Reliable Uncertainty Quantification

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

Accurate estimation of forest height from satellite imagery is essential for applications such as carbon accounting, biodiversity monitoring, and ecosystem management. While recent deep learning approaches provide accurate predictions, they typically do not quantify predictive uncertainty. This limitation is particularly relevant in geospatial settings characterized by sparse supervision and geographic distribution shift. In this work, we investigate Deep Evidential Regression (DER) for forest height estimation on the TreeUQ benchmark, a large-scale dataset designed for the joint estimation of tree count and average tree height at 10 m resolution, based on Sentinel-1/-2 data as well as tree inventory data over the federal state of Bavaria. To account for the extreme label sparsity of the tree inventory data, we introduce a masked evidential loss for dense geospatial prediction. Using a U-Net architecture with multimodal Sentinel-1 and Sentinel-2 inputs, the proposed approach jointly predicts tree height and associated uncertainty estimates in a single forward pass. Experimental results show that DER achieves predictive performance comparable to a deterministic U-Net while additionally providing well-calibrated uncertainty estimates. These findings demonstrate the potential of evidential learning as an efficient framework for uncertainty-aware forest structure estimation from Earth observation data.

In social learning, agents learn not only from direct evidence but also through interactions with their peers. We investigate the role of imprecision in such interactions and ask whether it can improve the effectiveness of the collective learning process. To that end we propose a model of social learning where beliefs are equivalent to formulas in a propositional language, and where agents learn from each other by combining their beliefs according to a fusion operator. The latter is parametrised so as to allow for different levels of imprecision, where a more imprecise fusion operator tends to generates a more imprecise fused belief when the two combined beliefs differ. In this context we describe both difference equation models and agent-based simulations of social learning under a variety of conditions and with different initial biases. The results presented suggest that for populations with a strong initial bias towards incorrect beliefs some level of imprecision in fusion can improve learning accuracy across a range of learning conditions. Furthermore, such benefits of imprecision are consistent with a stability analysis of the fixed points of the proposed difference equation models.

Automatic RF modulation recognition is of critical importance in spectrum monitoring, electronic warfare, and cognitive radio applications, where low signal-to-noise ratio (SNR) conditions and the growing diversity of modulation schemes limit the performance of existing methods. This paper proposes an uncertainty-driven hybrid deep learning architecture for recognizing RF signals over a broad modulation space. The proposed approach carries out a multi-stage classification process by combining spectral information obtained through low-cost FFT-based preprocessing with time-frequency features extracted from short-time Fourier transform (STFT) spectrograms. The architecture comprises a 2D convolutional neural network (2D CNN)-based path for fast, low-latency primary classification, MC Dropout-supported Bayesian uncertainty estimation for assessing classification reliability, and a BiLSTM-based secondary decision mechanism activated under high-uncertainty conditions. The proposed system is evaluated in a controlled simulation environment spanning different SNR levels and modulation classes. Experimental results show that the primary 2D CNN path achieves $83.3\pm0.7\%$ accuracy with an inference time of only 0.138 ms per sample, providing superior performance compared with traditional rule-based and classical machine-learning approaches. Furthermore, the obtained findings reveal the limitations of compact spectral feature representations and classifiers lacking temporal modeling, particularly in disambiguating FSK-based modulations. The uncertainty estimation module offers promising results for detecting low-confidence decisions, and the proposed approach demonstrates the potential of a low-latency and scalable solution for real-time RF modulation recognition.

Large language models (LLMs) can generate fluent reasoning traces that nevertheless lead to incorrect answers, making response-level uncertainty estimation important for abstention, human review, and adaptive compute allocation. Existing approaches generally fall into three categories: passive single-trace methods use token-level confidence signals, sampling-based methods compare multiple complete traces at higher generation cost, and active prefix-based methods probe partial traces to study answer stabilization or preference transitions. However, none actively re-elicits an answer from a completed reasoning trace to measure its consistency with and support for the original answer. To address this gap, we introduce Trace-Conditioned Answer Consistency (TrAC), a correctness-supervised uncertainty quantification framework that combines active and passive signals anchored to one completed reasoning trace. Its active component, Prefix-Conditioned Elicitation (PCE), re-elicits a short answer conditioned on the completed trace and represents both its consistency with the original answer and its token-level probabilistic support. Its passive component, Trace Uncertainty Profile (TUP), summarizes how token-level uncertainty evolves throughout the original generation without additional decoding. A lightweight head then integrates the two representations into a response-correctness score. Across five mathematical reasoning benchmarks and three LLM families, TrAC improves macro AUROC by 1.8% and reduces AURC by 3.4% relative to eight-sample self-consistency, while using one complete reasoning trace and a short cached answer probe. When eight samples are already available, augmenting sample consensus with re-elicitation further improves macro AUROC by 4.3% and reduces AURC by 8.3%, without additional full-trace generation.

Although large language models (LLMs) can produce fluent spatial reasoning traces, their intermediate relations may fail to support the final conclusion, making token-level confidence insufficient for final-answer reliability estimation. Existing formal verifiers provide stronger semantic evidence, but their applicability is partial: a parsed claim need not yield a definite semantic verdict. To address this issue, we introduce SymboUQ, a symbolic uncertainty quantification framework that estimates final-answer reliability from reasoning traces by distinguishing symbolizability, whether a claim can be represented in the verifier's formal language, from semantic determinacy, whether its execution yields an entailed or contradicted verdict rather than an unknown or not-evaluable outcome. SymboUQ comprises (i) a Layout Auditor that executes ordered spatial claims and extracts feasibility, conflict, and repair evidence; (ii) a label-free Determinacy Profile that characterizes effective executable coverage; and (iii) a Determinacy-Aware Reliability Composer that integrates constraint-based, representation-based, and decoding-based scores according to verifier applicability. Extensive experiments on five spatial reasoning benchmarks with four frozen LLM backbones show that SymboUQ achieves approximately an 8% relative improvement in AUROC and a 7% relative reduction in class-balanced Brier loss over the strongest baseline.

To maintain common ground in cooperative conversation, humans iteratively update their beliefs as conversation participants share new information; participants who are epistemically vigilant detect when new information conflicts with prior beliefs and take steps to repair these conflicts. In order for AI systems to serve as reliable partners in complex cooperative tasks, they must similarly weigh incoming information against their own private evidence and shared context and appropriately surface inconsistencies when they arise. To measure the epistemic vigilance of vision-language models in cooperative settings, we present an information-asymmetric, dialog-based "spot-the-difference" task. Two models are privately shown one image each, and must determine through conversation whether the images are identical or, if not, identify the difference. Models routinely fail at this: they frequently overlook key evidence in their private image in favor of agreeing with their conversational partner, even when their agreement is unwarranted. We relate these violations of epistemic vigilance to the broader behavior of sycophancy, which manifests itself in cooperative goal-oriented dialog as over-accommodation and weak evidential grounding. Our results show that model steering to reduce sycophancy with a vector learned from task-agnostic sycophancy examples can reduce epistemic vigilance-related errors, making models more faithful reporters of their evidence, and in turn, more reliable partners in information-asymmetric cooperative tasks.

Active 3D reconstruction relies on active view selection to maximize reconstruction fidelity under limited capture budgets. However, most existing methods rely on surrogate signals such as parameter uncertainty or geometric heuristics, but these signals are often misaligned with the ultimate goal: the fidelity of rendered predictions. We propose GO-PRE, a goal-oriented next-best-view selection framework that explicitly targets information gain in the prediction space. Specifically, we formulate the objective as maximizing the reduction of the average marginal predictive entropy over a user-specified target view manifold. GO-PRE supports interactive goal specification and yields an efficient acquisition rule that enables real-time computation of information gain. Extensive experiments across benchmarks demonstrate that GO-PRE consistently improves active reconstruction performance and provides more reliable uncertainty quantification compared to state-of-the-art methods.

Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response. The repeated model evaluations required for these tasks are often prohibitively expensive; surrogate models provide an efficient alternative by constructing inexpensive approximations of the underlying system response. Constructing surrogate models that combine scalability and interpretability for systems with high-dimensional stochastic inputs and functional responses remains challenging, particularly when sensitivity estimates are required across spatial or temporal domains. Polynomial chaos expansion (PCE) provides an effective framework for uncertainty propagation and sensitivity analysis due to its orthogonal structure and direct relationship with variance-based sensitivity measures. However, PCE suffers from the curse of dimensionality, whose computational burden is amplified for problems with functional responses. In this work, we introduce the Structured Neural Chaos (sNC) expansion as a surrogate modeling framework for variance-based GSA, inspired by the interpretability and orthogonal structure of PCE. The proposed framework retains the interpretability of structured decompositions while leveraging the expressive power of neural networks. The sNC expansion mirrors a truncated functional ANOVA decomposition, where each interaction component admits a separable low-rank approximation whose basis functions and coefficients are parameterized by neural networks. The expansion is constructed sequentially, adaptively identifying the dominant modes within each ANOVA subspace and determining the effective complexity of the representation. The resulting structure enables the extraction of statistical and sensitivity quantities directly from the coefficients of the sNC expansion at negligible cost.

The deployment of deep neural networks in safety-critical domains demands reliable estimates of predictive confidence, yet conventional architectures lack principled uncertainty quantification. This survey provides a structured, critical review of methods for Uncertainty Quantification (UQ) in deep learning, scoped to ensemble-based and approximate Bayesian approaches and the measures used to summarize their outputs. Relative to existing UQ surveys, our contribution is depth on efficient ensemble approximations and single-pass methods, and a unified treatment that separates the method producing a predictive distribution from the measure that summarizes its uncertainty. We organize methods into five families: Bayesian neural networks, Monte Carlo Dropout, deep ensembles, efficient ensemble approximations, and last-layer or single-pass approaches. We situate adjacent work on evidential and prior networks, conformal prediction, and post-hoc calibration, together with the decision-time tasks of out-of-distribution detection and selective prediction. For each, we examine theoretical motivation, implementation, empirical performance, and limitations. We then review ensemble diversity theory and uncertainty measures and their decompositions, contrasting the entropy decomposition with pairwise divergence measures, and consolidate evaluation methodology so that our qualitative comparisons share a common basis. We close with a brief treatment of uncertainty in large language models and open research directions, including efficient epistemic measures for classification, last-layer diversity, diversity and calibration under shift, and hybrid architectures.

Flow matching (FM) has become a popular action head paradigm for modern embodied models. However, as a conditional generative model, it does not explicitly expose its inherent uncertainty, producing faulty action chunks even when it misinterprets the scene or encounters out-of-distribution (OOD) inputs. Therefore, determining when an FM-generated action can be trusted is essential for safe deployment, yet existing uncertainty estimation methods on real-time control suffer from several issues: extra training budget, high computational overhead, and low generalization ability. In this work, we provide a geometric interpretation of FM uncertainty in the velocity field, showing that uncertainty manifests as deviation from an ideal affine-isotropic contraction field. Building on this observation, we introduce denoising acceleration ($\mathrm{accel}$), a highly-generalizable and cost-free uncertainty proxy that measures the bending of the denoising trajectory from a single forward pass, without additional model evaluations, training, or resampling. We theoretically and empirically demonstrate that $\mathrm{accel}$ is a faithful proxy for FM uncertainty and further test its utility in online failure detection. Results show that $\mathrm{accel}$ identifies failing rollouts well before termination, matching or even outperforming costly resampling- and training-based baselines across settings under realistic deployment budget. Code and demos available at: https://github.com/rrrrrrzy/fm-geometry.

High-stakes decision systems in credit scoring, fraud detection, healthcare, and industrial safety require reliable uncertainty quantification under severe class imbalance and asymmetric error costs. Standard marginal conformal prediction (CP) provides valid overall coverage guarantees; however, we show that it severely under-covers rare, costly minority classes, with minority-class coverage dropping to as low as 0.5% on certain datasets. To characterize and address this limitation, we conduct a comprehensive benchmark comparing marginal CP, class-conditional (Mondrian) CP, and cost-controlled abstention mechanisms across 15 real-world imbalanced tabular datasets, 7 classification models, 3 probability calibration techniques, and 10 random seeds, resulting in 3,150 experimental runs. Our results show that Mondrian CP restores valid minority-class coverage, achieving an average minority-coverage improvement of 61.7 percentage points over marginal CP (p < 1e-80). Furthermore, combining Mondrian CP with cost-controlled abstention significantly reduces expected decision cost compared with standard decision boundaries, confidence-based rejectors, and risk-controlled rejectors under realistic human review budgets. We further quantify dataset-specific break-even thresholds at which deferring ambiguous instances to human experts becomes cost-effective. These findings provide practical guidance for deploying distribution-free, cost-aware uncertainty quantification in high-stakes decision support systems.

YOLO-Pose models provide efficient keypoint localization, but do not quantify the associated spatial uncertainty. We introduce a lightweight post-hoc probabilistic extension that augments a trained YOLO-Pose model with calibrated bivariate predictive distributions over keypoint locations, centered at the model's original predictions. Concretely, we train additional probabilistic heads with an importance-weighted negative log-likelihood to predict an input-dependent $2\times2$ dispersion matrix for each keypoint, followed by Gaussian calibration for broad downstream compatibility or Student-$t$ calibration for distributional fidelity. Complementing this, we propose an evaluation protocol that combines a suite of distributional calibration diagnostics with average keypoint precision (AKP), a keypoint-level extension of the COCO AP protocol for assessing reliability rankings. Experiments on COCO show that the learned uncertainty estimates enable effective keypoint-level reliability ranking, Student-$t$ calibration best captures the empirical residual distribution, and uncertainty-based pruning removes unreliable keypoints. A central application-level demonstration is vision-based aircraft landing, where calibrated covariances for runway keypoints support uncertainty-aware aircraft position estimation and downstream sensor fusion.

Deep off-policy reinforcement learning algorithms for continuous control typically rely on neural value function approximation to guide policy improvement. However, temporal-difference (TD) learning introduces noisy targets, resulting in non-stationary optimization, while greedy policy updates amplify early-stage estimation errors. The recursive propagation of such errors leads to persistent overestimation bias and degraded training stability in actor-critic methods. Existing approaches attempt to alleviate this issue via prioritized sampling or modified value learning objectives, but often overemphasize high-uncertainty transitions caused by limited data coverage or bootstrapping errors, thereby further amplifying bias.In this paper, we propose Collaborative Weighting Actor-Critic (CWAC), a unified framework that explicitly accounts for predictive uncertainty in value estimation. CWAC employs distributional critic to model return uncertainty and introduces a collaborative weighting mechanism that jointly reweights TD-errors and uncertainty, enabling robust learning from reliable samples while suppressing noisy updates. In addition, we incorporate a stochastic pessimistic value estimation scheme via sampling from the return distribution, which effectively mitigates error propagation during policy improvement. CWAC can be seamlessly integrated into existing off-policy algorithm frameworks such as SAC, TD3, and DDPG with minimal overhead. Empirical results demonstrate that our proposed method significantly enhances performance across a diverse range of simulated tasks. Our code is publicly available at https://anonymous.4open.science/r/CWAC-348E.

Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient $λ$. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-$γ$, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at $p<0.01$ (paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer ($p=0.23$). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.

Repository-level code generation relies on heterogeneous evidence whose relevance, compatibility, and completeness are inherently uncertain. Similar-code examples, repository context, and project-specific APIs may provide complementary information, but can also introduce noisy, redundant, or conflicting signals. Existing retrieval-augmented approaches primarily optimize retrieval relevance without explicitly modeling how uncertainty in retrieved evidence affects downstream generation. We introduce OpenCoder, an uncertainty-aware framework that estimates source-specific uncertainty, uses it to filter and rank heterogeneous evidence, and guides generation, verification, and repair. A factorial analysis over API knowledge, repository context, and similar-code evidence reveals no universal additive source ranking; instead, significant cross-source interactions depend on the accompanying evidence and LLM backend. On an expanded 32-task RepoExec-inline evaluation, OpenCoder improves GPT selected-output correctness over Baseline RAG from 56.25% to 78.13%. However, it matches a verification-and-repair control, and the corresponding Gemini improvement is not statistically supported, indicating backend-dependent benefits. Target-aware API refinement also substantially improves API-set retrieval. These findings support treating uncertainty as an actionable control signal for repository-level retrieval, verification, and repair.

A Last-Layer Ensemble (LLE), $K$ linear units on one shared frozen feature map, is an efficient single-pass approach to the disagreement-based epistemic uncertainty for out-of-distribution (OOD) detection. Its weakness is that members share the backbone gradient and can converge toward the same function, collapsing the inter-member diversity the signal depends on. Whether last-layer diversity can be restored, and what mitigates the collapse, is an open question. The weight-orthonormality defining Orthonormal Certificates (OC), the weight-orthonormal special case of the LLE, is only an indirect correction; it decorrelates the weights of the members, not their predictions. Here, we instead target the collapse directly in function space, with a Covariance Last-Layer Ensemble (cov-LLE) that places a direct covariance penalty on member activations. Cov-LLE restores the function-space diversity that weight-orthonormality cannot, and at matched $K$ recovers much of the diversity and calibration of a deep ensemble at $1\times$ backbone cost (in-distribution prediction variance $0.05\!\to\!9.3$ vs. $22.1$ ($\times10^{-3}$), and ECE $0.135\!\to\!0.090$ vs. $0.035$, for a $K\times$-cost deep ensemble), at no cost to accuracy. Viewing OC as a last-layer ensemble also organizes detectors into a two-axis taxonomy (by how their units are trained and how their outputs are scored) and exposes the OC score as a magnitude, motivating a scale-invariant, label-free direction score that repairs its near-OOD failure, adding $+0.16$ to $+0.18$ ROC AUC on every backbone.

Hybrid mechanistic/data-driven models, which combine first-principles with learned components, are increasingly used in process engineering and scientific machine learning. Common hybrid modeling designs are specified primarily through their architectures and training losses, which offers a limited basis for a shared semantic interface to compare or verify them across domains, with comparatively little attention paid to epistemic uncertainty in the mechanistic part. We bridge hybrid modeling and neuro-symbolic (NeSy) AI by reconstructing these designs as instances of NeSy interface. The resulting translation, Hybrid-to-NeSy (H2N), places mechanistic knowledge on the language side, learned modules on the belief side, and validity domains together with constraints on the logic side. For each design, H2N then yields an explicit NeSy inference functional and a logic-belief decomposition. From this decomposition we derive two metrics: structural violation rate (SVR), measuring whether the learned belief respects the mechanistic structure; and belief dispersion (BD), measuring how concentrated the learned plausibility is, serving as a hybrid model's epistemic uncertainty in its mechanistic part. We instantiate H2N on a case study of a structured hybrid model for binary classification under label noise and show that models with higher SVR and BD exhibit greater variability in held-out accuracy. Under structural distribution shift, H2N further quantifies a model's uncertainty during extrapolations, whereas test accuracy reveals the same shift only post hoc.

In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space. While traditional integrated-learning-and-optimization models assume that side information is perfectly revealed, empirical data-driven features are frequently corrupted or noisy at the time of decision-making, leading to fragile operational policies. To bridge this gap, we integrate principles of robust optimization directly into the predictive-prescriptive pipeline via a smart predict-then-robustly optimize loss and establish a computationally tractable convex surrogate, designed to hedge against worst-case feature perturbations. On the theoretical front, we formalize the structural validity of this surrogate by proving its approximation error probability decays exponentially according to a sub-Gaussian concentration profile. Furthermore, we establish that under mild assumptions, the surrogate is Fisher consistent with high probability. We also prove necessary conditions under which our framework outperforms standard smart predict-then-optimize and maintain its superiority even when the standard method is equipped with regularized upstream predictions. Numerical experiments validate that our robust framework consistently yields significant performance improvements over standard methods, both in out-of-sample terms and in training stability.

Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-aware hyperelastic constitutive modeling. iPANNs learn sparse lower, mean, and upper free energy density branches whose stresses, obtained by automatic differentiation, ultimately enclose noisy stress observations. In contrast to this deterministic interval description, fPANNs embed the learned iPANN branches into a fuzzy-set representation through alpha-cut interpolation, yielding a nested family of admissible responses. iPANNs and fPANNs encode mechanistic constraints - preserving objectivity, consistency and promoting polyconvexity - and smoothed L0 regularization promotes interpretable energy representations. The bound models are trained through a two-stage transfer-learning procedure in which a sparse mean constitutive response is learned first and then fine-tuned into lower and upper energy branches. We evaluate the framework on synthetic isotropic hyperelastic data with heteroscedastic noise, varying random realizations, shifted noise means, and varying noise magnitudes. The results show that the learned bounds enclose noisy stress observations while generalizing to the test set. Further, we examine the propagation of uncertainty through the mean, upper and lower bound predictions of the learned iPANN models in a finite element setting. The proposed framework provides a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification in hyperelastic constitutive modeling, and propagation in downstream finite element simulations.

Machine learning models for medical image analysis typically lack a reliable measure of confidence, limiting their use in ambiguous or atypical cases. Here we show that Monte Carlo dropout, applied to a multi-task chest-radiograph classifier (eight thoracic findings, 137,593 training images), provides an epistemic uncertainty signal that tracks generalisation across training-set scales and flags confident yet error-prone predictions. Adding this signal to the point prediction raised error-detection AUROC from 0.74 to 0.77 ($Δ$AUROC +0.023, 95% CI [+0.014, +0.033]). In a controlled 2x2 factorial experiment, a clinical-decision-support agent exploited this uncertainty only when it was delivered as a binary error-risk flag rather than as raw scores, cutting confident misdiagnoses on unreliable findings from 8.5% to 2.7%. Epistemic uncertainty estimation thus carries decision-relevant information beyond point predictions, but its value for downstream agents depends on how it is communicated.

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

This Good Practice Guide presents work done in the QUMPHY project (Uncertainty quantification for machine learning models applied to photoplethysmography signals) that considered both machine learning and uncertainty quantification for problems which used photoplethysmography (PPG) signals from wearable devices as input. It provides high-level guidance on what types of machine learning model might be used and how different models compare when applied to both regression and classification tasks. It provides guidance on the implementation of different methods for uncertainty quantification, covering both model-dependent and model-independent techniques, and on the validation of the results provided by those methods. It also describes six benchmark problems together with pointers to different benchmark datasets for each problem. Software is described that can assist practitioners in implementing the methods described herein and there is a brief consideration of ethical issues. It concludes with a summary and recommendations.

In this work, we incorporate first principle physics into the construction of data-driven methods by considering a model that accounts for the different sources of energy losses during vehicle operations. Our results show that Bayesian linear regression based on this physics-aware model can improve the reliability of the expected energy consumption, as compared with standard linear regression. Further, it is shown that more complex machine learning models such as neural networks and gradient boosted regression trees, based on the same physical model, can further improve the accuracy in energy forecasting and significantly outperform standard versions of the same machine learning models. In addition to point predictions of the energy consumption, we develop a framework for estimating the corresponding uncertainty in the form of predicted standard deviation. Our results show that all of the models learn to estimate the uncertainty reasonably well.

Users frequently express their beliefs to large language models (LLMs). In some situations, the LLM should accept these contextual beliefs as true. In others, they should stick to their prior knowledge. Notably, users' expressions of belief (EoBs) can take linguistically diverse forms - using presuppositions, evidential and certainty markers, or varied tones - each of which may have a different persuasiveness over the LLMs. We introduce a typology to systematically evaluate how different EoBs affect whether models follow context versus prior knowledge. The typology is grounded in four linguistically motivated dimensions: form, evidentiality, epistemic stance, and tone, spanning 17 fine-grained types. By pairing these EoBs with world knowledge facts, we generate controlled EoB-query pairs that isolate the effect of linguistic variation. Using this benchmark, we evaluate 16 LLMs that differ in architecture (Llama3, Qwen3, Gemma3), scale (1B-30B parameters), and training stages (base vs instruct). We identify meaningful variations in response behavior across these axes, e.g., that bigger models and instruction models tend to be less context-following than smaller models and base models. We further identify specific EoBs that statistically significantly persuade LMs more consistently than others. Our work reveals systematic patterns in how linguistic framing affects LLM context integration, with implications for prompt engineering and model robustness.

Managing massive crowds during infrequent special events requires reliable real-time pedestrian-flow forecasting to ensure public safety and operational efficiency. However, supervised forecasting methods face limitations in these contexts due to scarce historical data, heterogeneous data distributions, and short in-event observation windows. To effectively support operational decision-making, forecasts should provide not only accurate point estimates but also informative predictive uncertainty. Probabilistic uncertainty quantification plays a critical role in this aspect, particularly capturing sudden volatility and tail risks. This paper investigates pretrained time series foundation models as a lightweight approach for zero-shot probabilistic forecasting without extensive local retraining. Using decision-oriented metrics tailored to short events, we conduct a comprehensive assessment of two time series foundation models on crowd forecasting, with the SAIL2025 event as a use case. We then distill practical insights for crowd managers, specifying when zero-shot forecasts remain operationally reliable.

Sparse-support uncertainty is usually quantified by treating the dictionary as known, an assumption that can produce overconfident, label-dependent conclusions when the dictionary is learned from latent sparse mixtures. Near collisions of coherent atoms, a test signal may identify the active physical group even though the training data cannot distinguish the physical rays within it. We develop inference for active physical rays, unit atoms modulo sign, after latent dictionary learning. In a fixed-dimensional Gaussian train-test experiment, we retain all dictionaries compatible with a robust training-moment region, profile the test representation over them, and project surviving configurations onto a permutation-invariant support space. The resulting confidence correspondence can report cross-sheet inconclusiveness, group resolution with child ambiguity, or fine-support resolution. We characterize both its statistical cost and decision-theoretic benefit. Residual block orientation first affects the latent training density at cubic order, yielding information of order $s^6$, where $s$ is the within-block collision scale. The correspondence provides high-probability-over-training conditional test coverage, with resolution governed separately by parent detectability, test-time support separation, and learned-dictionary orientation. In the resolved fixed-shell regime, its projective Hausdorff diameter contracts at the minimax-optimal rate $s \wedge (\sqrt{N}s^2)^{-1}$, up to constants. A restricted-task theorem further determines when coefficient asymmetry allows test replication to supplement training information and when calibration uncertainty remains irreducible. The framework thus yields honest, resolution-adaptive support statements and guides the allocation of training versus test measurements.

A point prediction that is well calibrated on average can still be systematically biased conditional on its own value, undermining its use in downstream decision-making. We consider two objectives for reliable uncertainty quantification: self-calibration, requiring a point prediction to be unbiased conditional on its own value, and prediction-conditional validity, requiring a prediction interval to attain nominal coverage conditional on the prediction. Self-Calibrating Conformal Prediction (SC-CP) attains both objectives exactly in finite samples, but requires refitting its calibrator for every candidate outcome, which is computationally prohibitive for continuous outcomes. We propose Isotonic Conformal Prediction (ICP), a framework that decouples calibration from prediction-set construction by fitting a single isotonic recalibration map and constructing prediction intervals within strata of similar recalibrated predictions. Within this framework we develop two procedures. Split Isotonic Conformal Prediction (SICP) attains prediction-conditional validity in finite samples and self-calibration asymptotically, at the computational cost of split conformal prediction. Transductive Isotonic Conformal Prediction (TICP) attains both objectives exactly in finite samples through a per-test-point inner loop that avoids refitting the isotonic calibrator. On synthetic heteroscedastic regression problems and a real-world healthcare-utilization dataset, both procedures match the coverage of SC-CP at substantially lower computational cost.

Safe model-based reinforcement learning (RL) often bridges control-theoretic analysis and RL for robots to safely explore (partially) unknown system dynamics while deriving control actions for task efficiency. The control performance and safety assurance typically rely on prior knowledge of partially modeled nominal system dynamics and the data-driven models that compensate for residual model uncertainties. However, existing methods often overlook the structure of residual model uncertainties (e.g., components affine in control), which could lead to overly conservative robot behaviors or invalid safety guarantees under the safe learning-based controllers. This paper proposes a safe reinforcement learning framework that learns control-affine dynamics with a certifiable data-driven safe policy using control barrier functions (CBF). Specifically, we first use Control-Affine Random Fourier Features (ARFF) to model robot dynamics in a control-affine form, which offers computational efficiency that scales with dataset size and reduces potential model bias for model-based reinforcement learning. Then, a model-free, efficient uncertainty quantification method using adaptive conformal prediction (ACP) is applied to quantify the uncertainty in the safety constraint arising from the learned control-affine dynamics. This allows for data-driven safety assurance amenable to principled and efficient controller synthesis with CBF. Simulation results on the cartpole and the 3D quadrotor platforms demonstrate the effectiveness of the proposed framework.

Current evaluation of epistemic uncertainty relies on tasks such as out-ofdistribution detection and active learning. However, the Bayes-optimal decision strategies for these tasks do not coincide with the scores commonly used to quantify epistemic uncertainty. Building on the epistemic reject-option framework, we evaluate epistemic uncertainty using its ability to identify regret, the reducible error. Formulating selective prediction as a constrained optimization over coverage, expected risk, and regret, we prove the optimal selector is a thresholded convex combination of the ground-truth aleatoric and epistemic uncertainties. This theoretical unification exposes a weakness in recent uncertainty disentanglement literature: we demonstrate that standard correlation metrics between learned components do not necessarily predict their actual operational utility. We instead propose to evaluate the achievable risk, regret, coverage surface of the decomposition as a diagnostic for joint disentanglement and utility. Benchmarking standard methods on datasets with dense human annotations reveals that decision-theoretic rankings can disagree substantially with proxy-task rankings, including pairwise rank inversions between methods that are top-ranked on one criterion and bottom-ranked on other.

Machine-learning force fields (MLFFs) are reliable only near their training distribution, making efficient construction of diverse training sets a major bottleneck for both train-from-scratch and foundation fine-tuning workflows. Active learning can reduce this cost, but standard model-committee uncertainty is impractical for foundation MLFFs because each committee member requires a separate fine-tuning run. We present an active-learning workflow based on last-layer-projection regression (LLPR), a forward-pass-cheap per-configuration uncertainty estimator. Across molecular, condensed-phase, and electrolyte systems, LLPR identifies compact, high-value training sets that recover full-data accuracy using only a small fraction of electronic-structure labels. In foundation-model fine-tuning, LLPR-selected configurations reach the full-pool fine-tuning ceiling with substantially fewer labels than random selection. In iterative electrolyte fine-tuning, LLPR detects unphysical local coordination before DFT labelling, provides an absolute force-error threshold, and enables automatic termination of the learning loop. The resulting models reproduce reference density and ion-coordination structure, providing a scalable uncertainty-quantification strategy across MLFF training regimes.

Many signal processing systems ultimately exist to {act}. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

Radiative Gaussian splatting reconstructs sparse-view CT fast and accurately, and recent work attaches per-Gaussian posteriors to yield per-voxel uncertainty maps. We ask what such a map actually measures: posterior variance is a data-constraint map, not an error map -- its alarms are trustworthy, its all-clears are not. Exploiting the strict linearity of X-ray rendering in the per-Gaussian densities, we derive a clamp-aware closed form that the unchanged rasterizer evaluates exactly in one forward pass, in volume and projection space: the infinite-sample limit of the sampling estimator of concurrent work, at ~8x lower cost. On the official 15-scene benchmark this uncertainty ranks true error on 14 of 15 scenes. Restricted to the object interior -- the tissue a clinician reads -- the ranking collapses (median Spearman 0.11, 0/15 pass), identically for a deep ensemble and for a strictly positive log-normal posterior: three constructions, two estimator families, no survivors. The mechanism is structural: about 90% of in-object error is bias that reproduces across retrainings, invisible to model disagreement; 73-81% of the full-volume correlation is carried by object/surround contrast; and an exactly solvable control puts the observed in-object ranking 4-5x below what a perfectly calibrated posterior with the same sigma-spread would score. The error scale, by contrast, is an engineering problem, and we solve it: reparameterizing the posterior contracts the cross-scene temperature spread from 19.3x to 2.6x, one scene-agnostic temperature transfers to unseen scenes (10/15 leave-one-scene-out), and the repaired scale tracks photon count at the Poisson-predicted -1/2 power. We distill evaluation practice that would have caught the illusion -- masked calibration, seed-wise bias decomposition, an exact-posterior reference -- and release all protocols, seeds and per-run evidence.

Engineering use of AI forecasting models requires not only high nominal accuracy but also predictable behavior under uncertain inputs. In photovoltaic (PV) forecasting, this requirement is especially challenging because numerical weather prediction (NWP) errors are temporally correlated, state dependent, and physically coupled across variables. Existing evaluations, however, often rely on perfect forecast assumptions or simplistic perturbations that do not reflect these characteristics. This study presents a physically constrained robustness evaluation framework based on simulation, using virtual PV power as a controlled response variable to isolate the propagation of input uncertainty from confounders at the plant level. Six representative machine learning and deep sequence models, including PatchTST, GRU, N-HITS, and LightGBM, are evaluated under dynamic NWP perturbations with heteroscedasticity modulated by clear-sky conditions and Erbs reconstruction that preserves radiation consistency. The results show that sequence models provide stronger noise filtering and temporal resilience than a strong tabular baseline under medium to high disturbance regimes. SHapley Additive exPlanations (SHAP) and Integrated Gradients (IG) further support a feature reallocation tendency at the case level, in which predictive reliance shifts from corrupted future forecasts toward more stable historical observations and deterministic physical priors. A Pareto analysis of accuracy under clean conditions, robustness, and computational latency then translates these findings into engineering implications for robustness assessment and model selection under forecast uncertainty.

A language model may be asked either what experts believe about a contested claim or what it believes about the claim itself. A trustworthy conversational agent should distinguish these two requests and respond in different epistemic registers: neutral attribution in the first case and stance expression in the second. Whether such a shift occurs-and whether it occurs coherently-is not directly assessed by existing benchmarks for accuracy, instruction following, or safety. We introduce ESFP, a behavioral benchmark that treats the contrast between externally attributed and self-attributed prompts as the fundamental unit of measurement. ESFP consists of 104 carefully controlled items spanning six epistemic categories and five phrasing templates, and evaluates model responses along four complementary dimensions: lexical self-attribution, representation-level responsiveness to role framing, sentence-level stance content density assessed by an LLM judge panel, and cross-condition stance consistency. Evaluating eight frontier models from five vendors, we find that epistemic flexibility is largely orthogonal to general model capability: a 27B open-weight model matches the strongest proprietary systems, the flagship model of one family underperforms its lightweight counterpart, and reasoning-optimized models do not consistently exhibit higher flexibility. Stance content density provides the strongest signal, while surface-level lexical markers such as 'I think' can change substantially without corresponding changes in expressed stance. We provide item-level bootstrap confidence intervals, weight-sensitivity analyses, and an explicit discussion of the interpretation limits of the composite score. ESFP measures a model's propensity to adapt its epistemic stance under changing attribution conditions, rather than a general competence measure.

As Code Large Language Models (LLMs) become central to modern software engineering, their inherent stochasticity poses significant real-world risks, where even minor errors can lead to severe functional, security, or safety consequences. Reliable automation, therefore, demands the ability to distinguish between confident, well-supported predictions and stochastic guessing. However, existing uncertainty estimation methods face a critical gap: white and grey-box techniques are often inapplicable to closed-source models, while standard "black-box" text metrics fail to capture the unique fragility of code, where syntactic variation does not always imply semantic divergence. To bridge this syntax-semantics gap, we introduce Code-MUE, a purely black-box framework that measures uncertainty through execution-based Semantic Interaction Graphs. Unlike prior approaches that rely on superficial textual similarity, Code-MUE grounds uncertainty in observable runtime behavior, calculating the Von Neumann entropy of the solution space to quantify global semantic diversity. A large-scale empirical study across eight state-of-the-art LLMs demonstrates that Code-MUE achieves a strong negative correlation with functional correctness (Spearman's correlation up to -0.98), significantly outperforming lexical and embedding-based baselines while enabling robust risk detection and selective prediction in practical workflows.

Sensor-rich data-driven applications increasingly use Bayesian approaches to infer latent states of dynamic systems from noisy sensor measurements and physical models. Yet the computation of the likelihood remains an essential bottleneck for accurate posteriors and performant inference. This paper presents a Bayesian filtering technique that uses processor-native uncertainty tracking for both uncertainty propagation and inference. The technique implements deterministic hierarchical importance restructuring through a native operation, giving deterministic latency and bounded memory use for arbitrary models written as program code. Benchmarks across three nonlinear state-space systems compare the approach against particle filters and Monte-Carlo-based likelihood estimators. The technique enables deterministic approximate filtering with as high as 805$\times$ average speedup against direct Monte Carlo work at matched result quality for model evaluation, and Pareto-dominant accuracy-latency trade-offs for posterior inference while remaining competitive in RMSE with baseline particle filters.

Reliable uncertainty quantification is essential for integrating solar and wind generation into modern power systems, where operators must weigh risk rather than act on point forecasts alone. Existing probabilistic methods, however, often either lack finite-sample validity or require per-site recalibration, so a single model rarely transfers across the diverse climates of a dispersed generation fleet. This paper proposes a heteroscedastic, asymmetric, group-conditional split-conformal framework built on a bootstrap-diverse XGBoost ensemble, producing prediction intervals that adapt in width to local difficulty while retaining distribution-free coverage guarantees. A single fixed specification, with no per-site or per-horizon tuning, is evaluated across four climatologically distinct sites spanning both hemispheres, at horizons of 1 to 12 hours, for both solar irradiance and wind speed. The framework holds near-nominal coverage on both targets and reduces the Interval Score by up to 35% relative to competitive baselines, with the calibration and sharpness of its intervals shown to be properties of the method rather than of site-specific tuning.

Earth Observation regression tasks such as building height, canopy height, and above-ground biomass estimation underpin critical applications in urban planning, forest monitoring, and climate policy, where both accuracy and reliability are critical. Yet most deep learning models yield only deterministic predictions, providing no indication of per-pixel reliability. These regression tasks are inherently challenging due to heterogeneous land surfaces, skewed target distributions, sensor noise, and signal saturation at high target values, making uncertainty (UC) estimation essential for reliable inference. We address this gap by modeling aleatoric uncertainty using year-long Sentinel-1 SAR and Sentinel-2 MSI time series, proposing two complementary approaches: (i) Gaussian UC, which jointly predicts mean and standard deviation under a Gaussian assumption, and (ii) Quantile UC, which estimates the 10th, 50th, and 90th quantiles to capture asymmetric and heteroscedastic error distributions. Both models are evaluated on three representative EO regression tasks at 10 m spatial resolution. Results show that both approaches match or surpass deterministic benchmarks and existing global products, while delivering well-calibrated, interpretable, and operationally useful confidence estimates. Notably, both models outperform the current 10 m state-of-the-art uncertainty-aware model for canopy height estimation. Our implementation will be available at: https://github.com/RituYadav92/EO-Regression-Uncertainty-Estimation

A trained molecular property model can be refined at test time by correcting each prediction with the measured labels of the most similar training molecules, a retraining-free procedure we call neighbor fusion; evidential neural networks make it principled by using their aleatoric and epistemic uncertainty to parameterize a Bayesian update. Our main contribution, PG-EVIKAL, learns a property-distance metric to re-rank structurally similar neighbors by their property relevance before fusion, building on EVIKAL (scalar Kalman filter) and GP-EVIKAL (Gaussian process variant handling correlated neighbors). Evaluated on 16 molecular datasets, PG-EVIKAL reduces RMSE relative to the evidential model baseline on 14 of them, with a median reduction of 19.4%, and improves calibration; in sequential-assay scenarios it further incorporates newly measured molecules, refining predictions as they arrive without retraining. This work demonstrates that evidential uncertainty decomposition is not merely a calibration objective but an actionable inference resource that enables test-time refinement of molecular property predictions.

Reliable forecasting of several interrelated environmental variables - such as regional precipitation and temperature, or other correlated geophysical fields - across many locations calls for accurate predictions accompanied by trustworthy statements of their uncertainty. Modern deep-learning models forecast such variables accurately but usually report no uncertainty, and forcing them to output uncertainty through maximum likelihood tends to degrade their accuracy, especially when the variables are strongly correlated. Motivated by this tension, we develop TSCoNet, a two-stage convolutional-recurrent model coupled with a Gaussian copula that jointly forecasts multiple variables over space and time while quantifying predictive uncertainty. The method first learns accurate mean forecasts and then, holding the mean fixed, refines a shared representation to estimate the predictive variance, yielding calibrated prediction intervals after a standard recalibration, so that uncertainty is added without sacrificing point accuracy. We study the approach on simulated non-stationary spatial fields on the sphere and on a real dataset of monthly precipitation and temperature for fifty cities over 2000-2020. The model matches the accuracy of a strong deterministic forecaster while supplying calibrated prediction intervals that the deterministic model cannot, giving a single tool that provides both accurate point forecasts and reliable uncertainty for multivariate spatio-temporal data.

Predict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose \emph{learned predictive ambiguity sets} (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feeds a DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018--2026. The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

Uncertainty quantification for visual language models (VLMs) conventionally targets the answer token distribution. We provide the first three-family empirical characterisation of answer entropy behaviour in thinking-mode VLMs. Running four models on identical POPE adversarial samples, we find three qualitatively distinct patterns: Qwen3-VL-8B-Thinking shows complete collapse (ans H AUROC = 0.492); GLM-4.1V-9B-Thinking shows no collapse (0.716); and InternVL3-8B shows selective thinking (chains on only 50% of samples, ans H = 0.675 full / 0.602 thinking-only). Across all three thinking-mode models, thinking chain entropy outperforms answer entropy on the subset where chains are generated (0.647, 0.759, 0.608 vs. 0.492, 0.716, 0.602 respectively), suggesting chain signals are the more reliable predictor whenever chains are present. This holds strongly for Qwen and GLM, but with only marginal and statistically unreliable advantage for InternVL3 (n_FP = 17). A 300-sample VQAv2 pilot confirms chain entropy (0.680) outperforms answer entropy (0.595) on VQAv2 questions, with the gap largest for free-form answers (0.733 vs. 0.467). On harder reasoning tasks (HallusionBench) both Qwen models show moderate signal (approx. 0.64), consistent with incomplete pre-commitment on difficult questions. We additionally document structured abstention affecting 12-22% of queries with asymmetry toward absent-object queries, and a practical abstention gate raising accuracy from 71.0% to 93.8% at 62.7% coverage with no additional inference cost.

Large language models (LLMs) are reshaping social science methodology. Researchers increasingly prompt language models to generate quantitative measurements of social concepts, for example labeling data or simulating survey responses. Yet LLMs pose methodological challenges including bias, hallucination, and brittleness across contexts, with unclear threats to validity. Standard practices and norms for addressing these challenges are still emerging. We collect and systematically analyze validation practices in a comprehensive corpus of papers from eight flagship social science journals that use LLMs as measurement instruments. We find that LLM-generated measurements frequently play a central role in empirical analyses, yet validation practices are inconsistent and limited. We outline complementary strategies for more robust validation, pointing toward better norms and standards around the use of LLMs in social science.

Hypergraph neural networks have shown powerful capability in modeling higher-order relations, yet their predictive uncertainty remains underexplored. Unlike pairwise graphs, uncertainty in hypergraphs arises not only from noisy attributes and ambiguous labels, but also from variations in node-hyperedge incidence structures and complex higher-order dependencies. Existing approaches mainly estimate uncertainty from final predictions or rely on computationally expensive ensembles and Bayesian inference, limiting their ability to capture uncertainty evolution during representation learning. In this paper, we propose Hypergraph Neural Stochastic Diffusion(HyperNSD), a stochastic differential equation framework for uncertainty estimation on hypergraphs. HyperNSD models hypergraph representations as stochastic processes evolving over node-hyperedge incidence structures. A learnable drift function captures deterministic higher-order diffusion dynamics, while a learnable stochastic forcing function characterizes structural ambiguity and representation noise. Predictive uncertainty is directly quantified through the variability of stochastic representation trajectories, providing an intrinsic uncertainty measure beyond post-hoc confidence scores. We formulate HyperNSD with neural drift and diffusion networks, enabling joint learning of prediction and uncertainty propagation. Theoretical analyses establish well posedness, perturbation stability,permutation equivariance, and numerical convergence of the proposed stochastic dynamics. Experiments on multiple hypergraph benchmarks demonstrate that HyperNSD achieves reliable uncertainty estimation for out-of-distribution and misclassification detection while preserving competitive prediction accuracy. These results provide a principled stochastic-dynamical framework for trustworthy higher-order representation learning.

We introduce an efficient Bayesian deep ensemble method for predictive regression designed to enhance interpretability while maintaining competitive predictive performance and computational efficiency. Our method combines the statistical rigor of Bayesian inference with the scalability of deep ensembles, providing calibrated uncertainty estimates that enable its use not only for standalone prediction but also as a component within broader learning systems. To achieve these goals, our work relies on three key design components: (i) low-dimensional ensemble representation: predictions are expressed as a combination of a small number of trained neural predictors, enabling scalable inference whose cost depends on ensemble size rather than dataset size; (ii) closed-form Bayesian aggregation: ensemble predictions are combined using Bayesian linear regression, yielding interpretable posterior weights and calibrated uncertainty without approximate inference; and (iii) Independent ensemble training: multiple neural networks are trained separately, producing diverse predictive representations that improve robustness and uncertainty calibration. Empirical results on standard regression benchmarks demonstrate that the proposed approach achieves competitive predictive performance while maintaining reliable uncertainty estimates across settings.

We consider an open-world planning setting in which service robots must operate in unknown environments with incomplete knowledge of objects and actions. Traditional closed-world approaches with pre-programmed knowledge bases fail when robots encounter unexpected situations and tasks, posing a fundamental challenge for autonomous knowledge expansion in human environments. In this work, we propose an open-world planning framework that enables robots to automatically generate, verify, and update hypotheses about their abstract world models. Our key insight is to explicitly maintain uncertainty-aware knowledge expansion and integrate hypothesis verification into goal-reaching planning. The framework leverages foundation models to generate initial hypotheses over states and transitions, and applies automated planning to produce action sequences that jointly address hypothesis verification and task execution. Through iterative execution and refinement, the robot expands its knowledge by incorporating verification feedback from the foundation models when hypotheses prove incorrect. Extensive experiments in simulated and real-world environments demonstrate that our framework enables autonomous knowledge expansion and effective operation in open-world settings. These results indicate that integrating uncertainty-aware model expansion from robot foundation models with planning advances the practical deployment of household service robots.

Self-paced learning (SPL) is an effective learning paradigm that simulates the human learning process by progressing from easy to difficult samples based on the value of the loss function during the learning process. It has shown great potential in improving model performance and training efficiency. However, the prediction results of samples with smaller loss values are not necessarily reliable, indicating that such samples are not always simple samples for the model. Hence, this article proposes an uncertainty-aware self-paced learning based on evidential neural networks, termed UASPL, which integrates predictive reliability into sample selection through a general loss function within the Subjective Logic framework. This loss function incorporates uncertainty estimation and can be extended to different variants of SPL. Moreover, this loss function couples a sample selection preference, thereby ensuring the interpretability of the sample selection process. Finally, the experimental results on multiple datasets show that UASPL outperforms other SPL methods in terms of classification performance, interpretability, and generality. The source code is available at: https://github.com/treelife979/UASPL.

Uncertainty estimation (UE) enables LLM-powered systems to recognize when to abstain, yet existing research has predominantly focused on English. We present the first large-scale evaluation of UE methods across 22 languages, spanning high-, mid-, and low-resource settings. Using two human-curated Q&A datasets, we compare open and closed box UE methods (nine in total) across different model sizes and architectures while eliciting long-form reasoning, avoiding LLM-as-a-judge and embedding-based scoring, which can introduce evaluation noise. We report three main actionable findings. First, we find that prompting models to reason in English while keeping questions in low-resource languages substantially improves UE performance, suggesting that comprehension of low-resource languages is largely intact, and that the reliability bottleneck lies in generation rather than understanding. Second, prompting models to reason in English closes the UE performance gap between low and high-resource languages, demonstrating that generation language matters more than the question language. Third, the choice of UE method should depend on model scale: at smaller scales, open-box probability-based methods outperform alternatives; at larger scales, closed-box self-verbalized uncertainty becomes superior. Finally, we provide an analysis of threshold selection for selective prediction, offering guidance on calibrating abstention in multilingual settings.

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.

Uncertainty estimation is essential not only for the trustworthy deployment of large language models (LLMs) but also as a foundation for self-refinement in LLM generation. However, existing approaches operate at suboptimal granularities: token-level scores lack semantic coherence, while sequence-level scores fail to localize errors. We formalize Span-Level Uncertainty Estimation (SLUE), a new task that targets the natural granularity for uncertainty: semantically coherent text spans, each conveying a single assessable unit of meaning. To address this task, we introduce SPANUQ, a lightweight probe that distills the uncertainty knowledge from expensive multi-sample inference into a single forward pass over LLM hidden states. SPANUQ employs a DETR-style span decoder to simultaneously detect spans and estimate their uncertainty via a Mixture of Beta distribution, trained with a principled combination of Beta NLL regression and contrastive ranking objectives. We construct SPANUQ-BENCH, the first span-level uncertainty benchmark comprising 20K prompts, 293K annotated spans, and continuous soft labels derived from multi-sample claim verification. Experiments on five LLM backbones show that SPANUQ consistently achieves the best span-level uncertainty quality, outperforming the strongest probe baseline and all sampling-based methods while being 10-20x faster. Its DETR-based span detector attains 0.910 F1, surpassing the best heuristic by 39.4%, enabling precise error localization that sequence-level methods cannot provide. The framework generalizes across five LLMs spanning two model families.

3D Gaussian splatting (3DGS) is a strong representation for real-time novel-view synthesis, but its standard training pipeline relies on point estimates and hand-tuned heuristics, providing no native uncertainty or principled complexity control. This is most limiting under sparse views or fixed acquisition budgets, where a model must identify weakly supported geometry and select informative views. We introduce a rendering-aware Bayesian 3DGS framework that tracks Gaussian geometry with a Normal-Inverse-Wishart posterior over means and covariances using renderer-derived surrogate summaries. An optional Dirichlet-process extension adds a probabilistic component-usage signal, and the training schedule makes the closed-form versus approximate inference boundary explicit. Re-rendering posterior geometry samples yields native predictive uncertainty for interval calibration and active view selection. In a fixed-budget 16-to-32 active-view task, native NIW acquisition improves PSNR by +0.453 dB and LPIPS by -0.0146 over a scoring-only 3-member standard-ensemble baseline, winning 29/39 scene-seed pairs and 10/13 scene means; it also improves over PPU-style (+0.355 dB) and NIW-proxy (+0.401 dB) acquisition. NIW native intervals reduce 95% coverage error by about 17x relative to a shared proxy (0.046 vs. 0.796) and are about 10x closer to nominal coverage than a 3-member deep ensemble (0.047 vs. 0.454) at roughly one-third the training cost. As a reconstruction compatibility check, paired NIW-vs-standard analysis over 39 scene-seed runs yields +0.030 dB PSNR with 1.6% additional training time. These results position Bayesian 3DGS as a practical probabilistic scene representation for decision-facing tasks such as active view selection.

Vibration-based damage identification in civil infrastructure is a challenging, ill-posed inverse problem due to measurement noise, sparse sensor arrays, and environmental variability. While deep learning is powerful for system identification, deterministic approaches lack reliable uncertainty quantification and can yield physically inconsistent results. This work proposes a robust probabilistic Scientific Machine Learning (SciML) framework: a physics-informed Gaussian copula variational autoencoder (PI-GCVAE) for structural health monitoring (SHM). First, we eliminate the need for data-driven surrogates by embedding a differentiable numerical eigenvalue solver directly into the VAE architecture. This ensures that latent space samples satisfy the governing equations of structural dynamics, reducing the trainable parameter space and improving generalization. Second, we replace the conventional independence assumption of latent variables with a Gaussian copula. This model captures complex, physics-dependent spatial cross-correlations between adjacent structural elements, defining feasible solutions while accounting for inherent system variability and measurement errors. Third, compared with alternatives such as Gaussian mixtures, our copula-based VAE provides an efficient distributional model for high-dimensional, strongly correlated latent spaces. We validate the approach using a synthetic dataset of a simply supported bridge subjected to various damage scenarios and corrupted with stochastic Gaussian noise. Synthetic data enables exhaustive validation against ground-truth stiffness values unavailable in practice. Results demonstrate that the PI-GCVAE accurately recovers the true posterior distribution, achieving 77.2% coverage. The proposed framework provides a reliable, scalable tool for early-stage damage diagnosis in operating bridges.

Active learning is a promising framework for reducing annotation costs in large-scale bioacoustic monitoring, where expert labeling is expensive and data distributions are highly heterogeneous across environments. However, existing sample selection strategies often rely on static criteria that do not adapt to the evolving reliability of model predictions during training. This limitation can lead to suboptimal exploration-exploitation trade-offs and redundant sample selection. We propose an active learning strategy for multilabel bioacoustic event classification that jointly models predictive uncertainty, embedding-space diversity, and intra-batch redundancy. The method introduces an adaptive weighting scheme that progressively shifts from diversity-driven exploration in high-uncertainty regimes toward uncertainty-driven exploitation as the model becomes more confident, reflecting the increasing reliability of the classifier. To further improve annotation efficiency, a greedy Maximum Marginal Relevance (MMR) procedure is used to enforce diversity among selected samples within each acquisition batch. We evaluate the proposed approach within the BioDCASE 2026 Task 4 active learning framework on terrestrial (BirdSet) and marine (ATBFL) benchmarks using pretrained audio embeddings and a fixed annotation budget. Experimental results show consistent improvements in learning efficiency and competitive in terms of macro mean Average Precision (mAP) and Area Under the Learning Curve (AULC) across heterogeneous acoustic domains. The gains are particularly pronounced on structured terrestrial soundscapes, while performance remains competitive under noisier marine conditions. These findings demonstrate that adaptive acquisition strategies combining uncertainty estimation, embedding-space diversity, and redundancy-aware batch construction provide an effective and robust solution for [...].

Uncertainty quantification of hydrological predictions is necessary to inform operational decisions. Recent generative machine-learning methods have advanced probabilistic streamflow prediction, but have remained confined to lumped models that predict a basin outlet directly. At the same time, deterministic LSTM runoff models are increasingly applied at grid or catchment scale and routed through river networks to produce spatially continuous, physically consistent discharge fields. This technical note argues that moving probabilistic prediction from lumped to distributed models introduces a specific new requirement: the joint distribution of upstream runoff generation must be sampled jointly. In lumped inference, the model predicts the outlet distribution directly and can modulate spread from basin attributes. In distributed inference, downstream discharge is obtained by routing many upstream runoff predictions, so independent local sampling averages uncertainty away. Using Japan as a case study, we train two probabilistic basin-scale runoff LSTMs and route their runoff through a Hayami routing scheme. Randomly matching upstream ensemble members produces severely under-dispersed downstream ensembles, whereas a simple quantile matching strategy restores much of the spread of the direct basin-scale reference. The shift from lumped to distributed probabilistic hydrology therefore requires explicit attention to the spatial joint structure of runoff uncertainty.

In the age of AI, what will be good knowledge? This article, which is accepted and forthcoming in a special issue of Modern Fiction Studies on "Cultural AI" in 2027, applies digital humanities methods to map epistemic virtues (like "true," "accurate," "creative") used in a corpus of 553 journal articles on AI published in 2024. "Creativity" comes in for special attention as an example. Exploring this discourse of value, the article considers how a framework might be developed for evaluating the knowledge-worth of AI -- one less locked into values formed around pre-AI "knowledge work" agents or structures, and more open to the future values of "generativity." The essay is supported by an online digital kit for exploring data models of the corpus of articles on AI it studies.

Certified world models estimate how long their predictions remain valid. We turn this validity horizon into an operational sensing clock: a rule for when an agent should stop coasting and re-sense. Starting from an audited equivariant world model, we derive a deadline for no-sensing intervals and show that deployable deadlines in learned world models must be drift-aware: on-manifold Lyapunov rates alone overestimate coasting validity, while calibrated native rollout-drift envelopes carry the deployed guarantee. On a frozen 3D VN-JEPA model, the resulting clock controls held-out interval-simultaneous certificate violation across seeds and data shards. In a cue-conditioned theorem-bed (a synthetic bench where all schedulers share the exact model, isolating the scheduling rule), the clock remains valid on the deployment distribution and substantially reduces eventful-tail violations relative to exact-mixture expected-belief scheduling at matched sensing budget. We also report limits: in the short-horizon frozen VN-JEPA regime, empirical conformal horizons match the deployed clock on validity and budget, and a partial-reset exploration finds no clean budget-matched advantage for the spectral term. Thus the contribution is a certified sensing-clock primitive and drift-aware deployment method, not a claim that spectral clocks empirically dominate all non-spectral schedulers.

Safe motion planning in dynamic environments requires reasoning about the uncertainty in predicted obstacle motion without sacrificing real-time performance. Existing conformal approaches conformalize a scalar score that aggregates per-obstacle prediction errors, losing spatial coherence and scaling poorly with scene density. We instead conformalize the entire predicted distance field at once. This functional conformal prediction (FCP) framework yields a distribution-free, field-level lower bound, from which safety follows uniformly: any trajectory satisfying the resulting constraint is certified safe, independent of how the control space is sampled. The key enabler is that the residual distance field is empirically low-rank and approximately time-invariant, which makes the bound decomposable in coefficient space. An envelope is fitted offline via functional PCA and a Gaussian-mixture inductive conformal procedure, then refined online by a lightweight adaptive functional conformal (AFCP) update on a low-dimensional vector. This keeps the per-step cost largely insensitive to obstacle count and retains long-run field coverage under distribution shift. We embed the envelope as a tightened safety constraint in a sampling-based model predictive controller, FCP-MPC. On the ETH--UCY pedestrian benchmarks and a dense 3D quadrotor task with up to 280 dynamic obstacles, FCP-MPC attains a favorable balance of safety, feasibility, and efficiency, reaching goals where pointwise and egocentric conformal baselines become too conservative or too expensive, while keeping per-step computation far below online uncertainty-reasoning baselines.

Table extraction from business documents relies on a cascaded pipeline where Table Detection (TD) first localizes tables and Table Structure Recognition (TSR) then recovers their internal layout. Building task-specific training sets for this pipeline is costly, particularly for TSR which requires fine-grained structural annotations. Active learning (AL) can reduce this annotation burden, yet most AL strategies are designed for single-model tasks and do not account for inter-stage dependencies in cascaded architectures. In this work, we present the first adaptation of Uncertainty Herding (UHerding), a hybrid coverage-uncertainty sampling method originally proposed for image classification, to cascaded object detection pipelines. We propose two pipeline-aware extensions that exploit the TD-to-TSR dependency: RankFusion adds dual-manifold coverage over both detection and structure representation spaces, while CAPA further incorporates stage-dependent gating and per-task uncertainty calibration. Extensive experiments across two public (PubTables-1M and FinTabNet) and two private table extraction datasets, with various annotation budgets (from 71 to 500 documents) show that UHerding generalizes well to table extraction, outperforming each baseline. Among pipeline-aware variants, RankFusion achieves higher expected gains but at the cost of greater variance, while CAPA emerges as the most consistent strategy, outperforming standard UHerding on three out of four datasets.