositions with finite-sample validity. Simulations and an analysis of a protein dataset demonstrate competitive predictive accuracy, reliable uncertainty quantification, and consistent recovery of the tensor structure.

Elynn Chen, Jiayu Li, Zheshi Zheng +1

New York University · University of Michigan · Duke University

Tensor Networks Uncertainty Quantification Tensor Decomposition Conformal Prediction Neural Network Approximation Theory

May 18, 2026cs.LG

The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows

Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interactions and limited sensing. In this work, we develop a non-intrusive reduced-order modeling framework for efficient Bayesian initial-state inversion with uncertainty quantification. The framework combines a convolutional autoencoder with a learned latent-space forward operator. The autoencoder compresses high-dimensional flow fields into a compact nonlinear latent representation, while the forward operator predicts final-time latent states from encoded initial conditions. This AE-ROM surrogate enables rapid forward evaluations and is embedded within a No-U-Turn Sampler (NUTS) for posterior exploration. The framework is demonstrated using 500 high-fidelity Sod shock tube simulations generated through Latin hypercube sampling and solved using a fifth-order WENO scheme. The inverse problem seeks to recover unknown left and right density and pressure states from sparse noisy observations of final-time density and pressure fields. Results show that the AE-ROM accurately reconstructs key shock-tube structures, including the rarefaction wave, contact discontinuity, and shock front. A latent dimension of 32 provides an effective balance between reconstruction accuracy and reduced-space compactness, while 250 training simulations are sufficient for accurate reconstruction. Increasing observation density significantly contracts posterior uncertainty, reducing the mean posterior standard deviation by approximately 78% for density and 76% for pressure. Overall, the proposed framework provides a computationally efficient and uncertainty-aware approach for inverse analysis of shock-dominated flows, with potential extensions to multidimensional compressible-flow and digital-twin applications.

Bipin Tiwari, Muhammad Abid, Omer San

Department of Mechanical and Aerospace Engineering, University of Tennessee, Knoxville Knoxville, TN 37996, USA.

Neural Surrogate Modeling Uncertainty Quantification Bayesian Inverse Problems Reduced-Order Modeling Computational Fluid Dynamics

May 18, 2026stat.ML

Flowing with Confidence

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run

k

ensembles or stochastic trajectories at

k\times

compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

Friso de Kruiff, Dario Coscia, Max Welling +1

CuspAI · AMLab, University of Amsterdam · mathLab, SISSA

Flow Matching Uncertainty Quantification Image Generation Generative Modeling Flow-Based Generative Modeling

May 18, 2026cs.RO

Confidence-Gated Robot Autonomy: When Does Uncertainty Actually Help?

Robotic systems often use predictive uncertainty to decide whether to act autonomously or defer to a fallback policy. In threshold-gated autonomy, uncertainty matters mainly through its ability to rank likely errors. Standard metrics such as expected calibration error and AUROC do not directly test whether uncertainty changes act/defer decisions. We therefore evaluate uncertainty using Spearman rank correlation, paired bootstrap equivalence testing, and act/defer agreement. Across three temporal activity-recognition benchmarks, we find a dataset-dependent competence regime below which uncertainty provides a weak and unstable error ranking. Above this regime, softmax heuristics, MC Dropout, and ensembles produce similar gating behavior, while threshold choice has a much larger effect on execution outcomes. A multi-seed embodied simulation shows the same pattern for collision rate and cost once realized autonomy is matched. Under temporal covariate shift, ranking quality remains stable, but fine grained semantic OOD detection remains near chance. These results suggest that simple uncertainty proxies can suffice for selective gating once the base model is competent, but not for semantic novelty detection.

Johannes A. Gaus, Jhon P. F. Charaja, Daniel Haeufle

Hertie Institute for Clinical Brain Research & Center for Integrative Neuroscience, University of Tübingen, Germany

Uncertainty Quantification Selective Prediction Robotics Decision-Making under Uncertainty

May 18, 2026cs.IR

Uncertainty-Calibrated Recommendations for Low-Active Users

A fundamental challenge in recommender systems is balancing reliability for Low-Active Users (LAUs) with diversity for High-Active Users (HAUs). The key to this balance lies in quantifying model uncertainty, which approximates the risk of prediction errors and reveals the limits of the model's current knowledge. On large-scale short-video and livestream platforms, model uncertainty can warn of low-quality recommendations that may lead to disengagement of LAUs and at the same time identify opportunities to diversify content recommendation for HAUs. To leverage this dichotomy, we introduce a unified, production-ready framework that calibrates uncertainty to drive differentiated strategies. Specifically, we implement a model-uncertainty-based risk-averse deboosting policy for LAUs to suppress unreliable recommendations, while employing a risk-seeking Upper Confidence Bound (UCB) strategy for HAUs to encourage exploration. Validated on a major livestream platform, our framework demonstrates significant improvements in retention (active hours) and satisfaction (quality watch time ratio) for LAUs as well as remarkable increases in interest diversity and category coverage for HAUs, proving the value of uncertainty-aware recommendation in industrial settings.

Bob Junyi Zou, Sai Li, Tianyun Sun +2

Stanford University · Stanford, CA, USA · ByteDance Inc. +2

Uncertainty Quantification Exploration-Exploitation Tradeoff Recommender Systems Uncertainty Calibration

May 18, 2026cs.CV

UST-Hand: An Uncertainty-aware Spatiotemporal Point Cloud Interaction Network for 3D Self-supervised Hand Pose Estimation

Manually annotating accurate 3D hand poses is extremely time-consuming and labor-intensive. Existing self-supervised hand pose estimation methods leverage the discrepancy between input images and rendered outputs, or multi-view consistency constraints, as the driving force to optimize networks and progressively refine pose accuracy. However, these methods are highly susceptible to noisy pseudo-labels and overlook the importance of fully exploiting fine-grained spatial correlations, which undermines the stability of model training. To address these issues, we propose UST-Hand, a self-supervised learning framework that estimates uncertainty distribution of hand pose and constructs a probabilistic point cloud feature space, which enables the complex spatiotemporal relationship modeling. UST-Hand employs a conditional normalizing flow model to capture hand pose distributions and samples diverse hypotheses, facilitating robust learning under noisy pseudo-labels supervision with enhanced stability. These multi-hypothesis are mapped to a unified probabilistic 3D point cloud space for multi-view and temporal feature interaction, comprehensively exploring hand motion patterns and fine-grained spatial correlations. Extensive experiments on three challenging datasets demonstrate that UST-Hand achieves state-of-the-art performance, outperforming existing self-supervised methods by up to 37.8% in Mean Per Vertex Position Error (MPVPE).

Tianhao Han, Haoyang Zhang, Liang Xie +5

School of Computer Science, Shanghai Jiao Tong University · Defense Innovation Institute, Academy of Military Sciences · Tianjin Artificial Intelligence Innovation Center +3

Uncertainty Quantification Self-Supervised Learning 3D Hand Pose Estimation Point Cloud Learning

May 17, 2026cs.RO

MUSE: Multimodal Uncertainty Quantification of State Estimation

Accurate visual state estimation has been a central topic in robotics with a wide range of applications in robot navigation, autonomous driving, and autonomous flight. Recent advances in robot perception have led to significant improvements in the accuracy and robustness of state estimation, yet a fundamental challenge remains in how to quantify and calibrate its precision, i.e., how confident we are in an estimate and whether failures can be detected. This issue is particularly pronounced in visual-inertial odometry (VIO), where the heteroscedastic and multimodal nature of the problem makes uncertainty quantification especially difficult. This paper introduces MUSE (Multimodal Uncertainty Quantification of State Estimation), a novel real-time learning-based framework that leverages the strong and efficient sequential modeling capacity of Mamba to estimate localization uncertainty from multiple asynchronous sensor streams. Experiments on both public and in-house datasets demonstrate that MUSE achieves superior reliability and robustness compared to existing uncertainty quantification methods, and ablation studies justify the benefits of its key design choices.

Minkyung Kim, Henry Che, Bhargav Chandaka +6

Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign, Champaign, IL 61801, USA · Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, Champaign, IL 61801, USA · Department of Electrical Engineering, University of South Carolina, Columbia, SC 29208, USA

Uncertainty Quantification Visual-Inertial Odometry

May 16, 2026stat.ML

Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under uncertainty, their practical use typically requires specifying the magnitude and structure of model uncertainties that are often unknown and difficult to infer from noisy measurements. To address this challenge, we develop a stochastic operator-learning framework that learns directly from noisy data and outputs both a mean solution field and a quantification of uncertainty. The proposed method, namely the Stochastic Operator Network (SON), is constructed by combining the structure of the Deep Operator Network (DeepONet) with Stochastic Neural Networks (SNNs) to model stochasticity and enable probabilistic prediction. The training procedure is carried out by minimizing a Hamiltonian-type loss and optimizing the resulting objective using the Stochastic Maximum Principle. Numerical experiments on benchmark SPDEs under multiple uncertainty sources demonstrate the accuracy and robustness of the proposed method in capturing solution structure and quantifying predictive uncertainty.

Phuoc-Toan Huynh, Richard Archibald, Feng Bao

Department of Mathematics, Florida State University, Tallahassee, FL, USA · Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

Uncertainty Quantification Deep Operator Networks Operator Learning Neural Operators

May 15, 2026cs.AI

Scalable Uncertainty Reasoning in Knowledge Graphs

Knowledge Graphs are pivotal for semantic data integration. The real-world data they model is often inherently uncertain. Within knowledge graphs, uncertainty manifests in three distinct levels: imprecise attribute values, probabilistic triple existence, and incomplete schema knowledge. However, current Semantic Web standards lack native support for reasoning over such uncertainty, and naïve extensions often incur computational intractability. In this thesis, I aim to develop a modular framework that addresses each level through tailored techniques: (1) defining probabilistic literals and a corresponding query algebra for continuous attributes; (2) a compilation-based framework transforming SPARQL provenance into tractable probabilistic circuits for uncertain triples; and (3) topology-aware geometric embeddings for statistical schema reasoning. The central hypothesis is that specialized reasoning mechanisms, namely algebraic, logical, and geometric approaches, can reconcile semantic precision with computational tractability.

Jingcheng Wu

University of Stuttgart, Stuttgart, Germany

Probabilistic Circuits Uncertainty Quantification Knowledge Graphs

May 15, 2026stat.ML

A numerical study into neural network surrogate model performance for uncertainty propagation

Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high interest because of the potential to significantly reduce the repeated evaluation of expensive forward models via traditional numerical solvers when conducting parametric analysis. However, many studies found in the literature primarily focus on the ability of neural network surrogate models to represent deterministic samples or mean field solutions and largely overlook surrogate model performance at the tails of the distribution. The present study examines in detail the ability of neural network surrogate models to capture the full distribution of solution fields over the entire probability space, while emphasis is placed at the tails of the distribution. Serving as a canonical problem is the heat conduction equation with a highly stochastic source term, inducing extremely large variation in the thermal solution field. Comparisons are made between a classic feed-forward fully connected network and a Deep Operator Network architecture, using both data-driven and physics-informed loss functions. Results show that the worst-case prediction errors are an order of magnitude larger than the mean field error, highlighting the importance of the outlier samples. The large errors associated with extreme samples result from the networks having to extrapolate beyond the bounds of the training data. A method for identifying these samples is presented along with a discussion of potential approaches to account of their errors. Among the models considered, the fully connected neural network trained using a weak form residual loss performs best in handling these extrapolated inputs, achieving the highest prediction accuracy for the numerically produced datasets.

Noah Wade, Kirubel Teferra

ASEE Postdoctoral Associate, U.S. Naval Research Laboratory, Washington, DC, 20375, USA · U.S. Naval Research Laboratory, Washington, 20375, DC, USA

Neural Surrogate Modeling Uncertainty Quantification PDE Surrogate Modeling OOD Generalization Deep Operator Networks Uncertainty Propagation

May 15, 2026cs.CV

Uncertainty-Aware Wildfire Smoke Density Classification from Satellite Imagery via CBAM-Augmented EfficientNet with Evidential Deep Learning

Rapid and accurate wildfire smoke severity assessment from satellite images is essential for emergency response, air quality modeling, and human health risk management. Existing deep learning approaches treat smoke detection as a binary task, producing point estimates without any measure of prediction confidence. We propose a probabilistic framework to categorize a satellite patch into Light, Moderate, and Heavy severity classes and to provide decomposed epistemic and aleatoric uncertainty in a single forward pass. Our architecture uses the backbone of a pre-trained EfficientNet-B3 and a CBAM module with an evidential deep learning head that predicts Dirichlet concentration parameters, directly estimating vacuity (epistemic) and dissonance (aleatoric) without Monte Carlo sampling. Evaluated on 16,298 real satellite patches derived from the Wildfire Detection dataset, our model achieves 93.8% weighted test accuracy (91.1% unweighted) with ECE=0.0274. Selective prediction retaining the most certain 50% of patches achieves 96.7% accuracy. As image quality degrades, uncertainty increases monotonically, and vacuity is a practical scan quality measure. The Moderate class represents transitional smoke conditions that exhibit the highest epistemic uncertainty (mean vacuity = 0.187), confirming the model correctly identifies ambiguous smoke boundary regions. CBAM spatial attention maps localize to structurally distinctive scene regions, and t-SNE demonstrates the clear cluster separation of Light and Heavy smoke.

Ranjith Chodavarapu

Kent State University

Remote Sensing Image Understanding Evidential Deep Learning Uncertainty Quantification Remote Sensing Uncertainty Calibration

May 15, 2026cs.LG

Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization

Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this structure typically requires Monte Carlo rollouts or grafted generative models, both of which surrender the one-shot efficiency and resolution invariance that define the operator paradigm. To resolve this, we draw on the Doob-Meyer theorem, which establishes that any semimartingale fundamentally decomposes into a predictable drift and an unpredictable, zero-mean martingale. Translating this theorem into an architectural prior, we introduce the Martingale Neural Operator (MNO). MNO maps an initial condition directly to the conditional mean and covariance of the terminal law, parameterized by a drift-like mean and a low-rank factor

B_φ

with

B_φ^\top B_φ

positive semi-definite by construction. For our experiments, we use a Gaussian residual instantiation. Across 1D SPDEs, rough volatility, and 2D operator tasks, MNO reduces Wasserstein distance by up to

120\times

on

φ^4

field theory and

68\times

on stochastic Burgers, evaluating

\sim 3\times

faster than a conditional diffusion baseline at matched wall-clock training budgets. On 2D tasks, MNO is comparable to FNO on zero-shot resolution transfer and turbulent flow, while quasi-deterministic systems such as Gray-Scott remain a failure mode.

Kai Hidajat

Department of Applied Mathematics University of Washington Seattle, WA, USA

Uncertainty Quantification Neural Operators