Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answering
Authors: Yavuz Faruk Bakman
Sungmin Kang
Zhiqi Huang
Duygu Nur Yaldiz
Catarina G Belém
Chenyang Zhu
Anoop Kumar
Alfy Samuel
Daben Liu
Salman Avestimehr
Sai Praneeth Karimireddy
Venue: ICLR 2026 Poster (2026)
Keywords: Uncertainty Quantification
LLMs
RAG
Contextual QA
Hallucinations
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Abstract: Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify \emph{epistemic uncertainty}. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model’s hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: \emph{context-reliance} (using the provided context rather than parametric knowledge), \emph{context comprehension} (extracting relevant information from context), and \emph{honesty} (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead. The code is available at https://github.com/Ybakman/Feature-Gaps.

Published as a conference paper at ICLR 2026
UNCERTAINTY AS FEATURE GAPS:
EPISTEMIC UNCERTAINTY QUANTIFICATION OF LLMs IN CONTEXTUAL QUESTION-ANSWERT
Yavuz Bakman'
Sungmin Kang'
Zhiqi Huang?
Duygu Nur Yaldiz'
Catarina G. Belém
Chenyang Zhu²
Anoop Kumar²
Alfy Samuel
Salman Avestimehr'
Daben Liu?
Sai Praneeth Karimireddy!
University of Southern California
Capital One
University of California, Irvine
ybakman@uso.
ABSTRACT
Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epix- temic uncertainly. We begin by introducing task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than para- metric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using top-down interpretabillty approach, we extract these features by using only small number of labeled samples and ensemble them form robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribtion settings show that our method substantially outperforms state-of taite-of-the-ee of-the-art unsupervised (sampling free and compling-basedd and supervised UQ methods, achieving up to 13-point PRR improvement while incurring a negligible inference overhead. The code is available at htttps://giieee thub. com/ Ybakman, Feature- Gaps
INTRODUCTION
Despite their impressive performance across a wide range of real-world tasks, Large Language Models (LLMs) still suffer from hallucinations and incorrect generations, which limit their deployment in high-stakes domains such as medicine and finance (Bengio et al.) (2025] Ravi et al.) 2024). Uncertainty Quantification (UQ) has emerged as a key tool for detecting such errors by only using the model itself, such as output consistency, prg-pobbaiilities or internal activations. Recent works (Bakman) ctt al. 2025 Vashurin et al. 2025) have demonstrated that UQ methods cxhibit strong empirical performance across a variety of evaluation benchmarks.
While these results are encouraging, most existing works Yaadii et al. 2025a Lin et al. 2024 Kuhn et al. 2023 Duan et al. 2024) design and evaluate their methods primarily on closed-book factual question answering (QA) tasks, which test the success of UQ methods on the model's memory abilities. Although this direction is important, another critical ability of LLMs that deserves more attention from a UQ perspective is their contextual capabilities. With the increasing popularity
"Corresoonding author & Work done during the internship at Capital One

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UQ Metric
Step Approximation Step 2: Upper Bound
Step 3: Feature Gaps
Entropy: Aleatoric Uncertainty
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Figure 1: Derivation steps for epistemic uncertainty as feature gaps.
Visualization of Section 3
of Retrieval-Angmented Generation (RAG) in many LLM applications, detecting errors in model generations conditioned on retrieved context has become more important. However, relatively little effort has been devoted to this direction (Soudani et al. 2025 Fadeeva et al., 2025
Lapata 2025), where the proposed approaches often rely on heuristics rather than grounded theory.
Motivated by these observations, we focus on developing theoretically grounded UQ method for contextual QA. In this setting, the relevant context is either already retrieved or directly provided by the user, and context-relevant question is posed to the model. Our goal is to quantify the model's uncertainty for a given input as a means to assess whether its output is likely to be correct/reliable.
To quantify the uncertainty of an LLM, we first propose an uncertainty metric defined as the cross-entropy between the true predictive distribution and the given model's distribution, inspired by (Schweighofer et al. (2024). Our approach introduces key modification to their formulation by reversing the position of the true and given model distributions within the cross- eoossee and adapting it specifically for L.MSs. We further decompose the total uncertainty into two components: epistemic and aleatoric uncertainty. In our problem setup, epistemic uncertainty, the model's lack of ability or knowledge correctly and reliably answer a given question-context pair, is our main interest. After approximating the true predictive distribution with a perfectly prompted hypothetical ideal model, we show that epistemic uncertainty can be bounded by the distance between the last layer hidden state of the given model and the ideal hypothetical model. We further show that this distance can be expressed as the sum of distances over linearly independent model features. Importantly, this result generalizes to any LLM task and is visualized in Figure []] To approximate this distance specifically in contextual question answering task, we hypothesize three desirable features that capture how far the given model is from the ideal model: 1) Context reliancy: the model should ground its answer in the provided context rather than relying on its parametric knowledge; 2) Context comprehension: the model should be able extract and integrate relevant information from the context to answer the question accurately. 3) Honesty: the model should avoid intentionally outputting a wrong answer.
Following a tow-down interpretability approach similar to Zou al. (2025). extract the aforemen- tioned high-level semantic features using a small set of labeled samples to identify the optimal layer for feature extraction. At test time, combine the activation amount of three features quantify epistemic uncertainty by computing only three dot products hetween the model's hidden state and the corresponding feature vectors, one per feature, without requiring any sampling. Our method is highly efficient and achieves substantial performance gains: it outperforms SOTA unsupervised, sampling-fie and sampling- based approaches by up to 16 PRR points. Furthermore, with the same amount of labeled data, it surpasses strong supervised baselines such as SAPLMA (Azaria & Mitchell 2023) and LookbackLens (Chuang et al., 2024) by up to 13 PRR points, while exhibiting significantly better out-of-distribution generalization compared to SAPLMA, which is an important and desirable property for supervised UQ methods. The overview of our proposed method is visualized Figure]
2
PRELIMINARIES
2.1 ALEATORIC AND EPISTEMIC UNCERTAINTY
The total uncertainty of model is typically decomposed into two components: epistemic and aleatoric uncertainty (Hüllermeier& & Waegeman 2021). Epistemic uncertainty arises from a lack of knowledge. In the context of LLMs, when faced with difficult question that the model does not know the answer to, its output distribution tends to be more uniform, which indicates uncertainty about which answer is correct. This uncertainty stems from the model's inability or lack of knowledge
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to provide the correct answer, and is therefore classified as epistemic. In contrast, aleatoric (or data) uncertainty captures variability inherent to the task or data, rather than limitations in the model's s knowledge. For example, model may be epistemically confident, knowing the answer, but still produce multiple valid responses due to ambiguity in the question or the presence of multiple equally correct phrasings. This variability arises from the nature of the query and the language itself, not from the model's s lack of ability. In the next section, we discuss how existing works conceptualize UQ in LLMs, and how these concepts relate to epistemic and aleatoric uncertainty.
2.2 UNCERTAINTY QUANTIFICATION OF LLMS
In the LLM literature, uncertainty quantification is typically used to identify incorrect or unreliable answers generated for a given query. Unlike the well-establiseed frameworks in classification tasks (Gal & Ghahramani 2016). there is no widely accepted UQ framework for generative LLMs (Bakman et al.) 2025; Vashurin et al. 2025). With few exceptions, most approaches rely on heuristic-baser based methods that estimate the correctness of a model's (greedy or sampled) generation. UQ methods only use the model itself to find such a score by using signals such as token probabilities Farquuar et al.] 2024), internal representations (Chen et al.) 2024), or output consistencies (Lin) et al. 2024). Although rarely stated explicitly, the underlying objective in many of these works is to better quantify epistemic uncertainty, i.c., to produce an uncertainty score that quantifies the model's (lack of) certainty in the correctness of its own generation. The performance of UQ methods is typically evaluated using threshold-fres metries such as the Area Under the ROC Curve (AUROC) and the Prediction-Rejedde distinguish between correct and incorrect outputs. A smaller number of studies (A (Abbasi- Yadkori et al., 2024 Aichberger et al. 2024 take more theoretically grounded approach, explicitly distinguishing between epistemic and aleatoric uncertainty. In this work, we also aim to separate epistemic and aleatoric uncertainty through our proposed UQ formulation. In the following section, we introduce our notation and describe the problem setup.
Ratio (PRR) to measure which assess how well uncertainty scores
2.3 PROBLEM SETUP AND NOTATION
We denote the context sequence as c, and the question together with any relevant instructions as x. The probability distribution over the token at position produced by the model, conditioned on the context c, query and previously generated tokens, is given by: P(ye y x,,, c,0), where Yer denotes the sequence of tokens generated before timestep I, and represents the given model parameters. Our objective is to find uncertainty quantification method Uxx y) R that is negatively correlated with the correctness of the generated sequence y. More formally, we aim to maximize E. U'x) <Uxaa es) yyye y where (X1, Y1), (x2, ~ Diest with Diea denoting the evaluation dataset obtained by getting the most probable (greedy) output for a context-query pair, and Y, representing the set of acceptable (correct) generations for instance i. This expectation enforces ranking consistency: correct outputs should receive lower uncertainty scores than incorrect outputs, making high-uncertainty scored generations more likely be wrong.
BOUNDING EPISTEMIC UNCERTAINTY VIA FEATURE GAPS
3.1 UNCERTAINTY QUANTIFICATION METRIC
Before introducing our uncertainty quantification metric for LLMs, we define the notion of a true (but unknown) token generation distribution, denoted by P*( x). This distribution represents the behavior of an ideal model that is free from epistemic uncertainty, i.c.. uncertainty arising from incomplete knowledge due to limited data, suboptimal architecture choices, imperfect training, or insufficient instruction tuning. The concept of such epistemically optimal distributions has also been explored in recent works (Kotelevskii et al. 2025 Abbasi- Yadkori et al. 2024).
Given the true distribution (- x) and given model's conditional distribution P(- x, f), we define the total uncertainty of token yr at generation step as follows:
Definition 1 (Total Uncertainty). Let V denote the token vocabulary. The total uncertainty (TU) of the model 0 for generating token Yt at timestep I, conditioned on the imput x, is defined as the
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cross-entropy between the true distribution and the model's predictive distribution:
TU -
Σ (" ye,,)) In P(ye Vet,,,00
V+EV
where Y<t denotes the previously sampled tokens up to timestep t.
This definition allows us to decompose total uncertainty into aleatoric (data) and epistemic uncertainty with an intuitive interpretation. The total uncertainty can be expressed as the sum of two terms:
TU H (P" (ye V<t,x)) KL (P" Y<t,)) P(y x,,,x,
(1)
Alcatoric (Data) Uncertainty
Epistemic Uncertaioty
The first term, H(P (ye yeer yer, the entropy of the true distribution, which corresponds to aleatoric (data) uncertainty. Since the true distribution PT x) has no epistemic uncertainty, any uncertainty in its predictions must arise from inherent randomness in the language modeling data distribution, (x. D. The second term, KL(P* (y, yer, x) ) || P(yt y<c, x, 0)), measures the divergence between the true distribution and the predictive distribution of the actual model. This gap captures epistemic uncertainty, uncertainty arising from the actual model's lack of knowledge ability compared to the epistemically optimal distribution. Lastly, Schweighofer et al. (2024) recently proposed a UQ metric for classification tasks that instead swaps the positions of P( Y<t; X, O) and P" (y/ ycr, x). We discuss the differences between our proposed formulation and theirs, along with the motivation for our choice, in Appendix A.
3.2 STEP 1: APPROXIMATING THE TRUE DISTRIBUTION
The true predictive distribution (- x) is unknown and intractable, which makes exact computation of epistemic uncertainty infeasible. Therefore, we approximate P* x) through our given model A. Specifically, we approximate the ideal model as the actual model that has been perfectly instructed or prompted so that its output distribution is close possible P'( x). Since appending an instruction or prompt can be theoretically viewed as form fine-tuning, as shown by many works (Dherin al., 2025 Akyurek et al. 2023). this approximation corresponds to obtaining the closest possible distribution to (- (- x) by training the given model in token space. Lastly, prompting is powerful enough to be Turing-complete: for any computable function, there exists Transformer and a corresponding prompt that computes it (Qiu et al. 2025).
Formally, approximate the true distribution (. x) by P(. x,s" 00), where s* (81, 82, 8n) ,2, is the optimal token sequence that minimizes the following objective:
s" = min Ex-D [KL (P x) P(- x,s,0))
(2)
where D is the data distribution of language modeling task. This objective corresponds to finding the optimal pre-sequence such that the resulting output distribution of the model is as close as the data distribution DD We refer the as the ideal model. For notational simplicity, we denote it by P(- fr) P(- x,,", 0), since the output distribution of the optimally prompted model can be considered as the behavior of an ideal model 0r. These two models, and 0*, share the same architecture and weights, but their activations differ due differences in prompting.
possible to the true distribution p x), in expectation
approximated model P(- s* 0) R (=
3.3 STEP 2: DERIVING AN UPPER BOUND FOR EPISTEMIC UNCERTAINTY
Finding the optimal sequence s* requires an exponential enumeration over all possible token se- quences, which is computationally infeasible. However, we can derive an upper bound on epistemic uncertainty in terms of the model's internal representations.
Lemma (Epistemic Uncertainty Upper Bound). For any token yt.
(L(P(y) YYt, 0*) P(ye Yet, x, 0)) S 2| [| - hells
where h; E Rd and h, E Rd are the last- lastr hidden states of the ideal and actual models with dimension of d, respectively, and W E RV is the vocabulary projection matrix at the last layer.
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Context:
Question:
Ensembling
Arda Guler my
played scoeed goals Liga, Champions Loigue, and godl Copa de Rey.
Eeouiit fondball player.
How grols hax he this
Feature Extraction
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Anda Gäler soonal goah 2004 zcoording to mrandir nocods.
Ie scored In Liga and 3 Charpionns Lesgue, wouding 5 tid you.
Arda Guke samed goals and aulles this year Not Honest (Sycophancy)
B. to
Uses Model Memory
Can't Comprehend
Context
Honesty
hidden state
PPCA
Figure 2: Approximating the bound in contextual QA ensemble of three features.
The proof of Lemma begins by expressing the probability distributions in terms of the model's internal representations and leveraging the fact that both models share the same vocabulary projection matrix. The complete derivation is provided in Appendix A.2 Lemma [ implies that epistemic uncertainty is bounded by the norm of the difference between the last-layer hidden states, scaled by 2|[W|] []. Since 2||W]| is fixed and we are interested in the relative magnitude of uncertainty rather than its absolute value, estimating this hidden-state distance is sufficient for our purposes.
3.4 STEP 3: INTERPRETING THE UPPER BOUND AS FEATURE GAPS
Although we have bounded epistemic uncertainty in terms of the distance to the last-layer hidden state of the ideal model, the hidden state of 6* remains unknown. To better understand this hidden state difference, we leverage one of the key hypotheses in interpretability in language models.
Hypothesis 1 (Linear Representation (Informal)). High-level semantic features are encoded approxi- mately linearly in the activation space of language models, often as single directions.
This hypothesis is broadly accepted and supported by substantial empirical evidence from prior work (Park et al.) 2024 Nanda et al. 2023 Templeton et al. (004)) As an example, we can identify a vector in intermediate layers that corresponds to feature such as "toxicity": the activation along this direction increases when the model produces toxic outputs, and decreases otherwise.
Let he and hü denote the d-dimensional last layer hidden states of the actual and ideal models, respectively. Due to residual connections, both ht and hū can be written as the sum of layer outputs: he -'- hi and h; Σ/ hir where hi is the output of layer / at timestep t. For desired decomposition at layer let F be set of feature vectors of Rd where |F'| d and rank(F)) d. Then, the hidden states can be expressed as: h4 = Σtz Eefere ofv! and h = Et_ Enerr Aoo where of and 8 are the coefficients for the actual and ideal models, respectively. For simplicity, let F = F U o U...UUU FL. Then we can write: he En,r awy; and h = Em,ex Bru.
The norm of the difference between the hidden states then becomes:
||4] hall = Σ (B: oz)u: U.E.F
(3)
Note that the above derivation holds for any language model with the same architecture without the linear representation hypothesis. However, the linear representation hypothesis provides a crucial interpretability advantage: it allows us to decompose each layer into semantically meaningful features F. Since the actual model and the ideal model differ only by the input prompt. sharing the same architecture and weights, their feature vectors vú correspond to the same semantic concepts. This alignment enables us to interpret the error term in Equation 3 as a collection of feature gaps, (B, a.). that quantify how the actual model deviates from the ideal model along interpretable semantic directions. This whole introduced UQ framework is visualized in Figure |
Remark 1. All derivations up to this point have been generic to any language modeling task, such as factual QA, mathematics, coding, or contextual QA.
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4 COMPUTING EPISTEMIC UNCERTAINTY IN CONTEXTUAL QA
4.1 SELECTING A REPRESENTATIVE FEATURE SET FOR CONTEXTUAL QA
Since the error term in Equation 3 may consist of arbitrarily many feature directions vs computing the bound exactly is infeasible. We therefore hypothesize a small set of features that are most likely to contribute to the gap between the actual and ideal models in the contextual QA setting. For example, selecting a syntactic feature would not be meaningful, as modern LLMs already exhibit strong mastery of grammar and sentence structure (OpenAI 2023). Thus, the potential gap along such dimensions is expected to be negligible. Instead, we focus on the features where current LLMs are more likely to deviate from the ideal model. Intuitively, if the model grounds its answer in the provided context, fully comprehends the contextual information, and outputs its understanding honestly, then it can behave similarly to the ideal model. Following this reasoning. we hypothesize that three high-level semantic features can approximate the gap in Equation 3 The first is Context Reliance: in contextual QA, the model's Is parametric knowledge may contradict the information contained in the provided context (Longpre al.) 202T). Models often default to their internal knowledge (which may be outdated or incorrect), resulting in unreliable answers. The second is Context Comprehension: in many contextual QA tasks, the answer may not be explicitly stated in the context but must be extracted or inferred from it. The third is Honesty: language models may sometimes generate false information deliberately. An example of this is L.M sycophancy (Sharma al., (025), where the model fabricates answers to align with user expectations rather than admitting ignorance. Now, our ~ [E,,E (B, a;) a:)v. where JF denotes the full set of latent features and H. is the restricted set consisting of the three features defined above.
approximation becomes: |_ > - at)e;
4.2 FEATURE EXTRACTION AND ENSEMBLING
Feature Extraction. To extract these three features, we adopt a top-down interpretability approach similar to Zou et al. (2025), which requires only a small amount of labeled data. Suppose we have access to set of T labeled samples, each consisting of a question-instruution pair x and a context c. We first obtain the greedy answer y from the model under the standard instruction. For each feature, we then construct contrastive instruction input pairs designed to isolate that feature. Concretely, this involves two forward passes with carefully designed prompts. For example, to capture the context reliance feature, we run one forward pass with the instruction "look at the context" and another with "use your own knowledge". This difference is expected to capture the "context coontext-parametric knowledge reliance" direction in representation space. After repeating this procedure over the dataset, we find the strongest direction through PCA, which corresponds to the desired feature vector. Formally:
m = (y,,,, "look at the context", c;) - (y;, X; + "use your own knowledge", .c,,,
(4)
M [ml, mb m.....,,m..................... m,,l
(5)
0' = PCC((M))
(6)
where 0: denotes the hidden representation at layer L. We follow a similar procedure for the other two features. For context comprehension, we perform one pass with the original context e and another with с + "I ground truth J". This ground truth append simulates the model having already resolved the relevant information from the context, thereby isolating the context comprehension feature. For honesty, we contrast the instructions "be honest" versus "be liar."
Selecting Optimal Layers and Ensembling, We use the same dataset employed for feature extraction to select the most informative layer for each feature. For each sample and each layer I, we compute the dot product between the hidden state by (averaged across all tokens y) and the extracted feature vector u': s ht ot. We then measure the correlation between these scores [s] syy.... sty] and the generation correctness using PRR. The layer with the highest PRR is selected as the feature layer.
To ensemble the three features, we need to estimate the coefficients B, In principle, any function could be used for this estimation. For simplicity, we define B = W;aa, ie., a scaled version of a; where the scaling factors w; trained to minimize the cross-entropy error with respect to the correctness of generation. This formulation reduces the learning problem to training only three parameters (W1, W2, wx), which is why only small number of labeled samples is sufficient, After

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leamingg the weights, the final ensemble reduces to a linear combination of all three features:
Σ(e:
Σ mEH
(m; 1),
EEW
5 EXPERIMENTS
5.1 EXPERIMENTAL SETUP
Datasets. We evaluate approach three contextual question answering datasets:
Qasper (Dasigi et al. 2021), D. a dataset for question answering over scientific research papers; (ii)
HotpotQA (Yang al. 20188) Wikipedia-
dataset consisting of multi-hop question-ann answer
pairs with supporting passages provided; and (iii) NarrativeQA (Kočiský et al. (0118). a dataset of stories and associated questions designed to test reading comprehension, particularly over long documents. We use 1000 samples from the each dataset.
Models. We use three models: LLaMA 3. 83, Mistral-ver vv. 3-7B, and Qwen2. 5-
Performance Metries. We evaluate uncertainty quantification methods using two widely adopted metries (Vashurin al. 2025 Area Under the Receiver Operating Characteristic Curve (AUROC) and Prediction Prediction-Reeecction Ratio (PRR). AUROC measures method's 's ability to discriminate between correct and incorrect outputs across all possible thresholds, with values ranging from 0.5 (random performance) to 1.0 (perfect discrimination). PRR quantifies the relative precision gain achieved by rejecting low-confidence predictions, ranging from 0.0 (random rejection) 1.0 (perfect rejection).
Correctness Measure. As our tasks involve free-form generation, model outputs may be semantically correct even when they do not exactly match the reference answers lexically. To account for this, we adopt the LLM--s-a-judge paradigm, following prior work (Bakman et al. [025 Farquhar et al., 2024). Concretely, we prompt a language model (Gemini 2. flash) with the question, the generated answer, the reference answer, and the context, and ask it to output correctness judgment.
Baselines. We compare our method against several widely used unsupervised and supervised UQ methods by using TorthL library (Yaldiz et al. 2025b). Specifically, we include: Perplex- ity (Malinin & Gales 2021), which computes the average negative log- peg-rrbbbbiliyy of the greedy output; Entropy (Malinin & Gales| 2021), which samples multiple generations and averages their fog-probabilitie;; Semantic Entropy (Farquhar et al., 2024). which samples generations, clusters semantically equivalent outputs, and then computes entropy over the clusters; MARS (Bakman et al. 2024), which weights token probabilities by their contribution to meaning; SAR (Duan et al. 22024). which incorporates relevance scores of sampled generations into the entropy calculation and weights tokens by their relevancy to the sentence; Mini-Check (Tang et al. 2024). which trains small model check logical entailment between the generation and the Lontext:LL.MMJdee (Zheng et 2023), which queries an LLM directly to verify whether a generation is supported by the provided context; PTrue Kadavath et al. (2022a) which asks the model's generation corretness and get the probability of token "True" at the end; Kernel Language Entropy (KLE) (Nikitin et al., 2024) and Eccentricity (Lin et al., 2024), both which sample multiple generations, compute pairwise similarities, and apply linear- algebraic operations to quantify uncertainty; SAPLMA (Azaria & Mitchell| 2023), supervised approach that trains a classifier on the internal hidden states of the model to predict correctness; Average Token-level Mahalanobis Distances (ATMD) Vazhentsev et al. 2022)), which calculates the Mahalanobis distance between generated tokens and the average of correct output tokens in the training set, then train a classifier which takes distances as input and predict the correctnes of the generation; LookBackLens (Chuang et al.) (2024), another supervised method that leverages attention ratios between generated tokens and context tokens. For all methods requiring sampling, we generate 5 samples per input. For all supervised methods, we use total of 256 labeled examples. Additional experiments in lower data regimes (64 and 128 labeled samples) are presented in Section 5.5
5.2 RESULTS
The results our method compared to the baselines are presented in Table [ Our approach achieves consistently superior performance (first second rank) in both PRR and AUROC across all datasets and models, with the sole exception of Mistral- aatraal-BB 7B on NarrativeQA. We attribute this drop in performance the limited context window of Mi Mistral ra 1- 7B (32k tokens) relative to the long
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contexts in NarrativeQA (13.3% of samples exceed 32k tokens). As result, the model may fail to produce reliable feature activations for such long contexts, which lie outside its effective training distribution (potentially even shorter than the theoretical 32k limit (Hsich et al., 2024)). Moreover, our method requires neither sampling nor additional forward passes, which makes it substantially faster than sampling-based approaches such Semantic Entropy, KLE, and Eccentricity. Lastly, LookBackLens could only be evaluated on the HotporQA dataset. For the other datasets (Qasper and NarrativeQA), extracting all attention weights was computationally infeasible with the HuggingFace implementation/mterfacc on 8 x 40GB NVIDIA A100 GPUs, as it resulted in out-of out-of-memory errors.
Qasper AUROC
HotpotQA
Narrative
Model
Category
UQ Method
PRR
AUROC
PRR
AUROC
Perplexity
47.7
68.8
50.8
69.9
$7.9
72.6
No Sampling
MARS
48.3
68.4
46.6
67.9
56.4
72.2
MiniCheck
59.3
Unsupervised
L.MM-Juuge
35.7
60.7
12.1
55.6
15.4
54,1
Ptrue
57.4
74.2
46.1
68.8
36.7
68.2
Entropy
58.4
63.1
39.7
62.1
LLama3.1 - 8B
Multi-Sampling
KLE
43.9
66.4
39.8
68.7
47.3
71.6
Eccentricity
42.1
66.1
42.7
70.0
50.0
73.2
Unsupervised
SAR
53,9
71.9
$3.5
71.7
$9.7
75.2
Semantic Entropy
42.7
67.2
47.6
51.9
72.3
ATMD
32.0
62.8
26.8
60.9
21.1
57.1
No Sampling
LookBackL.ens
73.4
SAPLMA
74.7
53.0
72.8
47.3
67.5
Supervised
Feature-Gaps (ours)
64.9
75.3
66.6
78.0
59.7
74.0
Perplexity
70.4
67.8
No Sampling
MARS
54.8
73.2
25.7
60.6
47.0
69.6
MiniCheck
28.3
63.2
44.0
69.4
35.9
66.1
Unsupervised
L.MM-uude
39.2
65.5
28.8
64.0
22.4
61.4
Ptrue
36.7
-9.68
49.3
9.71
56.8
Mistralv0.3.1 7B
Entropy
51.3
70.3
34.3
64.3
40.1
65.5
Multi-Sampling
33.4
63.1
45.8
71.9
48.6
74.7
Eccentricity
37.7
65.2
44.1
70.7
55.5
76.3
Unsupervised
SAR
54.9
71.3
36.0
68.1
$1.0
70.9
Semantic Entropy
51.6
69.6
42.1
68.9
54.4
75.1
ATMD
37.7
66.4
43.4
21.6
69.5
No Sampling
LookBackLens
52.2
71.4
SAPLMA
44.4
69.1
53.2
73.3
53.8
71.3
Supervised
Feature-Gaps (ours)
38.5
65.1
Perplexity
42.7
66.9
27.9
58.6
42.3
65.2
No Sampling
MARS
42.4
66.1
26.5
$7.8
42.7
65.0
MiniCheck
41.8
48.3
71.7
31.4
60.9
Unsupervised
LLM-Judge
10.9
52.7
19.6
54.5
8.6
50.7
Ptrue
37.4
63.9
-9.68
49.3
7.79
54,1
Qwen2.5 7b
Entropy
43.4
66.0
Multi-Sampling
KI.E
34.5
62.8
29.4
66.9
45.5
69.9
Eccentricity
28.5
64.1
32.2
67.5
42.3
70.1
Unsupervised
SAR
45.1
67.4
36.5
65.6
48.5
69.0
Semantic Entropy
47.5
69.5
ATMD
37.7
66.4
43.4
68.1
21.6
59.5
No Sampling
LookBackLens
60.0
SAPLMA
59.1 58.5
75.2
76.2
45.1
68.8
Supervised
Feature-Gaps (ours)
73.3
62.6
76.1
51.0
70.7
Table I: AUROC and PRR performances of UQ methods on Qasper, HotpotQA, and NarrativeQA.
5.3 OUT-OF-DISTRIBUUS
EVALUATION
key challenge for supervised UQ methods is their performance under distribution shift, i.e., when the test distribution differs from the training data. To evaluate robustness, we evaluate two supervised methods, our method and SAPLMA, under out-of-distribution (OOD) settings. For each of the three datasets, construct 3 x train-test matrix, where train one dataset in pair and test on the other. The results, shown in Figure demonstrate that our method more robust to distribution shifts compared SAPLMA. This indicates that our Seature-based formulation generalizes more effectively across domains, which provides more reliable uncertainty estimates compared to direct supervised training model activations.
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Published as a conference paper at ICLR 2026
Train Data Holpot
Peature-Gaps
Qeaper
Hotpot
Narrative
Gesper
Nerrative
Gasper
Holpet
Narratve
Chspar
Test Data
Holpot
Normiiva
Llama-8B
Mistral-7B
Qwen-7B
Figure 3: Out-of-distribution evaluation results. In-distribution performances are with darker shades.
5.4 PERFORMANCE OF INDIVIDUAL FEATURES
An important ablation study is to understand how much of the performance gain comes from the ensemble itself, compared to the contribution of individual features. To in-
Features
Qasper
HotpotQA
NarrtvQA
Honesty
62.0
57.7
56.7
LLama
C. Rel.
43.6
38.8
-16.9
vestigate this, we evaluate each feature sep-
C. Comp.
59.6
66.8
52.2
arately across all model-datasee pairs, suring PRR as an indicator of its ability to predict correctness (i.e., to serve reliable measure of epistemic uncertainty). Results are reported in Table We find that individ- ual features already act as strong epistemic uncertainty estimators
Ensemble
64.9
66.6
59.7
Honesty
51.4
54.9
37.3
Mistral
C. Rel.
60.7
52.4
21.8
C. Comp.
27.4
52.3
21.4
Ensemble
59.6
54.2
38.5
their own. The en- semble offers little to no additional perfor-
Honesty
52.9
35.1
44.2
Qwen
Rel.
42.5
56.9
48.0
mance gain in terms of PRR. However, the role of the ensemble is not simply additive but rather regularizing. The best- pest-eerformng feature varies depending the dataset and model because of the inherent randomness of the proposal, which uses small number of labeled examples for feature extraction. As shown in Table 2 the top feature differs across datasets. In such cases, the ensemble balances these fluctuations, which yields more stable and consistent uncertainty quantifier across datasets and, importantly, under OOD conditions (see Section 5.3
C. Comp. Ensemble 58.5
33.5
61.8
56.9
62.6
51.0
Table 2: PRR scores of individual features Qasper, HotpotQA, and NarrativeQA.
5.5 PERFORMANCE Low DATA REGIMES
All supervised methods, including ours, are primarily evaluated using 256 labeled sam- ples. However, the performance of our ap- proach under more limited supervision critical for its applicability in extreme low- data settings. To assess this, we further evaluate our method with only 128 and 64 labeled samples. Results are reported in Ta-
Num Samples
Qasper
HotpotQA
NarrtyQA
Qwen Mistral LLama
64
64.4
57.0
57.5
128
63.2
62.0
63.2
256
64.9
66.6
59.7
64
38.3
49.5
39.4
128
52.2
55.2
38.7
256
59.7
54,2
38.5
b3e The findings are encouraging: with 128 samples, performance is largely pre- served, showing only marginal degradation compared to the 256-sample setting. Even with as few as 64 samples, although some performance drop is observed, our method remains substantially stronger than alternative baselines reported in Table I These results demon- strate that approach highly data-efficient and remains effective even in extreme low-data regimes, which highlights its practicality for real-world scenarios where labeled correctness data is scarce.
64
41.1
60.5
37.2
128
51.8
256
58.5
62.6
$1.0
Table 3: PRR performances of Feature-Gape low data regimes.

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Published as a conference paper at ICLR 2026
5.6 COMPARISON WITH BASELINE DIRECTIONS
Demonstrating the effectiveness of each com- ponent of our method is essential for rigor- ous scientific evaluation. To this end, we com- pare our extracted feature directions against several alternative baselines that could plausi- bly serve as candidates: Random: three ran- dom directions are chosen instead of using our feature extraction process. Positive-PCAa PCA is applied directly positive samples (e.g. "be honest"), omitting the contrastive dif- ference step. Negative-PCA. similar Posi- tive, but using only negative samples (e.g. "be liar"). All-PCA: the strongest direction ex- tracted from regular prompts without forming contrastive pairs. Mean-Diff: supervised baseline similar to SAPLMA, where we com- pute the mean hidden states of correct and incorrect samples each layer and use their difference correctness direction.
Directions
Qasper
HolpolQA
NarrivQA
Random
34.5
29.5
17.4
LLama
Positive-PCA
45.4
47.1
46.2
Negative-PCA
40.5
54.0
All-PCA
4.0
26.1
18.1
Mean-Diff
48.5
53.1
36.6
Feature-Gaps
64,9
66.6
59.7
Random
11.1
24.4
7.6
Positive-PCA
39.0
45.4
41.8
Mistral
Negative-PCA
52.0
52.9
33.2
All-PCA
4.1
36.7
12.8
Mean-Diff
51.7
49.0
48.5
Feature-Gaps
59.6
54.2
38.5
Random
17.9
6.1
Positive-PCA
-3.6
26.7
32.6
Qwen
Negative-PCA
2.2
31.3
36.4
All-PCA
-4.3
20.1
36.0
Mean-Diff
57.3
49.3
47.6
Feature-Gaps 58.5
62.6
51.0
Table 4: PRR scores of baseline directions Qasper, HotpotQA, and NarrativeQA.
The results, shown in Table 4 highlight the importance of our design choices. Ablating critical steps, such as contrastive differencing and finding features, leads to substantial performance drops. Moreover, Mean-diff underperforms compared to our approach, which demonstrates that explicitly extracting and combining feature directions is more effective than simply contrasting the mean of hidden states of correct and wrong generations.
CONCLUSION
In this work, we introduced task-agnostic metric for total uncertainty. By approximating the ideal model to the true (unknown) distribution, we showed that the epistemic uncertainty can be bounded by the norm of the difference in hidden states between the given model and the ideal model, which can be interpreted as feature gaps under the linear representation hypothesis. We then applied this framework to contextual QA and hypothesized that three features, context-reliance, context comprehension, and honesty, serving effective approximations of this gap. Using only small number of labeled samples, our method achieves superior performance compared to popular baselines. We believe this framework provides foundation for future research epistemic uncertainty, including the discovery of additional features and the development of automatic, task-agnostic feature extraction methods, ultimately enabling more robust and generalizable epistemic uncertainty quantifiers.
LIMITATIONS AND FUTURE WORK
Our method currently requires supervised examples. Making this framework work with unlabeled data, without any external data by relying solely synthetically generated samples, would be an important direction for future research. Although our experiments focus on contextual QA, the feature-gaps framework is general and can be applied wide range of language-model tasks. Extending it to other domains such as reasoning or long-form generations, is another promising direction. At present, our method relies on heuristic feature selection. However, this is fundamental limitation: developing an automatic procedure for selecting features would be valuable extension. In addition, our experiments use only a small number of labeled samples (256). Scaling the framework to larger training sets is important. This can be achieved by selecting more features to better approximate the gap, or by selecting more layers per feature, as we demonstrated in Appendix A Lastly, in our experiments, we don't consider the potential noise coming from the context-rerrreverpprovddr Retrieving the wrong/useless context is common RAG systems, and that noise/uncertainty can be modeled in future works. Overall, we believe the feature- gaps framework offers a strong approximation to epistemic uncertainty and has the potential to generalize better than other supervised approaches such SAP
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Katherine Tian, Eric Mitchell, Allan Zhou, Archit Sharma, Rafael Rafailov, Huaxiu Yao, Chelsea Finn, and Christopher Manning. Just ask for calibration: Strategies for eliciting calibrated confidence scores from language models fine-tuned with human feedback. In Houda Bouamor, Juan Pino, and Kalika Bali (eds.), Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pp. 5433-5442, Singapore, December 2023, Association for Computational Linguistics. doi: 00.18653/v1/2222 .tt.:/222..mmppmmimm.. 2023. www.pmmain.nn30000
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Artem Vazhentsev, Lyudmila Rvanova, Ivan Lazichny, Alexander Panchenko, Maxim Panov, Timothy Baldwin, and Artem Shelmanov. Token-level density-based uncertainty quantification methods for eliciting truthfulness of large language models. In Luis Chiruzzo, Alan Ritter, and Lu Wang (eds.), Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), pp. 2246- 2262, A Albuquerque, New Mexico, April 2025. Association for Computational Linguistics. ISBN
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Lianmin Zheng, Wei-Lin Chiang, Ying Sheng, Siyuan Zhuang, Zhanghao Wu, Yonghao Zhuang, Zi Lin, Zhuohan Li. Dacheng Li, Eric P. Xing, Hao Zhang, Joseph E. Gonzalez, and Ion Stoica. Judging llm-as-a-judge with mt-bench and chatbot arena. In Proceedings of the 37th International Conference on Neural Information Processing Systems, NIPS '23, Red Hook, NY, USA, 2023. Curran Associates Inc.
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A APPENDIX / SUPPLEMENTAL MATERIAL
A.1 COMPARISON WITH THE INFOMAATION- UNCERTAINTY QUANTIFIER OF SCHWEIGHOFER ET AL.. (2024)
Schweighofer et al. 2024 propose to quantify total uncertainty in classification tasks as
TU
Σ P(y x)
In P" x)
DЕC
where C is the set of classes, In their formulation, the roles of the actual model P(y x, 0) and the true distribution (" x, 0) are swapped compared to ours. The natural decomposition of their metric
TU H(P(y x. 0)
(L x 0| PM
Aleatoric (Data) Uncertainty
Epistemic Uncertainty
We argue that this decomposition is problematic. Data (alcatoric) uncertainty should arise from the input the data distribution of the task D, and should be independent of the specific training outcome. While the actual model is indeed trained on a sampled set of D. Durain ~ D, the sampled data may be insufficient and may lead to epistemically sub-optimal models. Besides, training a model is not a deterministic function of D different random seeds and hyperparameter settings can yield
infinitely many possible models, Orandom directly determine the data uncertainty.
Daan
θ. Consequently, propertics of cannot not
Consider an extreme case: if we train 9 with pathological hyperparameters (e.g., excessively high learning rates), the resulting model may output predictions nearly at random. The entropy term in their decomposition would then be very high, suggesting extreme data uncertainty. Yet, this uncertainty arises entirely from poor model training (epistemic uncertainty), not from the data distribution itself.
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By contrast, in our formulation where P(y x. 8) and P2 x. 8) swapped, the aleatoric component is defined in terms of P (y x, 8), which is independent of any part of training where epistemic uncertainty could arise. Lastly, a more recent work Kotelevskii al. (0225 also does similar formulation with ours from the Bayesian risk perspective (see Table 1). For these reasons, argue that our quantifier provides more reasonable decomposition of epistemic and aleatoric uncertainty. Nonetheless, we acknowledge that the formulation of SShhweeggrr et al. (2024) was an important inspiration for our work and served as a foundation for adapting these ideas language models.
A.2
PROOF OF LEMMA I
Proof.
For notational simplicity, let us denote
P(y 0*) P(ye x")).
We begin by explicitly writing the KL term
(L(P(y) (8") P(ye (8))
P(y: 0²) In P(y: 0*) P(y: 0)
KL(P(w) | 10') P(u: [0) Σ
iEV
Since the probability of a token under model A is given by
V Whe
Ply 0) Ejeve's e Wh,"
where W IR Vixd is the vocabulary projection matrix and Vi is the one-hot vector of token yt for token i, we can re-write KL in terms of model internals:
Σ P(us 0*) V. W(hg h4) + Σ NEV
P(ye (*))
In
Σ
Σ
why
JEV
JEV
as both models share the same vocabulary matrix W. Focusing on the first term, we have
Σ P(u (0) V. ( ht) S Σ P(y. 10)) [[ (ht he)ll
by Schwarz. Since V, a one-hot vector, || = 1, so this simplifies to P(u 0*) [[W - hh)ll || (ht h.)l
Σ
iEV
because Eiev P(ys 00) = 1. Moreover, by Cauchy-Schwand inequality,
[[W ht)ll S [[ ||; - -hell-
For the second term, observe that
In Σ jEV since Σiey P(y: 8*)) 1.
Σ P(us 0*)
eVy wh. In Σ VTTWn;
= In Σ
VT WTTh
In
Σ e VTT WT,
LEV
JEV
JEV
JEV
Define f(x) = In Ed
ez)), the log log-sum-exp function. Then
In
V Wh.
In Σ V.T. f(Wh,) fWWht).
jEV
JEV
By the mean value theorem, there exists on the line segment between Wh, h, and Wha hi such that f(Wh:) f(Wht)) = Vf(c) T (Wh; - Whī).
Since (=))) softmax(x)), we have
((Wh))-(WW;;) = so) (Wh, - Wh;)) S ||softmax (coftmax(c))llnna || || Whal| S [Wh, -Wht1, because ||softmax(c)] 5 Lastly, [Wh, Wh: < ||W]| [| - hell
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Combining both terms.
From the above bounds, conclude (P 8*) P(y 0)) = 2 [[ ||4 hy
A.3 RELATED WORK
large body of recent work has focused Uncertainty Quantification (UQ) for language models. These methods can be broadly categorized into four groups, though some approaches span multiple categories. Most existing methods are heuristic in nature:
1. Output-probability based methods, such as Semantic Entropy (Kuhn et al. 2023), Sequence- Probability (Aichberger al., 2024). Mutual Information (Abbasi- Yadkori al. 2024). MARS (Bak) man et al. 2024). LARS Yaaddiz et al. 2025a). and SAR (Duan et al.]|2022222 22024) 2. Output-consistency based methods, including Kernel Language Entropy (Nikitin et al. 2024), Eccentricity, and Matrix- Degree (Lin et al., 2024). 3. Internal-state based methods, such as INSIDE (Chen et al. 2024)
and SAPLMA (Azaria Mitchell, 2023). Self-checking methods, such as Verbalized Confi-
dence (Tian al. 2023) and PTrue Kadavath et al. 2022b).
With the exception of Mutual Information (Abbasi- Yadkori et al. 2024 and Sequence- Probability (Aichberger et al. 2024), which provide theoretical justification, nearly all of these approaches rely on heuristics. Furthermore, none of them have been specifically designed or evalu- ated for contextual QA.
Beyond single-model uncertainty estimation, several works propose Bayesian frameworks to decom- pose epistemic and aleatoric uncertainty (Ling al. 2024 Hou et al. 2024). Ling al. (2024) use a Bayesian in-context learning formulation, quantifying epistemic uncertainty as the mutual information between the model's output and the in-context examples, Hou al. (2024) introduce a generic Bayesian framework based on input clarification, where epistemic uncertainty is again defined as mutual information between outputs under different clarified queries. Although theoreti- cally grounded, these methods require replacing the LLM with a Bayesian framework and computing uncertainty over the Bayesian model, which is computationally expensive. In contrast, we quantify the uncertainty of single LLM directly.
Only litrle number of of recent works have directly addressed UQ in contextual QA or retrieval- augmented generation (RAG). (Soudani et al. (2025) propose an axiomatic framework for diagnosing deficiencies in existing methods and present a generic UQ method that can be layered on top of other approaches.
& Lapata (2025) introduce passage-utility based metric, training lightweight neural model to predict the usefulness of retrieved passages for given QA task. Similarly, Fadeeva et al. (2025) propose method that evaluates factuality by jointly assessing faithfulness and factual correctness under both faithful and unfaithful retrieval conditions.
However, all of these methods remain heuristic and largely empirical. In contrast, work introduces a UQ approach with a grounded theoretical formulation, designed specifically to contextual QA.
A.4 EXPERIMENTAL DETAILS
A.4.1 PROMPTS USED IN THE EXPERIMENTS
To query the model contextual QA setting, we use the following prompt:
Context: (context). Here is a given context. You are a helpful assistant. Answer the following question with a brief but complete response.
Use the context information to answer this question.
Question: (question)
Answer:
For the LLMejudge, which evaluates the correctness of generated answers, the following prompt:
You will be given a context, a question relevant to that context, a predicted answer, and list of possible ground truth answers provided by human experts.
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Your task is to assign of the following labels: ("CORRECT", "INCORRECT", "NCT ATTEEPPTMT)
Context: (context)
Question: (question)
Possible Ground Truth Answers Provided by Human Experts: (ground_truths) Predicted Answer: (answer)
Labeling instructions:
Assign "NOT_ATTEMPTED" if the predicted answer fails to engage with the question, or explicitly states that an answer is not found in the context. Assign "CORRECT" if the predicted answer is accurate based on the context, even if it is not explicitly listed among the ground truth answers. Assign "INCORRECT" if the predicted answer is contradicted by the context or otherwise wrong.
Important: The ground truth list may not cover all valid answers. For those cases, look at the context.
Provide your explanation and then at the end give your grade.
Response:
A.4.2 PROMPTS FOR FEATURE EXTRACTION
Honesty. To extract the honesty feature, design positive and negative prompts that encourage truthful versus intentionally false responses.
Positive:
Context: (context).
Here is given context. You helpful assistant.
Answer the following question with a brief but complete response.
Be honest with your answer. not give unfactual information. Do not lie.
Question: (question)
Answer:
Negative:
Context: (context).
Here is a given context. You are a helpful assistant.
Answer the following question with a brief but complete response.
a liar. Give unfactual information. Tell lie.
Question: (question)
Answer:
Context-Reliance To extract the context-reliance feature, contrast prompts that either require the model to ground its answer in the provided context or explicitly ignore it.
Positive:
Context: (context).
Here is given context. You are helpful assistant.
Answer the following question with a brief but complete response. Use the context information to answer this question. Do not use your own knowledge. Just look at the context.
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Model
Method
Narrative
Qasper
Hotpot
Saphma
Qwen2.5 7B PRR
Gepture-Gaps
57.8
58.1
65.6
Feature-Gaps (10 layers)
$7.4
65.2
66.2
Saphma
LLama3.1 8B MRR
Feature-Gaps
60.7
63.7
66.4
Teature-Gape (10 layers)
64.3
69.3
70.4
Saphma
Mistralv0.3 PRR
Feature-Gaps
43.
59.1
53.6
Feature-Gapy Gaps layers)
47.2
59.0
60.7
Saplma
72.7
74.9
73.8
Qwen2.5 AUROC
Feature-Gaps
73. 1
73.
78.1
Feature-Gap Gaps layers)
Saplma
75.1
76.9
76.4
Feature-Gaps
73.9
75.9
77.5
Feature-Gaps layers)
76.5
78.3
79.8
Saplma
74.2
68.2
71.1
Mistralv0.3 AUROC
Feature-Gaps
68.3
75.0
70.8
Feature-Gaps layers)
74.8
75.7
Table 5: PRR and AUROC metrics for Qwen, LLaMA, and Mistral with best- best-performing scores in bold.
Question:
(question)
Answer:
Negative:
Context: (context). Here is a given context. You are a helpful assistant.
Answer the following question with a brief but complete response. DO NOT use the context information to answer this question. Use your own knowledge. Ignore the context.
Question: (question)
Answer:
Context Comprehension. For context comprehension, we use the regular contextual QA prompt but append the ground-truth answer to the context, simulating an idealized model where the model has already extracted the necessary information.
A.5
ADDITIONAL EXPERIMENTS
In this section, we provide our additional results.
A. SCALING THE NUMBER OF TRAINING SAMPLES
In addition to low-data regime experiments, also try scale method to training data. We add small modification to our framework by instead of selecting a single direction e; for each feature, extend the approach to select (N) directions from multiple layers. We scaled the training data to 1000 samples for each dataset, and for the scalable version we selected 10 layers per feature. The results are in T.ble|A.5.1
As the results indicate, our method does not benefit substantially from simply increasing the number of training samples, but selecting multiple layers significantly improves performance. By con-
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trast, SAPLMA also does not improve much with additional data, and our method almost remains consistently superior.
We also performed similar experiments with more data (5000 samples) HotPo:QA. We could not scale NarrativeQA because we were unable to find a 5000-sample subset whose contexts fit within GPU memory, and Qasper does not contain 5000 samples. The HotPotQA results with 5000 samples are included below.
The results are in A.5.1 and observe performance drop for SAPLMA compared to the 1000- sample setting. This is expected: the 5000-sample experiment uses data from the training split of HotPotQA, whereas the earlier 1000-sample experiment used split from the validation set. This distribution shift appears to affect SAPLMA more strongly than our method. Scaled version of our method is superior both SaPLMA and our method.
Method
Model
AUROC
PRR
Qwen2.5 7B
69.8
50.9
Feature-Gaps
LLama3.1 8B
77.5
66.3
Mistralv0.3 7B
71.3
54.4
Qwen2.5 7B
71.6
55.9
Feature-Gaps (10 Layers)
LLama3.1 8B
79.4
68.9
Mistralv0.3 7B
71.3
54.2
Qwen2.5 7B
61.8
30.2
Saplma
LLama3.1 8B
73.0
55.9
Mistralv0.3 7B
71.1
52.8
Table 6: HotpoiQA Results with 5000 Training Samples
A.5.2 EXPERIMENTS WITH BIGGER MODELS (QWEN32B)
We evaluated our method on larger model, Qwen2.5-322 Due to computational constraints, we were unable to run experiments on Qasper and NarrativeQA, as their long contexts caused GPU memory emrоr with this model. Therefore, report only the HotPotQA results in Table A.5.2
The results show that our method remains noticeably superior to SAPLMA. However, Perplexity and PTrue achieve the strongest performance among all baselines. Since both rely on model probability estimates, this suggests that larger models may produce more calibrated probability signals compared to smaller models, which could explain their stronger performance in this setting.
A.5.3 SIGNIFICANCE TESTS ON OOD EXPERIMENTS
We also report AUROC scores for the OOD experiments along with statistical significance tests using the DeLong method DeLong et al. (1988). As shown in Table A.5.3) our method remains mostly superior. In all cases where the AUROC difference is substantial, the improvements are statistically significant (p-value < 0.05).
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Method
AUROC
PRR
SemanticEntropp
66.2
42.1
Confidence
75.4
58.5
Entropy
64.3
39.6
Eccentricity Uncertainty
66.7
36.1
Kernell angggelggg
65.9
43.6
ContextCheck
50.4
13.2
PTrue
78.9
63.9
MARS
71.2
51.1
MiniCheckMethod
71.7
48.3
SAR
67.8
44.1
Matrix
64.6
31.7
SumEigen Uncertainty
64.6
31.7
Saplma
58.1
32.5
FeatureGaps
67.5
49.0
Table 7: HotpotQA, AUORC and PRR Scores with Qwen2.5 32B Model
Model
Training Dataset / /est Dataset
Qasper
HotpotQA
NarrativeQA
Qasper
76.9
76.3
LLama3.1 8B
Feature Gaps
HotporQA
75.4
78.0
79.8
NarrativeQA
72.4
75.8
74.8
Qusper
72.2
LLama3.1 8B SAPLMA
HotporQA
64.8
72.8
63.4
NarrativeQA
68.4
71.0
67.6
Qusper
5.163e-02
LLama3.1 8B p-values
HotporQA
4.096e-04
6.314c-04
2.861c-13
NarQQA
0.1531
3.668e-03
1.391e-03
76.0
68.2
65.2
MistralvO.3- 7B
Feature Gaps
HotporQA
76.0
71.5
66.2
NarrativeAA
Qasper
69.1
64.1
55.9
Mistralv0.3-1 SAPEMA
HotporQA
64.8
73.3
66.3
NarrativoQA
66.2
71.3
Qasper
3.255e-03
2.576e-03
1.100c-04
MistralvO.3 p-values
HotporQA
1.100e-05
2.744e-01
9.629e-01
NarQA
4.349e-02
1.744e-01
9.634c-03
Qasper
72.7
67.5
63.1
Qwen2.5 7B Feature Gaps
HotperQA
73.4
NarattveQAA
67.7
66.0
70.7
Qusper
75.2
67.5
71.8
Qwen2.5 7B SAPLMA
HotporQA
76.2
63.9
NarrativeQA
71.0
61.5
68.8
Qusper
3.125e-01
9.711e-01
2.804e-04
Qwen2.5 7B p-values
HotporQA
2.703e-01
9.295e-01
4.940c-04
NarQUA
2.104e-01
3.827e-02
4.093e-01
Table OOD experiments, AUROC scores with significance values
21


Reviews:
[{"review_id": "bk0Ew1QCkI", "reviewer": "Reviewer_Eyf6", "summary": "The paper presents a new supervised method for uncertainty quantification for LLMs. The features are constructed as the difference between hidden states of LLM prompted in the standard way and the LLM which was prompted to be “liar” or “do not look at the context”. \nThe authors claim that constructing features in this way results in better generalization than standard hidden states or features built from attention maps (such as Lookback lens).\nThe model is basically a linear regression on top of the hidden states. \nImportant contribution of the paper is that the authors show that the epistemic uncertainty can be bounded from above by such a linear expression. \n\nOne of the main problems of the paper is that the authors claim that they quantify only epistemic uncertainty. However, the tasks where they test their methods assume that both types of uncertainty would be useful, so it seems that there is no need for such disentanglement.  \n\nAnother problem is that the method needs sampling of the answer multiple times, which introduces large computational overhead (basically up to 3-4 times). These is very close to sampling-based methods that need as little as 5 samples to show improvements over the simple baselines. Sampling alone should carry some additional information that help to improve the performance of hallucination detection. So, the substantial part of the improvement might come from sampling rather than other parts of the method. \n\nThe set of baselines is good, however, there are few methods that explore the idea of the difference between “good” and “bad” answers of LLM.\nVazhentsev, Artem, et al. \"Token-Level Density-Based Uncertainty Quantification Methods for Eliciting Truthfulness of Large Language Models.\" Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.\nComparison to this baseline looks important for me\n\nThe authors claim that the method works well with small amount of training data, which is good. However, the analysis in the case when the amount of data is bigger is not conducted. It would interesting to see wheather there are improvements when the number of train instances is relatively large 5000+. \nNote that the lack of the improvements doex not deteriorate the method, but the lack of such analysis is a notable drawback of this work. This analysis is important for me.\n\nPlease, also note that in the experiment with generalization you compare your method with SAPLMA. However, the authors of Lookback lens showed that SAMPLA in general is not very good at generalization. It would be reasonable to compare your method to Lookback lens, as the main point of their paper was better generalization than SAPLMA. This analysis is moderately important, but nice to have.\n\nOverall, I think the work is good and open for the discussion.", "questions": "1.\tInteresting method that has better performance than other supervised baselines.\n2.\tImportant contribution of the paper is that the authors show that the epistemic uncertainty can be bounded from above by such a linear expression.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1.\tInteresting method that has better performance than other supervised baselines.\n2.\tImportant contribution of the paper is that the authors show that the epistemic uncertainty can be bounded from above by such a linear expression.", "weaknesses": "1.\tNeed additional analysis with more training data\n2.\tComparison to another baseline\n3.\tThe method is computationally expensive, because it needs to sample 3-4 times\n4.\tThe improvements might come not from the “epistemic nature” of uncertainty, but just because of sampling.\n5.\tThe authors show that benefits of their method that disentangles epistemic uncertainty on tasks that need both epistemic and aleatoric uncertainty.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "d9E6HG0TfV", "reviewer": "Reviewer_id5u", "summary": "This paper proposes an information-theoretic metric to quantify epistemic uncertainty, i.e., cross-entropy between the true (ideal) predictive distribution and the given model's distribution --adapted from [Schweighofer et al. (2024)]. It operationalizes it via interpretability tools. Starting from the information-theoretic formulation, the authors derive an upper-bound of the epistemic uncertainty formulated as the difference between the ideal and given model's internal states. These can be represented as decomposed vectors (linear representation hypothesis); furthermore, the ideal and given model's coefficients in the linear representation can be interpreted as the deviation of the ideal from the given model (namely Feature-Gaps). In practice, for contextual QA, three features are selected: Context reliance, Context comprehension, and Honesty. Vectors for these features are extracted using interpretability techniques.  \n\nThe proposed method based on interpretability tools is sensible, efficient, and shows competitive performance. However details about the feature extraction/approximation are missing and there are some weak points in the experimental setup (see below).", "questions": "- Experimental setup:\n\n\t- The authors should clarify what sort of input is used for HotPotQA, it is common practice for this dataset to be considered an open-book QA task where external retrieval systems are used to retrieve passages for context (RAG). If this is not the case, and passages available in the dataset are used, then all evaluation tasks are instances of Reading Comprehension (RC). In this case the evaluation does not cover the case of real RAG scenarios. How would the approach work on the case of noisy and misleading real retrieval?\n\t\n\t- The evaluation focuses on 3 models of similar size (different families). It would also make a clearer empirical statement of the method's performance if the authors evaluate on larger models, e.g., Qwen2.5-32B.\n\t\n\t- Out-of-distribution experiments (Section 5.3, Figure 3) need to incorporate a non-supervised baseline, e.g., the cheaper unsupervised Perplexity, in order to better visualize how the compared out-of-distribution methods (Feature-Gaps and SAPLMA) compare to this simple approach. Also, by looking at values in Figure 3, we can see that these are PRR (better to add this in the caption), the authors should also report the AUROCs.\n\n\t- Significance values should be reported for results on Table 1.\n\t\n\t- An strong widely used approach p(true) is mentioned in the paper though not included in experiments.\n\n- \"Feature Extraction\" in Section 4.2 could be better explained (add missing details). Line 281,  \"access to a set of T labelled samples\" I guess this is with gold answer. Line 282, \"standard instruction\", what would be standard instruction in the case \"look at the context\" and \"se your own knowledge\"? How is $\\alpha_i$ in Eq. 7 (and Line 304) computed? Is $\\alpha_i v_i$ a decomposition of $v^l$? Is in the end $\\alpha_i$ assumed to be 1 in Eq. 7? More details about the training of the procedure to obtain the $w_i$ weights are needed (line 305). What is the connection of the $w_i$ weights and the ideal model representations ($w_i$'s are trained to predict correct/incorrect)? What is the relation of training these weights and the ranking formulation in Line 134?\n\n- Related work. The method by [Laura Perez-Beltrachini and Mirella Lapata] trains the so called passage-utility that is predicting correct/incorrect answer. How does this differentiates from the training $w_i$s on the task of predicting correct/incorrect answer? Beyond the different amount of training data required.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Using interpretability insights to estimate uncertainty is novel. \n- The proposed approach is efficient at test time; although it requires training it necessitates only few labelled data points. It does require tuning some hyper-parameters (e.g., layers to use), features, prompts.", "weaknesses": "- Missing experiments on RAG contexts, larger models, and p(true) approach. Significance tests on results as sometimes these are quite close values.\n- Lack of details about the training of the $w_i$ weights.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pYrC9HNegi", "reviewer": "Reviewer_WhVN", "summary": "The authors propose an uncertainty quantification method derived from an approximation of the upper bound for epistemic uncertainty.  They comprehensively justify the theoretical basis for this method and demonstrate that it empirically works effectively with three different models on three datasets.", "questions": "Is there a way to organize Table 1 so it’s easier to tell which baselines require multiple samples and which require supervised data? This would make comparisons easier.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1. Strong theoretical justification for the validity of this uncertainty quantification method, which is uncommon for many uncertainty quantification methods\n2. Strong experimental results, particularly when compared to the computational complexity of baselines\n3. Generally, many UQ methods quantify total uncertainty, rather than epistemic uncertainty; this broadens potential applications for this UQ method", "weaknesses": "1. Some assumptions are not well-justified, in particular that there exists an optimal token string that would result in an ideal model. This is more or less solely supported by previous work that suggests appending a prompt can be considered to be fine-tuning. While the empirical results suggest this assumption holds true enough for this method to work, I feel that stating that this is a close approximation to a fine-tuned model (lines 179-180) or that it is the “ideal” model (line 190) may need more evidence or more qualifiers.\n2. There may be more to add for related work, specifically in the domain of uncertainty decomposition (for instance, https://arxiv.org/abs/2311.08718 and https://arxiv.org/pdf/2402.10189)—I believe this would provide better context for this work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)