Reliable operation of modern distribution networks requires timely identification of operational risks and anomalous events under pervasive uncertainty. In practice, operators must identify risks that are inherent in stochastic yet in-distribution conditions, and anomalies that correspond to out-of-distribution behaviors such as unusual load patterns, extreme weather or cyber-physical attacks. This paper addresses this joint risk and anomaly identification problem for optimal distribution network operation and proposes a deep reinforcement learning framework that is explicitly uncertainty aware. We integrate distributional and Bayesian deep reinforcement learning to realize a second- order uncertainty quantification scheme that decomposes total uncertainty into aleatoric and epistemic components, which are respectively used to characterize inherent risk and out-of- distribution anomalies. The resulting epistemic estimates drive both exploration during training and out-of-distribution detec- tion with fallback control during deployment, whereas aleatoric estimates are used to characterize intrinsic operational risk. Simulation results demonstrate the performance of our DRL agent and the effectiveness of the uncertainty quantification.
Troy Butler, Tianyi Jiang, João Silva +2stat.ML math.OC math.PR math.ST
Data-consistent inversion (DCI) constructs probability measures whose push-forward distributions agree with observed data, while iterative data-consistent inversion (iDCI) extends this framework to generalized stochastic inverse problems by enforcing multiple push-forward constraints sequentially. Although iDCI avoids the direct approximation of high-dimensional joint densities, its relationship to the original joint DCI solution has remained unclear. In this work, we establish this relationship through copula theory. Using Sklar's theorem, we derive a factorization of the DCI update into separate marginal and dependence transformations and show that the discrepancy remaining after convergence of the iDCI algorithm is entirely characterized by the copulas associated with the observed and predicted joint distributions. This characterization motivates a copula-transformed iDCI solution, and we prove that an exact copula transformation recovers the original DCI solution. We further establish convergence results for approximate copula transformations under converging sequences of reference measures and progressively enriched feasible sets. Numerical examples demonstrate how the geometry induced by the quantity-of-interest map governs the importance of the copula transformation, illustrate an adaptive reference-measure refinement strategy for improving computational accuracy under a fixed sampling budget, and demonstrate the progressive refinement of generalized stochastic inverse problems through heterogeneous, asynchronously acquired experiments.
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.
Md. Atabuzzaman, Christian Alexander, Chris Thomascs.CV cs.CL
Large Vision-Language Models (LVLMs) have achieved strong multimodal performance, yet ensuring the factual correctness of generated content remains challenging. Existing methods that provide statistical guarantees on factuality typically rely on external verifiers or generation-time confidence signals, which introduce auxiliary dependencies or often fail for confident but incorrect outputs. We argue that reliable factuality control can instead be achieved through introspective signals derived from the model itself. We introduce IntroConformal, a training-free Conformal Risk Control (CRC) framework that provides finite-sample, distribution-free factuality guarantees. We first instantiate it with layer-wise semantic stability, a conformity score derived from hidden-state representations, and then propose verification probability, a stronger score capturing the model's self-administered judgment on claim factuality. Across multiple LVLM architectures, IntroConformal satisfies the conformal risk guarantee while substantially reducing abstention and achieving competitive or superior claim-level discrimination relative to external verifier-based baselines.
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.
Fairness audits in clinical Artificial Intelligence convert continuous fairness metrics into binary pass-or-fail verdicts against operational thresholds, where hospital governance boards, payers, and regulators act on the resulting verdicts. Such audits are repeated over time and across hospital sites, thus the same verdict can flip between pass and fail across audits. Existing uncertainty methods such as Bayesian posteriors, bootstrap confidence intervals, and permutation tests address verdict instability only at the continuous-metric level. Converting metric-level uncertainty into a verdict-stability claim remains a manual step that scales poorly across the (model, metric, attribute) cells an audit covers. Existing uncertainty methods also leave open whether bias-mitigation steps, such as reweighing or per-group threshold shifts, yield a stable passing verdict at the cost of model discrimination measured as AUROC or AUPRC.To address this verdict-stability gap, we propose VFR-Audit, a framework built around the Verdict Flip Rate (VFR), a scalar bounded between 0 and 0.5 that measures the probability of verdict reversal under stratified bootstrap resampling. VFR-Audit reports VFR alongside three reliability axes, namely within-cohort resampling stability, audit-size sensitivity, and cross-hospital verdict agreement via Fleiss' kappa.
End-to-end weather forecasting systems produce skillful global gridded and station forecasts directly from raw Earth observations, replacing the numerical weather prediction pipeline, including data assimilation, at a fraction of its cost. These systems are deterministic and issue no uncertainty. Here we render the Aardvark Weather model probabilistic by attaching one stochastic mechanism to each component: learned, input-dependent noise at the observation encoder, capturing aleatoric uncertainty inherited from the observing system, and Monte Carlo dropout in the processor, capturing epistemic uncertainty in the learned dynamics. The resulting nested ensemble attributes forecast spread to the two sources through a law-of-total-variance decomposition, cross-checked by withholding observation streams. Probabilistic finetuning significantly improves the mean forecast, by 4.2% on average across variables and lead times. The ensemble is calibrated against ERA5 through the medium range (spread-skill ratio 0.98), keeps station RMSE within 2.4% of the deterministic model while beating it in CRPS at every lead time, and trails the operational ECMWF ensemble. The encoder branch behaves as observation-driven uncertainty. Component-attributed uncertainty makes end-to-end forecasts more transparent, a step toward observation-driven digital twins of the atmosphere.
Kehan Long, Yiqi Zhao, Pol Mestres +3math.OC cs.LG eess.SY
Uncertainty quantification from finite data is central to machine learning, optimization, and automation systems, where decisions must remain reliable under limited samples and test-time distribution shift. Conformal prediction (CP) and distributionally robust optimization (DRO) offer two complementary approaches: CP constructs data-dependent prediction sets with distribution-free finite-sample validity under exchangeability, while DRO optimizes worst-case performance over an ambiguity set around an empirical distribution. We develop a unified probabilistic perspective on CP and DRO by viewing both as ways to turn finite calibration data into a data-dependent quantile estimator that a test score falls below with high probability. From this perspective, CP and DRO correct the empirical quantile along two coordinates of the same family of estimators: CP inflates the quantile level, whereas DRO shifts the quantile value through an ambiguity radius. Both methods provide the same calibration-conditional guarantee for the true distribution, requiring the target coverage to hold with high probability over the calibration sample. Their constructions differ, however: CP uses a closed-form, distribution-free level correction, while DRO uses a value-space correction whose certified radius depends on properties of the unknown distribution and additionally guarantees coverage uniformly over the ambiguity set. This distinction emerges in the tails of the score distribution. Because CP relies on sparse upper-tail order statistics of the calibration samples, its level inflation barely moves the estimator when those samples are dense near the target quantile but overshoots when they are sparse, whereas a well-chosen DRO radius corrects in value space and may avoid this overshoot.
Early failure prediction is important for long-horizon agents, as it enables timely intervention and can reduce inference and tool-use costs. Uncertainty quantification, such as verbal confidence and perplexity, offers a promising approach to detecting agent failures; however, it has not been explored whether these signals retain their discriminative power during the intermediate stages of long-horizon execution. We evaluate mainstream uncertainty signals on deep-research tasks and find that verbal confidence reliably distinguishes failures at trajectory completion, achieving a mean AUROC of 0.85, whereas all evaluated signals offer limited predictive value earlier in execution, with none exceeding a mean AUROC of 0.60 at 50% trajectory progress. We identify an underlying mechanism explaining this gap: path switching, where agents frequently abandon their current search direction in-trajectory, breaking the link between early signal and final outcome. These findings challenge the assumption that intermediate uncertainty can reliably guide early intervention. They also motivate a practical recommendation for agent harnesses in deep-research settings: use final-step confidence to decide whether to restart, an approach that our experiments find more effective than in-trajectory intervention.
Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3% in NLL and 12.0% in ENCE compared with the uncalibrated GP-pro model. The proposed method mitigates posterior variance overestimation while maintaining predictive accuracy and reducing computational complexity. GP-pro-c provides a promising approach for uncertainty estimation in scalable GP models and may serve as a useful surrogate model for Bayesian optimisation with high-dimensional and large-scale data.
Momina Liaqat Ali, Muhammad Abid, Muhammad Abdullah +1cs.LG
Wind power ramp events which are sudden, large swings in turbine output over short windows are difficult to estimate, and standard models often miss them. Hybrid forecasting approach is built which augments semantic context to ramp-event forecast. Rather than applying an extensive language model directly to predict turbine operating data, we have implemented a pipeline where turbine operating data is converted to simplified text, which is then converted to dense embeddings to be used as inputs for ensemble models incorporated with other features. Testing runs are performed at multiple intervals within the SDWPF dataset, including 10-minute, 30-minute, and 60- minute horizons, with ramp events constituting the highest change in future power output. We check robustness against autoregressive, LSTM, and GRU baselines plus several ensemble configurations, using Diebold-Mariano tests and bootstrap confidence intervals, and we vary the ramp threshold, compress the embeddings with PCA, and validate externally on Kaggle SCADA and NREL data with uncertainty-aware scoring. The semantic-context features produce negligible yet statistically significant gains over the baselines in multiple paired ensemble runs, most clearly at the 30- and 60-minute horizons where these gains hold across different ramp-threshold definitions, and PCA compression helps in some longer-horizon cases. The best context- augmented ensembles rank near the top overall, though the GRU model still posts the lowest ramp-event RMSE at 30 and 60 minutes. External tests confirm the error reduction generalizes across datasets, but the size of the gain depends on both model and dataset. Prediction intervals cover most test cases well but weaken during ramp events, pointing to a localized shift in the data distribution.
Neural operators provide fast surrogate models for approximating operators between function spaces, but their predictions often lack uncertainty quantification. We develop a split conformal framework to guarantee that a calibrated pointwise band around the neural operator output contains the true solution on at least a $1-γ$ fraction of the evaluation domain, with probability at least $1-α$ over test and calibration inputs, where $α,γ\in(0,1)$. Our method reduces a normalized residual field to its spatial $(1-γ)$-quantile and computes a scaling factor using a held-out calibration dataset. We prove marginal coverage guarantees for measurable residual fields defined on arbitrary probability spaces, covering both continuum domains and fixed discretizations. Under mild assumptions on the data distribution, we show that the coverage conditional on the calibration set follows a Beta distribution, which we verify with numerical experiments on Darcy flow and Navier--Stokes equations, where our calibration yields bands consistently tighter than existing corrections while retaining the target coverage.
Real-time musculoskeletal (MSK) surrogates could support personalized rehabilitation for children with cerebral palsy (CP), but their credibility depends on subject-wise evaluation, low inference latency, and calibrated uncertainty. We develop a subject-conditioned causal neural surrogate using OpenSim-derived static parameters, temporal joint kinematics, true muscle capacities, and training-only perturbations. On a real pediatric CP gait dataset comprising nine children, we use leave-one-subject-out validation on six development subjects and evaluate a frozen configuration once on three locked test subjects. The surrogate accurately reproduces musculotendon lengths (R-square = 0.92 in development validation and approximately 0.95 on locked subjects; nRMSE < 8%) while requiring only sub-millisecond to few-millisecond neural inference, well below a 100 ms interactive-rehabilitation target. In contrast, direct muscle-force estimation remains unstable at this small, heterogeneous scale: pooled metrics can overstate within-subject, per-muscle accuracy. A Monte Carlo credibility pilot further shows that propagating only +/-5% anthropometry and muscle-capacity variation produces severely overconfident nominal 90% intervals (approximately 4% force coverage and below 1% MT-length coverage). These results establish a leakage-free evaluation and credibility framework for pediatric MSK surrogates, while identifying force modeling and epistemic uncertainty as the central next challenges for clinically credible digital twins.
Multi-organ ultrasound classifiers increasingly combine attention, mixture-of-experts routing, uncertainty gating, and evidential deep learning (EDL) objectives to address heterogeneous anatomy and acquisition. Yet a plausible design rationale does not by itself establish that an added component improves the trained system. We contribute a controlled complexity-audit framework, applied to the deployment decision between the maximal evidential candidate Full-EDL and simpler alternatives. Six candidates were evaluated on the primary dataset and three in an internal replication, using ten matched seeds, frozen image-level partitions, capacity- and optimisation-aware comparisons, symmetric temperature scaling, paired decision rules, and a separate out-of-distribution (OOD) veto. Retaining Full-EDL did not establish a reliable macro-F1 gain on either dataset, while the simplified alternatives remained inconclusive under the non-inferiority margin. Simple cross-entropy with temperature scaling (Simple-CE+TS) met the calibrated negative log-likelihood criterion on both datasets and showed favourable selective-risk ordering. The raw calibration advantage of evidential training disappeared after temperature scaling and did not recur on the second dataset. The gate had negligible observable influence at the audited checkpoints, and deleting the Full-only chain revealed no stable task or calibrated-loss benefit. Simple-CE nevertheless triggered the OOD veto against the fetal probe but not the lung probe, precluding an unconditional OOD-safety claim. We therefore selected Simple-CE+TS for the evaluated in-distribution objective while retaining Full-EDL as the maximal reference. Components should earn retention through functional and retraining-based evidence, and calibration and distribution-shift reliability should be evaluated separately.
Existing conversational plant-phenotyping platforms are difficult for plant scientists to use and lack the reliability scientific research demands: failed analyses are reported as valid measurements rather than flagged as missing, statistical tests run without checking assumptions, predictions carry no uncertainty estimate, and specialised hardware limits accessibility. We present PhenoIntel, a lifecycle-aligned multi-agent web platform that turns the full machine-learning workflow into a reliable, user-friendly phenotyping system. Nine specialised agents divide the analysis into stages, from image collection through model selection, inference, and reporting, rather than handing the whole task to one AI manager. Independent checks separate these stages, and every agent reads from and writes to one shared, fixed-structure record, so an inconsistent output from one stage is caught before it reaches the next. Uncertainty is matched to each model family, conformal prediction, detection-confidence spread, or Monte Carlo Dropout, rather than applied uniformly, and quality thresholds adapt to crop and task instead of one global cutoff. When no suitable model exists, PhenoIntel can propose, validate, and integrate a new one on its own. The model repository spans ten trained models across five crops and four imaging modalities. Classification models reach Macro F1 of 0.78-0.996; object-detection models reach 0.96 mAP@50 with a 54% reduction in counting error over an unoptimised baseline; and a temporal model reaches held-out Macro F1 of 0.7050. PhenoIntel runs in a browser on standard hardware, requiring no GPU, and a 1,200-test automated suite confirms complete pipeline execution. Every result carries calibrated uncertainty, validated statistics, and FAIR-compliant provenance, a combination existing conversational phenotyping tools do not offer.
Kiarash Rezaei, Mehdi Sattari, Javad Aliakbari +3cs.LG stat.ML
Reliable prediction of time-varying channel state information (CSI) is essential for efficient wireless communication. Each CSI frame is a matrix-valued representation of the wireless channel response, and a sequence of CSI frames forms a temporal channel trajectory. Modern deep learning-based CSI predictors, however, often provide only point predictions and lack calibrated uncertainty estimates. This limitation is particularly problematic in multi-step CSI prediction, where the target is a sequence of future CSI matrices, and downstream decisions such as beamforming or scheduling may fail if any part of the predicted trajectory is unreliable. We propose trajectory-adaptive calibration and error profiling with conformal risk control (TRACE-CRC), a method for trajectory-aware uncertainty quantification in multi-step CSI prediction. TRACE-CRC constructs Frobenius-norm uncertainty balls around predicted CSI matrices and controls the risk that at least one future frame is uncovered. Instead of calibrating each future step independently, TRACE-CRC combines future-step-dependent error profiling, trajectory difficulty stratification, and learn-then-test (LTT) risk control. Empirically, TRACE-CRC achieves reliable trajectory-level coverage with substantially smaller uncertainty balls than conservative multi-step corrections, while avoiding the trajectory undercoverage of compact stepwise and adaptive conformal baselines.
Jitao Xu, Christopher Cocuzza, Kevin Braga +3hep-ph cs.AI
Extracting transverse momentum dependent parton distribution functions (TMD PDFs) from semi-inclusive deep inelastic scattering (SIDIS) data is a central goal of the nucleon structure program at Jefferson Lab and the future Electron-Ion Collider. Traditional extraction methods rely on parameterized functional forms and iterative fitting, which can limit the flexibility of the resulting distributions and make uncertainty quantification cumbersome. We present a conditional diffusion model that learns to map raw SIDIS event kinematics directly to TMD PDFs, bypassing explicit functional assumptions. Evaluated on simulated SIDIS data at CLAS12 kinematics, the model recovers the underlying TMD with informative uncertainties that narrow steadily with increasing event statistics, and produces reliable estimates even with as few as 1,000 conditioning events, a statistics-limited regime directly relevant to ongoing and planned experiments.
Toni Karvonen, Chris J. Oatesstat.ML cs.LG math.NA math.ST
Kernels measure similarity or correlation in tasks such as regression and classification. The Gaussian kernel, other names of which include squared exponential and radial basis function kernel, is one of the most popular in Gaussian process regression. We argue that the Gaussian kernel is best avoided and should never be used as a default. The argument rests on two results demonstrating that the Gaussian kernel is extremely brittle. First, the Gaussian kernel gives rise to a conditional variance that is unrealistically small. If the variance is used to quantify predictive uncertainty, catastrophic overconfidence is almost inevitable. Second, a small variance goes hand in hand with numerical ill-conditioning, so that to use the Gaussian kernel in practice requires tricks such as nugget terms that effectively modify the underlying regression or classification model. These problems are caused by the unnatural smoothness of the Gaussian kernel, a fact we are far from the first to take notice of. The problem is not the Gaussian form itself but the analyticity of the kernel: Our argument is more broadly that analytic kernels are best avoided. For stationary kernels analyticity is essentially equivalent to an exponential decay of the spectral density.
Asir Intesar Tushar, Ioannis Sgouraliscs.LG stat.ML
Point-cloud data routinely captured by modern imaging and sensor technologies provide detailed geometric descriptions of objects and environments, but their analysis is hindered by large data volumes, localization noise, and missing information. In addition, existing point-cloud reconstruction pipelines typically return a single best-fit structure without uncertainty quantification. We introduce a fully Bayesian framework for representing point-cloud data and reconstructing closed curves, in which observed points are modeled as noisy perturbations of latent locations constrained to lie on the underlying curve that is regularized by a non-parametric prior. Posterior inference in our framework is carried out using a series of Markov chain Monte Carlo samplers tailored to point-cloud characteristics. Numerical experiments, including synthetic examples and real-world LiDAR datasets, show accurate reconstructions and quantified uncertainty over the recovered curves.
Forecasting a stochastic dynamical system rarely means a single number: one wants several observables---future state, threshold event, regime label---each with its own likelihood. Standard multi-task recipes balance per-task losses, tuned or learned. We instead compose the observables' likelihoods in per-task free-routed last-layer beliefs on a shared backbone; this absorbs unit-dependent loss scaling into likelihood parameters learned in the same gradient pass. Stochastic dynamics supply what static benchmarks cannot: computable ground truth for the predictive variance. Results land where theory puts them: on the well-specified, homoscedastic Ornstein--Uhlenbeck process the learned predictive law recovers the analytic kernel and correctly specified baselines tie. On heteroscedastic systems (stochastic Lorenz-63, real air-quality data) the belief's input-dependent variance separates: best single-run NLL on the state and regime tasks, calibration matched only by arms whose NLL it beats, at a fraction of the tuned grids' cost. On the real series the state margin holds across five rolling origins.
We address the simultaneous prediction of multiple high-dimensional physical fields governed by linear equality constraints, a setting that arises in many real-world applications in physics machine learning. Gaussian process (GP) regression is a widely used surrogate modeling approach due to its effectiveness in small-sample regimes and its ability to provide uncertainty quantification. However, applying GP models in this setting raises two major challenges: the high dimensionality of the discretized output fields and the enforcement of the physical constraint in predictions. For the latter, a common strategy consists in deducing one output from the others via the constraint relation. Through a benchmark, we show that this deductive approach is sensitive to the arbitrary choice of which output to deduce, affecting both predictive accuracy and uncertainty quantification. Consequently, there is a need for an approach that treats all fields symmetrically while strictly respecting the underlying physics. Motivated by these limitations, we propose a robust framework for jointly modeling constrained multi-field data. Our approach first leverages a specific PCA procedure for multi-field data, coined row-wise PCA, which has the interesting property of preserving the constraint in the latent space. Since standard PCA strategies for multi-field data do not preserve such constraints, we investigate theoretically the optimality of the row-wise choice. In a second step, we consider a linearly-constrained multi-output GP approach based on a specific kernel parametrization which is trained on the latent space of row-wise PCA. The proposed framework is validated on a population dynamics problem and on an industrial CFD application, which involves the prediction of Reynolds stress tensor components under the incompressibility constraint.
Qasim Siddiqui, Adrian Friebel, Maiju Myllys +4cs.CV
Liver fibrosis, the principal predictor of long-term outcome in chronic liver disease, is staged from histological estimates of collagen content. Sirius Red (SR) provides the standard quantitative readout (collagen proportionate area, CPA) but is not acquired at every clinical centre and consumes tissue, time, and reagent cost beyond the routine Hematoxylin and eosin (H&E) stain. AI-based virtual staining can generate SR directly from H&E, yet systematic benchmarks of unsupervised models are scarce and their predictive uncertainty has not been quantified, even though visually plausible outputs may not faithfully reproduce the underlying tissue structure. We therefore benchmark six unsupervised image-to-image architectures (GAN-based and diffusion-based) across 54 scaling configurations on a newly released paired H&E to SR mouse liver dataset, the first open resource for this translation task. Each configuration is evaluated jointly on perceptual, distributional, and task-specific axes plus a blinded expert reader study; the best per family is then retrained as a deep ensemble, the first systematic comparison of epistemic uncertainty across unsupervised stain-to-stain architectures. Across families, perceptual quality, task-specific error, and ensemble agreement measure largely independent axes of model fitness: GAN-based methods cluster tightly on perceptual metrics yet differ substantially on task error and ensemble agreement, while the diffusion-based method (CycleDiffusion) is qualitatively different on all three. No single metric captures these differences, so reliable virtual staining requires reporting and selecting on all three jointly. The dataset, tiling pipeline, models, and evaluation code are released publicly.
Leonhard F. Feiner, Manuel Nickel, Martin Menten +6cs.LG cs.CV
Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty -- aleatoric and epistemic -- focusing on their joint integration in high-dimensional regression tasks. For example, in applications like medical image segmentation or restoration, aleatoric uncertainty captures inherent data noise, while epistemic uncertainty quantifies the model's confidence in unfamiliar conditions. Modeling both jointly enables more reliable predictions by reflecting both unavoidable variability and knowledge gaps, whereas modeling only one limits transparency and robustness. We propose a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, capturing essential output correlations while avoiding the computational burdens of full covariance matrices. Unlike prior work, our method explicitly combines aleatoric and epistemic uncertainties into a unified second-order distribution that supports robust downstream analyses like sampling and log-likelihood evaluation. We further introduce stabilization strategies for efficient training and inference, achieving superior UQ in the tasks of image inpainting, colorization, optical flow, and depth estimation.
Uncertainty quantification (UQ) methods are widely used for hallucination detection in large language models (LLMs) in closed-book settings where ground-truth evidence is unavailable at inference time. Prior work has proposed combining UQ signals via learned ensembles, but empirical investigations into the robustness of these ensembles are limited. We study a supervised ensembling framework that trains a classifier over heterogeneous UQ-based scorer outputs on a small, domain-specific dataset of labeled LLM responses, then applies it to out-of-sample hallucination classification without retrieval, tools, or reference documents. Across four LLMs, nine datasets, and three generation regimes (short-form QA, long-form generation, and code generation), we provide a systematic robustness analysis along three axes: sample efficiency, in-domain dataset transfer, and generation regime dependence. We find that supervised ensembles outperform the best individual scorer in 30 of 32 settings, with gains realized from as few as 100 labeled instances. Ensembles retain most of their advantage in cases of in-domain transfer under distribution shift, outperforming the best non-ensemble scorer in 23 of 28 transfer settings. Sampling-based black-box ensembles are nearly as effective as full ensembles, while single-generation white-box ensembles offer limited benefit.
Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. While E(3)-equivariant neural networks excel at point estimates, they lack rigorous confidence measures. We focus on symmetric rank-2 tensor prediction, where the target has six Kelvin--Mandel coordinates and full uncertainty is represented by a $6\times6$ covariance matrix. We introduce a framework for E(3)-equivariant UQ, modeling the full predictive distribution where both mean and covariance preserve rotational symmetry. Our approach decomposes the covariance into irreducible representations $\mathrm{Sym}^2(ρ_c) \cong 2\times(l=0) \oplus 2\times(l=2) \oplus 1\times(l=4)$. By mapping from the flat Lie algebra $\mathfrak{sym}(6)$ to the curved SPD manifold via matrix exponentiation, we strictly ensure positive-definite covariances while maintaining exact equivariance. Furthermore, we formulate a Log-Euclidean Equivariant Scoring Objective (LE-ESO)---a robust surrogate loss based on the Multivariate Laplace distribution---providing robustness to heavy-tailed errors and stable optimization. Validation on ModelNet40 inertia tensors and Materials Project dielectric tensors demonstrates that our method achieves competitive performance and provides physically consistent, symmetry-preserving uncertainty estimates with useful risk and OOD sensitivity.
Wyatt A. Smith, Arkaitz Rodas, Marius D. Thomas +5hep-ph cs.LG nucl-th
Reconstructing scattering amplitudes from finite, noisy, and mutually inconsistent measurements is an ill-posed inverse problem common to many reactions relevant to particle physics. We introduce S-matrix informed neural networks (SINNs), and demonstrate their ability to learn scattering amplitudes directly from data while respecting first principles. We further develop a novel data selection procedure, which uses the response of constrained neural network ensembles to identify a set of experiments compatible with first principles, and with each other. We apply this framework to $ππ$ scattering, producing reusable amplitudes and correlated uncertainties without relying on a fixed functional form. We validate our results against residual model dependencies and training biases through closure tests and ablations. We find negligible impact of model architecture on our results. Our workflow unifies physics-constrained representation learning, data selection, and uncertainty quantification. Our strategy is transferable to other scattering processes, and other constrained physics problems limited by inconsistent data.
Markus B. Pettersson, James Bailie, Mohammad Kakooei +2cs.LG
Despite their critical importance for policy and research, high-resolution poverty data remain limited across much of Africa. Machine learning (ML) with earth observation (EO) imagery has recently emerged as a way to supplement these data by predicting (i.e., estimating) poverty where it has not been directly measured. Yet to be used reliably, decision-makers and analysts need assurances that they will not be misled by the errors in these predictions. To meet this need, we develop an uncertainty-aware EO-ML method for poverty mapping based on simultaneous quantile regression and a novel form of conformal prediction. Using a spatiotemporal transformer trained on sequences of Landsat and nighttime-light images, we produce prediction intervals for neighborhood-level International Wealth Index estimates across Africa which are statistically guaranteed to achieve their desired coverage rates. While our method's point-prediction performance matches the state of the art, its prediction intervals are wider than might be expected given its high $R^2$ of $0.75$. However, other models of similar accuracy likely suffer from comparable uncertainty, pointing to an inherent limitation: even with its remarkably high explanatory power, EO-ML cannot naively be relied upon for policy-making, such as when designing poverty-targeting programs. To handle this challenge, we develop a procedure to efficiently allocate aid using both ground-truth surveys and model predictions while provably ensuring the risk of excluding eligible neighborhoods remains below a prespecified level. In simulations, this approach delivers substantially more aid per eligible recipient than other strategies, thereby demonstrating that EO-ML can indeed be a reliable supplement to traditional data sources---as long as methods
Large language models (LLMs) often produce fluent but incorrect answers with unwarranted confidence. A central limitation is that standard LLMs represent uncertainty through a single predictive distribution, conflating epistemic ignorance with genuine ambiguity. We introduce Credal Large Language Models (CLLMs): an ensemble of LoRA adapters induces a credal set whose lower and upper probabilities expose the spread of plausible predictive distributions rather than collapsing to a single softmax output. From this representation we derive two complementary commitment scores. Credal Token Commitment (CTC) is a token-space score that combines lower-bound support, credal width, and intersection entropy, computed without additional generation. Semantic Commitment Consistency (SCC) extends commitment to semantic space using sampled completions, with SCC-Gap measuring the mismatch between token-level and semantic-level support. We evaluate hallucination detection, calibration, selective prediction, and reasoning on Gemma-2-9B, Llama-3.1-8B, and Qwen2.5-7B across OpenBookQA, CoQA, TriviaQA, and ARC-Challenge. CLLM is the best method on QA accuracy at competitive expected calibration error, and CTC tracks the best hallucination AUROC within 1.5 pp on most settings without additional generation. On selective prediction at 80% coverage, CLLM with SCC reaches 99.0% accuracy on OpenBookQA, and on ARC-Challenge CLLM with Csem confidence achieves <= 0.6% ECE across the three backbones.
Manos Giannopoulos, Yi Shen, Michael M. Zavlanoscs.LG
In high-stakes healthcare applications, machine learning models are frequently trained on data from one patient population and deployed on another, creating a distribution shift that degrades both accuracy and reliability. Semi-Supervised Domain Adaptation (SSDA) addresses this by leveraging labeled data from some source domain to improve model performance on a target domain where labels are scarce. However, existing SSDA methods optimize primarily for point-prediction accuracy and offer no principled uncertainty quantification --- a prerequisite for clinical trust. Conformal Prediction (CP) can address this limitation by providing prediction sets with rigorous, distribution-free coverage guarantees. However, applying CP post-hoc to a pre-trained model can yield prohibitively large prediction sets, as SSDA pre-training methods do not account for the nonconformity score geometry that determines conformal set size. Conformal Risk Minimization (CRM) has been used to resolve this issue in the fully supervised setting by integrating the CP objective directly into model training, but it requires a large labeled dataset to compute nonconformity thresholds during training, precisely the data that is scarce in the SSDA regime. We propose an end-to-end framework that integrates CRM into the SSDA training objective, enabling effective CRM in the limited-labeled-target-data regime. The key idea is to utilize Optimal Transport (OT) to generate pseudolabels for unlabeled target instances, providing the additional training signal needed by CRM to operate using only a small labeled target set. This results in a model jointly optimized for domain invariance and conformal efficiency, producing prediction sets that are compact, coverage-valid, and support domain-specific constraints such as excluding mutually contradictory diagnoses in skin lesion classification.
Rounak Sharma, Ananya B. Sai, Soumyabrata Palcs.AI
Black-box large language models need confidence scores that can separate likely-correct from likely-incorrect outputs, enabling systems to prioritize human review, route uncertain cases to stronger models, or choose abstention thresholds on development data. Yet existing confidence estimators face a cost-quality trade-off: verbal confidence is cheap but is often overconfident, while sampling-based uncertainty is more informative but scales linearly with the number of samples per query. We propose \textsc{POOL} (\emph{Propagated Uncertainty Over Lookalikes}),a cost-efficient framework that addresses this trade-off taking inspiration from group-testing.\textsc{POOL} clusters query stems with overlaps, evaluates a base estimator on representative medoids, softly propagates confidence scores to nearby queries, and selectively evaluates high-disagreement cases. We instantiate this framework with \textsc{Hy@}$p$, a hybrid estimator that combines verbal confidence with spectral answer diversity computed from the negative von Neumann entropy of sampled answer embeddings.Across six domains from three datasets and five black-box LLMs, \textsc{Hy@}5 achieves higher average AUROC than verbal confidence and \textsc{Vn@}10 sampling while using half as many samples as \textsc{Vn@}10. \textsc{POOL}-\textsc{Hy@}5 retains 93.5--97.9\% of its AUROC while saving 19.3--39.3\% of generations. On paraphrase-dense workloads, generation savings rise to 73-76\%, showing that semantic redundancy can be leveraged to lower confidence-estimation costs.