Uncertainty Calibration

Follow this topic Ask about this topic

Momentum

15 papers in the last four weeks, up 7% on the four weeks before. 0.1% of all new papers.

Jul 13Week of Sep 28

Latest papers 184

Jul 9, 2026eess.IV

Calibrated Hybrid CNN-Transformer for Retinal OCT Classification

Deep models for retinal optical coherence tomography (OCT) classification report high accuracy but rarely report whether their confidence can be trusted -- a gap that matters when a wrong-but-confident reading delays sight-saving treatment. We pair a hybrid convolutional-Transformer encoder with a gradient-boosting (XGBoost) classification head and a three-part clinical safety layer: confidence calibration, out-of-distribution (OOD) rejection, and per-prediction uncertainty flagging. On four-class OCT (84,495 scans) the model reaches 95.4% accuracy while cutting calibration error twelve-fold (expected calibration error, ECE = 0.0024), so the confidence it reports tracks its true accuracy. To our knowledge this is the first OCT classifier to validate all three safety mechanisms jointly, with public weights and reproducible multi-seed evaluation.

Animesh Kumar

School of Computing, Newcastle University, UK

Uncertainty Quantification Optical Coherence Tomography Uncertainty Calibration

Jul 7, 2026cs.LG

Heckman-Corrected Epistemic Uncertainty: Selection on Unobservables Defeats Importance Weighting

Training data for machine learning is routinely collected by a selection process the model never sees: loans are observed only when granted, outcomes only when a test was ordered. The standard fixes -- importance weighting, covariate-shift correction, MAR imputation -- assume selection is ignorable given observables. Econometrics solved the harder case in 1979: Heckman's two-equation model jointly fits a probit selection equation and an outcome equation linked through correlated errors, and the inverse-Mills-ratio term corrects for selection on unobservables, where importance weighting is structurally helpless. We instantiate this for deep epistemic uncertainty: a deep outcome network, a linear selection head, and a joint bivariate-normal likelihood over all units, ensembled for predictive variance. In a controlled generator where sampling probability depends on an unobservable correlated (rho up to 0.9) with the outcome noise, deep ensembles, MC dropout, and GP baselines are overconfident exactly where data was avoided: coverage of nominal-90% intervals falls to 64.4% at rho=0.9, and importance weighting with oracle propensities does not fix it (43.1%) -- reweighting corrects the covariate distribution, not the conditional bias E[y|x,selected] != E[y|x]. The Heckman correction restores coverage (88.9%) when the selection equation has an instrument -- a variable affecting selection but not the outcome -- and degrades measurably without one (40.3%); we chart this honesty curve rather than hide it. On real tabular data with induced MNAR selection, the corrected intervals are the best-calibrated (lowest region-ECE) non-oracle method in selected-against regions; baselines matching its raw coverage do so only by over-widening everywhere. Our estimators reproduce classic Stata output to seven digits. We state which identification regime a practitioner is in, and release the code.

Gunner Levi Howe

Independent Researcher

Selection Bias Uncertainty Calibration Regression Prediction Intervals Epistemic Uncertainty

Jul 6, 2026astro-ph.IM

Interpretable Human-Label-Free Deep Learning for Real-Bogus Classification with Uncertainty Quantification

Time-domain surveys generate many transient candidates, making Real-Bogus classification a critical step in automated discovery pipelines. Reliable labels are costly, while community labels can be noisy and survey-dependent. We aim to develop a Real-Bogus classification framework that can be trained without human-labeled data using injected transients and bogus-dominated survey data, remains robust under strong class contamination, and provides calibrated uncertainty quantification. We combine simulated transient injections with a contaminated survey class and train a dual-network model using asymmetric co-teaching for classes with different label-noise levels. We evaluate performance on a benchmark subset and analyze the learned representation with latent-space visualization tools. For uncertainty quantification (UQ), we compare MC dropout and deep ensembles and propose a low-cost hybrid strategy that exploits the dual-network setting to improve calibration. We extend the evaluation to the light-curve domain to assess recovery of light-curve classes. The method achieves strong Real-Bogus performance on the labeled subset and remains stable under severe class contamination. It recovers transient light-curve classes with high fidelity, while single-source identification is limited by ambiguity in light-curve-derived labels. Our hybrid UQ approach achieves competitive calibration relative to more expensive ensemble baselines. Latent-space analyses indicate that uncertainty aligns with the decision boundary and reveal subclasses within the bogus population. Our results show that injection-driven, weakly supervised training can enable scalable and consistent Real-Bogus classification without human-labeled training data while providing calibrated uncertainties. The method is suited for transfer to forthcoming surveys by re-running the injection-based training pipeline.

Raphaël Bonnet-Guerrini, Bruno Sanchez, Dominique Fouchez +5

Università degli Studi di Milano, Department of Computer Science, Milan 20133, Italy · Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France · Université Côte d’Azur, INRIA, CNRS, Laboratoire J.A.Dieudonné, Maasai team, Nice 06000, France +2

Weakly Supervised Learning Learning with Noisy Labels Uncertainty Calibration

Jul 6, 2026cs.SD

Towards Robust Uncertainty-Aware Speaker Modeling

Speaker embeddings aggregate frame-level acoustic features into compact representations for speaker recognition. Recent uncertainty-aware speaker modeling approaches further characterize the reliability of speaker embeddings by estimating their associated uncertainty. However, existing methods often suffer from inaccurate uncertainty estimation and uncertainty miscalibration under domain shifts. To address these challenges, we propose a robust uncertainty modeling framework from both estimation and adaptation perspectives. Specifically, we introduce an Inter- and Intra-Speaker-Aware Uncertainty Softmax that incorporates both inter-speaker separability and intra-speaker variability into uncertainty learning, enabling uncertainty estimates to better capture the reliability of speaker embeddings. Furthermore, we propose an Uncertainty-Calibrated Domain Adaptation (UCDA) framework to mitigate uncertainty miscalibration caused by domain mismatch. Extensive experiments on both in-domain and cross-domain benchmarks demonstrate that the proposed approach consistently improves uncertainty reliability and speaker recognition robustness.

Junjie Li, Yang Xiao, Kong Aik Lee

Department of Electrical and Electronic Engineering, The Hong Kong Polytechnic University, Hong Kong SAR · The University of Melbourne, Australia

Speaker Verification Uncertainty Quantification Domain Adaptation Uncertainty Calibration

Jul 5, 2026cs.CL

Uncertainty-Aware Abstention in Large Language Models with Provable Alignment Guarantees

Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level

α

, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least

1-δ

that the selected threshold, if non-null, controls the error rate among accepted answers at level

α

. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.

Sijin Dong, Hiroyuki Shinnou

1Ibaraki University, Japan.

Selective Prediction Confidence Estimation in Language Models Question Answering LLM Reliability LLM Uncertainty Estimation Uncertainty Calibration

Jul 4, 2026cs.AI

Evaluating LLM Uncertainty in Long-Form Generation Using Deterministic Ground Truth

As LLMs generate increasingly long outputs, effective uncertainty estimation must identify errors at fine-grained levels rather than discard entire responses. While such methods exist, evaluating uncertainty at any resolution (token to an entire generation) is challenging and highly sensitive to label imperfections, making zero-noise benchmarks essential; yet, long-form generation benchmarks tend to rely on fallible labels rather than deterministic ground truth. We introduce Single-answer Atomic Long-form Target (SALT), a benchmark of six procedurally generated tasks with single deterministic long textual ground truths, enabling unit-level evaluation of correctness, calibration, and ranking without external judges. Equipped with SALT, our analysis of 50+ LLMs reveals key insights: We identify which confidence functions dominate each uncertainty aspect and show that confidence ranking largely breaks at atomic resolution, even when clearer separability emerges at coarser line-level units. SALT further enables controlled atom-level interventions throughout generation, revealing two separable drivers of future errors: propagation from corrupted prefixes, dominated by global context correctness, and bounded degradation from increasing answer-context length. Finally, we demonstrate that reasoning, via Chain-of-Thought prompting or internalized through training, introduces a trade-off, improving accuracy while degrading confidence ranking. These findings directly impact risk-critical applications requiring reliable error identification and mitigation.

Ido Amit, Ido Galil, Ran El-Yaniv

1Technion · 2Nvidia

LLM Evaluation LLM Uncertainty Estimation Uncertainty Calibration

Jul 1, 2026cs.AI

Bayesian Uncertainty Propagation for Agentic RAG Pipelines: A Proof-of-Concept Study on Multi-Hop Question Answering

Trustworthy deployment of Agentic Retrieval-Augmented Generation (RAG) systems requires mechanisms for estimating when multi-stage reasoning pipelines may fail. This paper presents an uncertainty-aware Agentic Retrieval-Augmented Generation (RAG) framework in which planner, evaluator and generator stages produce uncertainty signals derived from semantic divergence and generator self-evaluation. These signals are propagated through a Bayesian Network (BN) to estimate system-level uncertainty and provide node-level indicators of potential failure points across the workflow. The approach is evaluated on StrategyQA and HotpotQA using GPT-3.5-Turbo and GPT-4.1-Nano, with Area Under the Receiver Operating Characteristic Curve (AUROC), Area Under the Accuracy-Rejection Curve (AUARC), Expected Calibration Error (ECE), and Brier Score used to assess discrimination, selective prediction and calibration. Results show that Bayesian propagation is more effective on HotpotQA, where uncertainty accumulates across multi-hop reasoning stages, while StrategyQA exposes limitations caused by miscalibration and unreliable upstream signals. The study positions Bayesian uncertainty propagation as a promising but preliminary mechanism for monitoring Agentic RAG systems, with future validation required in industrial domains such as Offshore Wind (OSW) maintenance decision support.

Louis Donaldson, Connor Walker, Koorosh Aslansefat +1

University of Hull, Hull HU6 7RX, UK

Uncertainty Quantification Agentic RAG LLM Uncertainty Estimation Uncertainty Propagation Uncertainty Calibration

Jun 30, 2026cs.LG

TRIE: An Evaluation Framework for Stochastic PDE Surrogates

Many scientific systems exhibit uncertainty from stochastic forcing, unresolved degrees of freedom, or imperfect observations, making reliable surrogate forecasting fundamentally distributional rather than pointwise. For such systems, deterministic neural surrogates fail to capture statistical measures and forecast uncertainty. We introduce TRIE, an evaluation framework for stochastic PDE surrogates that asks whether models reproduce invariant measures, provide trustworthy predictive uncertainty, and scale to efficient probabilistic generation. We demonstrate TRIE on two stationary chaotic spatially extended SPDEs, stochastic Kuramoto--Sivashinsky and stochastic Kolmogorov flow, across 11 parameter values. Our evaluation shows that standard pointwise-trained neural surrogates can produce plausible short rollouts while failing to match long-time statistical structure. Approximate uncertainty methods such as Monte Carlo dropout and heteroscedastic Gaussian likelihoods produce stochastic forecasts, but are often miscalibrated and overconfident under temporal and spatial uncertainty diagnostics. Across these criteria, generative models provide the most consistent performance, accurately capturing invariant measure statistics and achieving the lowest CRPS in all reported probabilistic settings. Finally, we show that latent generative models with automatic dimension discovery retain much of this statistical fidelity while reducing Kolmogorov inference time by roughly

12\times

. We release our code and data at https://github.com/scailab/TRIE-SPDE-Bench to support reproducible evaluation of stochastic PDE forecasting models.

Bharat Srikishan, Javier E. Santos, Nikhil Muralidhar +1

Stevens Institute of Technology · Los Alamos National Laboratory

PDE Surrogate Modeling Probabilistic Forecasting Generative Modeling Uncertainty Calibration

Jun 30, 2026cs.AI

Ask the World Before Acting: Environment Probing for Calibrated Agent World Models

Language agents acting over long horizons must maintain beliefs about tool states, object locations, graph edges, and subgoal dependencies. When these beliefs drift, failures can be fixed neither by longer reasoning traces nor by ordinary self-reflection, since the missing evidence lies in the environment. We formulate environment probing as a budgeted decision problem for structured agent world models: before acting, the agent may query the current value of one belief field, update its table, and pay one interaction step. We introduce EnvProbe, a simple scoring policy that combines task criticality, staleness, verbalized uncertainty, and dependency role. A type-stratified analysis separates the benefit of belief repair from the cost of displaced task actions and predicts different behavior for procedural and spatial beliefs. In three controlled environments with gold belief states, EnvProbe improves terminal world-state accuracy over periodic probing by 11.76 percentage points on procedural tool-dependency tasks, 3.79 points on spatial tasks, and 6.45 points overall. Ablations show that task-structural terms are the main source of the gains, while self-reported uncertainty is unreliable under confident wrong beliefs. The results suggest that agent calibration should be treated as an action-selection problem over environment evidence, not only as a model-internal reasoning problem.

Xinyuan Song, Zekun Cai

Emory University, Atlanta, GA, USA · The University of Tokyo, Tokyo, Japan · LocationMind, Tokyo, Japan

Belief-Space Planning World Model Learning Long-Horizon Agent Tasks Uncertainty Calibration

Jun 29, 2026cs.LG

Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias

Probabilistic downscaling models the conditional distribution of high-resolution fields given coarse inputs and is a core challenge in atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic mean predictor followed by a stochastic residual generator. While effective in idealized settings, this mean-residual approach frequently produces biased and underdispersive ensembles in real-world applications. We identify a fundamental source of this failure: residual target misspecification, where the residual distribution induced during training systematically differs from the correction distribution required at test time, a mismatch amplified by downscaling bias. We theoretically connect this misspecification to underdispersion through the spread-skill ratio and show that conditional residual distribution matching controls both residual-energy and conditional-mean mismatch. Motivated by this analysis, we introduce ReMatch (Residual Distribution Matching), which aligns training residual targets toward a held-out calibration regime via optimal transport. On a controlled synthetic benchmark with varying bias levels and a real-world HRRR-ERA5 wind-field downscaling task, ReMatch substantially reduces underdispersion, improves calibration, and outperforms strong mean-residual and super-resolution baselines. Our code is available at https://github.com/sdean-group/ReMatch.git.

Yujin Kim, Nidhi Soma, Sarah Dean

Department of Computer Science Cornell University Ithaca, NY, 14853

Probabilistic Forecasting Uncertainty Calibration

Jun 29, 2026cs.CV

Beyond Point Estimates for Glaucoma Visual Field Forecasting with Diffusion Models

Forecasting visual fields (VFs) is critical for personalized monitoring and treatment planning in glaucoma. This is inherently uncertain due to heterogeneous disease progression and measurement variability, yet most existing methods produce single deterministic predictions that fail to represent this uncertainty. We formulate VF forecasting as a probabilistic prediction problem and the use of conditioned denoising diffusion models to generate distributions of plausible future VFs from longitudinal observations with irregular follow-up intervals. Experiments on two independent VF cohorts show that diffusion-based predictions produce well-calibrated distributions for clinically relevant VF measures. When reduced to a standard point-estimate, the proposed approach achieves state-of-the-art accuracy compared to clinical baselines and prior learning-based methods. Our results highlight the advantages of distributional modeling for VF forecasting and support a shift from point-estimate prediction toward uncertainty-aware, clinically interpretable risk assessment in glaucoma.

Marta Colmenar Herrera, Pablo Márquez Neila, Şerife Seda Kucur Ergünay +2

ARTORG Center for Biomedical Engineering Research, UniBe, Switzerland · PeriVision SA, Epalinges, Switzerland · Department of Ophthalmology, Inselspital, Bern, Switzerland

Spatiotemporal Forecasting Uncertainty Calibration Probabilistic Time Series Forecasting Diffusion Models

Jun 29, 2026cs.CV

Uncertainty Estimation in Pathology Foundation Models via Deep Mutual Learning

Pathology foundation models (PFMs) offer generalizable representations for whole-slide image (WSI) analysis, yet their clinical adoption remains limited. Specifically, their predictions lack reliable confidence estimates, and no single PFM is universally best across tasks, which severely undermines trust in medical settings. To overcome this, we propose

\mathtt{DICE}

, a plug-and-play framework that ensembles

K

frozen PFMs and models their disagreement as a proxy for uncertainty estimation. To ensure this proxy yields meaningful estimates, we align the ensemble members via deep mutual learning, and theoretically show that this objective upper-bounds the model uncertainty. Additionally, we demonstrate that the ensemble's consensus localizes abnormalities at the patch level without any explicit supervision. We evaluate

\mathtt{DICE}

on three challenging WSI benchmarks. Notably, our framework provides reliable uncertainty estimates that accurately flag failure-prone cases under in- and out-of-distribution settings, while matching or outperforming SOTA baselines in classification, calibration, and localization. Overall,

\mathtt{DICE}

takes a crucial step toward translating PFMs into uncertainty-aware decision-support systems.

Gbègninougbo Aurel Davy Tchokponhoue, Sevda Öğüt, Ali Idri +2

EPFL, Lausanne, Switzerland · UM5, Rabat, Morocco

Pathology Foundation Models Deep Ensembles Uncertainty Calibration Whole-Slide Image Analysis

Jun 29, 2026cs.LG

Bandwidth Selection in Kernel Density Estimation for Model Calibration

As deep learning models are increasingly deployed in high-stakes applications, providing well-calibrated uncertainty estimates has become as critical as achieving high predictive accuracy. While Kernel Density Estimation (KDE) has emerged as a smooth and continuous alternative to traditional binning for quantifying miscalibration, its reliability is heavily dependent on the choice of the kernel bandwidth. Standard selection techniques, such as Maximum Likelihood Estimation (MLE), often fail to produce optimal bandwidths for calibration tasks. In this work, we introduce Risk Alignment (RA), a novel optimization framework that determines the optimal bandwidth by aligning KDE-reconstructed risk with empirical risk. We theoretically demonstrate that this alignment minimizes calibration estimation bias across the data distribution, establishing a principled bandwidth selection criterion applicable to various metrics, including the challenging case of canonical calibration error. Extensive experiments across multiple architectures and datasets show that RA consistently outperforms standard bandwidth selection methods, yielding more reliable calibration assessments.

Han Zhou, Teodora Popordanoska, Matthew Blaschko

Department ESAT, Center for Processing Speech and Images, KU Leuven, Leuven, Belgium

Model Calibration Kernel Density Estimation Uncertainty Calibration

Jun 28, 2026cs.CR

The Calibrated Deepfake Trust Score (CDTS): Competence-Coupled Trust Degradation Across Deepfake Detectors

Modern deepfake detectors are rarely consumed as bare classifiers. In moderation, provenance, and verification pipelines their output probability is read as a degree of trust, so its calibration matters as much as raw accuracy. We reframe deepfake detection as a calibrated, self-auditing trust instrument, the Calibrated Deepfake Trust Score (CDTS), and identify what governs its trustworthiness. Our central finding is a competence-calibration coupling: the calibration of the trust score degrades as the detector's discriminative competence falls. We establish it across 32 configurations (pooled Pearson r = -0.81), demonstrate it within a single dataset, reinforce it by inducing low competence directly, and replicate it on a fourth held-out dataset the detectors never trained on. It holds across three architecturally distinct detectors, two convolutional networks and a CLIP vision transformer (r = -0.88, -0.83, -0.86). The result is also deployable: a single calibrator frozen on in-domain data fails on exactly the low-competence generators the coupling flags (its error tracks competence at r = -0.98), and competence is estimable without labels, so a label-free monitor flags calibration risk on unseen generators and routing source-batches on a reference-free competence estimate lowers overall AURC and improves the low-to-mid coverage operating region relative to confidence-based routing. The same competence factor also drives calibration inequity across demographic subgroups (distinct from accuracy inequity) and explanation faithfulness. We therefore argue that detector trustworthiness is organized by competence as a shared driver, that competence is the right quantity to estimate and condition on, and that trust scoring must be competence-aware. We offer the CDTS wrapper as the mechanism, and report openly where the unification is tight and where it is architecture-specific.

Md Anas Biswas

School of Computing, University of Portsmouth, Portsmouth, United Kingdom

Deepfake Detection Model Calibration Uncertainty Calibration

Jun 25, 2026stat.ML

Ribbon: Scalable Approximation and Robust Uncertainty Quantification

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for modern machine-learning models because they require posterior sampling or repeated model refitting. We introduce Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty. Ribbon replaces repeated refitting with an influence-function linearization around a single fitted model, preserving the first-order data-reweighting structure of the Bayesian bootstrap while requiring only post-hoc linear algebra. Ribbon approximates the Bayesian-bootstrap or weighted-likelihood-bootstrap refitting target. With a general concentration parameter, Ribbon gives a calibrated Dirichlet-reweighting family whose uncertainty scale can be tuned on validation data. We show that Ribbon is asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification and recovers the robust sandwich covariance under misspecification. Across synthetic regression, MNIST classification, and California Housing benchmarks, Ribbon provides competitive predictive performance and improved calibration in several settings while avoiding repeated model retraining.

Graham Gibson, John Tipton, Kellin Rumsey +1

Uncertainty Quantification Uncertainty Calibration

Jun 25, 2026cs.LG

Just how sure are you? Improving Verbalized Uncertainty Calibration in Medical VQA

Multimodal large language models (MLLMs) applied to Medical Visual Question Answering (VQA) tend to produce overconfident outputs regardless of actual correctness, and existing verbalized confidence calibration methods, developed primarily for text only LLMs, do not account for the multimodal nature of medical image understanding. This work proposes a training based framework that finetunes MLLMs to improve their calibration using a composite loss function combining a Brier style calibration term, an anchor regularizer that prevents confidence collapse toward extreme values, a contrastive image text alignment term, and a KL based model stabilization term. The alignment signal is derived from a

2 \times 2

factorial perturbation design that crosses image presence with text integrity, probing the reliance of the model on visual modality input versus language priors. Finally, a top K KL divergence regularizer is used to protect the answering ability of the model during finetuning. Across three Medical VQA benchmarks and two architectures (MedGemma 4B IT and Qwen2 VL 7B Instruct), our method reduces calibration error by 60% or more, and improves discrimination by 26% or more, while preserving predictive accuracy. On average across benchmarks, the technique outperforms prompting based, sampling based, and training based approaches, and ablation experiments confirm that each component of the loss function is indeed necessary for improving the calibration. All code for the experiments is publicly available.

Eren Senoglu, Federico Toschi, Nicolo Brunello +2

Politecnico di Milano

Medical VQA Language Model Calibration Medical VLMs VLM Calibration Uncertainty Calibration

Jun 24, 2026cs.LG

Uncertainty Quantification for Computer-Use Agents: A Benchmark across Vision-Language Models and GUI Grounding Datasets

Computer-use agents turn vision-language model (VLM) predictions into executable GUI clicks, so reliable uncertainty estimates are essential for rejection, calibration, miss-severity ranking, and spatial safety regions. Yet evidence on post-hoc uncertainty quantification (UQ) for these agents is fragmented across isolated model and dataset pairs, leaving it unclear whether UQ rankings stay stable when the agent, benchmark, or observable interface changes. We present Argus, a cross-regime benchmark for post-hoc UQ in single-step executable GUI grounding: a 27-method open-weight matrix over 4 VLM agents and 4 datasets, plus an 8-method closed-source matrix across 3 frontier vendors where logits, hidden states, and attention maps are unavailable. Evaluated methods span logit-based scores, sampling and consistency measures, hidden-state and density estimators (Mahalanobis, SAPLMA), attention-based scores, P(True) and verbalised-confidence prompting, and split-conformal prediction. The main finding is selective transfer: UQ rankings are stable across datasets for a fixed model, but degrade across model classes and observable interfaces. Hidden-state and density methods are the most stable open-weight family, while CoCoA-1MCA, Focus, sampling-based scores, and verbalised self-assessment win in specific regimes. Within-model ranking transfer is strong (Spearman rho up to 0.969), but cross-tier transfer to closed-source vendors averages only +0.08, so closed-source UQ should be reranked on the target rather than extrapolated. Conformal click regions show score-level discrimination is not enough for deployment: locally weighted disks shrink radii by 40-60% when the plug-in UQ is calibrated, but coverage degrades under calibration-test or interface mismatch. We release per-item records, calibration/test splits, UQ scores, and analysis scripts for regime-aware UQ selection in GUI agents.

Divake Kumar, Sina Tayebati, Devashri Naik +5

University of Illinois Chicago · Intel Labs · Capital One AI Labs

Computer-Use Agent Benchmarks Uncertainty Quantification Computer-Use Agents GUI Grounding Conformal Prediction AI Agent Benchmarks+1

Jun 23, 2026cs.LG

Enhancing Clinician Decision-Making via Uncertainty-Aware Multi-Expert Fusion for Stroke Rehabilitation

Tailoring stroke rehabilitation requires assessing how movements are organized, not merely if they succeed. Currently, this assessment is a rate-limiting bottleneck. Instruments like the Action Research Arm Test (ARAT) compress rich behavioral observations into single ordinal endpoints, discarding the movement-quality details that distinguish recovery from compensation. Automated alternatives typically chase accuracy on noisy, single-observer labels to output opaque scores - a technology-centric approach that rarely reaches clinical practice. To address this, we present xAARA: an engine designed to augment rather than replace clinical judgment. From multi-view video, xAARA returns ARAT assessments with calibrated uncertainty and explanations across task, movement-phase, and movement-quality levels. Treating clinical scoring as an ill-posed inference problem, xAARA composes 692 calibrated multimodal models via a Dynamic Bayesian Network with entropy-based gating. It qualifies results against clinical validity rules and defers low-confidence cases. In 105 stroke survivors (788 exercises), xAARA achieved 94.2% task accuracy (Cohen's kappa=0.934) and 81.3% movement-phase accuracy (kappa=0.727), reducing predictive uncertainty by 96.1% compared to single-clinician scoring. For subjective cases, it matched at least one rater 100% of the time and never returned out-of-range scores. Four independent clinicians validated the assessments and indicated willingness to adopt the system. We argue that principled uncertainty quantification and clinician-aligned explainability are the critical bridges moving automated assessment from technical demonstration to a deployable clinical tool.

Tamim Ahmed, Thanassis Rikakis

Bioemdical Engineering, University of Soutehrn California,, Los Angeles, 90007, CA, USA.

Clinical Decision-Making Multimodal Model Interpretability Multimodal Fusion Uncertainty Calibration

Jun 20, 2026cs.LG

Neural Conjugate Aggregation: Identifiable Unsupervised Multi-Sensor Regression under Heterogeneous Sensor Bias

We study regression-based data fusion under uncertainty, where multiple noisy and biased measurement sources are available but ground-truth labels are absent during training. This setting arises in sensor networks, simulation ensembles, and scientific monitoring systems where supervision is costly or infeasible. We propose the Neural Conjugate Aggregation Model (NCAM), a hierarchical Bayesian framework that combines neural networks with conjugate Gaussian inference for unsupervised multi-source fusion. NCAM learns source-specific bias and reliability conditioned on contextual covariates, yielding an analytically tractable posterior over a latent target variable with decomposed epistemic and aleatoric uncertainty. Structural non-identifiability is resolved through sensor anchoring and variance regularization, enabling stable and interpretable posterior aggregation. To complement Bayesian uncertainty with finite-sample guarantees, we integrate locally adaptive Monte Carlo conformal prediction, producing heteroscedastic prediction intervals with coverage guarantees under exchangeability assumptions. Experiments on synthetic and real-world air-quality datasets demonstrate improved predictive accuracy and well-calibrated uncertainty compared to unsupervised baselines, including mean aggregation, probabilistic PCA, and Kalman filtering.

Muhammed Faruk Aytin, Zehra Demir, Alper Unal +2

AI and Data Engineering Department, Istanbul Technical University, Istanbul, Türkiye · Eurasia Institute of Earth Sciences, Istanbul Technical University, Istanbul, Türkiye · Civil & Environmental Engineering, University of Washington, Seattle, WA, USA

Bayesian Inference Uncertainty Calibration Multimodal Sensor Fusion

Jun 19, 2026cs.CV

Quantile Adaptive Temperature Scaling for Confidence Calibration

Deep neural networks often produce poorly calibrated confidence estimates, overstating their certainty even when predictions are incorrect. Temperature Scaling remains the most widely used posthoc calibration method due to its simplicity and effectiveness, yet its global, uniform rescaling of logits fails to correct the highly heterogeneous structure of miscalibration observed across the confidence spectrum. In particular, the largest correctness confidence discrepancies arise in different quantile regions depending on the setting, low confidence predictions, where uncertainty matters most, tend to exhibit the largest correctness confidence discrepancies, which standard TS leaves largely unaddressed. We introduce Quantile Adaptive Temperature Scaling (QaTS), a simple and efficient post hoc calibration method that adapts the temperature as a function of a predictions empirical confidence quantile. By mapping confidences into the quantile space, QaTS normalizes the calibration problem, makes the structure of miscalibration explicit and enables a monotone temperature function that adapts across quantiles while leaving well calibrated high confidence predictions largely unchanged. preserving high confidence behavior. This quantile aware formulation aligns naturally with a reparameterized Expected Calibration Error (ECE) objective and yields a sample wise temperature that is robust across a variety of challenging scenarios, such as class imbalance and distributional shifts. Across a broad range of datasets, architectures, evaluation scenarios and diverse tasks, QaTS consistently, and substantially, outperforms state of the art post hoc calibration methods, delivering more reliable and trustworthy confidence estimates without modifying model predictions.

Omprakash Chakraborty, Leo Fillioux, Ismail Ben Ayed +1

1 ÉTS Montréal, Canada · Université Paris-Saclay, CentraleSupélec, Gustave Roussy, INSERM, CDSU, IHU PRISM, Gif-sur-Yvette

Post-Hoc Calibration Probability Calibration Model Calibration Uncertainty Calibration

Jun 19, 2026cs.LG

Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling

Machine learning models are increasingly used to model chemical process systems, yet they often lack principled uncertainty quantification and mechanisms to enforce physical constraints. We propose a probabilistic neural network framework that guarantees satisfaction of linear equality constraints within a given tolerance, while capturing aleatoric uncertainty. Compared to state-of-the-art methods, our formulation demonstrates improved predictive accuracy, uncertainty calibration, and adherence to constraints on reduced data. It also demonstrates competitive performance, but with significantly faster training times when evaluated on large data regimes. We evaluated this on two batch reactor case studies, enforcing mass balances.

Matthew Marsh, Benoit Chachuat, Antonio del Rio Chanona

The Sargent Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, UK

Neural Surrogate Modeling Bayesian Neural Networks Uncertainty Quantification Uncertainty Calibration

Jun 19, 2026cs.LG

Continuous-Time Probabilistic Correctors for Uncertainty-Aware Physics-Based Spacecraft Trajectory Forecasting

Long-horizon spacecraft trajectory forecasting suffers from error accumulation due to the absence of corrective observations in the forecast regime, making reliable uncertainty estimation crucial for safety-critical decision-making such as space domain awareness and conjunction assessment. While high-fidelity physics-based orbit propagators provide accurate deterministic forecasts, they typically lack calibrated uncertainty estimates over long horizons. We introduce a Predictor--Corrector framework in which a physics-based continuous-time

\textit{deterministic}

forecaster is augmented with a learned continuous-time

\textit{probabilistic}

Corrector that models forecast errors. The proposed Corrector can be wrapped around an existing deterministic propagator to improve forecast accuracy while producing sharp and calibrated full-covariance uncertainty estimates. The Corrector is based on Latent Neural Controlled Differential Equations (Latent NCDEs) and models the probabilistic temporal evolution of forecast errors in continuous time, naturally supporting irregular sampling and missing features. We further introduce a loss function that promotes calibration and sharpness in long-horizon uncertainty propagation. We evaluate the proposed framework on long-horizon spacecraft trajectory forecasting using real-world data from NASA's Crustal Dynamics Data Information System (CDDIS), wrapping the Corrector around NASA's General Mission Analysis Tool (GMAT). Across forecast horizons of 2--4 days without observations and six rolling test windows, the proposed approach consistently improves accuracy and uncertainty calibration compared to deterministic baselines and Latent ODE-based correctors, demonstrating the effectiveness of the continuous-time probabilistic Corrector for trajectory forecasting.

Muhammad Bilal Shahid, Zhanhong Jiang, Soumik Sarkar +1

Iowa State University, Ames, Iowa, 50011, USA

Neural Controlled Differential Equations Uncertainty Quantification Probabilistic Forecasting Uncertainty Propagation Trajectory Prediction Uncertainty Calibration

Jun 18, 2026cs.AI

Toward Calibrated Mixture-of-Experts Under Distribution Shift

Calibration aligns a model's predictive uncertainty with the frequencies of its empirical outcomes and is important for understanding and trusting reported probabilities. Recent work shows that enforcing calibration at the level of individual predictors can improve ensemble accuracy and calibration, with mixture-of-experts (MoE) models showing strong empirical improvements in particular; however, the conditions under which calibration helps MoE are not well understood. In this work, we study how MoE models behave under distribution shift, focusing on how routing mechanisms interact with expert-level calibration. We show that expert calibration is sufficient to ensure calibration of the overall model under a broad class of distribution shifts in hard-routed models, but is insufficient for calibrating soft-routed models. To address this, we propose an adversarial reweighting that penalizes calibration errors of the routed aggregate under distribution shift, and we demonstrate that it improves the accuracy-calibration tradeoff both on average and on difficult subsets of the data, across model classes, prediction tasks, and distribution shifts.

Gina Wong, Drew Prinster, Suchi Saria +2

Johns Hopkins University, Baltimore, MD, USA.

Distribution Shift Robustness Model Calibration Mixture-of-Experts Models Uncertainty Calibration

Jun 17, 2026cs.CV

Confidence is Not Reliability: Rethinking MC Dropout in Brain Tumour Segmentation

Glioma segmentation in multiparametric MRI is a critical component of treatment planning. A segmentation model that fails silently on treatment-critical sub-regions represents a patient safety risk that overlap-based metrics such as Dice scores cannot expose. We ask whether voxel-level uncertainty estimation via Monte Carlo (MC) Dropout can reliably identify segmentation errors in clinically critical sub-regions, and whether calibration failure modes are detectable from standard reporting metrics alone. In an empirical two-model case study on 126 BraTS21 patients, we evaluate a high-performance pretrained SegResNet and a locally trained UNet with residual units (UNet-Res). MC dropout preserved segmentation accuracy (

|Δ\text{Dice}|

<0.01

) while achieving strong uncertainty-error alignment (AUROC for entropy (H)

\approx

0.97), indicating uncertainty correctly ranks erroneous voxels above correct ones. Entropy-based patient stratification identified a high-uncertainty subgroup with substantially lower segmentation performance (median whole-tumour Dice

0.835

vs.

0.925

), supporting uncertainty as a practical triage signal. However, global alignment can mask important region-specific differences. Despite similar AUROC, UNet-Res exhibited near-zero enhancing tumour entropy (

0.054

) and Expected Calibration Error (ECE) of

0.915

, with a Dice of only

0.714

, indicating severely miscalibrated confidence on the most clinically critical sub-region, a failure mode invisible to standard Dice and AUROC reporting. These findings demonstrate that strong uncertainty-error alignment is necessary but insufficient for clinical safety: sub-region-specific calibration assessment must accompany AUROC evaluation when selecting models for clinical deployment.

Xin Ci Wong, Duygu Sarikaya, Kieran Zucker +2

Centre for Doctoral Training in AI for Medical Diagnosis and Care, School of Computing, University of Leeds · School of Computer Science, University of Leeds · Leeds Cancer Centre, St James’s University Hospital, Leeds, UK

Segmentation Uncertainty Estimation Uncertainty Calibration Brain Tumor Segmentation

Jun 16, 2026cs.LG

Amortized Probabilistic Retrieval of Atmospheric CO2 from OCO-2 Spectra Using Deep Learning with Laplace Approximations and Normalizing Flows

Space-based monitoring of atmospheric carbon dioxide (CO

_2

) constrains the global carbon budget. NASA's Orbiting Carbon Observatory-2 (OCO-2) estimates column-averaged dry-air mole fractions of CO

_2

(XCO

_2

) from high-resolution spectra, but operational retrievals are computationally expensive and impose stringent Gaussianity assumptions on the retrieved posterior. We present a deep learning framework that addresses both through amortized probabilistic inference. Lacking ground truth for real observations, we train and evaluate on a high-fidelity OCO-2 simulation ensemble with calibrated forward-model errors, comparing against the version-10 ACOS full-physics retrieval on the same radiances. Our architecture encodes each spectral band separately and estimates posteriors of the full CO

_2

column, or summaries thereof, with Laplace approximations and conditional normalizing flows. Once trained, inference costs milliseconds per sounding rather than minutes, and calibrated posteriors are attainable at that cost. Trained on simulations that explicitly include forward-model discrepancy, our retrievals are more accurate than the operational one for XCO

_2

on both data partitions we consider, and competitive on profiles. The flow represents asymmetric posteriors that a Gaussian cannot, a gain attributable to shape rather than scale, and its advantage in predictive density persists where its accuracy advantage does not. These results are established on a land-only ensemble against one configuration of the operational algorithm. On reference soundings withheld from training and on two unseen months the XCO

_2

and density advantages persist while calibration degrades under sparsely sampled observing conditions, pointing to the diversity of the simulated scene population rather than the method as the main obstacle.

Alejandro Calle-Saldarriaga, Felix Jimenez, Jack Grosskreuz +3

Department of Statistics, University of Wisconsin–Madison · Jet Propulsion Laboratory, California Institute of Technology

Amortized Inference Remote Sensing Uncertainty Calibration

Jun 15, 2026cs.LG

Calibrated Sampling-Free Uncertainty Estimation in Bayesian Deep Learning

Modern deep learning models remain notoriously prone to overconfidence, limiting their reliability in high-stakes applications. Bayesian methods aim to counter this by learning a distribution over model parameters, and recent advances now make this feasible for large-scale architectures at costs comparable to AdamW. However, a challenge remains at test time: predictions must be averaged across many forward passes with weights sampled from the posterior, which is prohibitively expensive. Variance propagation offers an efficient alternative, computing layer-wise analytical approximations of uncertainty in a single forward pass. While such techniques are effective for MLPs, their extension to modern architectures remains challenging, due to increased depth and diversity of layer types. To fill this gap, we propose Calibrated Variance Propagation (CVP), which introduces a new propagation method for normalization layers, combines it with recent techniques for handling activation functions, and absorbs residual error through a light calibration step. CVP yields comparably accurate uncertainty estimates to MC sampling across transformers and CNNs, at a fraction of the cost. Against prior variance propagation work, CVP improves coverage at

0.5\%

risk from

8.2\%

to

14.6\%

with BEiT-3 on Visual Reasoning (NLVR2) and from

2.6\%

to

10.8\%

with ViLT on VQAv2, with gains extending to convolutional architectures.

Tobias Jan Wieczorek, Leon de Andrade, Thomas Möllenhoff +1

TU Darmstadt & hessian.AI, Darmstadt, Germany · RIKEN Center for Advanced Intelligence Project, Tokyo, Japan

Bayesian Neural Networks Uncertainty Quantification Uncertainty Propagation Uncertainty Calibration

Jun 13, 2026cs.LG

Bayesian 3D Steerable CNNs: Enabling Equivariance and Uncertainty Quantification Simultaneously

Steerable convolutional neural networks (Steerable-CNNs) guarantee SE(3)-equivariance by parameterizing kernels as linear combinations of steerable basis functions, but their deterministic nature precludes uncertainty quantification - limiting their use in settings where confidence estimates are essential. We propose a Bayesian Steerable-CNN that places posterior distributions over the basis coefficients, yielding stochastic kernels while preserving equivariance exactly. The loss function of the model is obtained via variational inference and minimized by Bayes-by-Backpropagation. The framework admits a decomposition of predictive uncertainty into epistemic and aleatoric components. Empirically, the model attains competitive classification accuracy alongside an expected calibration error of 0.0263 and outperforms its deterministic counterpart by up to 6.17% under distributional shift induced by additive Gaussian noise. Furthermore, we leverage the model's uncertainty estimates to enhance its performance significantly, achieving a notable gain - approximately 4% higher accuracy across 84% of the test dataset. A statistically significant negative correlation between epistemic uncertainty and prediction error confirms that the learned posterior variance is semantically meaningful. The framework unifies Bayesian uncertainty quantification with the inductive bias of equivariant CNNs.

Abhishek Keripale, Ponkrshnan Thiagarajan, Susanta Ghosh

Department of Mechanical and Aerospace Engineering, Michigan Technological University, Houghton, MI 49931 · Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD 21218 · The Center for Artificial Intelligence at the Institute of Computing and Cybersystems, Michigan Technological University, USA

Bayesian Neural Networks Uncertainty Quantification Equivariant Neural Networks 3D CNNs Uncertainty Calibration

Jun 11, 2026cs.LG

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods -- the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) -- are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms -- diversity, smoothness, and stochasticity -- within the language of PAC-Bayesian and large-deviation theory.

Luis A. Ortega

Department of Computer Science Machine Learning Group Madrid

Bayesian Neural Networks Neural Network Generalization PAC-Bayesian Generalization Bounds Uncertainty Quantification Variational Inference Uncertainty Calibration

Jun 11, 2026cs.LG

Reliability of Probabilistic Emulation of Physical Systems

Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

Sam F. Greenbury, Radka Jersakova, Paolo Conti +4

The Alan Turing Institute · Autodesk Research · PhysicsX +3

Surrogate Modeling Probabilistic Forecasting Generative Modeling Spatiotemporal Forecasting Uncertainty Calibration

Jun 10, 2026cond-mat.mtrl-sci

Modelling magnetic material properties with uncertainty-aware neural networks

Machine learning is increasingly used to accelerate materials discovery across large compositional and structural design spaces, but limited and heterogeneous data make reliable uncertainty estimation essential. In this work, we investigate uncertainty quantification for permanent magnet modeling across three complementary studies. First, on a public Curie temperature surrogate dataset, we benchmark Gaussian process regression, random forest bagging, and dropout-based Bayesian neural networks and show that calibration, sharpness, and confidence curve diagnostics reveal differences in uncertainty quality that are not visible from point-prediction metrics alone. Second, we transfer this framework to the prediction of intrinsic magnetic properties in Nd2 Fe14 B-based magnets. Third, we extend the same uncertainty-aware perspective to coercivity prediction from microstructural information using a graph neural network. Together, these studies show that uncertainty quantification improves the trustworthiness of magnetic material property predictions and can be transferred from composition-based surrogate models to more complex structure-sensitive learning tasks.

Clemens Wager, Heisam Moustafa, Alexander Kovacs +10

Christian Doppler Laboratory for magnet design through physics informed machine learning, University for Continuing Education Krems, Wr. Neustadt, 2700, Austria · Vienna Doctoral School in Physics, Vienna, Austria · Department for integrated sensor systems, University for Continuing Education Krems, Wr. Neustadt, 2700, Austria +1

Uncertainty Quantification Materials Property Prediction Uncertainty Calibration