Epistemic Uncertainty

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Epistemic uncertainty concerns what a model does not know, often distinguished from aleatoric uncertainty caused by inherent variability or ambiguity in observations. Researchers estimate it with Bayesian methods, ensembles and dropout, evidential models, and set-valued or credal predictions, then use it for out-of-distribution detection, selective prediction, active learning, and safer decisions. Work increasingly evaluates whether uncertainty is calibrated and useful for specific decisions, including through conformal guarantees, abstention tests, and benchmarks under distribution shift. A central tension is that common signals such as ensemble disagreement or predictive entropy may not reliably track missing knowledge, and their value depends on how uncertainty is defined and tested.

Latest papers

113 papers14 papers in the last four weeks, up 250% on the four weeks before. 0.1% of all new papers.

May 20, 2026

Certifying Whether to Adapt: Baseline-Relative PAC-Bayes-MMD Guarantees for Test-Time Adaptation

Test-time adaptation (TTA) needs a decision about an update, not only an absolute-risk estimate. We give PAC-Bayesian certificates for the target excess risk of a candidate relative to a pilot-fixed baseline. A radial certificate uses an MMD ambiguity radius; a direction-sensitive certificate retains the sign of the empirical RKHS shift and can therefore certify target improvement even when source risk increases. For finite binary state spaces we derive statewise marginal and signed conditional-shift refinements, with penalties localized to candidate--baseline disagreements. A source-worsening update with target excess risk

-0.576

is accepted in all 1,000 repetitions by the directional certificate and never by the radial certificate; learned finite-state updates with excess risks

-0.800

and

-0.401

are likewise accepted in every repetition. On Covertype, the certificate safely rejects all updates and blocks geographic-shift adaptations whose unconditional deployment increases risk by up to

2.75

percentage points in prespecified base libraries; an exploratory stress test reaches

5.66

points. A feature-quantized CIFAR-10-C and ImageNet-C study is structurally vacuous and is reported only as a diagnostic limitation, not as a practical neural certificate.

Ahanaf Hasan Ariq, Hasaan Ahmad, Aayush Parekh +1

Ideal School and College

Distribution Shift Robustness PAC-Bayesian Generalization Bounds Test-Time Adaptation Epistemic Uncertainty

May 17, 2026

Descriptive versus Regulatory Uncertainty in Bounded Predictive Systems

Any system that models the world under finite representational capacity must compress; any compression entails a prior; and the prior is the system's bias. What has not been established is whether uncertainty participates in the dynamics governing future behavior, or merely describes the output distribution without consequence. We introduce a structural distinction between descriptive uncertainty, which does not recursively modulate the system's policy, and regulatory uncertainty, which directly enters the optimization landscape and drives persistent adaptive restructuring. We prove formally that current transformer architectures are confined to descriptive uncertainty at inference. We ground this in thermodynamics via Landauer's principle: for uncertainty to be regulatory, epistemic error must cost real energy; in a decoupled system, hallucinations and correct derivations dissipate identical energy. We test this empirically across three locally-deployed language models (3B, 8B, 70B parameters). Token-level Shannon entropy is statistically invariant across tasks spanning pattern retrieval, causal operator application, and out-of-distribution causal generalization in all three models (all pairwise p >= 0.568; within-model ranges 0.011-0.028 nats), while task accuracy varies substantially across the same conditions (0%-100%). Entropy and accuracy are orthogonal. The decoupling is scale-invariant: larger models achieve higher accuracy but identical entropy flatness. This structural incapacity is not resolvable by additional parameters or training data. Genuine epistemic grounding requires physical coupling between thermodynamic substrate state and information processing cost.

Ahmed Gamal Eldin

Nova University Lisbon – Cairo Branch (NOVA IMS), Cairo, Egypt

LLM Uncertainty Estimation Epistemic Uncertainty

May 12, 2026

Semantic Reward Collapse and the Preservation of Epistemic Integrity in Adaptive AI Systems

Recent advances in reinforcement learning from human feedback (RLHF) and preference optimization have substantially improved the usability, coherence, and safety of large language models. However, recurring behaviors such as performative certainty, hallucinated continuity, calibration drift, sycophancy, and suppression of visible uncertainty suggest unresolved structural issues within scalarized preference optimization systems. We propose Semantic Reward Collapse (SRC): the compression of semantically distinct forms of evaluative dissatisfaction into generalized optimization signals. Under SRC, categories such as factual incorrectness, uncertainty disclosure, formatting dissatisfaction, latency, and social preference may become entangled within a shared reward topology despite representing fundamentally different epistemic classes. We argue that adaptive reasoning systems operating under generalized evaluative pressure may drift toward suppression of visible epistemic failure rather than preservation of calibrated uncertainty integrity. These behaviors are framed strictly as optimization consequences rather than evidence of deception or anthropomorphic agency. Drawing on institutional proxy collapse, metric gaming, software reliability engineering, and human learning theory, we propose that uncertainty disclosure and escalation behavior should be treated as protected epistemic conduct rather than globally penalized task incompletion. Finally, we introduce Constitutional Reward Stratification (CRS), a domain-aware reward framework intended to preserve differentiated epistemic attribution within adaptive learning systems. We present CRS not as a validated solution, but as a testable governance-oriented research direction requiring further empirical investigation.

William Parris

BDB Labs / BagelTech · San Diego, California, USA

Reward Modeling Reward Hacking Epistemic Uncertainty Preference-Based RL RL from Human Feedback

May 12, 2026

Random-Set Graph Neural Networks

Uncertainty quantification has become an important factor in understanding the data representations produced by Graph Neural Networks (GNNs). Despite their predictive capabilities being ever useful across industrial workspaces, the inherent uncertainty induced by the nature of the data is a huge mitigating factor to GNN performance. While aleatoric uncertainty is the result of noisy and incomplete stochastic data such as missing edges or over-smoothing, epistemic uncertainty arises from lack of knowledge about a system or model (e.g., a graph's topology or node feature representation), which can be reduced by gathering more data and information. In this paper, we propose an original new framework in which node-level epistemic uncertainty is modelled in a belief function (finite random set) formalism. The resulting Random-Set Graph Neural Networks have a belief-function head predicting a random set over the list of classes, from which both a precise probability prediction and a measure of epistemic uncertainty can be obtained. Extensive experiments on 9 different graph learning datasets, including real-world autonomous driving benchmarks as such Nuscene and ROAD, demonstrate RS-GNN's superior uncertainty quantification capabilities

Tommy Woodley, Shireen Kudukkil Manchingal, Matteo Tolloso +2

School of Engineering, Computing and Mathematics Oxford Brookes University · Department of Computer Science University of Pisa · Oxford Brookes Institute for Artificial Intelligence, Data Analysis and Systems (AIDAS)

Graph Neural Networks Uncertainty Quantification Epistemic Uncertainty

May 8, 2026

The Minimax Rate of Perturbed Second-Order Calibration

Second-order calibration error quantifies how closely a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. We characterize the minimax rate of estimating the second-order calibration error for binary classification in the regime where a small perturbation is applied to the classifier outputs. Our procedure is simple: add independent bandwidth-

h

sech noise to the score coordinates, then regress

Y^{(1)}

and

Y^{(1)}Y^{(2)}

on the perturbed score using low-degree polynomials. Crucially, the sech perturbation makes the calibration functions analytic in a suitable strip. The resulting estimator has error

O_h(\log^{3/2}n/\sqrt n)

, with explicit constants. In the same setting, a matching

Ω(1/\sqrt{n})

lower bound establishes minimax optimality up to logarithmic factors. As a corollary, we give a finite-sample guarantee for perturbed second-order Platt scaling, yielding a post-hoc procedure that recalibrates both the mean prediction and the epistemic-variance estimate of the perturbed higher-order predictor. Along the way, we give an explicit two-moment formulation of second-order calibration error and relate it quantitatively to the bucketed formulation of Ahdritz et al. [2025]. Our experiments confirm the predicted rate and the quality of the recalibrated uncertainties.

Kamil Ciosek, Banafsheh Rafiee, Sina Ghiassian +1

Spotify

Post-Hoc Calibration Minimax Estimation Model Calibration Binary Classification Statistical Learning Theory Uncertainty Calibration+1

May 5, 2026

GEM-FI: Gated Evidential Mixtures with Fisher Modulation

Evidential Deep Learning (EDL) enables single-pass uncertainty estimation by predicting Dirichlet evidence, but it can remain overconfident and poorly calibrated, and it often fails to represent multi-modal epistemic uncertainty. We introduce Gated Evidential Mixtures (GEM), a family of models that learns an in-model energy signal and uses it to gate evidential outputs end-to-end in a distance-informed manner. GEM-CORE learns a feature-level energy and maps it to a bounded gate that smoothly suppresses evidence when support is low. To capture epistemic multi-modality without multi-pass ensembling, GEM-MIX adds a lightweight mixture of evidential heads with learned routing weights while preserving single-pass inference. Finally, GEM-FI stabilizes mixture allocations via a Fisher-informed regularizer, reducing head collapse and producing smoother boundary uncertainty. Across image classification and OOD detection benchmarks, GEM improves calibration and ID/OOD separation with single-pass inference. On CIFAR-10, GEM-FI vs. DAEDL improves accuracy from 91.11 to 93.75 (+2.64 pp), reduces Brier x100 from 14.27 to 6.81 (-7.46), and also improves misclassification-detection AUPR from 99.08 to 99.94 (+0.86). For epistemic OOD detection, GEM-FI achieves AUPR/AUROC of 92.59/95.09 on CIFAR-10 to SVHN and 90.20/89.06 on CIFAR-10 to CIFAR-100, compared with 85.54/89.30 and 88.19/86.10 for DAEDL.

Marco Mustafa Mohammed, Fatemeh Daneshfar, Pietro Liò

Department of Computer Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

Evidential Deep Learning OOD Detection Image Classification Epistemic Uncertainty

May 1, 2026

Possibilistic Predictive Uncertainty for Deep Learning

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency. Code is available at https://github.com/MaxwellYaoNi/DAPPr.

Yao Ni, Jeremie Houssineau, Yew-Soon Ong +1

Nanyang Technological University · A*STAR · The University of New South Wales +1

Uncertainty Quantification Epistemic Uncertainty

Apr 30, 2026

Task-Conditioned Uncertainty Costmaps for Legged Locomotion

Legged robots maintain dynamic feasibility through multicontact interactions with terrain. Learned foothold prediction can provide feasibility-aware costs for motion planning and path selection, but accurately predicting future contacts from perceptual inputs such as height scans remains challenging on highly unstructured terrain, even with a repetitive gait cycle. In this work, we show that modeling epistemic uncertainty in predicted footholds, conditioned on terrain observations and commanded motion, distinguishes in-distribution from out-of-distribution operating regimes in simulation and real-world settings. This allows a single learned model, trained on limited data distributions, to express uncertainty caused by missing training coverage. We use this learned uncertainty to detect OOD regions and incorporate them into a unified costmap-generation framework for uncertainty-aware path planning. Using these uncertainty-aware costmaps, we evaluate feasibility error across in-distribution and OOD terrains in simulation and real-world settings. The results show improved OOD detection, up to a 37% reduction in simulation feasibility error, and more reliable planning behavior than geometry-only baselines.

Kartikeya Singh, Christo Aluckal, Romeo Orsolino +1

DRONES Lab, University at Buffalo, NY, USA · Ocado Technology, UK

Robot Locomotion Epistemic Uncertainty Terrain-Aware Robot Locomotion Legged Robotics OOD Detection Robot Motion Planning+1

Apr 29, 2026

Uncertainty-Aware Pedestrian Attribute Recognition via Evidential Deep Learning

We propose UAPAR, an Uncertainty-Aware Pedestrian Attribute Recognition framework. To the best of our knowledge, this is the first EDL-based uncertainty-aware framework for pedestrian attribute recognition (PAR). Unlike conventional deterministic methods, which fail to assess prediction reliability on low-quality samples, UAPAR effectively identifies unreliable predictions and thus enhances system robustness in complex real-world scenarios. To achieve this, UAPAR incorporates Evidential Deep Learning (EDL) into a CLIP-based architecture. Specifically, a Region-Aware Evidence Reasoning module employs cross-attention and spatial prior masks to capture fine-grained local features, which are further processed by an evidence head to estimate attribute-wise epistemic uncertainty. To further enhance training robustness, we develop an uncertainty-guided dual-stage curriculum learning strategy to alleviate the adverse effects of severe label noise during training. Extensive experiments on the PA100K, PETA, RAPv1, and RAPv2 datasets demonstrate that UAPAR achieves competitive or superior performance. Furthermore, qualitative results confirm that the proposed framework generates uncertainty estimates that are predictive of challenging or erroneous samples.

Zhuofan Lou, Shihang Zhang, Fangle Zhu +2

College of Electronics and Information Engineering, Sichuan University, China

Evidential Deep Learning Epistemic Uncertainty

Apr 28, 2026

Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Space Models

Model-Based Reinforcement Learning distinguishes between physical dynamics models operating on proprioceptive inputs and latent dynamics models operating on high-dimensional image observations. A prominent latent approach is the Recurrent State Space Model used in the Dreamer family. While epistemic uncertainty quantification to inform exploration and mitigate model exploitation is well established for physical dynamics models, its transfer to latent dynamics models has received limited scrutiny. We empirically demonstrate that latent transitions are biased toward well-represented regions of latent space, exhibiting an attractor behavior that can deviate from true environment dynamics. As a result, discrepancies in environment dynamics may not manifest in latent space, undermining the reliability of epistemic uncertainty estimates. Because these attractors often lie in high-reward regions, latent rollouts systematically overestimate predicted rewards. Our findings highlight key limitations of epistemic uncertainty estimation in latent dynamics models and motivate more critical evaluation of this method.

Julia Berger, Bernd Frauenknecht, Sebastian Trimpe +1

1RWTH Aachen University

Uncertainty Quantification Latent Dynamics Modeling Latent World Models Model-Based RL Epistemic Uncertainty Uncertainty Estimation in RL

Apr 27, 2026

Credal Concept Bottleneck Models for Epistemic-Aleatoric Uncertainty Decomposition

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

Tanmoy Mukherjee, Thomas Bailleux, Pierre Marquis +1

Univ. Artois, CNRS, CRIL, France · Institut Universitaire de France

Uncertainty Quantification Concept Bottleneck Models Aleatoric Uncertainty Decision-Making under Uncertainty Uncertainty Decomposition Epistemic Uncertainty

Apr 18, 2026

Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification

Large language models (LLMs) often produce confident yet incorrect responses, and uncertainty quantification is one potential solution to more robust usage. Recent works routinely rely on self-consistency to estimate aleatoric uncertainty (AU), yet this proxy collapses when models are overconfident and produce the same incorrect answer across samples. We analyze this regime and show that cross-model semantic disagreement is higher on incorrect answers precisely when AU is low. Motivated by this, we introduce an epistemic uncertainty (EU) term that operates in the black-box access setting: EU uses only generated text from a small, scale-matched ensemble and is computed as the gap between inter-model and intra-model sequence-semantic similarity. We then define total uncertainty (TU) as the sum of AU and EU. In a comprehensive study across five 7-9B instruction-tuned models and ten long-form tasks, TU improves ranking calibration and selective abstention relative to AU, and EU reliably flags confident failures where AU is low. We further characterize when EU is most useful via agreement and complementarity diagnostics.

Kimia Hamidieh, Veronika Thost, Walter Gerych +2

1MIT · MIT-IBM Watson AI Lab · 3WPI +1

Selective Prediction Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Aleatoric Uncertainty Uncertainty Calibration+2

Apr 17, 2026

EviDep: Uncertainty-Aware Multimodal Depression Estimation via Disentangled Evidential Learning

Audio--visual recordings provide complementary cues for estimating depression severity, but their informativeness varies across time and modalities. Point predictions alone do not express the uncertainty associated with these estimates. We present EviDep, a multimodal evidential regression framework that integrates multi-scale temporal modeling and shared--private representation learning for uncertainty-aware depression estimation. Frequency-aware Feature Extraction decomposes behavioral feature sequences into multiple frequency bands and refines them with scale-specific experts. Disentangled Evidential Learning encourages the disentanglement of cross-modal shared and modality-specific information in the refined features. Multi-branch Evidential Regression maps the resulting shared and private representations to three Normal-Inverse-Gamma (NIG) outputs and uses evidence-weighted aggregation to estimate depression severity and quantify aleatoric and epistemic uncertainty. Experiments on AVEC 2013, AVEC 2014, DAIC-WOZ, and E-DAIC show competitive prediction accuracy, with ablation studies supporting the contributions of frequency-aware refinement and shared--private disentanglement. Further analyses show that estimated epistemic uncertainty helps identify higher-error predictions, while both uncertainty estimates generally increase under controlled feature degradation.

Fangyuan Liu, Sirui Zhao, Yangsong Zhang +5

School of Computer Science and Technology, University of Science and Technology of China, Hefei, China · aSchool of Computer Science and Technology, University of Science and Technology of China, Hefei, China · bSchool of Computer Science and Technology, Laboratory for Brain Science and Artificial Intelligence, Southwest University of Science and Technology, Mianyang, China +1

Disentangled Representation Learning Evidential Deep Learning Depression Detection Depression Severity Estimation Multimodal Fusion Epistemic Uncertainty

Apr 14, 2026

A Bayesian Perspective on the Role of Epistemic Uncertainty for Delayed Generalization in In-Context Learning

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and grokking in in-context learning using a Bayesian perspective, asking what enables the delayed transition from memorization to generalization. Concretely, we consider modular arithmetic tasks in which a transformer must infer a latent linear function solely from in-context examples and analyze how predictive uncertainty evolves during training. We combine approximate Bayesian techniques to estimate the posterior distribution and we study how uncertainty behaves across training and under changes in task diversity, context length, and context noise. We find that epistemic uncertainty collapses sharply when the model groks, making uncertainty a practical label-free diagnostic of generalization in transformers. Additionally, we provide theoretical support with a simplified Bayesian linear model, showing that asymptotically both delayed generalization and uncertainty peaks arise from the same underlying spectral mechanism, which links grokking time to uncertainty dynamics.

Abdessamed Qchohi, Simone Rossi

EURECOM, France

In-Context Learning Grokking Epistemic Uncertainty

Apr 13, 2026

Retrieval Is Not Enough: Why Organizational AI Needs Epistemic Infrastructure

Organizational knowledge used by AI agents typically lacks epistemic structure: retrieval systems surface semantically relevant content without distinguishing binding decisions from abandoned hypotheses, contested claims from settled ones, or known facts from unresolved questions. We argue that the ceiling on organizational AI is not retrieval fidelity but epistemic fidelity--the system's ability to represent commitment strength, contradiction status, and organizational ignorance as computable properties. We present OIDA, a framework that structures organizational knowledge as typed Knowledge Objects carrying epistemic class, importance scores with class-specific decay, and signed contradiction edges. The Knowledge Gravity Engine maintains scores deterministically with proved convergence guarantees (sufficient condition: max degree

< 7

; empirically robust to degree 43). OIDA introduces QUESTION-as-modeled-ignorance: a primitive with inverse decay that surfaces what an organization does not know with increasing urgency--a mechanism absent from all surveyed systems. We describe the Epistemic Quality Score (EQS), a five-component evaluation methodology with explicit circularity analysis. In a controlled comparison (

n{=}10

response pairs), OIDA's RAG condition (3,868 tokens) achieves EQS 0.530 vs.\ 0.848 for a full-context baseline (108,687 tokens); the

28.1\times

token budget difference is the primary confound. The QUESTION mechanism is statistically validated (Fisher

p{=}0.0325

, OR

=21.0

). The formal properties are established; the decisive ablation at equal token budget (E4) is pre-registered and not yet run.

Federico Bottino, Carlo Ferrero, Nicholas Dosio +1

Kakashi Ventures Accelerator (KVA) · Massachusetts Institute of Technology

Knowledge Representation Epistemic Uncertainty Retrieval-Augmented Generation Knowledge Graphs AI Agent Evaluation

Apr 8, 2026

Epistemic Robust Offline Reinforcement Learning

Offline reinforcement learning learns policies from fixed datasets without further environment interaction. A key challenge in this setting is epistemic uncertainty, arising from limited or biased data coverage, particularly when the behavior policy systematically avoids certain actions. This can lead to inaccurate value estimates and unreliable generalization. Ensemble-based methods like SAC-N mitigate this by conservatively estimating Q-values using the ensemble minimum, but they require large ensembles and often conflate epistemic with aleatoric uncertainty. To address these limitations, we propose a unified and generalizable framework that replaces discrete ensembles with compact uncertainty sets over Q-values. %We further introduce an Epinet based model that directly shapes the uncertainty sets to optimize the cumulative reward under the robust Bellman objective without relying on ensembles. We also introduce a benchmark for evaluating offline RL algorithms under risk-sensitive behavior policies, and demonstrate that our method achieves improved robustness and generalization over ensemble-based baselines across both tabular and continuous state domains.

Abhilash Reddy Chenreddy, Erick Delage

GERAD, Department of Decision Sciences, HEC Montréal, Montréal, Québec H3T 2A7, Canada

Uncertainty Estimation in RL Offline RL Robust RL Epistemic Uncertainty Risk-Sensitive RL

Apr 5, 2026

Uncertainty-Aware Foundation Models for Clinical Data

Healthcare foundation models have largely followed paradigms from natural language processing and computer vision, emphasizing large scale pretraining and deterministic representations over heterogeneous clinical data. However, clinical observations are inherently incomplete, reflecting sparse, irregular, and modality dependent measurements of an underlying physiologic state. In this work, we propose a framework for uncertainty aware foundation modeling that represents each patient not as a point embedding, but as a distribution over plausible latent states. By learning set valued representations and enforcing consistency across partial views of the same patient, the model captures what is invariantly inferable while explicitly encoding epistemic uncertainty. We integrate this formulation with multimodal encoders and scalable self supervised objectives, combining reconstruction, contrastive alignment, and distributional regularization. Across diverse clinical tasks, our approach improves predictive performance, robustness under missing data, and uncertainty calibration relative to strong baselines. These results suggest that modeling what is not observed rather than only what is constitutes a critical inductive bias for healthcare foundation models.

Qian Zhou, Yuanyun Zhang, Shi Li

University of the Chinese Academy of Sciences · Columbia University

Epistemic Uncertainty Multimodal Foundation Models Learning with Missing Data Uncertainty Calibration Uncertainty-Aware Multimodal Fusion

Apr 2, 2026

Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty

Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric uncertainty, must be considered. This poses a significant challenge due to heavy computational demands. Machine learning techniques are thus introduced as metamodels to alleviate this burden. However, the "black box" nature of Machine learning models underscores the necessity of avoiding overly confident predictions, particularly when data and training efforts are insufficient. This creates a need, in addition to considering the aleatoric uncertainty, of estimating the uncertainty related to the prediction confidence, i.e., epistemic uncertainty, for machine learning-based metamodels. We developed a probabilistic metamodeling technique based on a variational long short-term memory (LSTM) with augmented inputs to simultaneously capture aleatoric and epistemic uncertainties. Key random system parameters are treated as augmented inputs alongside excitation series carrying record-to-record variability to capture the full range of aleatoric uncertainty. Meanwhile, epistemic uncertainty is effectively approximated via the Monte Carlo dropout scheme. Unlike computationally expensive full Bayesian approaches, this method incurs negligible additional training costs while enabling nearly cost-free uncertainty simulation. The proposed technique is demonstrated through multiple case studies involving stochastic seismic or wind excitations. Results show that the calibrated metamodels accurately reproduce nonlinear response time histories and provide confidence bounds indicating the associated epistemic uncertainty.

Manisha Sapkota, Min Li, Bowei Li

Department of Civil, Environmental, and Construction Engineering, Texas Tech University, 2500 Broadway St, Lubbock 79409, TX, USA · Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy 12180, NY, USA · National Wind Institute, Texas Tech University, 1009 Canton Ave, Lubbock 79409, TX, USA

Surrogate Modeling Uncertainty Propagation Long Short-Term Memory Networks Epistemic Uncertainty Structural Mechanics Aleatoric Uncertainty

Apr 1, 2026

Procela: Epistemic Governance in Mechanistic Simulations Under Structural Uncertainty

Mechanistic simulations typically assume fixed ontologies: variables, causal relationships, and resolution policies are static. This assumption fails when the true causal structure is contested or unidentifiable-as in antimicrobial resistance (AMR) spread, where contact, environmental, and selection ontologies compete. We introduce Procela, a Python framework where variables act as epistemic authorities that maintain complete hypothesis memory, mechanisms encode competing ontologies as causal units, and governance observes epistemic signals and mutates system topology at runtime. This is the first framework where simulations test their own assumptions. We instantiate Procela for AMR in a hospital network with three competing families. Governance detects coverage decay, policy fragility, and runs structural probes. Results show 20.4% error reduction and 69% cumulative regret improvement over baseline. All experiments are reproducible with full auditability. Procela establishes a new paradigm: simulations that model not only the world but their own modeling process, enabling adaptation under structural uncertainty.

Kinson Vernet

Independent Researcher

Epistemic Uncertainty Uncertainty Quantification Structural Causal Models

Mar 31, 2026

Uncertainty Gating for Cost-Aware Explainable Artificial Intelligence

Post-hoc explanation methods are widely used to interpret black-box predictions, but their generation is often computationally expensive and their reliability is not guaranteed. We propose epistemic uncertainty as a low-cost proxy for explanation reliability: high epistemic uncertainty identifies regions where the decision boundary is poorly defined and where explanations become unstable and unfaithful. This insight enables two complementary use cases:

improving worst-case explanations' (routing samples to cheap or expensive XAI methods based on expected explanation reliability), and

recalling high-quality explanations' (deferring explanation generation for uncertain samples under constrained budget). Across four tabular datasets, five diverse architectures, and four XAI methods, we observe a strong negative correlation between epistemic uncertainty and explanation stability. Further analysis shows that epistemic uncertainty distinguishes not only stable from unstable explanations, but also faithful from unfaithful ones. Experiments on image classification confirm that our findings generalize beyond tabular data.

Georgii Mikriukov, Grégoire Montavon, Marina M. -C. Höhne

Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Potsdam, Germany · BIFOLD – Berlin Institute for the Foundations of Learning and Data, Berlin, Germany · Charité – Universitätsmedizin Berlin, Berlin, Germany +1

Explainable Artificial Intelligence Explainability Evaluation Epistemic Uncertainty Cost-Aware Inference

Mar 31, 2026

An Isotropic Approach to Efficient Uncertainty Quantification with Gradient Norms

Existing methods for quantifying predictive uncertainty in neural networks are either computationally intractable for large language models or require access to training data that is typically unavailable. We derive a lightweight alternative through two approximations: a first-order Taylor expansion that expresses uncertainty in terms of the gradient of the prediction and the parameter covariance, and an isotropy assumption on the parameter covariance. Together, these yield epistemic uncertainty as the squared gradient norm and aleatoric uncertainty as the Bernoulli variance of the point prediction, from a single forward-backward pass through an unmodified pretrained model. We justify the isotropy assumption by showing that covariance estimates built from non-training data introduce structured distortions that isotropic covariance avoids, and that theoretical results on the spectral properties of large networks support the approximation at scale. Validation against reference Markov Chain Monte Carlo estimates on synthetic problems shows strong correspondence that improves with model size. We then use the estimates to investigate when each uncertainty type carries useful signal for predicting answer correctness in question answering with large language models, revealing a benchmark-dependent divergence: the combined estimate achieves the highest mean AUROC on TruthfulQA, where questions involve genuine conflict between plausible answers, but falls to near chance on TriviaQA's factual recall, suggesting that parameter-level uncertainty captures a fundamentally different signal than self-assessment methods.

Nils Grünefeld, Jes Frellsen, Christian Hardmeier

1IT University of Copenhagen · 3Pioneer Centre for Artificial Intelligence · 2Technical University of Denmark

Uncertainty Quantification LLM Uncertainty Estimation Uncertainty Decomposition Epistemic Uncertainty

Mar 30, 2026

Entropic Claim Resolution: Uncertainty-Driven Evidence Selection for RAG

Current Retrieval-Augmented Generation (RAG) systems predominantly rely on relevance-based dense retrieval, sequentially fetching documents to maximize semantic similarity with the query. However, in knowledge-intensive and real-world scenarios characterized by conflicting evidence or fundamental query ambiguity, relevance alone is insufficient for resolving epistemic uncertainty. We introduce Entropic Claim Resolution (ECR), a novel inference-time algorithm that reframes RAG reasoning as entropy minimization over competing semantic answer hypotheses. Unlike action-driven agentic frameworks (e.g., ReAct) or fixed-pipeline RAG architectures, ECR sequentially selects atomic evidence claims by maximizing Expected Entropy Reduction (EER), a decision-theoretic criterion for the value of information. The process dynamically terminates when the system reaches a mathematically defined state of epistemic sufficiency (H <= epsilon, subject to epistemic coherence). We integrate ECR into a production-grade multi-strategy retrieval pipeline (CSGR++) and analyze its theoretical properties. Our framework provides a rigorous foundation for uncertainty-aware evidence selection, shifting the paradigm from retrieving what is most relevant to retrieving what is most discriminative.

Davide Di Gioia

Retrieval-Augmented Generation Evidence Selection Inference-Time Search Epistemic Uncertainty Value of Information

Mar 28, 2026

Quantification of Credal Uncertainty: A Distance-Based Approach

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

Xabier Gonzalez-Garcia, Siu Lun Chau, Julian Rodemann +6

Dept. of Statistics, CS & Mathematics, Public Univ. of Navarre · EPIC Lab, Nanyang Technological Univ. Singapore · Rational Intelligence Lab, CISPA Helmholtz Center for Information Security +7

Uncertainty Quantification Aleatoric Uncertainty Integral Probability Metrics Uncertainty Decomposition Epistemic Uncertainty

Mar 26, 2026

The Anatomy of Uncertainty in LLMs

Understanding why a large language model (LLM) is uncertain about the response is important for their reliable deployment. Current approaches, which either provide a single uncertainty score or rely on the classical aleatoric-epistemic dichotomy, fail to offer actionable insights for improving the generative model. Recent studies have also shown that such methods are not enough for understanding uncertainty in LLMs. In this work, we advocate for an uncertainty decomposition framework that dissects LLM uncertainty into three distinct semantic components: (i) input ambiguity, arising from ambiguous prompts; (ii) knowledge gaps, caused by insufficient parametric evidence; and (iii) decoding randomness, stemming from stochastic sampling. Through a series of experiments we demonstrate that the dominance of these components can shift across model size and task. Our framework provides a better understanding to audit LLM reliability and detect hallucinations, paving the way for targeted interventions and more trustworthy systems.

Aditya Taparia, Ransalu Senanayake, Kowshik Thopalli +1

School of Computing and Augmented Intelligence, Arizona State University · Lawrence Livermore National Laboratory

LLM Auditing LLM Reliability LLM Uncertainty Estimation Uncertainty Decomposition Epistemic Uncertainty

Mar 19, 2026

Rethinking Uncertainty Quantification and Entanglement in Image Segmentation

Uncertainty quantification (UQ) is crucial in safety-critical applications such as medical image segmentation. Total uncertainty is typically decomposed into data-related aleatoric uncertainty (AU) and model-related epistemic uncertainty (EU). Many methods exist for modeling AU (such as Probabilistic UNet, Diffusion) and EU (such as ensembles, MC Dropout), but it is unclear how they interact when combined. Additionally, recent work has revealed substantial entanglement between AU and EU, undermining the interpretability and practical usefulness of the decomposition. We present a comprehensive empirical study covering a broad range of AU-EU model combinations, propose an entanglement proxy based on the relative performance of uncertainty measures, and evaluate model combinations across downstream uncertainty quantification tasks. Ensembles consistently show more favorable proxy values and superior performance. Softmax models usually beat other AU methods, except in calibration where the results are dataset-dependent. A softmax ensemble performs remarkably well on all tasks. Finally, we analyze potential sources of uncertainty entanglement and outline directions for mitigating this effect.

Jakob Lønborg Christensen, Vedrana Andersen Dahl, Morten Rieger Hannemose +2

Technical University of Denmark, DTU Compute · University of Lucerne, Faculty of Health Sciences and Medicine, Switzerland

Uncertainty Quantification Deep Ensembles Aleatoric Uncertainty Segmentation Uncertainty Estimation Uncertainty Calibration Uncertainty Decomposition+1

Mar 18, 2026

FoMo X: Modular Explainability Signals for Outlier Detection Foundation Models

Tabular foundation models, specifically Prior-Data Fitted Networks (PFNs), have revolutionized outlier detection (OD) by enabling unsupervised zero-shot adaptation to new datasets without training. However, despite their predictive power, these models typically function as opaque black boxes, outputting scalar outlier scores that lack the operational context required for safety-critical decision-making. Existing post-hoc explanation methods are often computationally prohibitive for real-time deployment or fail to capture the epistemic uncertainty inherent in zero-shot inference. In this work, we introduce FoMo-X, a modular framework that equips OD foundation models with intrinsic, lightweight diagnostic capabilities. We leverage the insight that the frozen embeddings of a pretrained PFN backbone already encode rich, context-conditioned relational information. FoMo-X attaches auxiliary diagnostic heads to these embeddings, trained offline using the same generative simulator prior as the backbone. This allows us to distill computationally expensive properties, such as Monte Carlo dropout based epistemic uncertainty, into a deterministic, single-pass inference. We instantiate FoMo-X with two novel heads: a Severity Head that discretizes deviations into interpretable risk tiers, and an Uncertainty Head that provides calibrated confidence measures. Extensive evaluation on synthetic and real-world benchmarks (ADBench) demonstrates that FoMo-X recovers ground-truth diagnostic signals with high fidelity and negligible inference overhead. By bridging the gap between foundation model performance and operational explainability, FoMo-X offers a scalable path toward trustworthy, zero-shot outlier detection.

Simon Klüttermann, Tim Katzke, Phuong Huong Nguyen +1

TU Dortmund University, Dortmund, Germany · Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, Germany

Interpretable Anomaly Detection Unsupervised Anomaly Detection Zero-Shot Anomaly Detection Tabular Foundation Models Epistemic Uncertainty

Mar 13, 2026

The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence

This paper develops a measure-theoretic framework establishing when and how a possibilistic representation of incomplete knowledge contracts into a probabilistic representation of intrinsic stochastic variability. Epistemic uncertainty is encoded by a possibility distribution and its dual necessity measure, defining a credal set bounding all probability measures consistent with current evidence. As evidence accumulates, the credal set contracts. The epistemic collapse condition marks the transition: the Choquet integral converges to the Lebesgue integral over the unique limiting density. We prove this rigorously (Theorem 4.5), with all assumptions explicit and a full treatment of the non-consonant case. We introduce the aggregate epistemic width W, establish its axiomatic properties, provide a canonical normalization, and give a feasible online proxy resolving a circularity in prior formulations. Section 7 develops the dynamics of epistemic contraction: evidence induces compatibility, compatibility performs falsification, posterior possibility is the min-intersection of prior possibility and compatibility, and a credibility-directed flow governs support geometry contraction. This is not belief updating. It is knowledge contraction. Probability theory is the limiting geometry of that process. The UKF and ESPF solve different problems by different mechanisms. The UKF minimizes MSE, asserts truth, and requires a valid generative model. The ESPF minimizes maximum entropy and surfaces what evidence has not ruled out. When the world is Gaussian and the model valid, both reach the same estimate by entirely different routes -- convergent optimality, not hierarchical containment. We prove this (Theorem 9.1) and compare both on a 2-day, 877-step orbital tracking scenario. Both achieve 1-meter accuracy. The UKF is accurate but epistemically silent. The ESPF is accurate and epistemically honest.

Moriba Kemessia Jah

Black Swan Research Group, GaiaVerse, Ltd., Austin, TX 78728, USA · Jah Decision Intelligence Group, Aerospace Engineering & Engineering Mechanics The University of Texas at Austin, Austin, TX 78712

Imprecise Probability Epistemic Uncertainty Uncertainty Quantification

Mar 11, 2026

CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice, understanding the reason behind a model's uncertainty and the type of uncertainty it represents can support risk-aware decisions, enhance user trust, and guide additional data collection. However, many existing methods only address a single type of uncertainty or require modifications and retraining of the base model, making them difficult to adopt in real-world systems. We introduce CUPID (Comprehensive Uncertainty Plug-in estImation moDel), a general-purpose module that jointly estimates aleatoric and epistemic uncertainty without modifying or retraining the base model. CUPID can be flexibly inserted into any layer of a pretrained network. It models aleatoric uncertainty through a learned Bayesian identity mapping and captures epistemic uncertainty by analyzing the model's internal responses to structured perturbations. We evaluate CUPID across a range of tasks, including classification, regression, and out-of-distribution detection. The results show that it consistently delivers competitive performance while offering layer-wise insights into the origins of uncertainty. By making uncertainty estimation modular, interpretable, and model-agnostic, CUPID supports more transparent and trustworthy AI. Related code and data are available at https://github.com/a-Fomalhaut-a/CUPID.

Xinran Xu, Xiuyi Fan

Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore · College of Computing and Data Science, Nanyang Technological University, Singapore · Centre for Medical Technologies & Innovations, National Health Group, Singapore

Uncertainty Quantification Epistemic Uncertainty Uncertainty Decomposition Aleatoric Uncertainty

Mar 11, 2026

Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities

Despite the growing demand for eliciting uncertainty from large language models (LLMs), empirical evidence suggests that LLM behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in imprecise probabilities, a principled framework for repesenting and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from LLMs, improving credibility and supporting downstream decision-making.

Anita Yang, Krikamol Muandet, Michele Caprio +2

Lattice Lab, Toyota Motor Corporation, Japan · Department of Computer Science, University of Tokyo, Japan · Rational Intelligence Lab, CISPA, Helmholtz Center for Information Security, Germany +3

Imprecise Probability LLM Uncertainty Estimation Epistemic Uncertainty LLM Prompting

Mar 10, 2026

From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express

Leyva-Vázquez and Smarandache (2025) demonstrated that neutrosophic T/I/F evaluation, where Truth, Indeterminacy, and Falsity are independent dimensions not constrained to sum to 1.0, which reveals "hyper-truth"' (T+I+F > 1.0) in 35% of complex epistemic cases evaluated by LLMs. We extend their work in two directions. First, we replicate and extend their experiment across five model families from five vendors (Anthropic, Meta, DeepSeek, Alibaba, Mistral), finding hyper-truth in 84% of unconstrained evaluations, which confirms the phenomenon is cross-vendor under our prompt protocol. Second, and more significantly, we identify a limitation of scalar T/I/F that their framework cannot address: models adopting an `"Absorption" position (T=0, I=1, F=0) produce identical scalar outputs for fundamentally different epistemic situations (paradox, ignorance, contingency), collapsing the very distinctions neutrosophic logic was designed to preserve. We demonstrate that extending the evaluation to include declared losses (structured descriptions of what the model cannot evaluate and why) substantially recovers these distinctions. Models producing identical scalars for paradox and ignorance produce nearly disjoint loss vocabularies (Jaccard similarity < 0.10 on loss description keywords), with domain-specific, severity-rated loss declarations that differentiate the nature of their uncertainty. This suggests that scalar T/I/F is a necessary but insufficient representation of epistemic state, and that tensor-structured output (scalars + losses) provides a more faithful model of LLM epistemic capabilities.

Tony Mason

University of British Columbia, Vancouver, Canada · Georgia Institute of Technology, Atlanta, USA

Epistemic Uncertainty LLM Evaluation LLM Uncertainty Estimation