Uncertainty Gap in AI & Models

• Uncertainty gap is the misalignment between a system’s expressed uncertainty and the ideal benchmark, impacting calibration in diverse domains.
• It encompasses discrepancies in adversarial settings, evaluation theory, contextual QA, and creative tasks, highlighting a divergence between metric performance and inherent ambiguity.
• The concept stresses that improvements in accuracy or likelihood do not automatically resolve miscalibration, necessitating targeted strategies in model training and evaluation.

Searching arXiv for papers on “uncertainty gap” and closely related formulations across AI, control, and scientific modeling. In recent literature, “uncertainty gap” is used in several related but non-identical senses rather than as a single canonical quantity. Across machine learning, scientific modeling, evaluation theory, and decision analysis, it denotes a mismatch between the uncertainty a system ought to express and the uncertainty it actually expresses, between benchmark scores and the ceiling imposed by ambiguous ground truth, or between uncertainty representations and the human or dynamical behaviors they are expected to support. Representative formulations include adversarial over-confidence in zero-shot CLIP, the collapse of expert-versus-random distinguishability under uncertain labels, semantic feature mismatches in contextual question answering, and the lower-uncertainty profile of model-generated fiction relative to human-authored writing (Lu et al., 15 Dec 2025, Elangovan et al., 9 Jan 2026, Bakman et al., 3 Oct 2025, Sui, 18 Feb 2026).

1. Terminological scope and recurring structure

Across the surveyed literature, the term appears in at least five recurring forms.

Domain	Gap formulation	Representative paper
Adversarial VLMs	uncertainty decreases as perturbations make predictions less reliable	(Lu et al., 15 Dec 2025)
Evaluation theory	aggregate metrics cannot separate expertise from chance under uncertain labels	(Elangovan et al., 9 Jan 2026)
Contextual QA	epistemic uncertainty is a hidden-state feature gap to an ideal model	(Bakman et al., 3 Oct 2025)
Human/model alignment	model uncertainty weakly matches human-perceived uncertainty	(Mendes et al., 18 Jun 2025)
Chaotic surrogates	probabilistic objectives improve while dynamics-oriented certification worsens	(Herz et al., 29 May 2026)

A common pattern is that the gap is not simply “high uncertainty” or “low uncertainty.” Rather, it is a structural misalignment between an uncertainty signal and some external criterion: correctness under attack, expert consensus, latent semantic adequacy, human intuition, fairness across groups, or local tangent dynamics. This suggests that the phrase functions as a family resemblance term: each paper instantiates a domain-specific discrepancy, but the discrepancy is always between a nominal uncertainty mechanism and a target notion of reliability.

A second recurring pattern is that many papers distinguish aleatoric and epistemic components rather than treating uncertainty as a scalar monolith. In the CLIP setting, Dirichlet concentration separates ambiguity across classes from overall evidence strength; in contextual QA, cross-entropy is decomposed into $H(p^*)$ and $KL(p^* \| p_\theta)$; in long-context in-context learning, total uncertainty is decomposed into epistemic and aleatoric terms; and in human-perception studies, by contrast, only total uncertainty is measured (Lu et al., 15 Dec 2025, Bakman et al., 3 Oct 2025, Wang et al., 27 May 2025, Mendes et al., 18 Jun 2025).

2. Adversarial calibration and zero-shot vision-LLMs

In zero-shot CLIP, the uncertainty gap is defined as a failure of uncertainty to rise when inputs become harder under adversarial perturbation. “Calibrating Uncertainty for Zero-Shot Adversarial CLIP” reports that under AutoAttack with $\epsilon=1/255$, the average Shannon entropy of CLIP’s predictions on adversarial examples is often lower than on clean inputs across 16 zero-shot datasets, even though adversarial perturbations degrade accuracy (Lu et al., 15 Dec 2025). The paper quantifies the effect as

$$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$

with

$H[p] = -\sum_k p_k \log p_k.$

In practice, the phenomenon manifests as severe miscalibration, high Expected Calibration Error under attack, and spuriously confident errors.

The paper’s technical response is to reinterpret CLIP logits as concentration parameters of a Dirichlet distribution. With cosine-similarity-based logits

$\ell_k(x) = \langle v(x), t_k\rangle / T,$

and a secondary calibration temperature $T'$, the construction is

$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$

so that $\alpha_k \ge 1$. The resulting Dirichlet density over $\Delta^{C-1}$ is

$KL(p^* \| p_\theta)$0

Its mean is

$KL(p^* \| p_\theta)$1

and when $KL(p^* \| p_\theta)$2, this coincides exactly with $KL(p^* \| p_\theta)$3 by Lemma 4.3 of the paper (Lu et al., 15 Dec 2025).

This Dirichlet reinterpretation yields closed-form aleatoric and epistemic uncertainty estimates:

$KL(p^* \| p_\theta)$4

$KL(p^* \| p_\theta)$5

The proposed Uncertainty-Calibrated Adversarial fine-Tuning (UCAT) keeps CLIP’s text encoder frozen, generates adversarial examples with standard $KL(p^* \| p_\theta)$6-PGD, and optimizes

$KL(p^* \| p_\theta)$7

where $KL(p^* \| p_\theta)$8 is text-guided cross-entropy on the adversarial embedding and $KL(p^* \| p_\theta)$9 is a Dirichlet-level KL alignment

$\epsilon=1/255$0

The stated rationale is that Dirichlet-level alignment preserves both inter-class semantic geometry and total evidence $\epsilon=1/255$1, unlike logit matching or softmax-level KL.

Empirically, the method fine-tunes CLIP-B/32 on TinyImageNet under 2-step PGD ($\epsilon=1/255$2) and 10-step PGD ($\epsilon=1/255$3), evaluates zero-shot on 16 single-label datasets plus MS-COCO, and measures robustness with PGD-100, CW-100, and AutoAttack while assessing calibration with ECE, NLL, and AUROC on AU/EU for separating correct from incorrect predictions (Lu et al., 15 Dec 2025). Under the light PGD-2 regime and AutoAttack, UCAT reaches an average robust accuracy of approximately $\epsilon=1/255$4, compared with approximately $\epsilon=1/255$5 for the best prior zero-shot method, while reducing ECE by over $\epsilon=1/255$6 relative to vanilla CLIP. The paper further reports that replacing the Dirichlet KL with a softmax-level KL yields inferior calibration, and that on MS-COCO multi-label evaluation UCAT improves top-$\epsilon=1/255$7 F1 under CW attack by nearly 3 points over the previous state of the art.

A common misconception is that adversarial fine-tuning is primarily a robustness intervention. In this setting, the paper argues that robustness-oriented logit matching can leave a separate reliability defect unresolved: perturbations may suppress uncertainty rather than amplify it. The “uncertainty gap” is therefore presented as a calibration failure beyond conventional adversarial accuracy (Lu et al., 15 Dec 2025).

3. Ground-truth ambiguity and evaluation ceilings

In medicine and related evaluation settings, the uncertainty gap is defined differently. Elangovan et al. describe it as the phenomenon whereby, when the “ground truth” label is itself uncertain because experts disagree, standard single-point metrics such as accuracy and F1 can no longer distinguish a true expert from a weak or even random annotator (Elangovan et al., 9 Jan 2026). The key mechanism is majority-vote uncertainty: if a fresh expert agrees with the majority label only with probability $\epsilon=1/255$8, then even perfect expertise is bounded by the ambiguity of the label set.

For binary classification, the paper gives closed-form expected metrics:

$\epsilon=1/255$9

and, with positive-class fraction $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$0,

$$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$1

which imply

$$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$2

These expressions depend only on the agreement rate $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$3 and class balance $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$4, not on any hidden notion of system capability (Elangovan et al., 9 Jan 2026).

The paper therefore recommends estimating $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$5 from expert agreement, computing $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$6 as the fraction of experts voting for the majority label on each item, and stratifying evaluation by certainty bins. It gives example bins of $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$7 and $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$8, and states that stratification becomes critical when overall performance drops below a threshold of $$\Delta_{PU} = H[p_{\mathrm{CLIP}}(y \mid x)] - H[p_{\mathrm{CLIP}}(y \mid x_{\mathrm{adv}})],$$9 (Elangovan et al., 9 Jan 2026). Without such stratification, an AI system can appear “expert-level” simply because a test set is dominated by intrinsically ambiguous items on which random and expert behavior are both close to the same ceiling.

The toy examples make the logic explicit. On balanced data with $H[p] = -\sum_k p_k \log p_k.$0 and expert agreement $H[p] = -\sum_k p_k \log p_k.$1, both a random labeler and an expert have approximately zero probability of exceeding $H[p] = -\sum_k p_k \log p_k.$2 accuracy on $H[p] = -\sum_k p_k \log p_k.$3 items. By contrast, at $H[p] = -\sum_k p_k \log p_k.$4, the expert “pulls away.” On imbalanced data with $H[p] = -\sum_k p_k \log p_k.$5, the expected F1 for $H[p] = -\sum_k p_k \log p_k.$6 is approximately $H[p] = -\sum_k p_k \log p_k.$7, whereas for $H[p] = -\sum_k p_k \log p_k.$8 it is $H[p] = -\sum_k p_k \log p_k.$9 (Elangovan et al., 9 Jan 2026).

This formulation relocates the uncertainty gap from the predictor to the benchmark itself. It is therefore a direct counterexample to the assumption that low aggregate accuracy necessarily implies low capability. In the presence of uncertain labels, the aggregate score may instead be limited by the attainable expert ceiling.

4. Language-model formulations: feature gaps, in-context uncertainty, and creative writing

A distinct formulation appears in contextual QA. “Uncertainty as Feature Gaps” defines total token-level uncertainty as the cross-entropy between the unknown true distribution $\ell_k(x) = \langle v(x), t_k\rangle / T,$0 and the model distribution $\ell_k(x) = \langle v(x), t_k\rangle / T,$1:

$\ell_k(x) = \langle v(x), t_k\rangle / T,$2

Using

$\ell_k(x) = \langle v(x), t_k\rangle / T,$3

the paper isolates epistemic uncertainty as $\ell_k(x) = \langle v(x), t_k\rangle / T,$4 and approximates $\ell_k(x) = \langle v(x), t_k\rangle / T,$5 by an idealized, perfectly prompted model (Bakman et al., 3 Oct 2025). It then derives the upper bound

$\ell_k(x) = \langle v(x), t_k\rangle / T,$6

where $\ell_k(x) = \langle v(x), t_k\rangle / T,$7 and $\ell_k(x) = \langle v(x), t_k\rangle / T,$8 are final-layer hidden states under the ideal and actual models. Under the Linear Representation Hypothesis, the hidden-state discrepancy is interpreted as a gap over semantic feature directions, yielding the paper’s feature-gap conception of epistemic uncertainty.

For contextual QA, the paper hypothesizes three dominant features: context reliance, context comprehension, and honesty. These are extracted using a top-down, contrastive PCA procedure from a small labeled set, and combined into a weighted uncertainty score. On Qasper, HotpotQA, and NarrativeQA, with LLaMA-3.1 8B, Mistral 7B, and Qwen 2.5 7B, the method is reported to outperform both supervised and unsupervised baselines by up to a 13-point PRR improvement while incurring negligible inference overhead (Bakman et al., 3 Oct 2025).

A related but not identical use of the phrase appears in long-context in-context learning. “Uncertainty Unveiled” states that in-context learning often yields models that appear confident yet still err at a non-negligible rate, and names this discrepancy the uncertainty gap (Wang et al., 27 May 2025). The paper defines total uncertainty as the entropy of the aggregated predictive distribution and decomposes it into epistemic uncertainty and aleatoric uncertainty via averaged entropies across sampled demonstration sets. Its core empirical claim is that more in-context examples reduce total uncertainty by injecting task-specific knowledge and thereby diminishing epistemic uncertainty. The effect depends on diversity rather than repetition: Figure 1 is described as showing that repeating the same examples many times does not lower epistemic uncertainty, whereas adding distinct examples does (Wang et al., 27 May 2025). A concrete example given for Qwen-2.5-14B is that on AG_News, total uncertainty drops from $\ell_k(x) = \langle v(x), t_k\rangle / T,$9 at 2-shot to $T'$0 at 256-shot, epistemic uncertainty from $T'$1 to $T'$2, and accuracy rises from $T'$3 to $T'$4; on LD5, total uncertainty drops from $T'$5 to $T'$6 and accuracy rises from $T'$7 to $T'$8 (Wang et al., 27 May 2025).

Creative writing introduces yet another formalization. Sui et al. argue that literary quality depends on indeterminacy and ambiguity, and operationalize the uncertainty gap as the model-normalized difference between human-authored and model-generated story continuations (Sui, 18 Feb 2026). For a continuation $T'$9 under context $$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$0, they define

$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$1

$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$2

and PMI- and CPMI-based quantities. The uncertainty gap is then measured by

$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$3

and

$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$4

Across 28 LLMs and two professionally curated fiction corpora, the paper reports median $$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$5–$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$6, median $$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$7–$$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$8, and New Yorker $$\alpha_k(x)=\exp h(\ell_k(x)), \qquad h(\ell)=(T\ell+1)/T',$$9 to $\alpha_k \ge 1$0 nats, indicating that human continuations are systematically less predictable than model outputs (Sui, 18 Feb 2026). Instruction-tuned and reasoning variants are reported to widen the gap relative to base models, and the gap is described as more pronounced in creative writing than in functional domains.

Taken together, these LLM papers suggest that “uncertainty gap” can denote at least three different objects: a representational distance to an ideal model, a confidence–reliability discrepancy under prompting, and an information-theoretic shortfall in creative indeterminacy. The shared intuition is epistemic inadequacy, but the operational definitions differ substantially.

5. Human, fairness, and interactional gaps

One line of work treats the gap as a divergence between model uncertainty and human-perceived uncertainty. “Uncertainty Estimation by Human Perception versus Neural Models” defines human uncertainty from a soft label distribution

$\alpha_k \ge 1$1

with human entropy

$\alpha_k \ge 1$2

and compares it to model predictive entropy

$\alpha_k \ge 1$3

On CIFAR-10H, CIFAR-N, and ImageNet-16H, Pearson correlations between human and model uncertainty are reported as weak or negligible, ranging from approximately $\alpha_k \ge 1$4 to $\alpha_k \ge 1$5 across baselines (Mendes et al., 18 Jun 2025). Replacing one-hot targets with human-derived soft labels,

$\alpha_k \ge 1$6

raises the correlation from $\alpha_k \ge 1$7 to $\alpha_k \ge 1$8 on CIFAR-10H and from $\alpha_k \ge 1$9 to $\Delta^{C-1}$0 on ImageNet-16H, with no significant drop in top-1 accuracy and 20–30% relative improvement in calibration metrics (Mendes et al., 18 Jun 2025). Here the uncertainty gap is a human–model alignment problem rather than a purely statistical one.

Fairness work gives the term an explicitly demographic interpretation. “FairlyUncertain” defines the uncertainty gap between protected groups as the absolute difference in mean predicted uncertainty:

$\Delta^{C-1}$1

It further proposes two axioms for fair uncertainty estimates: consistency across similar learning pipelines and calibration to observed randomness (Rosenblatt et al., 2024). For binary classification, the benchmark argues for a simple estimator obtained from Bernoulli NLL training with

$\Delta^{C-1}$2

and reports that this “Binomial NLL” method is more calibrated and among the most consistent on five binary datasets. The paper also states that abstaining on high-uncertainty cases reduces error but does not systematically alleviate statistical parity or equalized-odds disparities, whereas in regression, Normal NLL-based heteroscedastic uncertainty improves uncertainty-aware statistical parity by 20–50% without explicit fairness constraints (Rosenblatt et al., 2024).

Human-computer interaction work shows that even the display granularity of uncertainty can create its own gap between intended and realized user behavior. In a between-subjects study with $\Delta^{C-1}$3, “Not All Uncertainty Is Equal” compares output-level, relation-level, and token-level uncertainty displays for medical yes/no questions (Villavicencio et al., 27 May 2026). Token-level uncertainty increases agreement with the AI; output- and relation-level uncertainty reduce participants’ confidence in their own answers; and relation-level uncertainty reduces external verification such as link clicks and web searches. The paper therefore defines an uncertainty gap as a mismatch between the quantity and granularity of uncertainty information provided and the resulting user outcomes. A plausible implication is that “more uncertainty information” is not intrinsically trust-calibrating; its behavioral effect depends on representation and task context.

6. Dynamical, control-theoretic, and decision-analytic formulations

Outside mainstream ML calibration, related gap formalisms arise in control and scientific modeling. In “Probabilistic Robustness in the Gap Metric,” the gap is the gap metric between a nominal LTI plant and a stochastic perturbation:

$\Delta^{C-1}$4

with $\Delta^{C-1}$5 (Renganathan, 14 Jul 2025). Under a Lipschitz condition,

$\Delta^{C-1}$6

which yields the tail bound

$\Delta^{C-1}$7

The paper derives probabilistic robust-stability and $\Delta^{C-1}$8-performance guarantees in terms of this random gap, as well as bounds on the expected gap (Renganathan, 14 Jul 2025). Here the relevant gap is a random robustness radius, not a miscalibration statistic.

Chaotic surrogate modeling introduces a stronger consistency notion. “The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling” defines a DPC gap for a parameter update $\Delta^{C-1}$9 when a finite-horizon probabilistic score improves while a scientific certification loss deteriorates:

$KL(p^* \| p_\theta)$00

The paper attributes the gap to core collapse, noise masking, and blind uncertainty, and proposes KAFFEE, an EKF-based training framework that scores one-step innovations while transporting covariance through learned Jacobians (Herz et al., 29 May 2026). On stochastic hyperchaotic Lorenz-96, KAFFEE is reported to reduce the failure modes, improve dynamical invariants relative to open-loop objectives, and maintain competitive predictive scores. A key message is that better likelihood can actively degrade the very dynamical structure that uncertainty is supposed to reflect.

A separate, older tradition concerns information-gap decision theory rather than “uncertainty gap” in the same terminological sense. The comprehensive energy review defines Information-Gap Decision Theory as a non-probabilistic framework centered on a horizon of uncertainty $KL(p^* \| p_\theta)$01 and the functions of robustness and vulnerability:

$KL(p^* \| p_\theta)$02

$KL(p^* \| p_\theta)$03

$KL(p^* \| p_\theta)$04

In this literature, the gap is the allowable deviation from a nominal forecast before a requirement fails, with applications to renewable generation, market prices, unit commitment, and transmission planning (Majidi et al., 2019). Harp and Vesselinov’s contaminant-remediation analysis develops the same logic for uncertain contaminant flux, deriving robustness and opportuneness from nested uncertainty sets around a nominal flux $KL(p^* \| p_\theta)$05 (Harp et al., 2011).

Rougier and Crucifix use “uncertainty gap” at the policy-science interface. They define it as the mismatch between academic climate science, focused on high-resolution simulation and explanation, and policy climate science, which requires total uncertainty quantification across interventions, scenarios, model structures, parameters, and judgments (Rougier et al., 2014). Their designed-experiment example computes

$KL(p^* \| p_\theta)$06

model-years of simulation for a policy tableau spanning interventions, socioeconomic scenarios, simulator configurations, and forecast years. The gap is therefore institutional and epistemological as much as statistical.

7. Synthesis, limitations, and recurring misconceptions

Taken together, these works suggest that the uncertainty gap is best understood as a class of alignment failures rather than a single metric. The aligned quantity may be adversarial difficulty, label ambiguity, semantic adequacy, human perception, demographic parity in uncertainty assignment, user verification behavior, local tangent dynamics, or policy needs (Lu et al., 15 Dec 2025, Elangovan et al., 9 Jan 2026, Bakman et al., 3 Oct 2025, Mendes et al., 18 Jun 2025, Rosenblatt et al., 2024, Herz et al., 29 May 2026, Rougier et al., 2014).

Several misconceptions recur across the literature. First, improved prediction or likelihood does not guarantee improved uncertainty behavior. UCAT is motivated precisely because logit matching can preserve or improve adversarial objectives while leaving over-confidence unresolved; DPC-gap work shows that finite-horizon probabilistic training can degrade dynamics; and FairlyUncertain shows that abstention lowers error without systematically improving fairness (Lu et al., 15 Dec 2025, Herz et al., 29 May 2026, Rosenblatt et al., 2024). Second, uncertainty is not interchangeable with calibration. In medicine, the core issue may be uncertainty in the benchmark rather than in the predictor; in creative writing, higher uncertainty can correlate with quality rather than with unreliability; and in human-facing interfaces, the display of uncertainty can alter verification in undesirable ways (Elangovan et al., 9 Jan 2026, Sui, 18 Feb 2026, Villavicencio et al., 27 May 2026). Third, scalar uncertainty alone is often insufficient. Multiple papers replace scalar confidence with structured objects: Dirichlet distributions in CLIP, feature directions in contextual QA, certainty strata in benchmark evaluation, and Jacobian-grounded covariance transport in chaotic surrogates (Lu et al., 15 Dec 2025, Bakman et al., 3 Oct 2025, Elangovan et al., 9 Jan 2026, Herz et al., 29 May 2026).

The main methodological consequence is that closing an uncertainty gap usually requires modifying the representation or protocol that produced it. Examples include aligning entire Dirichlet distributions rather than logits, stratifying results by expert agreement, learning semantic feature probes with small labeled sets, training on human soft labels, or coupling probabilistic losses to the same Jacobians that define the learned dynamics (Lu et al., 15 Dec 2025, Elangovan et al., 9 Jan 2026, Bakman et al., 3 Oct 2025, Mendes et al., 18 Jun 2025, Herz et al., 29 May 2026). A plausible implication is that uncertainty quality is rarely a purely post-hoc property. In the surveyed work, it is typically entangled with training objectives, data collection, model interfaces, and the operational definition of correctness itself.