Uncertainty Quantification

The recent emergence of Time Series Foundation Models (TSFMs) has significantly advanced multi-step forecasting performance, enabling accurate predictions over extended future horizons. However, existing TSFMs often suffer from significantly inherent uncertainty, which typically manifests as derived forecast branches emerging at each time step and spreading to subsequent steps; different forecast branches often exhibit varying forecasting performance, thereby undermining the credibility of TSFM forecasts. In this paper, we propose the Slicing-Graphing-Alignment (SGA) method to quantify the uncertainty of multi-step TSFM forecasts. The proposed SGA first characterizes the topology of all potential forecast branches using a directed acyclic graph, such that the graph complexity bounds the uncertainty of multi-step forecasts, and then precisely measures the graph complexity by integrating both topological information and TSFM-inherent stochasticity. Experimental results conducted on 11 TSFMs and 27 datasets demonstrate that (i) SGA achieves the best performance when ranking predictive errors with uncertainty estimates; (ii) SGA works with a more extensive and more precise sampling coverage than those of existing UQ methods, deriving a quantification mechanism fundamentally different from those of established ones; and (iii) larger model scales of TSFMs correlate with lower uncertainty estimates of multi-step forecasts, suggesting another empirical scaling law for uncertainty quantification of multi-step TSFM forecasts.

KITE queries a typed behavioral kernel once per unique state, then executes populations of any size from the table with event-keyed randomness and common random numbers. An expensive flagship model is reserved for sparse paired anchors that estimate intervention effects. Measured human-model discrepancy is propagated as shared error into every conclusion. Population-experiment cost thus scales with unique states and anchors, while uncertainty is governed by evidence about people rather than Monte Carlo noise. On Epstein experiments with 9,070 participants, anchors covering 1.7% of states reduced effect error by 41% (absolute MAE reduction 0.0125). On 37 held-out SocSci210 experiments, 0.5-1.5% anchor coverage raised captured decision gain from 0.27 to 0.39. The kernel passed content-fidelity criteria in all 15 new countries of a 16-country study. Shared discrepancy yielded retrospective coverage of 93% and 96% at nominal 80% and 90%, versus 29% and 36% from human sampling uncertainty alone. A million agents executed 20 tabulated steps in 0.9 seconds on a laptop. This architecture offers a route to screening candidate interventions before human trials, multi-country content audits, and uncertainty-aware policy comparison at the cost of a few thousand kernel calls with sparse flagship anchors. Property-specific evidence records connect each use to its validation scope, correction provenance, and uncertainty, making these applications auditable.

Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncertainty quantification (UQ) approaches behave when adapted to geometry-conditioned neural surrogates. We compare one closed-form and two sampling-based approaches-a Gaussian process (GP)-based method, concrete Monte Carlo (MC) dropout, and deep ensembles-and evaluate them on three large, industry-relevant CAE datasets for external aerodynamics and crash dynamics. We examine whether predicted uncertainties have credible magnitudes, identify locations with larger prediction errors, respond to unfamiliar inputs, and remain informative for derived engineering quantities. On the DrivAerStar dataset, where all three methods are compared, each generally assigns higher uncertainty to locations with larger prediction errors, and validation-based rescaling brings interval coverage close to nominal on a disjoint in-distribution test set. Results on AirFRANS and automotive crash also show useful error ranking and interval estimates, but the relative performance of the methods changes with the dataset and evaluation criterion. UQ methods and evaluation metrics should therefore be selected based on the intended downstream CAE decision.

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

Generative models are increasingly used to solve scientific inverse problems, but existing evaluations still focus primarily on whether a method can produce a single plausible reconstruction. This is insufficient for ill-posed problems, where multiple solutions may be consistent with the same sparse or noisy observations. In these settings, a method can achieve strong pointwise accuracy while still failing to capture the true posterior through mode collapse, overconfident uncertainty, or averaging incompatible solutions. We introduce PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers. PosteriorBench evaluates four physics-based inverse problems: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. For each task, we construct high-fidelity reference posteriors using computationally heavy but established procedures such as rejection sampling and Markov chain Monte Carlo, enabling direct assessment of whether solvers recover the full set of solutions rather than the single best sample. We pair these references with a five-metric posterior evaluation suite: posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error. These metrics assess pointwise accuracy, marginal uncertainty, distributional alignment, and global frequency fidelity. The benchmark spans sparse sensing, low-resolution observations, nonlinear forward models, varying noise levels, and multimodal priors, with a unified pipeline for distribution matching and uncertainty quantification. Our experiments reveal substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness, and guidance weights and generation noise are key to posterior-variance calibration.

Active subspace methods provide a framework for quantifying predictive uncertainty in high-dimensional models by identifying and performing inference along parameter directions that have the greatest influence on the model output. However, the construction of active subspaces requires storing many full-dimensional model gradients, which becomes prohibitive as model size increases. We address this limitation by proposing Compressed Active Subspaces (CAS), a scalable approach that first maps the model parameters to a compressed space using a structured isometric embedding and then constructs the active subspace within this reduced parameterization. Our approach substantially reduces the memory required for active subspace construction and enables Bayesian inference for large models where standard active subspace methods become impractical. We demonstrate the scalability of CAS on neural networks of increasing size while maintaining predictive performance and robust uncertainty estimates.

Dynamic facial expression recognition (DFER) benchmarks such as DFEW provide multiple annotator votes per clip, yet most models collapse them to a majority label and cannot represent human disagreement at inference time. We propose a disagreement-aware DFER framework that trains directly on the raw annotator count vector using a Dirichlet-Multinomial likelihood. Unlike mean-only soft-label objectives, the proposed likelihood provides scale-sensitive supervision for the Dirichlet concentration while preserving the predictive mean. A separate ambiguity head predicts annotation entropy for unseen clips, and a monotone Chow-style reject rule combines predicted ambiguity, vacuity, temporal instability, and input quality for selective prediction. On DFEW, the method preserves recognition accuracy while reducing ECE by 30% and AURC by 15%, and predicted ambiguity reaches a Spearman correlation of 0.52 with the annotation entropy of test clips. The calibration and selective-prediction gains transfer to FERV39k and remain under identity- and movie-disjoint DFEW splits.

Tracking the energy transition requires reliable statistics on renewable deployment. Rooftop photovoltaics (PV) are especially hard to track, owing to their decentralised nature, and the resulting inaccuracies in official statistics are known but not quantified. Remote sensing offers an independent way to identify rooftop PV systems. We introduce a Bayesian framework to estimate the ground-truth rooftop PV capacity from remote sensing detections, turning an imperfect detector into an uncertainty-aware measurement instrument. Applied to France, the corrected detections estimate a capacity of 4.03 GWp [3.96--4.11] (99% credible interval) of rooftop PV below 36 kWp, matching the transmission system operator's connection data within 3.3% nationally, while identifying local under-reports of up to 61% of local capacity. We also document and quantify a significant truncation bias in French rooftop PV open data. Beyond France, the approach paves the way for more reliable estimates of rooftop PV capacity worldwide.

Streaming geometric foundation models are emerging as a compelling alternative to SLAM systems. Yet this streaming nature introduces a fundamental issue: each prediction is made from limited context, which is vulnerable to dynamic objects and weak textures. Small local errors accumulate into severe geometric distortion and long-horizon scale drift. We argue that reliable streaming reconstruction requires geometric foundation models to be not only predictive, but also self-correcting. We introduce SURE-Map, a self-correcting framework built upon two complementary principles. First, we explicitly model cross-view geometric uncertainty. Unlike conventional depth or point confidence, which primarily reflects the reliability of individual-view prediction, our uncertainty directly measures whether the jointly predicted pose and depth induce geometrically consistent cross-view pixel correspondences. Second, because local correction alone cannot eliminate slowly accumulating scale errors, we introduce multi-timescale self-correction: fast consecutive-frame inference preserves streaming efficiency, while sparse keyframe-window inference provides longer-range geometric evidence to periodically recalibrate the scale of recent trajectories. SURE-Map establishes new state-of-the-art performance for online feed-forward reconstruction across long-horizon benchmarks, reducing ATE-RMSE from 24.00 to 17.24 m on KITTI, 5.11 to 4.74 m on Oxford Spires, and 31.37 to 28.58 m on VBR, with further improvements to 15.17, 4.63, and 22.12 m when incorporating loop-closure refinement. Project page: https://mingkai-liu.github.io/projects/sure-map/.

Kolmogorov-Arnold Networks (KANs) with spline activations have recently shown promise for interpretable function approximation. Distance-Aware Error for Kolmogorov Networks (DAREK) introduces a computationally efficient bottom-up approach to uncertainty quantification by equipping KANs with distance-aware error bounds; yet, in high-dimensional settings, the theoretical guarantees can be weakened by the emergence of fictitious knots. Inspired by the Kolmogorov-Arnold representation theorem, DAREK adopts a componentwise formulation in which each input dimension is treated separately; as a result, induced knot locations may appear in the combined input space without corresponding to actual training data. These fictitious knots mislead the DAREK uncertainty estimator into reporting low uncertainty far from any real observation, violating the distance-awareness guarantee. We identify this failure mode precisely, characterize its geometric structure, and propose a drainage uncertainty mechanism that restores distance-awareness by constructing a monotonically decreasing uncertainty path from any fictitious knot region toward the nearest real knot. The proposed drainage method provides a practical heuristic correction that mitigates the fictitious-knot failure mode while restoring theoretical distance-awareness in high-dimensional settings. Experiments on a 2D synthetic benchmark and a 100-dimensional face dataset show that drainage raises sampled distance-awareness (SDA) from 85% to 98-99%, matching Gaussian processes at lower computational cost.

While homographies are fundamental to many computer vision tasks, the majority of conventional estimation techniques provide only point estimates without directly quantifying uncertainty introduced by noisy observations. Uncertainty, though, propagates to subsequent processing steps such as camera calibration and 3D reconstruction and is particularly relevant in safety-critical and socially relevant fields including medical imaging, autonomous driving, and defense. We present a fast Bayesian formulation for homography estimation from point correspondences that explicitly incorporates measurement uncertainty and prior knowledge while providing a posterior distribution over the homography parameters. A closed-form solution of the posterior mean of the homography is derived in homogeneous coordinates and supplemented by an iterative Bayesian approach to handle non-linearities. Synthetic experiments demonstrate the applicability to projective transformations and show improved estimation accuracy over DLT under varying noise conditions. Image stitching experiments further demonstrate applicability to real image correspondences while additionally providing uncertainty information.

Vision-language models are increasingly explored for clinical prediction from electronic health records and medical images, where identifying unreliable predictions is important for safe deployment. Uncertainty estimation (UE) enables detecting such predictions, but its evaluation depends on a correctness criterion that determines whether each model output is correct. If this criterion disagrees with human judgement or distorts downstream UE performance, conclusions about model reliability can be misleading. We introduce a two-axis framework that evaluates correctness criteria by their agreement with human judgements and fidelity to human-referenced UE performance. We assess eight criteria across three clinical prediction tasks and three models using 450 predictions annotated by two reviewers. Across the audited tasks, canonical exact matching (EM) achieved the highest observed human agreement and lowest UE distortion, while the BERT-based matching (BEM) and LLM-judge also showed strong human agreement. Across four UE methods and 23,254 clinical predictions, criterion choice changed error-detection AUROC by up to 0.146 and reversed the relative ranking of UE methods. The LLM-judge also selectively accepted invalid or uncertain outputs, accepting 16 of 30 such human-identified errors. These results demonstrate that correctness assessment is an integral component of clinical UE evaluation and should be validated before UE methods are compared.

Neural operators such as the Fourier Neural Operator (FNO) achieve remarkable accuracy in approximating solutions to partial differential equations (PDEs). However, providing rigorous uncertainty estimates remains an open challenge. We propose Physics-Informed Conformal Prediction (PI-CP), a framework that embeds PDE residuals into the nonconformity score of split conformal prediction, producing prediction intervals that are (i) distribution-free with provable coverage guarantees, and (ii) spatially adaptive when the PDE residual correlates with prediction error -- tighter where physics is well-satisfied, wider where it is violated. Additionally, we prove that FNO's translation equivariance creates a fundamental approximation barrier for PDEs with Dirichlet boundary conditions, and show that coordinate channels resolve this with up to 63x error reduction. We validate PI-CP across six physics scenarios -- heat conduction (2D/3D), structural mechanics (2D/3D), Darcy flow, and Navier-Stokes -- demonstrating consistent 89-91% coverage for all four Conformal methods, while MC Dropout and Deep Ensembles are unstable (82-100%). FNO outperforms CNN and DeepONet by 10-12x.

Strategic flight plan validation in Advanced Air Mobility (AAM) environments requires robust methods for predicting aircraft state uncertainty and detecting potential conflicts with dynamic airspace hazards. This paper presents a novel framework for uncertainty-conditioned trajectory prediction combined with polyhedra hazard representation for pre-flight conflict detection. We introduce a closed-form uncertainty estimation method that couples non-uniform rational B-spline (NURBS) curve fitting for kinematic trajectory generation with a Kalman Filter for state covariance propagation. Drawing from the Light Propagation Algorithm (LPA) paradigm, we employ a sigmoid-blended measurement noise model that captures the uncertainty reduction behavior of flight management systems approaching the required time of arrival (RTA) for waypoints. The resulting temporal uncertainty bounds are derived through a velocity-to-time variance transformation, enabling probabilistic assessment of arrival time deviations along the flight path. For hazard representation, we develop an operator-conditioned classification scheme that transforms gridded environmental data, specifically weather phenomena, into three-dimensional polyhedra volumes with intensity-based stratification. These hazard polyhedra incorporate aircraft-specific safety buffers computed from vehicle performance characteristics. Conflict detection is performed through mesh intersection algorithms operating on the spatial uncertainty tube surrounding the mean trajectory against the hazard polyhedra and temporal overlap. The framework enables the continuous strategic validation of flight plans throughout the pre-flight planning time horizon as environmental conditions evolve.

We present BEAST, the first-ever Bayesian Swin Transformer for atmospheric forecasting on 0.25$^\circ$ global resolution able to accurately quantify both aleatoric and epistemic uncertainty. To overcome the associated computational bottlenecks, we devise an orthogonal 4D-parallelization scheme that introduces a unique domain-tensor-parallelism strategy and a novel uncertainty parallel method, enabling us to fully leverage GPU capacity and efficiently scale model training. For a 2.4-billion-parameter model, we achieve a peak performance of 3.96 EFLOP/s on 20,480 NVIDIA GH200 GPUs on the JUPITER supercomputer. We train BEAST as a 700-million-parameter model with 96 random weight samples on 384 nodes on 40 years of data for nearly one million gradient updates. This model achieves predictive skill scores competitive with state-of-the-art probabilistic atmospheric AI models and numerical models, and can predict extreme events with exceptional skill, while generating large ensembles 3 to 4 times faster than the current-best AI model. Our contribution unlocks the potential of high-fidelity uncertainty quantification in atmospheric AI models, heralding a new era for AI-based models in climate and Earth system sciences.

Earth system modeling is shifting from task-specific predictors toward foundation models with general spatiotemporal representation capabilities. Although these models can jointly encode dynamic Earth fields, external forcings, and static geographic context for multistep forecasting, accurate point predictions or statistically calibrated intervals alone are insufficient for high-impact applications such as extremeweather warning, flood control, renewable-energy dispatch, and emergency resource allocation. What matters in practice is whether predictive uncertainty can be translated into reliable decision risk under specific actions, loss functions, and risk preferences. We propose a decision-oriented uncertainty quantification framework for Earth system spatiotemporal foundation models. The framework produces predictive distributions of future states and uses a decision risk adapter to map forecast samples, decision context, and utility functions into action-conditional risks. A utility-aware calibration module further enforces reliability at the downstream decision-loss level rather than only at the forecast-value level. Calibrated risks are then used to select warning, dispatch, inspection, or resource-allocation actions. Compared with the strongest baseline, the proposed method reduces decision regret by 18.7%, lowers the missed-event rate from 14.2% to 9.1%, and improves expected utility by 11.6%, while maintaining 90.4% predictive coverage and reducing decision calibration error from 0.083 to 0.047. These results suggest that decision-oriented uncertainty quantification can improve the robustness and operational value of Earth system foundation models in risk-sensitive applications.

Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible values of model elements and can introduce inconsistencies, i.e., situations in which models can no longer be jointly satisfied. While existing approaches can determine consistency for a given uncertainty configuration, they provide limited support for systematically exploring, analyzing, and explaining inconsistency across large uncertainty spaces. We address this challenge by reformulating inconsistency as an intervention response modeling problem. Using Saltelli sampling and multi-fidelity Monte Carlo estimation, we generate intervention-response datasets and train a surrogate model that directly predicts inconsistency from the propagated uncertainty geometry. Experiments on 48 scenarios and 10 CPS domains show that the surrogate matches Monte Carlo estimates while reducing evaluation time from milliseconds to microseconds, enabling orders-of-magnitude more response-surface evaluations within fixed computational budgets. Building on the learned response surfaces, we perform sensitivity analysis to identify dominant uncertainty drivers and introduce a gradient-based consistency recourse method to determine minimal uncertainty interventions that restore consistency. The results show that inconsistency under uncertainty can be effectively learned, analyzed, and repaired through response-surface modeling, providing a scalable foundation for uncertainty-aware consistency management in CPS development.

Test-Time Adaptation (TTA) enhances the robustness of models against distribution shifts but faces two critical challenges: error accumulation from noisy pseudo-labels and catastrophic forgetting of source knowledge. Uncertainty-based approaches designed to mitigate error accumulation often yield overconfident or computationally expensive estimates, while strategies intended to prevent forgetting via prototype replay rely on static representations that easily become misaligned as the model adapts. To address these issues, this paper proposes a novel framework, Distilling Image Prototype for Guided Test-Time Adaptation (DIPTTA). The core of the proposed approach is the introduction of a Distill Image Prototype (DIP), a compact set of synthetic images that serves as a dynamic and regenerative anchor of source knowledge. This prototype enables a dynamic feature replay mechanism that continuously generates feature prototypes aligned with the current state of the model, thus effectively preventing catastrophic forgetting. Furthermore, the DIP anchors a source-calibrated uncertainty estimation method, which provides a less biased measure of sample reliability by leveraging stable source knowledge, thereby robustly suppressing error accumulation. Extensive experiments on multiple benchmarks demonstrate that DIPTTA significantly outperforms state-of-the-art methods, particularly under severe domain shifts. The source code is available at https://github.com/LiwenWang919/DIPTTA.

Sea-ice stage of development (SoD) describes the age and associated thickness of sea ice and provides important information for navigation, and operational ice monitoring. SoD labels are obtained from operational ice charts, where trained analysts interpret satellite observations and assign standardized stage codes to regions with similar ice conditions. These codes often represent ranges of compatible ice thicknesses rather than exact physical values. Deep-learning methods can automate SoD mapping and commonly adopt operational ice charts as reference labels for training. These annotations are not exact, however; this is because chart interpretation relies on analyst judgement and on the observations available at the time, so different ice services may assign different SoD labels to the same conditions. We term this variation across independently produced expert annotations multi-annotator label uncertainty; collapsing the annotations into a single deterministic target discards this variation. A second source of uncertainty originates in the learned model itself. In this paper, we quantify both sources: annotation uncertainty from disagreement among independent ice-service charts and model uncertainty from the learned predictive models. We then evaluate their relationship by testing whether model uncertainty is higher where ice services disagree. We observe that supervision incorporating information from multiple annotators can improve this correspondence, with soft supervision achieving the highest overall correlation of 0.256. The relationship becomes substantially stronger near the ice edge, where model predictive uncertainty closely tracks multi-annotator disagreement, reaching a correlation of 0.704 within 0--10 km. Among the uncertainty-estimation approaches, Monte Carlo dropout provides the best-calibrated confidence estimates, with an expected calibration error of 0.050.

Sensor-based AI systems are rarely operated under the conditions under which they were trained: devices, personnel and recording epochs change, and each change degrades performance in ways a random train-test split cannot reveal. We propose a staged, accountable evaluation protocol that treats the evaluation of a deployed model as a measurement with declared reference levels and a quantified uncertainty. Four cumulative generalisation stages hold out devices, subjects and time. Each stage is judged on quantiles of repeated trainings against chance references with the correct class count, an out-of-present-scope rate exposes silent misdirection towards classes that are no longer present in deployment relative to training, and an explicit decision rule ties roll-out decisions not to means but to 5% quantiles. We demonstrate the protocol on infrastructure-free geomagnetic localisation with smartphone-based recurrent classifiers in two real underground mines, including a replication of the scheme's training stages at the second site. Unchanged models are re-evaluated on data recorded 34 months after the training campaign, on a device generation unknown at training time and with a held-out surveyor. The 5% quantile of their present-conditioned precision there is 0.39 over 299 repeated trainings, 16.5 times the chance level; across the composition of the 42 reachable location classes the figure varies by +/-0.08, several times the spread between repeated runs. Repeated trainings of a single configuration show why means mislead: a bimodal configuration passes a mean-based test decisively while its 5% quantile lies more than an order of magnitude below chance.

We address the challenge of scalable uncertainty quantification in large-scale scientific applications, where complex state-of-the-art machine learning methods are often computationally infeasible. Our primary contribution is a simple yet effective empirical Bayes method for automatically tuning the hyperparameters of a flexible, heteroscedastic Spectral-normalized Neural Gaussian Process. This approach retains the expressiveness and uncertainty-awareness of semi-Bayesian neural models while significantly reducing the computational burden by integrating hyperparameter learning directly into the training loop. We demonstrate the practical impact of our method on the task of estimating the dynamic aperture in circular particle accelerators, a fundamental problem in high-energy physics colliders and storage rings, using simulation data from the case of the Large Hadron Collider at CERN. Traditional approaches to DA estimation require extensive particle-tracking simulations, which are prohibitively time-consuming and resource-intensive. Our results show that the proposed method achieves competitive predictive performance and well-calibrated uncertainty estimates at much lower computational cost than state-of-the-art approaches. We stress that, beyond this application, the proposed empirical Bayes framework offers a general solution for training heteroscedastic neural models in situations where manual hyperparameter tuning is impractical. Accordingly, we anticipate that this framework can be applied to other domains that encounter comparable computational limitations.

Machine-learning weather models (MLWMs) now match or outperform operational numerical weather prediction (NWP) at global medium-range forecasting, at far lower inference cost. Many deployed MLWMs are deterministic, producing a single forecast with no estimate of its own uncertainty, whereas a growing family of trained-probabilistic models generate calibrated ensembles directly, at the price of a dedicated training run. We ask instead how much uncertainty can be extracted from a deterministic checkpoint that already exists, without retraining it. Where physical ensembles represent model uncertainty by stochastically perturbing parametrisation tendencies, we perturb the network's raw weight tensors at inference time, a scheme we call stochastically perturbed weights (SPW). We also ask whether it works, where and on which scales to inject the noise, and where it fails. A three-phase ablation across four deterministic backbones, Aurora, GraphCast, SFNO, and AIFS, selects one production baseline per model, benchmarked against the trained-probabilistic AIFS-ENS, FourCastNet 3 and Atlas as well as the operational ECMWF ensemble (IFS-ENS) over 112 initialisation times. At a 240 h (10-day) lead time the SPW ensembles reach continuous ranked probability skill scores (CRPSS) between 0.04 and 0.13 below the best trained-probabilistic baseline, at zero marginal training cost. No injection site works across models: the productive tensor group is architecture-specific, so SPW is at present a tuning procedure rather than a plug-and-play recipe. Its main failure mode is a coherent whole-field offset that overdisperses the domain mean, and restricting the noise to coarse scales or perturbing the initial conditions each repair part of it.

Several geometry-aware approaches to low-rank adaptation have emerged for parameter-efficient fine-tuning of large pre-trained models. These methods aim to take full advantage of the geometric structure of low-rank manifolds for improving the efficiency in subspace utilization and reducing redundancy by enforcing orthogonality constraints during optimization. The strong empirical results of these techniques have motivated further study into whether predictions from such geometry-based adaptation methods could be overconfident. In this paper, we build on the singular value decomposition factorization of adapters to develop a framework based on Stein variational gradient descent (SVGD). In this formulation, the low-rank matrices are transported along the Stiefel manifold to match the targeted distributions while retaining their crucial geometric structure. Since this geometry-aware SVGD approach provides multiple solutions during inference, it supports uncertainty quantification and produces better-calibrated adapters on the Stiefel manifold. Extensive experiments show that our method delivers strong model calibration and attains higher prediction accuracy than SVGD and related uncertainty estimation methods that are formulated in Euclidean space.

Machine learning models are widely used in clinical applications, social media, law enforcement and critical infrastructure. Verifying whether their outputs are biased against disadvantaged groups or individuals is crucial to ensuring they are fair and allowing their use in such settings. A rigorous risk assessment of possible fairness violations requires quantifying the uncertainty associated with selecting and estimating such models. Yet, this is rarely done in the literature, which focuses on identifying a single model with a suitable trade-off between predictive accuracy and fairness. In this paper, we move beyond point estimation and discuss frequentist and Bayesian approaches to uncertainty quantification for fair machine learning, with practical examples and implications for simulated and real data.

Ensuring the reliability of deep learning models in real-time industrial defect detection is critical for high-stakes quality inspection. To mine uncertain samples within continuous industrial media streams, thereby enhancing the reliability of the detection system, this paper proposes a streaming active learning method based on the Fuzzy Dual-dimensional Uncertainty (FuDU) framework. Specifically, we first design a Prototype-based Global Uncertainty Quantification (PGUQ) module on the backbone to evaluate image-level uncertainty via normal/defective feature prototypes. A Dual-entropy defect Uncertainty Evaluator (DeUE) is then integrated into the detection head to quantify box-level uncertainty. Finally, by modeling uncertainty as systematic error, we propose a fuzzy dual-dimensional uncertainty-aware strategy that leverages fuzzy inference to fuse dual-dimensional uncertainties, enabling expert knowledge-driven adaptive sampling decisions. Comprehensive experiments demonstrate that FuDU is efficient and flexible, making it well-suited for challenging industrial inspection tasks such as the detection of nuclear fuel rod defects. Our code is publicly available at: https://github.com/wangzhaoyang-508/FuDU.

Post-hoc out-of-distribution detectors are fitted on a finite reference set, so every score they produce is an estimate. If we had chosen a different set, some verdicts would have moved. We measure that movement by resampling the reference set and recording the bootstrap standard deviation of the score, which we call verdict instability. It admits a closed form with no fitted parameters. The instability of a verdict is the within-class dispersion of the assigned class along the query's direction, divided by the square root of that class's reference count. That count is what separates verdict instability from the geometry of the score distribution, and it is identifiable only under class imbalance. Instability grows with the local dispersion. Far-OOD queries lie along the low-variance directions of an anisotropic embedding, so every distance-based score we test assigns its highest values to the verdicts that are most reproducible. Only estimators of local dispersion carry the sign a practitioner expects. We give a rule that predicts this sign for any score from a single label-free correlation, and abstention driven by a wrong-signed score turns out worse than abstention at random on every dataset we test.

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.

Background and Objective: Quality control is a prerequisite for whole-slide image analysis, yet the benchmarks on which quality-control methods are compared share four properties that make their reported differences hard to interpret: few independent slides, annotation concentrated in a minority of them, pooled ratio metrics with no closed-form standard error, and a single inherited train/test partition. We propose a reliability protocol for such benchmarks. Methods: The protocol quantifies four sources of variability - test-set sampling, training stochasticity, partition composition, and undocumented preprocessing - a claim is reportable only if it survives all four; three of the four cost minutes of compute. We apply it to an independent reconstruction of a published diffusion-based artifact detector, evaluated on the original 24-slide partition and against a supervised baseline. Results: The method's central mechanism reproduces: the auxiliary contrastive term improves pooled F1 from 0.673 to 0.688 and replicates under a second seed (+0.0156, p = 0.031; +0.0190, p = 0.005), although it acts on pen marking rather than the artifact types cited to motivate it. Its comparative claims do not: differences between design variants, and against the supervised baseline, fall inside the uncertainty of the evaluation. Four of 24 slides carry 70% of scored annotated pixels, giving an effective sample size of 6.2, and the inherited partition sits at the 7th percentile. An unreported tissue-restriction step excludes 41.4% of out-of-focus annotation against 2.6% of air bubble; such a gate is confounded with blur by construction. Conclusions: Small-cohort benchmarks support far weaker conclusions than current reporting implies. The four checks are cheap enough to accompany any evaluation on such a resource and separate reproducible effects from differences the evaluation cannot resolve.

Natural-language tasks can elicit different verdicts from protocol-following evaluators that receive the same declared information. We study aggregate disambiguation systems (ADSs). Given a task and a candidate solution, each evaluator casts a binary vote on whether the solution should be accepted, and the system aggregates the votes of a finite panel. The target is protocol reproducibility relative to an explicitly declared evaluator reference, not semantic truth. We separate fixed finite censuses, probabilistic evaluator populations, and growing-census limits, since their endpoint laws and guarantees are not interchangeable. In the population setting, we use finite samples to estimate how often a finite panel reaches the same decision as the declared evaluator population. We provide a lower confidence bound on the fraction of candidate solutions for which the disagreement probability is at most a chosen tolerance. The calculation accounts separately for sampling candidate solutions and sampling evaluators. The construction permits arbitrary dependence among columns induced by shared evaluator rows and uses exact binomial intervals at the evaluator layer and an exact one-sided binomial inversion at the generator layer. Simulations check the implementation against known population coverages and expose power limitations.

Reliable uncertainty estimation is a crucial requirement for deploying large language models (LLMs) and vision-language models (VLMs) in safety-critical settings, especially when the model parameters are not accessible (black-box). We propose BiG-SURE, an uncertainty estimator based on cross-temperature semantic agreement. The method samples low-temperature responses as stable semantic anchors and high-temperature responses as probes under meaning-preserving input transformations. It then constructs an anchor-probe Bipartite Graph (BiG) using NLI-based entailment scores and defines confidence through the normalized squared spectral energy of this matrix, with uncertainty given by its complement. This bipartite graph-based Semantic Uncertainty and Reliability Estimation (SURE) score measures whether high-temperature probes remain semantically aligned with the model's stable low-temperature belief or not. We evaluate BiG-SURE on text QA, multilingual QA, and multimodal QA tasks across multiple model families. In these experiments, BiG-SURE improves average abstention AUROC over prior black-box uncertainty estimators, while remaining simple, unsupervised, and applicable to black-box model settings.