Uncertainty Quantification

Also known as UQ

Follow this topic Ask about this topic

Momentum

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

Jul 13Week of Sep 28

Latest papers 431

Jun 8, 2026cs.CV

Real-time body pose non-verbal communication with a consistency-based reliability measure

Body movement communicates intent at distances and in conditions where neither the face, nor speech can be captured. We study the recognition of communicative intent from 2D body pose alone. We argue that body motion is a reliable signal especially in scenarios that require real time low-cost on-device person-to-robot communication in long distance environments, such as rescue missions. However, existing resources do not isolate this signal. Affective corpora combine body, face, voice and text, while skeleton action-recognition benchmarks label the action performed rather than the message conveyed. We release a dataset of real frames of full-body pose covering ten communicative intents and we compare it against other real (IPC) and synthetic (MotionLCM, VEO3.1, Kimodo) ones that span a range of difficulty. We target systems that can run on a robot's limited onboard hardware. We benchmark multiple models, from skeleton graph classifiers to joint motion-forecasting networks, and report performance metrics together with frame rate on an embedded GPU (NVIDIA Orin~Nano), since speed matters as much as accuracy in our scenario. Finally, we show that a model's own autoregressive self-consistency works as an unsupervised reliability signal. We give a short proof that bounds the probability that a self-consistent prediction is correct, show that this probability grows with the number of consistent steps, and identify the conditions under which a confident prediction can still be false, benchmarked against industry-standard metrics.

Alina Marcu, Dragos Costea, Cristina Lazar +1

National University of Science and Technology "Politehnica" Bucharest · "Simion Stoilow" Institute of Mathematics of the Romanian Academy · NORCE Norwegian Research Centre AS

Uncertainty Quantification Gesture Recognition Human-Robot Interaction

Jun 8, 2026cs.RO

Taming Perception Jitter: Uncertainty-Aware LiDAR Object Detection for Reliable Motion Classification

Reliable motion classification is critical for autonomous driving, as false dynamic predictions of static objects can cascade into unnecessary planner interventions. Unstable bounding box predictions can lead to spurious velocity estimates in tracking and falsely predicted trajectories. We present a deployment-friendly mitigation strategy that augments a 3D object detector with aleatoric uncertainty estimates and applies a two-sample z-test over short observation windows to separate true motion from jitter. Integrated into Autoware with minimal changes, the approach reuses existing data association for minimal compute overhead. Empirical results show parity with velocity thresholding on nuScenes, but substantially fewer false dynamic predictions and unnecessary stops in real-world test drives, explained by the presence of an intermediate jitter band in the recorded data that speed-only rules misclassify. This demonstrates that uncertainty-aware detection and lightweight statistical testing can deliver practical performance gains for autonomous driving in noisier real-world settings.

Cornelius Schröder, Žygimantas Marcinkus, Markus Lienkamp

Institute for Automotive Engineering, Munich Institute of Robotics and Machine Intelligence, School of Engineering and Design, Technical University of Munich

Lidar-Based 3D Object Detection Uncertainty Quantification Autonomous Driving 3D Object Detection Statistical Hypothesis Testing

Jun 8, 2026cs.CV

A practical probabilistic framework for deformable image registration uncertainty in radiotherapy dose propagation

Deformable image registration (DIR) is widely used in radiotherapy for dose propagation and accumulation, but uncertainty in the underlying deformation can substantially affect clinically relevant dose estimates. We present a practical probabilistic framework for propagating DIR uncertainty to voxel-wise dose statistics and dose-volume histograms (DVHs). The method models the mapped correspondence at each voxel as a random variable governed by a transparent local certainty map that can be defined by simple safety margins, structure-boundary mismatch, or structure-wise conservative uncertainty values. This yields interpretable quantities such as dose probabilities, expected dose, confidence bounds, and induced DVH envelopes. The framework is designed to remain lightweight and interpretable: it avoids complex biomechanical or ensemble-based uncertainty models and instead emphasizes simple parameterization, computational feasibility, and transparent dose metrics. We further introduce a structure-guided in/out strategy as an optional refinement that restricts mapping probabilities to anatomically plausible target regions. The approach is demonstrated on a prostate radiotherapy case study and used to compare different certainty-map strategies and probability kernels. The experiments show that the certainty-map design has a stronger effect on resulting dose and DVH uncertainty bounds than the specific kernel choice, while the additional benefit of the in/out strategy is case-dependent and modest in the present example. Overall, the proposed framework provides a transparent way to incorporate DIR uncertainty into radiotherapy dose assessment and to study how modelling choices affect propagated dose metrics.

Stefan Heldmann, Sven Kuckertz, Nasim Givehchi +4

Fraunhofer Institute for Digital Medicine MEVIS, Lübeck, Germany · Varian, a Siemens Healthineers company, Dättwil, Switzerland · Icon Group, South Brisbane, QLD, Australia

Uncertainty Quantification Oncology Uncertainty Propagation Deformable Image Registration

Jun 8, 2026stat.ME

Data augmented bootstrap: Unifying confidence interval construction by approximate invariance

We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI. Meanwhile, DAB also recovers the classical bootstrap method, which exploits the dataset's approximate invariance under uniform sampling of data indices as the dataset size grows. For all DAB methods, we establish theoretical coverage results that interpolate between finite-sample and asymptotic guarantees according to the strength of the invariance, and without assuming a group structure. The approximate invariance is measured in the Kolmogorov distance and, for statistics that satisfy Gaussian universality, reduces to conditional mean and variance matching. This allows us to incorporate data augmentation (DA), a widely used machine learning heuristic based on approximate invariances, into known statistical methods. We empirically test the performance of incorporating DA into bootstrap, wild bootstrap and conformal prediction for simulated settings as well as for image, language and scientific data.

Kevin Han Huang

Department of Statistics, University of Warwick

Confidence Region Estimation Uncertainty Quantification Data Augmentation Conformal Prediction

Jun 7, 2026stat.ML

Rank Intervals for Leaderboards: A Hierarchical Framework for Model Evaluation

Pretrained models are often evaluated on multi-task leaderboards to measure their applicability in diverse contexts. However, current methods for aggregating performance across tasks into leaderboard-level rankings do not address the uncertainty and variability at the task level. While recent works have proposed interval-based model rankings, the principled aggregation of uncertainty from individual tasks to leaderboard-level rankings remains unaddressed, and variation in models' performance across tasks is frequently obscured. In this work, we introduce a hierarchical framework that constructs model rank intervals with statistical guarantees at both levels: task-level rank confidence intervals from pairwise comparisons, and leaderboard-level rank prediction intervals using a conformal approach. This enables reliable quantification of model rank for each observed task and for new potential tasks. Experiments on simulated data and the TabArena and PromptEval (MMLU) benchmarks show that our method yields statistically valid and informative intervals, enabling reliable, uncertainty-aware model ranking on leaderboards.

Bitya Neuhof, Yuval Benjamini

Department of Statistics and Data Science The Hebrew University of Jerusalem

Uncertainty Quantification

Jun 7, 2026cs.LG

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime

In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated uncertainty for spatiotemporal field predictions. Our approach wraps a trained Fourier Neural Operator (FNO) with split conformal prediction and constructs the local uncertainty scale by comparing the predictions of two operators trained on nearly identical datasets: one on the original labels and one on labels perturbed by small Gaussian noise. We consider this procedure in the data-scarce regime, where the total label budget is fixed and methods that require a separate uncertainty network must divide training data between multiple models. On the 2D Navier--Stokes benchmark, the perturbation-based method produces substantially narrower conformal bands than existing methods under matched total data budgets while maintaining the target simultaneous coverage. These results suggest that perturbation sensitivity is a practical and sample-efficient uncertainty proxy for conformalized neural operators.

Weinan Wang, Bowen Gang, Hao Deng

Department of Mathematics, University of Oklahoma, Norman, OK, USA · Department of Statistics and Data Science, School of Management, Fudan University, Shanghai, China

Uncertainty Quantification Conformal Prediction Operator Learning Uncertainty Calibration

Jun 7, 2026cs.LG

Conformal Prediction for Neural Operators: Distribution-Free Uncertainty Quantification in Physics Simulation

Neural operators such as the Fourier Neural Operator (FNO) have emerged as powerful surrogates for solving partial differential equations (PDEs), achieving speedups of several orders of magnitude over traditional numerical solvers. However, deploying these models in safety-critical engineering applications -- such as thermal management of electronic components and battery systems -- requires not only accurate point predictions but also rigorous uncertainty guarantees. Existing uncertainty quantification (UQ) methods for neural operators, including Monte Carlo Dropout and Deep Ensembles, provide only relative uncertainty estimates without formal coverage guarantees. In this work, we propose the first application of split conformal prediction to neural operator-based physics simulation, providing distribution-free prediction intervals with finite-sample coverage guarantees. We further introduce a normalized conformal prediction scheme that leverages MC Dropout uncertainty to produce adaptive-width intervals, yielding tighter intervals in regions of low uncertainty and wider intervals where the model is less certain. Full-scale experiments (33.7M parameters, 800 training samples, 5 ensemble members, NVIDIA V100) on steady-state heat conduction benchmarks demonstrate that our method achieves 89.1% empirical coverage at the target level of alpha=0.1, while producing spatially adaptive prediction intervals that reflect the underlying physical uncertainty structure. We also provide an uncertainty decomposition framework that separates epistemic uncertainty (68% of total) from aleatoric uncertainty (32% of total), offering actionable guidance for data collection and model improvement. Our method is implemented in an open-source platform with REST API endpoints and interactive 3D visualization.

Michael Chin

Independent Researcher

Uncertainty Quantification PDE Surrogate Modeling Conformal Prediction Neural Operators Regression Prediction Intervals

Jun 6, 2026cs.CV

Remember with Confidence: Uncertainty Quantification for Spatio-temporal Memory with Probabilistic Guarantees

Long-horizon robot operation requires spatio-temporal memory to record the environment state and recall it for downstream reasoning. Scene graphs and retrieval-augmented systems ground VLM descriptions to persistent 3D entities with rich semantic descriptions. However, VLM captions are noisy and viewpoint-inconsistent, and existing systems treat them as an oracle with no mechanism to detect unreliable stored descriptions. We introduce object-level semantic uncertainty for multi-view VLM memory: a score that measures object-centric cross-view semantic scatter of captions and identifies semantically unresolved objects. Then, we include our uncertainty scores in an advanced spatial-semantic memory system, that we dub UQ-DAAAM. UQ-DAAAM uses this score to actively refine uncertain objects under a fixed query budget by selecting high-quality views and fusing the resulting multi-view captions into a single object description. We also derive probabilistic guarantees showing that higher-quality candidate views (as selected by our approach) are more likely to reduce uncertainty. Our experiments show that uncertainty quantification can make embodied 4D memory systems more reliable and more effective. In particular, on the OC-NaVQA benchmark, UQ-DAAAM achieves substantially larger uncertainty reduction and better spatio-temporal question answering performance than baselines.

Harry Zhang, Nicolas Gorlo, Luca Carlone

MIT

Multi-View Consistency Uncertainty Quantification VLMs for Robotics Memory-Augmented Agents

Jun 6, 2026math.NA

Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs

Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Nathanael Bosch

EPFL, Lausanne, Switzerland

Dynamical Systems Uncertainty Quantification Algorithmic Stability

Jun 6, 2026cond-mat.mtrl-sci

Inverse design of bespoke interatomic potentials via active learning by information-matching

Interatomic potentials (IPs) enable large-scale atomistic simulations beyond the reach of first-principles methods, but their predictive reliability depends critically on the selection of training data, quantified uncertainty, and model expressiveness. Active learning (AL) provides a principled framework for constructing efficient and accurate IPs, yet most strategies reduce parameter uncertainty without explicitly accounting for the specific material properties being predicted. The information-matching (IM) approach addresses this limitation by requiring that the selected training data provide at least as much parameter space information as needed to achieve prescribed uncertainty targets for selected quantities of interest (QoIs). Here, we apply IM to develop bespoke IPs specifically tailored for predicting plastic strength in metals. Due to the high computational cost of simulating plastic strength, we employ an indirect IM strategy that targets inexpensive intermediate QoIs that correlate with strength. The IM method enables precise parameter constraints with minimal training data, yielding precise predictions for both the intermediate QoIs and plastic strength. Yet, model error remains a key limitation, and a post hoc uncertainty inflation correction provides a viable means to mitigate this limitation. These findings illustrate both the promise and limits of uncertainty-aware AL for predicting complex material properties.

Yonatan Kurniawan, Logan D. Williams, Amit Samanta +6

Department of Physics and Astronomy, Brigham Young University, Provo, UT, USA · Department of Physics and Astronomy, Brigham Young University, Provo, UT, USA. · Lawrence Livermore National Laboratory, Livermore, CA, USA +7

Uncertainty Quantification Machine Learning Interatomic Potentials Active Learning Materials Property Prediction

Jun 5, 2026astro-ph.IM

Beyond Point Estimates: Benchmarking Uncertainty Quantification Methods on the AION-1 Astronomical Foundation Model

Foundation models for astronomical surveys offer powerful learned representations that can be transferred to downstream regression tasks such as galaxy property estimation. However, point predictions alone are insufficient for scientific inference; reliable uncertainty quantification (UQ) is essential. We compare seven UQ methods on galaxy property regression using frozen AION-1 foundation-model embeddings, predicting redshift, stellar mass, stellar-population age, gas-phase metallicity, and specific star-formation rate, from Legacy Survey photometry/imaging and DESI spectra, with PROVABGS-derived labels. Distribution-free conformal methods achieve marginal coverage within

\sim

1,pp of the nominal 90% across all properties, while non-conformal baselines (Deep Ensembles, MC~Dropout) fail to calibrate reliably. Among conformal approaches, Conformalized Quantile Regression (CQR) delivers the best coverage in the bin with the poorest model predictions. More importantly, only the Locally Valid and Discriminative (LVD) framework -- particularly when operating on AION-1 embeddings -- also provides finite-sample \emph{local validity}, producing intervals that adapt to each galaxy's local prediction difficulty rather than relying on marginal guarantees alone. These results establish conformal prediction, and LVD in particular, as the preferred UQ framework for uncertainty-aware inference on foundation-model embeddings in astrophysics.

Karla Tame-Narvaez, Aleksandra Ćiprijanović, Shubhendu Trivedi

Scientific Computing Division Fermi National Accelerator Laboratory Batavia, IL 60510 · Department of Astronomy and Astrophysics University of Chicago Chicago, IL 60637 · Fermi National Accelerator Laboratory Batavia, IL 60510 +1

Uncertainty Quantification AI-Assisted Scientific Research Conformal Prediction Regression Prediction Intervals

Jun 5, 2026math.NA

No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty

Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper develops a no-harm certification-and-selection framework for physics-informed inverse learning. A learned reconstruction is accepted only when its residual-calibrated radius is no worse than the baseline radius, namely when

R_{\mathrm{learn}}\le R_{\mathrm{base}}+\varepsilon_{\mathrm{safe}};

otherwise, the method returns the baseline. The certificate combines data, physics, boundary or initial-condition, and optimization residuals. Under a conditional stability estimate, these residuals yield an a posteriori reconstruction-error bound and a deterministic uncertainty radius. A high-probability certificate is also derived for physics residuals estimated from independent random collocation points. Numerical tests on Poisson source recovery, inverse heat reconstruction, limited-angle tomography, elliptic coefficient identification, and stochastic residual validation show that the selector accepts certified improvements, rejects shifted, hallucinated, or unfinished candidates, and becomes conservative in strongly ill-posed regimes. The framework is therefore a certification-and-selection layer, not another reconstruction architecture.

Ronald Katende

Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda

Uncertainty Quantification Physics-Informed ML PDE Inverse Problems

Jun 4, 2026cs.CV

Architecture-Adaptive Uncertainty Fusion for Deepfake Detection

Deepfake detection systems achieve near-perfect accuracy on benchmarks, yet forensic deployment demands reliable prediction uncertainty. Existing uncertainty quantification (UQ) methods rely on single sources and ignore that optimal uncertainty composition varies across architectures. We propose Correlation-Optimized Fusion (COF), an architecture-adaptive framework that fuses five complementary uncertainty sources -- epistemic, aleatoric, calibration, conformal, and distributional -- by maximizing Pearson correlation between fused uncertainty scores and prediction errors via constrained optimization on the probability simplex. COF requires no model modifications and only 42 s of weight optimization, compared to 20--45 h for a 5-model Deep Ensemble. Evaluation across eleven architectures on FaceForensics++ reveals a fundamental trade-off: under matched train/evaluation protocol, non-linear methods achieve approximately 5--6% higher in-domain correlation than COF (mean r = 0.438), but this reverses under distribution shift. On CelebDF, COF outperforms Random Forest in 9/11 architectures with up to 7.3x higher correlation (MaxViT-B: r = 0.249 vs. 0.034); RF degrades 85% cross-domain to r = 0.071, whereas COF retains substantially more signal (74% drop to r = 0.116). Cross-dataset evaluation on CelebDF and DFDC reveals catastrophic generalization failure across all methods: in-domain correlations of 0.41--0.47 collapse to near-zero externally (mean degradation 90.7%), with seven of eleven architectures exhibiting uncertainty inversion. These results establish COF as a practical, interpretable framework for controlled-distribution deployment and identify domain-adaptive UQ as the central open challenge for forensic deployment.

Ritesh Sharma, Mohammad Ghasemigol, Yuichi Motai

Uncertainty Quantification Digital Image Forensics Domain Generalization Deepfake Detection

Jun 4, 2026cs.LG

Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression

Symbolic regression (SR) is a class of methods that systematically explore the space of mathematical functions to discover models that accurately capture the underlying relationships in a dataset. Despite recent advances in the field, a lack of support for uncertainty quantification (UQ) limits its adoption in real-world decision processes. In regression analysis, UQ provides important information about the model reliability, which can both help to avoid overfitting by accounting for uncertainty in the data, and provide insights for decision-making. This survey is the first to clearly address this issue, with the objective of introducing essential UQ concepts and reviewing the current literature on UQ in SR, which can be broadly organized into three research directions: frequentist, Bayesian, and model selection. Despite its importance, UQ in SR is still underexplored, which motivates further research into reliable UQ methods for SR.

Julia Reuter, Fabricio Olivetti de Franca

Center for Mathematics, Computation and Cognition (CMCC), Federal University of ABC, Brazil

Uncertainty Quantification Symbolic Regression

Jun 4, 2026cs.NE

Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process

Uncertainty quantification in neural networks prediction is a main issue for usual applications. Our approach seeks at reducing computation costs by directly evaluating uncertainty using PDE's information on the asymptotic variance, rather than the deep ensemble method which may be seen as a Monte Carlo estimation of the prediction, requiring the training of multiple networks. We thus study the law of the limiting process describing the random fluctuations around the mean-field limit of wide two-layer neural networks trained by stochastic gradient descent in a weak-noise regime. Building on a recent trajectorial central limit theorem, in which this limit is characterized as the weak solution of a linear stochastic evolution equation, we identify its law explicitly. More precisely, we show that it is a centered Gaussian process in the dual of a weighted Sobolev space, and we derive a closed covariance representation for the finite-dimensional distributions obtained by testing it against smooth functions. This covariance is expressed through the solution of a backward transport equation with a nonlocal source term, whose coefficients are driven by the mean-field trajectory. As a consequence, by testing against the activation function at a fixed input, we obtain an expression for the limiting variance of the corresponding network-output fluctuations. We illustrate this result numerically on a one-dimensional regression example.

Arnaud Descours, Arnaud Guillin, Geoffrey Lacour +3

LSAF · LMBP · MaIAGE +1

Uncertainty Quantification Neural Network Training Dynamics

Jun 3, 2026cs.AI

Uncertainty Aware Functional Behavior Prediction and Material Fatigue Assessment for Circular Factory

Returned products in circular factories re-enter production with heterogeneous degradation states, usage histories, and remaining capability. Reuse cannot be decided from the current inspection alone, because future function fulfillment and component integrity may evolve differently under the next service scenario. Existing PHM approaches support degradation prediction, but often target fixed operating conditions or isolated component benchmarks, while material-fatigue assessment is rarely linked to system-level functional prognosis. This paper addresses this gap for an angle grinder by combining uncertainty-aware functional prediction with component-level fatigue assessment in an instance-specific reliability workflow. The proposed framework combines the current tool state with recent force--torque usage windows. A convolutional encoder extracts loading patterns from spindle forces and shaft torque, and an LSTM backbone predicts nine functional variables as Gaussian mean and variance estimates. In parallel, the same loading history is translated into output-shaft fatigue information through finite-element-supported stress reconstruction, S--N/Miner damage evaluation with Haibach extension, and Paris-law crack-growth analysis. A streaming replay algorithm consolidates both branches into functional, material, and system reliability trajectories. Held-out tests show mean

2\%

-tolerance accuracy of 0.9652 across nine outputs. Thermal variables are predicted near-perfectly, while drive motor current and load speed remain the most demanding dynamic outputs, with

R^2

values of 0.9750 and 0.9924. Torque history is especially important for these variables, and the conventional LSTM outperforms GRU and xLSTM in the short-history setting. Reliability calibration is most informative for drive motor current, where predicted and observed exceedance probabilities ...

Nehal Afifi, Mehdi Khabou, Victor Mas +5

Uncertainty Quantification Predictive Maintenance

Jun 3, 2026cs.CV

Instance-Level Post Hoc Uncertainty Quantification in Object Detection

Object detection is a safety-critical component of autonomous driving. It is essential to quantify the uncertainty in bounding-box predictions for safety assurance. Post hoc uncertainty quantification without retraining aligns with real-world deployment requirements; therefore, we employ the Laplace approximation. Because instance-level uncertainty is needed, linearized inference methods that require multiple backpropagations are not time-efficient, and sampling-based methods are not fully post hoc. We propose Monte-Carlo generalized linearized model (MC-GLM), which provides instance-level and approximately post hoc uncertainty quantification. The number of samples required in the Monte Carlo step is constant and independent of the number of output instances, so it can be parallelized. Experiments on the nuScenes dataset with the CenterPoint detector validate the effectiveness of our method, and the resulting uncertainties exhibit good quality.

Chongzhe Zhang, Zifan Zeng, Qunli Zhang +2

RAMS Lab, Huawei Heisenberg Research Center, Munich, Germany · Technische Universität Berlin, Berlin, Germany · Technische Universität München, Munich, Germany

Uncertainty Quantification Autonomous Driving Perception Object Detection

Jun 3, 2026cs.LG

Smart Picks in the Dark: Towards Efficient RLVR for Reasoning via Tracing Metacognitive Pivots

Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset. To this end, data-efficient RLVR methods have been widely studied from two perspectives: (i) data selection methods identify a small subset of "golden" samples that yield near-full-data performance, but they rely on a pre-existing pool of labeled data. (ii) unsupervised RLVR methods train the model using its own internal supervision signals on large-scale unlabeled data, yet they exhibit suboptimal performance. Accordingly, we investigate the "pick in the dark" setup for RLVR, which aims to select, without prior supervision, unlabeled samples that are most beneficial for training and worthy of annotation. Through systematic analysis, we demonstrate that smart picks hinge on a well-calibrated uncertainty estimator to enable strategic partitioning of data for adaptive training regimes. Building on this insight, we propose PivotTrace, a three-way data triage framework that leverages attention dynamics to trace metacognitive pivots during reasoning. By precisely quantifying uncertainty through pivot density, PivotTrace achieves automated data routing to synergistically maximize both annotation and training efficiency. Empirically, PivotTrace surpasses the fully supervised LRM with only 29.3% annotated samples and 2.75 faster convergence.

Guangcheng Zhu, Shenzhi Yang, Haobo Wang +7

1Zhejiang University · 2Ant Group

Uncertainty Quantification RL for Language Model Reasoning Active Learning Reinforcement Learning with Verifiable Rewards Data-Efficient Learning

Jun 2, 2026cs.LG

Integrating Local and Global Entropy for Uncertainty Quantification in LLMs

Large language models hallucinate confidently, making uncertainty quantification (UQ) essential for reliable deployment. Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic.

Johanne Medina, Tianyi Zhou, Keivin Isufaj +2

Qatar Computing Research Institute, HBKU Doha, Qatar · KTH Royal Institute of Technology Stockholm, Sweden

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

Jun 2, 2026cs.CL

Clustered Self-Assessment: A Simple yet Effective Method for Uncertainty Quantification in Large Language Models

Large language models (LLMs) demonstrate remarkable performance across diverse tasks, but they often generate responses that appear plausible while being factually incorrect. This problem is compounded by the lack of explicit uncertainty estimates, which makes it difficult for users to judge the reliability of model outputs. Existing uncertainty quantification methods typically rely on indirect signals, such as entropy across sampled generations. These signals can be difficult to interpret and do not fully leverage the model's ability to assess its own uncertainty. We propose a simple yet effective self-assessment method for uncertainty quantification in LLMs. Our approach groups sampled generations into semantically distinct clusters, converts them into answer options in a structured multiple-choice question, and uses the probability assigned by the LLM to each option as a confidence estimate. Experiments across multiple models and datasets show that our method consistently outperforms baseline approaches. Notably, it achieves competitive performance with as few as two additional samples, demonstrating both its effectiveness and efficiency.

Qi Cao, Takeshi Kojima, Andrew Gambardella +3

The University of Tokyo, Japan

LLM Evaluation Uncertainty Quantification Confidence Estimation in Language Models Language Model Self-Assessment LLM Reliability LLM Uncertainty Estimation+1

Jun 2, 2026cs.LG

APIC: Amortized Physics-Informed Calibration using Neural Processes

Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration (APIC), a population-level extension of KOH that leverages Neural Processes to perform scalable Bayesian inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, APIC enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka-Volterra system, and the advection-diffusion PDE with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.

Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler

Computer Vision Group, Friedrich Schiller University Jena, Germany

Uncertainty Quantification Amortized Inference Model Calibration Physics-Informed ML

Jun 1, 2026cs.CV

FUSE: Quantifying Uncertainty in Vision-Language Models by Bayesian Fusing Epistemic and Aleatoric Uncertainty

Vision-language models (VLMs) are playing an increasingly important role across multiple domains. In many applications, such as robotics, it is crucial to quantify the uncertainty in the output of these models. } We develop FUSE, a probabilistic framework for capturing two complementary sources of uncertainty in vision-language modeling: (i) aleatoric embedding-level uncertainty derived from input data vision-language ambiguity, and (ii) epistemic model-level uncertainty estimated from the semantic response diversity of VLMs. Our approach formulates a Bayesian fusion mechanism that analytically combines these uncertainty sources to produce a scalar measure of uncertainty. This measure can be used to reliably predict the model's output correctness for downstream applications. We demonstrate that our method outperforms baselines and achieves SOTA uncertainty calibration.

Harry Zhang, Luca Carlone

Massachusetts Institute of Technology

Uncertainty Estimation for VLA Models Vision-Language Models Uncertainty Quantification VLM Calibration Uncertainty Calibration

Jun 1, 2026cs.LG

Scalable Uncertainty Quantification for Extreme Weather Forecasting via Empirical Neural Tangent Kernels

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (

k \leq 10

), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37% sharper prediction intervals at 90% coverage, and uniquely produces \emph{adaptive} intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Jose Marie Antonio Miñoza, Rex Gregor Laylo, Sebastian C. Ibañez

Center for AI Research · Department of Education · Makati, Philippines

Uncertainty Quantification Independent Component Analysis Neural Tangent Kernel Regression Prediction Intervals Weather Forecasting

Jun 1, 2026cs.CL

The Role of Ambiguity in Error Prediction via Uncertainty Quantification

The task of Error Prediction, namely predicting whether a model output is correct, is commonly tackled with Uncertainty Quantification (UQ). However, while uncertainty metrics capture when models lack knowledge or capacity to make a prediction, they also reflect aleatoric uncertainty, which is inherent in the model input and context. This paper presents a method for improving error prediction for Large Language Models (LLMs), by disentangling input ambiguity from UQ signal. We conduct experiments on the task of Question Answering (QA) with six UQ metrics and show that UQ metrics are more predictive of errors on unambiguous instances than on questions with multiple plausible answers. We use Gated Experts and Selective Prediction to incorporate gold and predicted ambiguity labels into the error prediction pipeline. We find that ambiguity information improves error prediction scores across model families, training and evaluation paradigms, datasets (including allegedly unambiguous ones), and sources of aleatoric uncertainty, yielding improvements of over 10 points of PRR for individual UQ metrics on standard datasets.

Ieva Raminta Staliūnaitė, James Bishop, Andreas Vlachos

University of Cambridge · The Alan Turing Institute

Uncertainty Quantification LLM Uncertainty Estimation

Jun 1, 2026physics.app-ph

Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraints

Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and probabilistic exceedance mapping. The model predicts both the temperature field and a spatially varying predictive uncertainty field using a graph-attention-based mean-residual architecture trained with a Gaussian negative log-likelihood. Sensor placement is addressed using a Proper Orthogonal Decomposition with QR factorization (POD-QR) strategy with a 4 km minimum inter-sensor distance constraint and is compared with random feasible placement and farthest-point sampling. The framework is evaluated over a Montreal-area polygon using Daymet v4.1 daily temperature data (1 km resolution) under a strict temporal hold-out protocol (training: 2020-2023; testing: 2024). Across sensor budgets (10-40 sensors), the proposed GNN consistently outperforms inverse distance weighting and ordinary kriging in RMSE and MAE on unobserved nodes. Sensor-placement effects are most pronounced at low budgets and diminish at higher budgets, with a practical saturation regime emerging around 30 sensors under the imposed spacing constraint. Probabilistic evaluation further shows improved uncertainty calibration with increasing sensor density and a better sharpness-calibration trade-off than kriging. These results support the proposed framework as an effective tool for uncertainty-aware temperature field reconstruction and decision-oriented heat-risk mapping.

Reda Snaiki, Abdelatif Merabtine

Department of Construction Engineering, École de Technologie Supérieure, Université du Québec, Montréal, Québec, Canada

Graph Neural Networks Uncertainty Quantification

May 31, 2026stat.ML

Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics

Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings. However, modern-sized datasets have made overparameterized deep networks the preferred methods of choice due to their predictive power and favorable computational scaling. While many posterior approximations exist, all incur approximation errors. Recent work accounts for this error in the form of computational uncertainty but comes at the cost of quadratic complexity and assumes fixed model hyperparameters. Here we extend this development to model selection, including a novel training loss and optimization scheme, which yields tractable inference in large state-spaces. We introduce a framework, the Computation-Aware State-Space Model (CASSM), specifically designed for the scale-imbalanced regime, where the number of trials is significantly lower than the number of recorded neurons. In this regime, for both synthetic and real data, we show that our method is competitive with data-hungry deep networks, with significantly improved uncertainty calibration over previous attempts to scale Bayesian methods. Our experiments provide a roadmap to neuroscience researchers in choosing from a host of potential dynamical latent variable models given key dataset properties and constraints.

JR Huml, Jonathan Wenger, John P. Cunningham

Department of Statistics, Columbia University; Zyphra Technologies · Department of Statistics, Columbia University; Zuckerman Institute

Dynamical Systems Bayesian Filtering Uncertainty Quantification Latent Dynamics Modeling State Space Models

May 31, 2026stat.ML

On the Uncertainty Quantification Ability of Tabular Foundation Models

Foundation models (FMs) have achieved substantial success in generalizing across tasks without problemspecific training or fine-tuning. However, many critical applications in mechanics and computational science require not only accurate predictions but also reliable uncertainty quantification (UQ). Herein we investigate the UQ capabilities of tabular FMs in regression tasks through a comprehensive empirical study comparing Tabular Prior-Data Fitted Networks (TabPFN) against Gaussian processes (GPs). We systematically evaluate these two methods across a host of regression problems with varying complexity, dataset sizes, and input dimensionalities. We use a default setting to build all the GPs and for a fair comparison against TabPFN v2.5. Our findings highlight an important trade-off between explicit and learned priors: while TabPFN achieves highly competitive performance for complex, high-dimensional problems with sufficient data, GPs often provide superior predictive accuracy and UQ in data-scarce settings. Moreover, when the chosen kernel constitutes a good prior for the underlying function, GP performance can substantially exceed that of TabPFN. Our results can be reproduced from https://github.com/kianswarehouse/GPvsPFN.

Tyler R. Johnson, Kian Ben-Jacob, Nima Negarandeh +2

Department of Mechanical and Aerospace Engineering, University of California, Irvine · Department of Civil and Environmental Engineering, University of California, Irvine

Tabular Foundation Models Uncertainty Quantification Prior-Data Fitted Networks Tabular Regression Gaussian Process Regression

May 29, 2026stat.ML

Parameter-Free and Group Conditional Online Conformal Prediction

Uncertainty quantification (UQ) is critical for the deployment of machine learning predictors in real-world scenarios where the data distribution may shift over time (i.e., data may not be exchangeable). Online conformal prediction (OCP) methods address this issue at the expense of either (i) group-wise error control or (ii) learning-rate independent implementation. Group-conditional coverage is essential for fairness across different collections of data points and for providing finer UQ guarantees. Parameter-free optimization is crucial for robustness to adversarial and unknown data shifts. We propose a parameter-free algorithm for group-conditional OCP and demonstrate that it achieves the best group-conditional coverage guarantees. We evaluate our algorithm on synthetic and real-world data, demonstrating that our method not only improves the reliability of existing parameter-free OCP methods but also provides prediction intervals that are comparable in size to well-tuned group-conditional approaches. By unifying group-conditional coverage with parameter-free online algorithms, our work lays a foundation for fair and robust uncertainty quantification in shifting environments.

Beepul Bharti, Ambar Pal, Jacopo Teneggi +1

1Johns Hopkins University · 2Amazon Responsible AI

Uncertainty Quantification Group-Conditional Conformal Prediction Conformal Prediction

May 29, 2026cs.LG

Large-scale Uncertainty Quantification for Latent Variable Models Using Subsampling Markov Chain Monte Carlo

Stochastic gradient Langevin dynamics combined with Gibbs updates (SGLD--Gibbs) provides a highly scalable approach to approximate Bayesian inference in latent variable models. However, it remains unclear how to tune the algorithm's hyperparameters in a principled manner to ensure the uncertainty estimates are statistically meaningful. In this work, we address this gap in tuning guidance by developing a statistical scaling limit theory for SGLD--Gibbs. We derive a joint asymptotic limit for the global parameters and latent variables under appropriate space-time rescaling. We show that global parameters converge to a diffusion-type limit, while each latent variable converges to a jump process, reflecting the use of intermittent Gibbs updates. This joint jump-diffusion structure reveals how latent-variable randomness contributes to the stationary distribution of the global parameters. We leverage our results to propose explicit guidance on hyperparameter tuning for SGLD--Gibbs that ensures meaningful uncertainty quantification. Numerical experiments show that SGLD--Gibbs with our tuning guidance leads to better parameter estimates, uncertainty quantification, and predictive performance than stochastic variational inference.

Xiaoyu Wang, Jonathan H. Huggins

Department of Mathematics & Statistics, Boston University · Faculty of Computing & Data Sciences, Boston University

Markov Chain Monte Carlo Stochastic Gradient Langevin Dynamics Latent Variable Models Uncertainty Quantification Langevin Dynamics Bayesian Inference

May 29, 2026cs.LG

Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlo

Tuning algorithms such as stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD) for approximate sampling and uncertainty quantification remains challenging, particularly in the practically relevant settings when the batch size is large or the model is misspecified. Existing theory that provides tuning guidance relies on continuous-time limits or strong statistical assumptions, which can become quantitatively inaccurate in these regimes. We address these shortcomings by proposing new discrete-time approximations to SG(L)D with and without momentum, which enables accurate predictions of the stationary covariance, iterate average covariance, and integrated autocorrelation time. Moreover, we prove quantitative, non-asymptotic error bounds showing that these estimates are sufficiently accurate for practical tuning and uncertainty quantification. Numerical experiments demonstrate that our theory yields improved tuning guidance across a range of models and data-generating distributions where existing approaches fail, including when using the

β

-divergence rather than log-loss to obtain statistically robust inferences.

Yu Wang, Jie Ding, Jonathan H. Huggins

Department of Mathematics & Statistics, Boston University · Questrom School of Business, Boston University · Faculty of Computing & Data Sciences, Boston University

Markov Chain Monte Carlo Stochastic Gradient Langevin Dynamics Uncertainty Quantification Langevin Dynamics Bayesian Inference Stochastic Gradient Descent