Reliable Uncertainty Quantification

Language models increasingly act as epistemic proxies, synthesizing evidence from multiple sources to inform decisions. Whether they evaluate the quality of that evidence, or merely aggregate it based on surface presentation, remains poorly understood. We show that models possess the capability to detect fabricated statistics in isolation but do not recruit this capability during multi-source synthesis, producing similar numeric estimates whether the statistics are fabricated or valid. Specifically, source influence is governed by a methodology-register gate that responds to the distributional register of analytical text but not to numeric validity: for example, statistically impossible confidence intervals receive the same weight as valid ones. The behavioral dissociation replicates across six models from four families (Anthropic Claude, Qwen, OLMo, and OpenAI GPT-5.4) and three professional domains. Mechanistic analyses, including causal tracing, linear probes, and component-level attribution, converge on the same account: the model encodes and causally uses a methodology-register representation that transfers across domains, while numeric-validity signals, decodable in isolation, are suppressed to chance during multi-source synthesis. Prompting-based mitigations, even an oracle checklist naming the exact statistical checks, produce blanket skepticism rather than selective discernment, and the post-training pipelines we examine reinforce the shortcut without building numeric verification. Unlike sycophancy, which tracks user preference, this failure tracks whether a source presents as analytically credible, not whether its claims are consistent. We term this \textit{epistemic alignment}: like preference and safety alignment, the question is not capability but deployment.

Returned products in circular factories re-enter production with heterogeneous degradation states, usage histories, and remaining capability. Reuse cannot be decided from the current inspection alone, because future function fulfillment and component integrity may evolve differently under the next service scenario. Existing PHM approaches support degradation prediction, but often target fixed operating conditions or isolated component benchmarks, while material-fatigue assessment is rarely linked to system-level functional prognosis. This paper addresses this gap for an angle grinder by combining uncertainty-aware functional prediction with component-level fatigue assessment in an instance-specific reliability workflow. The proposed framework combines the current tool state with recent force--torque usage windows. A convolutional encoder extracts loading patterns from spindle forces and shaft torque, and an LSTM backbone predicts nine functional variables as Gaussian mean and variance estimates. In parallel, the same loading history is translated into output-shaft fatigue information through finite-element-supported stress reconstruction, S--N/Miner damage evaluation with Haibach extension, and Paris-law crack-growth analysis. A streaming replay algorithm consolidates both branches into functional, material, and system reliability trajectories. Held-out tests show mean $2\%$-tolerance accuracy of 0.9652 across nine outputs. Thermal variables are predicted near-perfectly, while drive motor current and load speed remain the most demanding dynamic outputs, with $R^2$ values of 0.9750 and 0.9924. Torque history is especially important for these variables, and the conventional LSTM outperforms GRU and xLSTM in the short-history setting. Reliability calibration is most informative for drive motor current, where predicted and observed exceedance probabilities ...

Designing a neural network processor is an end-to-end co-design problem: network architecture and training budget determine the inference workload; hardware mapping decisions determine chip area, latency, and energy; and these characteristics govern fabrication yield and manufacturing cost. In practice, these decisions are made in separate stages, and existing co-design methodologies are tightly coupled to specific algorithms, making it difficult to improve one component without reworking the entire pipeline. This paper presents a unified framework, grounded in monotone co-design theory, that composes four interoperable design blocks spanning network training, chip mapping, wafer-level fabrication, and compute resource allocation. Each block exposes only a functionality-resource interface to the rest of the system, so any block can be refined without structural changes elsewhere. A central contribution is the treatment of uncertainty: rather than collapsing stochastic outcomes into point estimates, the framework introduces Confidence, the inverse of success probability, as an explicit and optimizable resource alongside cost, time, and power. Three case studies validate the approach. The first recovers Pareto-optimal implementations across heterogeneous application scenarios. The second confirms that Confidence functions as a continuously tunable design knob rather than a post-hoc diagnostic. The third demonstrates that improving a single block's implementation set automatically propagates to the global Pareto front, without modifying the co-design diagram.

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

Multi-step time series forecasting (MSF) is commonly evaluated using point-wise error metrics such as mean squared error (MSE), implicitly treating the conditional mean as a sufficient target. We show that this can be misleading under conditional uncertainty, where the conditional expectation becomes unrepresentative of typical realized values at longer horizons. We formalize this effect through a conditional uncertainty gap and prove that whenever this gap is nonzero, no deterministic predictor can simultaneously minimize MSE and match the marginal distribution of realized futures. This establishes a fundamental, model-agnostic trade-off between point accuracy and marginal realism in MSF evaluation. Using controlled stochastic dynamical systems and nine real-world forecasting benchmarks, we empirically characterize the resulting accuracy--realism frontier and \textbf{quantify the practical cost of MSE-only model selection}. As conditional uncertainty increases with forecast horizon, the attainable set expands into a pronounced Pareto front, separating MSE-optimal but under-dispersed predictors from methods that trade accuracy for realistic marginal variability. \textbf{Across benchmarks, we find that small relaxations in MSE ($\boldsymbol{\le 5\%}$) frequently unlock disproportionate gains in marginal realism, with median improvements of $\mathbf{17.3\%}$ and gains exceeding $\mathbf{30\%}$ in some datasets.} We further show that common forecasting strategies systematically occupy different regions of this frontier: direct multi-output predictors concentrate near the accuracy-optimal extreme, while recursive strategies and sample-based inference favors marginal realism. Together, these results expose a structural failure mode of MSE-based evaluation in long-horizon forecasting and recast strategy and inference selection as navigation of an unavoidable accuracy--realism trade-off.

Data samples used for training often differ from those encountered during fine-tuning and deployment, and while ML models show promise, their performance remains limited when only small annotated datasets are available. Performance often degrades under distribution shifts caused by diverse sensors, populations, and application settings. Although pre-training helps, models frequently encounter out-of-distribution (OOD) data in real-world settings, leading to reduced robustness. Existing adaptation methods usually assume fixed distribution shifts and struggle when multiple types or severities occur. In particular, they overlook shift severity, for example treating adaptation to a large familiar dataset the same as adaptation to a small dataset with a new task, which limits generalisation. To address this, we propose ADAPTOOD, a novel framework that leverages data uncertainty to quantify distribution shift severity and guide fine-tuning for time series. This uncertainty measures how strongly samples from the target deployment distribution deviate from the pre-training distribution, providing a direct signal of OOD severity. Our framework combines this uncertainty with low-rank model updates and adaptive hyperparameter optimisation to improve adaptation. We show that ADAPTOOD achieves up to 7% higher accuracy and 12.9% higher precision than existing methods in OOD tasks, maintaining strong performance as distribution shift severity increases.

Modeling temporal evolution is important to analyzing and reasoning about scientific phenomena, yet most machine learning methods provide deterministic forward predictions that overlook multiple plausible outcomes and rarely support backward reasoning, limiting their usefulness in practical scientific workflows. We present a framework that integrates diffusion-based generative modeling with interactive visual analytics for scientific exploration. We introduce DiffUNet^2, a conditional diffusion model that enables bidirectional, any-to-any generation across time and captures distributions of plausible system evolutions. Built upon the model, our interactive system supports branching timeline exploration, user-guided state editing, and probability-space navigation, enabling scientists to actively explore alternative hypotheses rather than passively observe predictions. We evaluate the model on 5 datasets across different scientific domains to validate its predictive accuracy and probability-space ensemble quality. In collaboration with domain experts, we demonstrate the effectiveness of our approach in supporting practical scientific temporal data analysis workflows. By integrating modeling and visual interaction, our approach enables scientists to interactively explore system dynamics, transforming generative models into tools for hypothesis-driven scientific analysis.

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2α$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-α$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.

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

Complex, dynamic, and interactive driving environments pose significant challenges for autonomous driving, primarily due to the pervasive uncertainty of surrounding traffic. A fundamental bottleneck in current systems is the disconnect between highly expressive uncertainty modeling and interpretable, safe motion planning. In this paper, we propose a novel sample-conditioned differentiable planning framework that bridges this gap by explicitly incorporating diffusion-generated future trajectories into the optimization process. Rather than compressing predictions into a single deterministic future or relying on black-box end-to-end architectures, our approach leverages a conditional diffusion model to generate a diverse set of plausible future scenarios. Crucially, these samples are directly fed into a differentiable planner, which explicitly mitigates predictive uncertainty via an empirical Conditional Value-at-Risk (CVaR) tail-risk constraint. This allows the planner to optimize a physically interpretable trajectory that is robust to rare yet safety-critical interactions. Furthermore, we introduce a directed graph representation for scene context that yields substantial improvements in both predictive effectiveness and computational efficiency. Validated through extensive open-loop and closed-loop evaluations on the Waymo Open Motion and Argoverse 2 datasets, our framework significantly outperforms state-of-the-art baselines in safety, efficiency, and ride comfort.

Extracting reporting obligations from EU legislation is critical for assessing and reducing regulatory reporting burden. However, distinguishing reporting requirements from structurally similar provisions requires specialised legal understanding. Current legal NLP methods lack specialised datasets with clear guidelines and comparative evaluation of extraction paradigms and domain adaptation strategies. We curate EURO-5K, a corpus of sentence-level reporting obligations and challenging negative examples from 136 EU legislative acts. On this dataset, we train and compare discriminative token-classification models (BERT-style) and generative span-extraction models (LLMs), evaluating both full fine-tuning and parameter-efficient QLoRA against baselines (pattern and dependency-based extraction, few-shot prompting). Results show that fully fine-tuned generic and legal BERT models achieve similar performance (0.89 F1), while fine-tuned LLMs match encoder accuracy for sentence-level extraction. Legal pretraining offers only small gains for generative models. In contrast, it is clearly beneficial when adaptation capacity is constrained, as parameter-efficient tuning of Legal-BERT outperforms its generic counterpart. Learning curve analysis demonstrates that legal pretraining accelerates early learning with minimal data. All approaches converge around 3K samples with diminishing returns thereafter, validating dataset sufficiency. Cross-dataset evaluation on two external regulatory corpora shows that our models behave as specialised reporting obligation extractors rather than generic regulatory classifiers. We release EURO-5K, trained models, and an interactive demo with explainability visualizations and structured RDF export. These demonstrate that both paradigms and parameter-efficient training provide practical tools for regulatory compliance automation.

Current research primarily focuses on model performance, while comparatively less attention has been devoted to uncertainty estimation, particularly in settings where LLMs are increasingly used to generate annotated data. We introduce a framework combining conformal prediction with Collaborative Filtering-style annotators' representation to model LLM behavior in relation to human annotators and to analyze patterns of agreement and disagreement. Using Non-Conformity Scores, we introduce the Ghost Prediction metric and the Ghost Annotator representation to quantify cases in which model predictions diverge from all available human annotations. We compute cosine similarity measures to explore differences in model behavior across sociodemographic axes. We evaluated four LLMs of different size and families across four content moderation datasets. Our finding shows that while we find that all models uncertainty increases with annotator disagreement, larger models tend to be more confident in the classification of texts that are not aligned with any human annotation. Finally, the Ghost Annotator framework reveals a consistent and robust pattern of demographic misalignment, suggesting a structural bias likely rooted in pretraining corpora.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation ($k \leq 10$), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37% sharper prediction intervals at 90% coverage, and uniquely produces \emph{adaptive} intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the conditional mean and conditional volatility. At the inference stage, it generates predictive distributions by resampling normalized residuals. ProbRes is applicable to both univariate and multivariate time series and remains robust under a wide range of error distributions, including non-Gaussian innovations with conditional heteroskedasticity. Theoretical results demonstrate ProbRes's validity and experiments on both synthetic and real-world datasets show that ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.

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

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

We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose DistMatch, a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov-Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

Energy consumption prediction is essential for efficient grid management, demand-side optimization, and sustainable energy planning. Although advanced machine learning methods have been employed for better prediction performance, existing works have two key limitations: (1) they usually formulate this task as a purely time-series prediction problem without explicitly modeling the spatial dependencies among different regions, and (2) they fail to provide reliable predictions with uncertainty estimates under abnormal situations such as extreme weather events. To advance existing research, we propose EnergyMamba, an uncertainty-aware spatiotemporal learning framework for accurate and reliable energy consumption prediction, which comprises two key components: (i) a novel Graph-Enhanced Selective State Space Model (GE-Mamba) that injects spatial context learned from the grid topology into the temporal dynamics, enabling coupled spatiotemporal modeling, and (ii) an Adaptive Sequential Conformalized Quantile Regression (AS-CQR) module, which includes locally adaptive normalization and an online feedback mechanism to dynamically calibrate prediction intervals under potential distribution shifts. We evaluate EnergyMamba on four large-scale real-world datasets from Florida, New York, and California. Results show EnergyMamba achieves around 5% improvement in prediction accuracy and 6% improvement in uncertainty quantification over 15 state-of-the-art baselines.

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

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

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

Nonlinear conservation laws are at the heart of many of the most important dynamical systems in science and engineering. In practical applications, such systems are often subject to various sources of uncertainty, e.g. due to sparse or noisy measurements. Inferring physical quantities and fields of interest then becomes an ill-posed problem which both classical numerical methods and modern deep learning-based methods struggle to treat appropriately. Recent work has framed classical numerical methods as Bayesian inference under Gaussian process priors, resulting in a physics-aware treatment of uncertainties. Following this line of work, we develop a novel numerically conservative method for uncertainty-aware simulations of nonlinear conservation laws. We use recent sparse approximation techniques to scale up to large-scale forward and inverse problems. For forward simulation, we inherit the accuracy of classical solvers while providing structured uncertainty quantification. On inverse problems, we recover posteriors over nonparametric source fields in seconds -- outperforming neural baselines that take minutes to produce a less accurate point estimate.

Public consultations generate large volumes of data in the form of stakeholder submissions that are practically unfeasible to analyse manually. We present an end-to-end LLM-based pipeline and interactive dashboard for structured topic extraction from regulatory consultation submissions, demonstrated on the European Commission's Digital Fairness Act (DFA) public call for evidence as a case study. The system processes raw PDF attachments and web-form responses, extracts topic annotations, and grounds every extraction in a verbatim quote from the source text. Applied to 4,322 DFA submissions, the pipeline produced 15,368 topic annotations supported by 20,951 verbatim evidence quotes. Three principles govern the proposed design: verbatim grounding, full traceability, and transparency by design. The dashboard exposes the full extraction dataset through five analytical views, from dataset-level topic overviews to individual paragraph drill-downs, with every result traceable to its source. Beyond the predefined DFA topic categories, the pipeline generated certain stakeholder concerns, such as Age Verification, Payment Processor Censorship, and Digital Ownership, that a fixed-taxonomy approach would have missed. The pipeline is domain-generic; adapting it to a new consultation requires only a prompt update and a new dataset. A live demo is available at https://dfa-dashboard.thalesbertaglia.com/. The code and processed data are publicly available at https://github.com/thalesbertaglia/dfa-dashboard.

Epistemic uncertainty quantification (UQ) for deep neural networks (DNNs) is a requirement for safe adoption of AI in mission-critical settings. Several leading methods for UQ linearize DNNs to form Bayesian Generalized Linear Models (GLMs), where epistemic uncertainty is modeled via the predictive posterior distribution. Linearizing around the parameters of the final connected layer of a DNN is a commonly used approximation for reducing the computational burden of such GLMs, though it is often believed to come at the cost of degraded performance. In this work, we compare GLMs arising from full-network and last-layer linearization using both theoretical and empirical approaches. We first employ tools from random matrix theory to conduct a theoretical comparison; this analysis reveals no meaningful improvement in the UQ capabilities of full linearization. Coupled with a large-scale empirical evaluation across a range of modern machine learning tasks, we arrive at the following conclusion: a last-layer approximation yields comparable UQ performance while offering substantially improved computational efficiency.

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Engine Health Management (EHM) depends on reliable forecasting of Remaining Useful Life (RUL) and on tracking thermal indicators such as turbine gas temperature (TGT). In practice, real-world fleet data are heterogeneous and non-stationary, and point predictions alone are insufficient for risk-aware maintenance decisions. This paper presents a multi-task scientific machine learning framework for turbine prognostics that jointly predicts turbine gas temperature untrimmed (TGTU), Delta Turbine Gas Temperature (DTGT), and RUL, with quantified uncertainty in the form of prediction intervals whose empirical coverage is evaluated. A shared sequence encoder (convolutional front-end with residual bidirectional LSTM layers and attention pooling) feeds task-specific heads, including mean--variance estimation for probabilistic regression and, optionally, a survival head for threshold-based event modeling. The framework is designed to be tunable via a small set of practitioner-facing parameters (e.g., DTGT thresholding rules and RUL target construction) so that deployment can align with in-house policies and proprietary criteria. The predictive performance of the proposed framework is evaluated using both point and interval metrics, including mean absolute error (MAE), prediction interval coverage probability (PICP), mean prediction interval width (MPIW), and the coverage--width criterion (CWC). Results are reported both in aggregate and stratified by flight phase and maintenance segment to highlight operational-context effects and to support uncertainty-aware monitoring.

Effective prognostics and health management of modern engines relies on accurate turbine gas temperature predictions and robust uncertainty quantification to ensure reliability and safety. This paper investigates five major approaches for constructing prediction intervals -- namely the Delta method, Bayesian Monte Carlo Dropout, Bootstrap method, Lower-Upper Bound Estimation, and Mean-Variance Estimation -- as a means of capturing the uncertainty in neural network predictions of turbine gas temperature. Each approach is implemented within a unified experimental framework that employs cross-validation for hyperparameter selection, repeated train-test splits for performance robustness, and multiple metrics to evaluate both the accuracy and tightness of the intervals. In particular, Coverage Probability, Normalized Mean Prediction Interval Width, and the Coverage Width-based Criterion are measured to comprehensively assess each method's reliability and sharpness. Experiments conducted on a representative turbine gas temperature dataset reveal distinct trade-offs among the five methods in terms of interval coverage, width, and stability. These findings provide a practical guide for selecting and tuning prediction interval methods in engine health management and prognostics, ensuring both interpretability and precision in real-world applications.

Offline reinforcement learning requires careful conservatism to mitigate distribution shift, yet most existing methods apply a fixed penalty uniformly across all states regardless of local data coverage. We present UNIQ (Uncertainty-Informed Quantile), an offline RL method that introduces state-adaptive conservatism through conformally calibrated uncertainty estimation. Built on the Implicit Q-Learning (IQL) backbone, UNIQ trains a multi-expectile value ensemble, computes distribution-free uncertainty estimates using split conformal prediction, and maps the resulting signal to a state-dependent expectile that relaxes conservatism in well-covered regions while strengthening it in uncertain regions near the data frontier. On D4RL MuJoCo benchmarks, UNIQ consistently improves over IQL, with the largest gains observed on Walker2d and replay-heavy tasks. At the same time, UNIQ operates at near-IQL memory cost (approximately 250 MB peak VRAM), providing roughly a 10x reduction compared to EDAC. Rather than pursuing overall state-of-the-art performance, we position UNIQ as a practical mechanism contribution that improves the performance-efficiency trade-off in offline reinforcement learning.

Human reasoning has long been theorised to operate socially, not through isolated individual cognition, but through collective adversarial discourse, a framework known as the Argumentative Theory of Reasoning (ATR). Rather than relying on individual "intellectualist reasoners" as the primary vehicle for truth-seeking, ATR reconceptualises truth as an emergent property of social epistemology: the product of imperfect individual reasoning refined under the adversarial pressure of debate. This distributed method of collective intelligence has guided humanity to ever-greater epistemic heights and underpins the foundational principles of all democratic systems. This thesis breaks new ground by, for the first time, simulating ATR through the multi-agent debate (MAD) of large language models (LLMs). With rigorous empirical analysis, we demonstrate that, when correctly engineering an epistemically diverse set of models, LLM-MAD can significantly improve truth-seeking performance on questionnaire-based tasks, even when individual debate participants exhibit limited standalone performance. Furthermore, we present strong empirical evidence that this performance gain is mechanistically grounded in the central principles of ATR, suggesting that collective reasoning may be universally favourable over individualist reasoning, rather than a quirk in biology or evolution. Finally, drawing on our analysis of debate dynamics, we propose a novel benchmarking methodology that leverages LLM-MAD to measure intrinsic model properties (such as hallucination propensity) in order to compare models in ways that current static benchmarking approaches cannot support.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

Irregular multivariate time series forecasting is critical in many real-world applications, where time series are irregularly sampled and exhibit dynamically evolving missingness patterns. Although existing methods perform well in offline settings, they often suffer from significant performance degradation when deployed online due to dynamic shifts in data distribution. Maintaining forecasting capability in such dynamic scenarios typically necessitates online adaptation techniques. Since irregular sampling fundamentally undermines temporal continuity and periodicity, we cannot leverage these widely studied characteristics from regular MTS for online learning. To this end, we study the problem of online IMTS forecasting and propose Under-Cali, an uncertainty-driven dual-expert calibration framework consisting of three core components: an uncertainty estimator, a dual-expert calibration module, and an adaptive routing module. We design an uncertainty estimator that serves as the core control signal to jointly manage inference and adaptation processes. In our framework, the uncertainty estimator first assesses uncertainty for each incoming batch. The adaptive routing module then directs samples with high uncertainty to the unreliable expert for calibration, while low uncertainty samples remain with the reliable expert. Subsequently, the system updates the reliable expert and the uncertainty estimator using well-calibrated reliable samples, and updates the unreliable expert with challenging samples, enabling stable and efficient online learning. Under-Cali keeps the source forecasting model frozen and performs adaptation only through a lightweight, model-agnostic calibration module, enabling efficient adaptation. Extensive experiments on IMTS benchmarks demonstrate consistent improvements with low computational cost. Our code is available at https://github.com/HaonanWen/Under-Cali.

Chance-constrained Model Predictive Path Integral (MPPI) control is increasingly adopted for navigation in dynamic environments to explicitly bound collision risk. However, these probabilistic guarantees implicitly assume that upstream uncertainties from localization and perception are well-calibrated. In practice, estimators are often miscalibrated, inducing characteristic closed-loop failure modes: overconfidence leads to systematic safety violations, while underconfidence triggers overly conservative freezing or probability dilution. To address this critical gap, our primary contribution is a rigorous evaluation methodology applying proper scoring rules to assess the statistical validity of predicted collision risks during closed-loop execution. Concurrently, Dual-Uncertainty Chance-Constrained Tube MPPI (DUCCT-MPPI) is proposed as a real-time, risk-aware planning architecture. DUCCT-MPPI jointly integrates localization uncertainty via a one-tube Unscented Transform (UT) approximation and dynamic obstacle prediction uncertainty via Monte Carlo aggregation. Through extensive physics-based simulations, the framework demonstrates robust failure-mitigation, seamlessly transitioning to safe, conservative maneuvering without succumbing to functional deadlocks in highly cluttered environments. In highly cluttered environments, DUCCT-MPPI achieves superior robustness, outperforming established Monte Carlo MPPI baselines by nearly 28% in navigation success rate, while simultaneously recording the lowest travel times and minimizing induced social forces. Ultimately, these findings establish that reliable probabilistic safety in autonomous navigation dictates not only expressive risk models but statistically valid uncertainty estimates throughout the entire autonomy stack.

In safety-critical robotics applications, guaranteed and practical uncertainty quantification (UQ) in perception is vital. Many existing works either offer no formal containment guarantee, rely on restrictive modeling assumptions, or focus only on pose estimation rather than a complete SLAM pipeline. This paper presents provably guaranteed UQ algorithms for 3D-3D landmark-based SLAM. The algorithms consist of three basic UQ modules: forward UQ for mapping, backward UQ for pose tracking, and pose compound. Each module produces a certified uncertainty set; when the input uncertainty bounds are deterministic, the output sets inherit deterministic guarantees, i.e., they provably contain the true poses and landmarks. Specifically, we use polytopes to represent uncertainty sets, enabling tractable computations and a unified treatment of pose uncertainty. To enhance algorithms' practical usability, we incorporate conformal prediction to calibrate measurement uncertainty from data with prescribed probability. Simulations and experiments demonstrate that the proposed algorithms provide both strong theoretical guarantees and practical usability. The code is open-sourced at https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification.

As large language models (LLMs) are increasingly integrated into high-stakes decision-making, the ability to reliably quantify uncertainty has become a critical requirement for safety and trust. However, current uncertainty quantification methods primarily operate at the output level, often failing to distinguish whether uncertainty arises from the model's lack of knowledge or from ambiguity in the user's input. While input-centric uncertainty quantification has recently emerged as a promising direction, it remains relatively underexplored and typically relies on coarse, input-level information. Consequently, users are provided with scalar uncertainty scores that offer little actionable guidance on which parts of the input should be clarified to improve reliability. To address this limitation, we propose Shapley-based input uncertainty Quantification (ShaQ), a framework for span-level attribution of input-induced uncertainty. Our approach models ambiguous spans in the input as players in a cooperative game and quantifies their contributions using Shapley values, defined via the weighted average of marginal reductions in conditional entropy obtained by clarifying each span coalition. Unlike existing input-level approaches, our formulation captures complex interactions among spans and provides a principled decomposition in which individual attributions sum exactly to the total input-induced uncertainty. We evaluate ShaQ on the AmbigQA and AmbiEnt benchmarks, where it achieves state-of-the-art performance in ambiguity detection. We further demonstrate its utility on MediTOD, showing that ShaQ can localize under-specified clinical utterances and facilitate human-AI collaboration in high-stakes settings. Overall, ShaQ improves uncertainty estimation and provides actionable insights for targeted input clarification.

Knowledge distillation is a powerful method for model compression, enabling the efficient deployment of complex deep learning models (teachers), including large language models. However, its underlying statistical mechanisms remain unclear, and uncertainty evaluation is often overlooked, especially in real-world scenarios requiring diverse teacher expertise. To address these challenges, we introduce \textit{Multi-Teacher Bayesian Knowledge Distillation} (MT-BKD), where a distilled student model learns from multiple teachers within the Bayesian framework. Our approach leverages Bayesian inference to capture inherent uncertainty in the distillation process. We introduce a teacher-informed prior, integrating external knowledge from teacher models and task-specific training data, offering better generalization, robustness, and scalability. Additionally, an entropy-based weighting mechanism adaptively adjusts each teacher's influence, allowing the student to combine multiple sources of expertise effectively. MT-BKD enhances the interpretability of the student model's learning process, improves predictive accuracy, and provides uncertainty quantification. We validate MT-BKD on both synthetic and real-world tasks, including protein subcellular location prediction and image classification. Our experiments show improved performance and robust uncertainty quantification, highlighting the strengths of our MT-BKD framework.

Existing training approaches for large language models learn a single set of parameters, based on large volumes of data, which is typically heterogeneous, conflicting and often outright contradictory. As a result, the model is forced to compress conflicting goals, and inherent uncertainties into a single, averaged pattern of behaviour. We propose an $α$-Rényi variational framework for learning distributions over post-training parameters, offering an uncertainty-aware alternative to deep ensemble approaches. The resulting variational objective interpolates between classical variational Bayes and predictively oriented posterior learning, balancing between globally plausible individual models against systems of complementary specialists. We identify local stability criteria, demonstrating how model misspecification can make non-degenerate posterior spread locally favourable, manifesting contradictory or conflicting data as epistemic uncertainty. We apply our framework to LLM post-training, learning an ensemble of LoRA adapters attached to a shared, frozen base model, providing a scalable training procedure for both supervised fine-tuning and preference optimisation. Our approach enables training examples to be softly routed across ensemble members, promoting model specialisation and providing actionable uncertainty estimates across different tasks.

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood $p \sim \text{Beta}(α, β)$ and outcome $y \sim \text{Bernoulli}(p)$, with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

Large language models (LLMs) are known to abandon their initial stance to conform to user pushback. While prior research largely attributes this behavior to sycophancy learned during reinforcement learning from human feedback, we hypothesize that conformity is also driven by a model's epistemic uncertainty at inference time. In this paper, we introduce MUSE, a two-stage evaluation framework to disentangle the mechanisms driving LLM conformity. Specifically, MUSE maps a model's epistemic uncertainty in responding to a query against its likelihood to yield to user pushback in a subsequent turn. We demonstrate that the mechanisms driving conformity extend beyond sycophancy alone. Specifically, we characterize two distinct factors that jointly drive conformity: sycophantic conformity, where a model aligns with user pushback even with absolute certainty in its initial response, and uncertainty-driven conformity, where a model's likelihood for conformity increases alongside its uncertainty. Furthermore, we conduct ablation studies to demonstrate that both sycophantic conformity and uncertainty-driven conformity grow with 1) the LLM's perceived expertise of the user and 2) the plausibility of the user's suggestions. More broadly, MUSE informs more targeted intervention strategies by distinguishing alignment-induced sycophancy and training-corpora-driven uncertainty.

Estimating how much an intervention helps a given individual the conditional average treatment effect (CATE) is increasingly central to decision-making in medicine, economics, and policy, where an estimate is most useful when accompanied by a calibrated uncertainty interval. We study the few-placebo regime, in which one treatment arm is much smaller than the other, as arises in unequal-allocation trials and small-holdout $A/B$ tests. The standard estimator in this setting is the X-Learner, and a natural way to obtain credible intervals is to make its second stage Bayesian. We show that these intervals under-cover: they contain the true effect less often than their nominal level. We trace this to a structural cause the X-Learner's regression target inherits the bias of a nuisance model fitted to the small arm, so the posterior is centered away from the true effect and we find that the standard remedy, regressing an orthogonal doubly-robust score, is also unreliable here, since the regime's limited overlap leaves the estimator either highly variable or, once stabilized, biased once more. Both consequences reflect a pattern that extends beyond causal inference: a separately estimated variance is attached to a point estimate of a hard-to-learn quantity, and the point estimate's bias is not captured by that variance. We propose GP-CATE, which models each arm's outcome surface with a Gaussian process, so the scarce arm's uncertainty enters the posterior directly rather than as an unmodelled bias. Across synthetic and semi-synthetic benchmarks, GP-CATE attains calibrated coverage where the estimators we compare against including Causal Forest and BART do not, at the cost of intervals that are appropriately wide when the data are uninformative.

Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB), a concave integer optimization framework that reallocates a fixed sampling budget based on per-question uncertainty estimated at no additional inference cost. In Phase 1, every question receives one generation; its average negative log-likelihood (ANLL), extracted directly from output log-probabilities, serves as a difficulty signal while the generation contributes to the final vote. In Phase 2, the remaining budget is allocated by a marginal-greedy algorithm that solves a concave coverage-maximization surrogate exactly: uncertain questions receive more sampling budget while confident questions receive fewer additional samples. Evaluated on six open-weight and black-box models spanning 1.5B to 27B parameters and five reasoning benchmarks covering math, logic, and preference tasks, UAB outperforms baselines by up to +3% in average accuracy and up to +5% on individual benchmarks, with the largest gains in low-resource settings, requiring no auxiliary model or additional LLM call. Code is publicly available at https://github.com/manhitv/UAB.

Neural cellular automata (NCA) provide a lightweight alternative to encoder-decoder segmentation networks. However, it can be difficult to decide when a prediction should be trusted. Here, we study uncertainty estimation for NCA-based medical image segmentation without modifying the underlying architecture or retraining the model. Our approach is motivated by viewing the NCA as a dynamical system where convergent attractors correspond to confident predictions. Concretely, we propose resilience, a simple measure that leverages the intrinsic iterative structure of NCAs by probing the stability of the final prediction under small perturbations of the automaton state. Predictions that return to the same solution are deemed confident, while those that change substantially are flagged as uncertain. We evaluate uncertainty by its ability to predict segmentation quality using selective prediction metrics ($Δ$Dice@90 and AURC) and ranking metrics (AUROC and AUPRC). Across multiple medical segmentation benchmarks, resilience identifies failure cases more reliably than baselines, improving trust and safety in NCA-based models.

Over the centuries, probability theory has grown from the calculus of games of chance into a central framework for reasoning under uncertainty. This article interprets that evolution not merely as a mathematical history, but as a transformation of rationality itself. From Pascal and Fermat's combinatorial symmetry to the inductive logic of Bayes and Laplace, from Poisson's statistics of events to Kolmogorov's axiomatic formalization, probability progressively incorporated uncertainty, time, and coherence into scientific judgment. This trajectory reaches a mature epistemological form in modern Bayesian inference, especially in Tarantola's view of probability as a logic of information, where prior knowledge and data are combined coherently. Yet this framework also exposes a limit: probability quantifies uncertainty about well-defined propositions, but does not by itself formalize the vagueness of the concepts used to describe them. The article therefore examines how rationality extends beyond probability. Fuzzy logic is presented as a rigorous language for graded meaning and qualitative judgment, while deep learning is analyzed as a distinct, powerful mode of prediction based on geometric interpolation and optimization rather than explicit inference. By situating probability, fuzzy logic, and deep learning in a common historical and epistemological perspective, the article clarifies their roles and limits. It argues that contemporary scientific rationality cannot be reduced to data-driven performance alone, but requires the explicit articulation of uncertainty, vagueness, and inference.

Reliable uncertainty quantification in continuous-time (CT) representation learning remains nascent, particularly within CT attention literature. We introduce the Neuronal Stochastic Attention Circuit (NSAC), a novel biologically-inspired CT attention architecture that reformulates attention logit computation as the solution of an Ornstein-Uhlenbeck stochastic differential equation modulated by input-dependent, nonlinear interlinked gates derived from repurposed C. elegans Neuronal Circuit Policies (NCPs) wiring mechanism. It induces a Gaussian distribution over logits that propagates principled stochasticity through a logistic-normal distribution over attention weights to yield probabilistic output. A two-term objective function combining Gaussian negative log-likelihood with an epistemic-separation regularizer enforces higher predictive variance under distributional shifts and enables joint quantification of aleatoric and epistemic uncertainty. Theoretically, we provide: (i) state stability bounds; (ii) closed-form guarantees; and (iii) frozen-coefficient error approximation. Empirically, we implement NSAC in a diverse set of learning tasks including: (i) irregular CT function approximation; (ii) multivariate regression; (iii) long-range forecasting; (iv) Industry 4.0; and (v) lane-keeping of autonomous vehicles. We observe that NSAC remains competitive against several baselines in terms of accuracy and produces informative uncertainty estimates while being interpretable at the neuronal cell level.

We introduce Fuzzy PyTorch, a framework for rapid evaluation of numerical variability in deep learning (DL) models. As DL is increasingly applied to diverse tasks, understanding variability from floating-point arithmetic is essential to ensure robust and reliable performance. Tools assessing such variability must be scalable, efficient, and integrate seamlessly with existing frameworks while minimizing code modifications. Fuzzy PyTorch enables this by integrating stochastic arithmetic into PyTorch through Probabilistic Rounding with Instruction Set Management, a novel library interfacing with Verificarlo, a numerical analysis compiler. The library offers stochastic rounding mode and a novel mode; up-down rounding. Comparative evaluations show Fuzzy PyTorch maintains model performance and achieves runtime reductions of 5x to 60x versus Verrou, a state-of-the-art tool. We further demonstrate scalability by running models from 1 to 341 million parameters, confirming applicability across small and large DL architectures. Overall, Fuzzy PyTorch provides an efficient, scalable, and practical solution for assessing numerical variability in deep learning, enabling researchers and practitioners to quantify and manage floating-point uncertainty without compromising performance or computational efficiency.

Recent advances in uncertainty quantification increasingly emphasise the distinction between aleatory and epistemic uncertainty in machine learning, motivating the need for more unified frameworks. However, despite much progress in producing reliable predictions, existing methods often lack rigorous guarantees when generalising beyond the training domain. We propose a conformalised imprecise inference framework for robust extrapolation, which is model-agnostic and augments predictive models with imprecision and distance awareness. The proposed approach yields imprecise predictions (probability boxes) that remain valid under distributional shift, maintaining coverage while adaptively expanding uncertainty in extrapolation regimes. Experiments on synthetic and benchmark datasets demonstrate improved robustness and reliable coverage compared to standard probabilistic approaches, particularly under limited data.

Epistemic uncertainty is often viewed as a reducible uncertainty that vanishes with increasing data. This perspective implicitly assumes parameter identifiability and equates epistemic uncertainty with predictive variability. In overparametrized neural networks, however, model parameters are typically non-identifiable due to symmetries and redundant representations. As a consequence, substantial parameter uncertainty can persist even when the underlying function is fully identified. In this work, we analyze epistemic uncertainty through the lens of non-identifiability and characterize both discrete and continuous sources of residual uncertainty. Focusing on one-hidden-layer ReLU networks, we thoroughly analyze the resulting posterior structure and validate our theoretical insights through empirical studies.

Reliable forecasting of renewable energy generation is a foundational requirement for grid stability energy trading battery scheduling and carbon aware operational planning Solar and wind resources are inherently intermittent their output fluctuates with cloud cover wind speed atmospheric turbulence seasonal patterns and local terrain The proliferation of IoT and edge devices spanning smart meters inverters anemometers pyranometers weather stations and grid interface sensors has created an unprecedented volume of real time operational data that conventional forecasting pipelines are ill equipped to exploit fully This review investigates how large language model LLM agents can enhance renewable energy forecasting by integrating heterogeneous sensor streams weather API data historical generation records grid constraints and contextual reasoning into unified decision support workflows We survey classical forecasting methods statistical time series models deep learning architectures physics hybrid approaches and emerging LLM agent frameworks for explanation uncertainty communication and operator guidance A six layer taxonomy is proposed covering data acquisition preprocessing feature engineering model inference uncertainty estimation and natural language reporting The review identifies twelve open challenges spanning real time deployment model drift under distribution shift uncertainty quantification hallucination control in LLM agents interoperability of edge hardware and integration with energy management systems The paper concludes by recommending a research agenda centred on open benchmarks physics informed LLM grounding and federated forecasting architectures

Guided Soft Actor-Critic (GSAC) distills knowledge from a privileged full-state teacher to a partial-observation student for autonomous driving, but uses a fixed distillation coefficient lambda regardless of the agent's uncertainty. We present Belief-Aware GSAC (BA-GSAC), which modulates lambda via ensemble disagreement, and use it as a testbed for a systematic empirical study asking: when does adaptive guidance actually help? Evaluating five strategies (fixed lambda in {0.01, 0.1}, adaptive, linear decay, and vanilla SAC) across three POMDP difficulty levels on Highway-Env, we find that preliminary single-seed runs suggest benefits under mild and moderate partial observability, but under severe occlusion (evaluated with 3 seeds for all methods) the adaptive coefficient collapses to lambda_min within about 3K steps. We trace this to an observability blindness phenomenon: because the ensemble predicts partial observations, it achieves low disagreement even under heavy occlusion, modeling what is visible but unable to detect what is missing. We diagnose the root cause and propose an architectural fix (training the ensemble on full-state predictions using the guiding actor's privileged access); while not validated here, we show that even with current limitations, the warmup phase provides measurable stabilization (CV=13.3% vs. 29.8% for constant lambda=0.01). In fact, a simple deterministic linear decay schedule achieves the best severe-POMDP performance across all metrics (mean 116.5, CV=8.9%), suggesting that the scheduling effect, not the ensemble, drives the stability benefit. These findings provide practical guidance for designing uncertainty-aware teacher-student frameworks and highlight ensemble prediction targets as an important design choice.

Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits scalability. Monte Carlo (MC) Dropout, initially introduced as a regularization technique, has been shown to approximate Bayesian inference by enabling probabilistic modeling through multiple stochastic forward passes. In this work, we enhance uncertainty estimation in deep learning by integrating a Dirichlet-based framework within MC Dropout. Specifically, we leverage the formulation proposed by Sensoy et al. (2018), where class probabilities are modeled using a Dirichlet distribution, allowing for a more informative uncertainty representation. The proposed approach maintains the computational efficiency of MC Dropout while improving the quality of uncertainty estimates. We discuss the theoretical foundations of our method and compare it with existing uncertainty quantification techniques. The results highlight the effectiveness of the proposed method in producing well-calibrated uncertainty estimates, offering a practical solution for uncertainty-aware deep learning models.

LLM-based multi-agent systems can fail even when planned actions are executed correctly because agents may misjudge their knowledge when evaluating plan feasibility, a phenomenon we term epistemic miscalibration in planning. Unlike execution errors, epistemic miscalibration is latent during planning, as generated plans can remain self-consistent and executable without observable errors; the miscalibration is also dynamic, as new information can alter feasibility assessments, potentially obscuring past miscalibration signals and causing them to recur over time. To address this, we propose the Epistemic Planning Calibration Agentic Workflow (EPC-AW), which assesses whether plans remain supported under varying information conditions rather than directly verifying feasibility. EPC-AW employs Information-consistency-based Plan Selection, selecting plans whose evaluations are stable across agents, together with Consistency-guided Epistemic State Refinement to adapt calibration over time by leveraging past discrepancies to guide future planning. Experiments show that EPC-AW improves system-level success by an average of 9.75%.

Large Language Models (LLMs) are predominantly governed by probabilistic frameworks in which the sum of outcome probabilities is constrained to unity. This architectural limitation, often imposed by Softmax layers, leads to a collapse of uncertainty that makes it difficult to differentiate between epistemic uncertainty, paradox, and vagueness. We present an empirical investigation of the application of Neutrosophic Logic, a framework that treats Truth (T), Indeterminacy (I), and Falsity (F) as three independent dimensions, to model epistemic states in LLMs. We conducted experiments on a family of four OpenAI GPT models across five linguistic phenomena: logical paradoxes, epistemic ignorance, vagueness, ethical contradictions, and future contingencies, under three prompting strategies: neutrosophic, probabilistic, and entropy-derived. Our findings reveal that the neutrosophic approach, by allowing T+I+F > 1, a state we term hyper-truth, provides a richer representation of a model's internal state. In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox. We demonstrate that this approach preserves truth values in fuzzy contexts and offers a robust method for identifying and quantifying internal model conflict. We conclude that the integration of neutrosophic evaluation layers is a critical step toward more transparent, reliable, and ethically aware AI systems.

Decision trees assign identical confidence to instances near and far from each split threshold. We introduce ternary decision trees, which augment each split node with an uncertainty zone of half-width delta. A decision-theoretic framework characterises the optimal zone width delta* as the solution to a node-local cost-minimisation problem; four formal properties are established: accuracy decomposition, a sufficiency condition for decided accuracy improvement, an exact efficiency characterisation (eta = Dec-Acc minus Acc_u, the accuracy gap between decided and boundary-uncertain predictions), and asymptotic consistency of the margin method. Instances within the zone receive predictions by weighted blending of both child subtrees and are flagged as boundary-uncertain. We propose and evaluate five delta-estimation methods: quality-plateau (plateau width of the split criterion curve), class-overlap (empirical class-distribution overlap), gain-ratio (split quality relative to split entropy), node-bootstrap (threshold variance under node-level resampling), and margin (SVM-inspired distance to the nearest cross-class training example). All methods reuse statistics already computed during standard CART split finding, requiring no external noise specification. Evaluated across 71 of the 72 OpenML-CC18 datasets with 5-fold cross-validation, all five methods with probabilistic routing significantly outperform standard CART on decided accuracy (Wilcoxon signed-rank, p < 0.001). The margin method achieves the best efficiency (0.104 accuracy gain per unit flagging rate), wins on 42 of 72 datasets, and requires zero hyperparameters. Analysis on Breiman synthetic benchmarks confirms margin is self-calibrating on clean data. On mammography, node-bootstrap achieves +0.71% decided accuracy by flagging 10.8% of cases as boundary-uncertain.

Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for inverse problems with multimodal posteriors. By the law of total variance, point estimators trained to minimize MSE or MAE produce a marginal spectrum strictly narrower than the truth whenever the posterior has nonzero width. The resulting bias is independent of architecture, training, and dataset size, and it compresses precisely the spectral features - tails, modes, shapes - that downstream scientific measurements rely on. We propose a three-part evaluation protocol where each step targets a failure mode the others miss: per-event distributional accuracy via CRPS, population-level marginal accuracy via a spectrum-fidelity diagnostic, and uncertainty trustworthiness via coverage-based calibration. On a synthetic benchmark with an analytic posterior and on a realistic many-to-one inverse problem from particle physics, model rankings reverse between pointwise and distributional metrics, and calibration further separates architectures indistinguishable under CRPS. The evaluation protocol, not the model, determines the scientific conclusion.

Accurate wind power forecasting requires reliable uncertainty quantification, yet most existing methods report a single predictive uncertainty that conflates epistemic and aleatoric sources. This paper applies the law of total variance to the joint setting of heteroscedastic neural network regression and Bayesian posterior approximation, deriving an explicit decomposition of total uncertainty (TU) into aleatoric (AU) and epistemic (EU) components. The resulting estimators are compatible with standard posterior-approximation methods and with $β$-NLL training to regulate the mean--variance learning trade-off. A wind power--specific evaluation framework is proposed to validate disentanglement without access to ground-truth uncertainty labels, comprising three modules: controlled synthetic experiments to verify responses to heteroscedastic noise and distribution shift; data-property--driven validation on a real-world wind turbine SCADA dataset; and dataset-size scaling experiments to examine the predicted asymptotic behavior of EU. Across synthetic and real-world experiments, the decomposed AU and EU components respond in theoretically consistent directions to noise structure, distributional shift, and training-scale variation, supporting the theoretical consistency and operational utility of the proposed decomposition and evaluation protocol.

Deep learning models, including Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), have achieved state-of-the-art performance on various computer vision tasks such as object classification, detection, segmentation, generation, and many more. However, these models are data-hungry as they require more training data to learn millions or billions of parameters. Especially for supervised learning tasks, curating a large number of labeled samples for model training is an expensive and time-consuming task. Active Learning (AL) has been used to address this problem for many years. Existing active learning methods aim at choosing the samples for annotation from a pool of unlabeled samples that are either diverse or uncertain. Choosing such samples may hinder the model's performance as we pool based on one dimension, i.e., either diverse or uncertain. In this paper, we propose four novel hybrid sampling methods for pooling both easy and hard samples, which are also diverse. To verify the efficacy of the proposed methods, extensive experiments are conducted using high and low-confidence samples separately. We observe from our experiments that the proposed hybrid sampling method, Least Confident and Diverse (LCD), consistently performs better compared to state-of-the-art methods. It is observed that selecting uncertain and diverse instances helps the model learn more distinct features. The codes related to this study will be available at https://github.com/XXX/LCD.

Post-training has become central to improving reasoning and alignment in large language models, where critic-free models enable scalable learning from model-generated outputs but lack principled mechanisms to distinguish informative from noisy signals. Recent approaches leverage response-level measures as uncertainty signals to regulate group-based optimization methods such as GRPO. Yet their empirical success remains unstable and unclear in how they influence optimization dynamics. In this paper, we provide, to our knowledge, the first principled formulation that interprets uncertainty signals as mechanisms for characterizing and regulating gradient variance and learning signal quality. Based on both empirical and theoretical analysis, we identify two critical gaps of current entropy-based estimators: The anisotropic gap and The calibration gap. Motivated by this analysis, we propose Geometric-aware Calibrated Policy Optimization (GCPO), a novel framework integrating geometry-aware measures to capture semantic disagreement with reward-based calibration to align uncertainty with learning signal strength. Experiments on multiple benchmarks show that our approach more faithfully tracks gradient variability and consistently improves post-training performance. Our results highlight the importance of designing uncertainty signals that are aligned with optimization dynamics, offering a principled perspective for robust post-training.

Test-time adaptation (TTA) methods improve model performance under distribution shift but lack formal guarantees connecting shift magnitude to prediction reliability. We develop a PAC-Bayesian framework yielding generalization bounds explicitly parameterized by the maximum mean discrepancy (MMD) between source and target distributions. Our principal contribution is interpreting MMD-balls around the source distribution as credal sets in Walley's imprecise probability theory, yielding natural epistemic uncertainty quantification. We establish: (i) a PAC-Bayesian bound with an MMD-dependent shift penalty under an RKHS-Lipschitz loss assumption; (ii) a finite-sample version via MMD concentration; (iii) a uniform worst-case risk bound over all distributions in the credal set, with a lower-upper risk decomposition; and (iv) geodesic preservation bounds explaining why kernel-guided adaptation protects local feature geometry. The credal set interpretation separates epistemic from aleatoric uncertainty and provides a principled decision criterion for when adaptation is warranted.

Machine learning models for chronic kidney disease (CKD) risk prediction often post strong discrimination scores on internal test sets. Calibration and uncertainty quantification get far less attention, leaving clinicians without reliable information about whether the probability outputs are accurate. We trained five classifiers on the UCI CKD dataset (400 patients, 62.5% CKD prevalence): logistic regression, random forest, XGBoost, SVM with Platt scaling, and Gaussian naive Bayes. We evaluated each across calibration quality, conformal prediction coverage, and an eight-criterion deployment readiness framework. A distributional stress-test applied the best-calibrated variant of each model to the open-access MIMIC-IV demo cohort (97 patients, 23.7% CKD) to assess behaviour under prevalence shift and feature missingness. We measured calibration before and after Platt scaling and isotonic regression using Expected Calibration Error and Brier Score, and quantified uncertainty through split conformal prediction targeting 90% marginal coverage. All five models reached AUROC 1.00 on the UCI test set. Isotonic recalibration reduced internal ECE to 0.000-0.022. On MIMIC-IV, AUROC fell to 0.48-0.58, ECE rose to 0.68-0.76, and conformal coverage dropped from 0.80-0.98 to 0.21-0.25 against a 90% target. No model scored above 4 out of 16 on the deployment readiness checklist. Near-perfect internal performance did not transfer. Calibration stability and conformal coverage should be evaluated on external data before any clinical prediction model moves toward deployment.