Enhancing Hallucination Detection through Noise Injection
Authors: Litian Liu
Reza Pourreza
Sunny Panchal
Apratim Bhattacharyya
Yubing Jian
Yao Qin
Roland Memisevic
Venue: ICLR 2026 Poster (2026)
Keywords: Bayesian Inference
Uncertainty Quantification
Hallucination Detection
Primary area: generative models

Abstract: Large Language Models (LLMs) are prone to generating plausible yet incorrect responses, known as hallucinations. Effectively detecting hallucinations is therefore crucial for the safe deployment of LLMs. Recent research has linked hallucinations to model uncertainty, 
suggesting that hallucinations can be detected by measuring dispersion over answer distributions obtained from multiple samples drawn from a model. While drawing from the distribution over tokens defined by the model is a natural way to obtain samples, in this work, we argue that it is sub-optimal for the purpose of detecting hallucinations. We show that detection can be improved significantly by taking 
into account model uncertainty in the Bayesian sense. To this end, we propose a very simple, training-free approach based on perturbing an appropriate subset of model parameters, or equivalently hidden unit activations, during sampling. We demonstrate that our approach significantly improves inference-time hallucination detection over standard sampling across diverse datasets, model architectures, and uncertainty metrics.

Published as a conference paper at ICLR 2026
ENHANCING HALLUCINATION DETECTION THROUGH NOISE INJECTION
Litian Liu Reza Pourreza' Sunny Panchal
Apratim Bhattacharyya' Yubing Jian
Yao Qin Roland Memisevic
"Qualcomm AI Research" 2 UC Santa Barbara
ABSTRACT
Large Language Models (LLMs) are prone to generating plausible yet incorrect responses, known as hallucinations. Effectively detecting hallucinations is there- fore crucial for the safe deployment of LLMs. Recent research has linked hallu- cinations to model uncertainty, suggesting that hallucinations can detected by measuring dispersion over answer distributions obtained from multiple samples drawn from a model. While drawing from the distribution over tokens defined by the model natural way to obtain samples, in this work, we argue that is sub- optimal for the purpose of detecting hallucinations. We show that detection can be improved significantly by taking into account model uncertainty in the Bayesian sense. To this end, we propose very simple, training-free approach based on perturbing an appropriate subset of model parameters, equivalently hidden unit activations, during sampling. We demonstrate that our approach significantly improves inference-time hallucination detection over standard sampling across diverse datasets, model architectures, and uncertainty metrics.
INTRODUCTION
Output
Large Language Models (LLMs) have made significant advances in recent years (Achiam et al., [023 Zhao et al. 2023). However, despite these advances, LLMs sometimes generate plau- phenomenon known as hallucination (li at. 2023 Kuhn et al.) 2023a IT In light of this, effective hallucination detection during inference has gained significant attention and is essential for the safe deployment of current LLMs. One line work detects hallu- cinations in single sample by training sepa- rate model (Azaria & Mitchell| Kossen et al. 2024 Liu al.; Manakul et al. [023] Su al. 2024.. allowing for evaluation on pre-defined question-answer benchmarks such HaluEval (Li et al.) 2023). This approach adds computa- tional cost and can suffer from train-test distri- bution shift Kossen et al. 2024). In contrast, we focus on an alternative line of work that detects hallucinations by assessing uncertainty across multiple samples directly drawn from model (Chen al. 2024 Kuhn al.] 2023a
Aleatoric
Softmax
Sampling
at Prediction Stage
Linear
sible yet incorrect responses
Epistemic
Feed
Forward
Noise Injection at Earlier Stages
Nx
Attention
Embeddings
Input
Figure 1: Inference-time hallucination detec- tion typically relies solely on prediction layer sampling, capturing mainly aleatoric uncer- tainty (Gao et al.) 2024). We introduce noise injection to perturb intermediate repre- sentations. By combining noise injection with prediction layer sampling, our sampling approach captures both epistemic and aleatoric uncertainty.
Lin et al. 2024 2022 Malinin & Gales 2021
"Correponddene: liti fu@qti qua comm. com, rmemi sevêqti. quaala comm. com "Qualcomm Al Research an initiative Qualcomm Technologies, Inc.
'Recent work (Kalai et al. (2055) notes that hallucinations fundamentally stem from current training paradigms and may be inevitable without radical changes.

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Experiments
Noise UCO, 0.07)
Exgerments w/ T 0.5, Noise
Experiments w/ 0.5, U10, 0.07)
Hall adiraian
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Hellucraton
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Answer Entropy
Answeer Entropy
Ansseer Entropy
(a) Standalone Effect Intermediate Layer Noise [Epistemic]
(b) Combined Effect of Intermediate Layer Noise and Sampling (Epistemic Aleatoric]
Figure 2: Effect of Intermediate Layer Noise on Hallucination Detection. (a) Standalone Effect. Noise injection induces epistemic uncertainty, where the LLM shows greater uncertainty for hallucinations (grey) than non-hallucinations (blue), as reflected by larger answer entropy (Equa- tion 4. (b) Combined Effect. Combining noise injection with prediction layer sampling (b Right) improves
separation compared to using prediction layer sampling alone (b Left), enhancing detection effectiveness. This highlights the importance combining epis- temic uncertainty with aleatoric uncertainty in sampling for hallucination detection. Evaluation on GSM8K with Llama-2 7B 7B-chat model across 10 samples.
Manakul et al. 2023 For example, Lin et al. 2022 2024) use semantic consistency and lexical similarity. Chen et al. (2024) quantifies uncertainty from the hidden activations of multiple samples. The core principle underlying this line of work simple: the greater the observed uncertainty, the higher the likelihood of hallucination.
Since language model defines the probability distribution over the next tokens, an obvious way to generate samples is to repeatedly draw from the conditional distribution over tokens given the context so far. This way of sampling stays faithful to the probability distribution defined by the deviations from the training distribution), and it makes sense when the goal is to generate multiple answers, say, to given prompt.
model (up to any temperature-indee
However, in the case of hallucination detection, the purpose of sampling is not to generate diverse set of alternative answers to a given prompt. Instead, it is to estimate the coherence among sampled responses to prompt. via kind of "'sensitivity analysis" that makes it possible to assess the like- lihood of given prompt to elicit a hallucination in a model. A distribution of responses that is coherent under perturbations considered evidence for the model knowing the correct response for a given prompt and accordingly, for the generated answers to be considered truthful.
More formally, sampling from the model using next-token prediction be considered capture uncertainty in the data distribution, whereas to detect hallucinations, we are also interested finite training set. The distinction
way to
in the model uncertainty, which is the result of training between these two types of uncertainty has been studied formally by Osband (2016), who refers to the former as aleatoric (data uncertainty), and the latter as epistemic (model uncertainty).
This distinction is also reflected in a Bayesian perspective, where uncertainty over the model param- eters reflects the epistemic uncertainty, and the model's output distribution reflects the aleatoric uncertainty. However, full Bayesian treatment is challenging for LLMs, which contain billions of parameters and are trained on datasets that contain billions, and sometimes trillions, of tokens (Hou et al.) 2024). It is also not feasible to apply approaches that cast dropout training as approxi- mate Bayesian inference (Gal & Ghahramani] (2016)), since dropout not included in many popular LLMs (see Appendix In this work, we devise novel, simple yet effective training free approach to approximate surrogate distribution over models that are plausible given the training data, using pre-trained model weights starting point illustrated in Figure
To perform this approximation, we consider random perturbations of the parameters of a pre-trained model, which, as show, is equivalent to perturbing hidden unit activations in some layers of the LLM for an appropriately chosen subset of parameters. Conveniently, the hidden activations also tend to capture the abstract and high-level representations of given phrase "thought"
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[LeCun al. 2013). This differentiates them from the output logits, which represent meaning at much lower, syntactic level, potentially making stability of hidden activations a better candidate to assess model'ss faithfulness to the prompt in the context of detecting hallucinations.
Concretely, our surrogate distribution is uniformly distributed and centered at the pre-trained param- eter weights of the hidden units and whose variance is defined by single hyper-paramett parameter. This retains the ability of models in the surrogate distribution to explain the training data well, while possessing sufficiently high coverage of plausible models to capture key aspects of the additional model uncertainty. This is illustrated in Figure where we show the uncertainty associated with a prediction in the case of hallucination, highlighting the effectiveness of jointly capturing epistemic and aleatoric uncertainty in a Bayesian framework.
In this work, we show how this insight leads to a very simple and efficient sampling approach to incorporate model uncertainty into inference-time hallucination detection. We demonstrate its effec- tiveness empirically across wide range of datasets, model architectures, and uncertainty metrics.
BAYESIAN FRAMEWORK
Prior work (Chen al. 2024, Kuhn et al. 2023a Lin al., 2024; 2022; Malinin & Gales 2021
Manakul et al.] 2023) connects hallucination detection to estimation of model uncertainty. Given an input context a, the task of detecting hallucination can be formulated as a binary classification problem:
[(x)- Noollaalluinnation if())) <
Hallucination
Hf 2T²
where y = (1r y. ......, x*) denotes K samples generated by the model given æ, H(-) is an uncertainty metric, and 7 is a detection threshold.
Prior work has primarily focused on designing uncertainty metrics, relying on standard sampling methods to remain faithful to the model's predictive distribution. Instead, we shift the focus to the sampling process and account for both aleatoric (data) and epistemic (model) uncertainty when drawing samples. To capture epistemic uncertainty. rather than relying on single LLM, we consider the distribution of plausible models given the training data D. Under this Bayesian formulation, the predictive probability of sequence y = [yoo V1...., Mt-1], given input context æ and the training
data D, can be expressed as (Malinin Gales 2021)
/ II (())(W( dw,
D)
where denotes the model parameters and p(w (D) is the posterior parameters given the training data D.
Since p(w D) is not directly accessible in practice, it is common to approximate it with surrogate distribution q(w). One approach to estimate q(w) is to minimize the KL divergence between g(w) and the true posterior DD) using a variational lower bound (MacKay 2003 Gal & Ghahramani] 20165). However, this approach remains challenging for large pre-trained LLMs, whose training data are often proprictary and whose retraining is computationally expensive. To address this, we propose training- -free surrogate distribution g(w), which concentrates the parameter distribution around the pre-trained checkpoint while allowing controlled perturbations for a subset of parameters S. Concretely, we define q(w) as
(ww) II 8(w; w.) II q: (w; w; a): RES
(3)
E
where w; represents the 7th parameter the model, W; is the value of w; the pre-trained check- point, and gi is perturbation distribution centered around w,, with perturbation magnitude bounded by a to prevent unstable behaviors in the tails. For parameters in S, we perturb according to qi- For parameters not in S, fix them at their checkpoint values, efffectively applying Dirac delta distribution 8()) centered at the pre-trained value. Our choice q(w) is inspired by Kendall & Gal (2017), who show that distribution parameters concentrate training data increases. Given
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Table 1: Example of Answer Entropy Computation on the GSM8K dataset. For each response, the answer string is marked in bold, with the remaining text representing the reasoning part. We estimate uncertainty by counting the occurrence of each answer string. In this example, with K
samples, (V) -066 x log 0.67 0.33 x log 0.33 0.275.
Responses for A robe takes 2 bolts of blue fiber and half that much white fiber. How many bolts in total does take?
Answer Frequency
Answer
Half of 2 bolts of white fiber is 2/2 bolt. So, it takes 2 + 1 = =3 bolts in total. The answer is 3.
67%
2 bolts of blue fiber and half that much white fiber is 2 + half of 2 2
== 3 bolts. The answer
2 bolts of blue fiber and half that much white fiber is 2 x 2 = 4 bolts of
33%
blue fiber. The answer
the massive scale of LLMs, we expect this concentration to be even more pronounced, making narrowly centered ((w) a computationally efficient proxy for the true posterior.
In this work, we demonstrate the effectiveness of the Bayesian view with simple and efficient approximation. Specifically, we restrict S to the bias terms in the MLP blocks, which have a similar effect to weight-based perturbations (see Appendix [B. We implement the bias perturbation approx- imately via noise injection into the MLP activations. This design offers significant computational advantages: directly perturbing the model parameters would require separate forward pass for each sampled model to generate every y E V. In contrast, injecting noise into the activations allows independent noise per sample within batch, enabling multiple models be sampled and multiple outputs to be generated in parallel in single forward pass. This preserves the Bayesian effect at fraction of the computational cost.
Given that the activations are biased to be non-negen non-negative due to the SiLU nonlinearity in most models, we inject non-negative uniform noise into the activations. This corresponds defining
(w's W; a) L(w,; úü 20; + a:)
which yields a naturally bounded perturbation to prevent unstable behaviors in the tails. Further details of our algorithm are presented through a case study in Section 3 As shown through extensive experiments in Section 4 this lightweight noise-injection approach substantially improves halluci- nation detection effectiveness. We explore alternative perturbation designs, including zero centered noise (Appendix H.. bounded Gaussian distribution (Appendix C). and perturbation of a different set of model parameters (Appendix B). All results corroborate the framework' 's effectiveness across these variations.
UNCERTAINTY AND HALLUCINATION DETECTION
In this section, conduct a study to investigate the effectiveness of the surrogate model distribution g(w), as described above, in capturing epistemic uncertainty. We first hypothesize and validate that when sampling under the model distribution ((w) (Equation (2). the responses exhibit
greater variability when the model hallucinates. We then observe that such epistemic uncertainty has complementary effect when compared aleatoric uncertainty for hallucination detection. Overall, combining epistemic and aleatoric uncertainty yields the best performance.
3.1 CASE STUDY SETUP
We perform an initial case study using the GSM8K dataset (Cobbe et al., 2021). Section 4 demon- strates that our algorithm also generalizes to knowledge-be baaed iesttiio-and--anee tasks.
In this study, we use the GSM8K test set, containing 1319 questions, together with in-context learning examples from Wei al. (2022). The dataset consists of mathematical question-responss pairs {x, y), where each response includes both the reasoning and the answer: y = [r. a). As shown in Table following in-context learning examples, LLM produce coherent yet incorrect
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answers ie., ballucinations hallacinaatons-hihhigghhnn highlighting the need for effective hallucination detection in such reasoning tasks.
For effective hallucination detection for GSM8K through uncertainty estimation, design an uncertainty metric as described in Equation T As illustrated Table reasoning chains can be extensive, although the final answer holds greater importance. Consequently, assigning equal weight to all tokens during uncertainty estimation may be suboptimal. Since the final answer in GSM8K numerical, metrics such as lexical similarity (Lin al. 2022) semantic entropy (Kuhn al.) 2023b) are less applicable. Instead, we estimate uncertainty by counting the number of occurrences of each final answer and introduce the metric of Answer Entropy:
Hans (2) = - Σ p(ay) p(a,)
(4)
where p(a,) is the empirical probability of each unique answer aj among the K extracted final An example of the answer entropy
answers fa a², ......a} from responses y {y* .....,, (K
computation is provided in Table
In practice, for the GSM8K dataset in this section, and more generally for datasets with formatted answers (e.g., numeric responses or multiple-choie options), we count answer occurrences using exact string matching. For datasets with free-form answers, we instead group semantically equiva- lent responses using BERT embeddings, following the standard protocol of Li et al. (2020).
In the following, we focus on the with additional datasets, uncertainty metrics, and models are discussed in Section
model (Touvron et 2023) Experiments
3.2 HALLUCINATION DETECTION UNDER EPISTEMIC UNCERTAINTY
We capture epistemic uncertainty through noise injection and study its effect on model hallucina- tions. Specifically, we inject uniform noise (0, 0.07) to perturb the MLP activations of layers 20 - 32 of the transformer. This approximately modifies the MLP bias and thus effectively samples a model e from our surrogate distribution q(w). To isolate this effect, we set the prediction layer sampling temperature zero and decode greedily to eliminate alcatoric uncertainty from sampling.
We generate 10 samples for each question and compute answer entropy following Equation (4) We classify model hallucination a question level; model responses to question are considered as hallucinating if the majority- answer from the K = 10 samples are incorrect, and as non- hallucinating otherwise. In Figure (left,, compare answer entropy between hallucinating and non-hallucinating cases by overlaying the histograms of the two groups. We observe that with the model stochastically sampled from q(w),, responses exhibit greater variability when hallucinating (grey), as evidenced by higher entropy values. This shows the effectiveness of using noise injection for capturing epistemic uncertainty and thus detecting hallucinations.
We also remark that our experiments show strong correlation between model reliability and the robustness of model output perturbations. This aligns with findings out-of-distribution (OOD) detection research (Liu & Qin (025). where OOD test samples-i.e samples with classes not seen during training are flagged for eliciting unreliable outputs. particular, [Luu & Qin (2024) show that OOD samples often lie near decision boundaries and exhibit decreased robustness to perturbations compared to in-distribution (reliable) samples. Our results suggest that hallucinations in LLMs behave similarly, manifesting as measurable instability in model output under perturbation.
3.3
COMPLEMENTARY EFFECT OF ALEATORIC AND EPISTEMIC UNCERTAINTY
We now examine the interplay between aleatoric and epistemic uncertainty and their impact on model performance.
Epistemic Uncertainty: We inject noise sampled from (1 0.07) and set sampling temperature to zero as Section 3.2
Aleatoric Uncertainty: We set temperature as T = 0.5 and inject no noise. This inference scheme
leverages the aleatoric uncertainty as captured by the original model.
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For each setup, assess answer entropy across
K 10 samples for each question following Equation 4. In the scatter plot in Figure B we display each question of the GSM8K test set as point, with the x-value representing answer entropy under aleatoric uncertainty, and the y-value representing the same under epis- temic uncertainty. The plot shows that model performance under the two types of uncertainty is weakly correlated, with a Pearson correlation of 0.58. This suggests that there a positive but complementary relationship. We further validate the complementarity in Section
Arower Entropy. T=o, Nobre Uio. 0.01)
3.0-
2.5
8.0
5.0
0.5
1.3
2.0
2.5 3.0
Answer Entropy. Tm0.5. No Noise
Figure 3: Complementary Effect of Epistemic
3.4 NOISE-ENIAANCED SAMPLING FOR HALLUCINATION DETECTION
and Aleatoric Uncertainty. The x-axis presents answer entropy (Equation 4 with prediction layer sampling only, which mainly captures aleatoric uncertainty. The y-axis presents answer entropy under intermediate layer noise injection only, which mainly captures epistemic uncer- tainty. A Pearson correlation of 0.58 indicates complementary relationship between the two types of uncertainty.
To capture both epistemic and alcatoric uncer- tainty, as suggested by Section 3.3 we incor- porate noise injection alongside prediction layer sampling and propose our noise-enhanced sampling for hallucination detection. The algo- rithm is described in detail in Algorithm
First, capture epistemic uncertainty, inject noise into MLP activations, effectively sampling models from our model distribution à ~ g(w) (see Equation in Section 3.2 As LLMs include skip connections. adding independent noise across layers may cancel out; to prevent this, we instead use the same noise sample across all selected layers (see Appendix [oor further discussion). Second, to capture aleatoric uncertainty, we sample from the temperature-adjuster categorical distribution ply,ly<c x, W). To detect hallucinations, we compute the answer entropy over samples and apply a threshold.
Algorithm Noise Enhanced Sampling for Hallucination Detection
input input context x, sample size K, uncertainty metric H(.)), model dimension d, temperature T, surrogate model distribution g(w) (built from noise magnitude a, perturbed layers L1-L2).
output Hallucination detection score: s(x)
1: for k = to K do
2: // Sample model from @ ~ g(w) 11
3: Sample noise: e e~ a0)
4: for each token yリ e do
5: for each layer do
6:
Compute h' using the potentially perturbed prior layer representations.
7:
if [T,, La] then
Perturb the MLP activations: fí' h1 + end if end for
8:
9:
11: // Sample tokens from model à //
12: Sample token y ~ p(y: x,() with temperature T.
13: end for
14: end for
return Hallucination detection score sxx = H(O)), where y = (y-, .2..,
Empirical Validation. In Table 2 we validate the effectiveness of our scheme under the case study setup. We perturb the MLP activation of layers 20 to 32 with additive uniform noise of magnitude a = 0.07, sampled from (0, 0.07). and evaluate over K = 10 samples. In practice, the noise magnitude can be selected based on the validation set, and we present an ablation study on different noise magnitudes in Section 4.4 Following Cellowing/Chen et al. (2024); Kuhn et al. (2023a); Lin et al. (2024) assess the effectiveness of hallucination detection using the
2022); Malinin & Gales 2021

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Table 2: Case Study: Effectiveness of Noise Injection for Enhancing Hallucination Detection. With the same aleatoric uncertainty fixed by sampling temperature, noise injection (first row) intro- duces epistemic uncertainty, improving detection effectiveness over no noise (second row), as shown by higher AUROC. Such improvement is achieved without degrading model generation accuracy (ACC). Evaluation on GSM8K dataset with L1 1aama-2-7----- model across 10 samples.
AUROC
ACC
Answer Entropy w/ T 0.5, no noise Answer Entropy w/ T = 0.5. noise ~ 21(0, 0.07)
71.56
23.64
76.14
24.09
threshold-free free metric, the area under the receiver operating characteristic curve (AUROC), where a higher value indicates better detection performance. As shown in Table [ our scheme effectively detects hallucination instances with AUROC value > 50.
We further compare approach with prior schemes that solely rely prediction layer sampling without noise injection and thus do not capture epistemic uncertainty. The setup without noise injec- tion follows Section 3.3 As shown in Table 2 our approach significantly improves detection effec- tiveness and achieves a higher AUROC value. The improvement is also visualized in Figure 2 (b), where noise injection increases the separation and reduces the overlap in the histograms from left to right, significantly reducing high uncertainty hallucinations (Simhi et al. (2025).
(Simi
Finally, we evaluate model accuracy on the GSM8K dataset by applying majority voting on the generated samples; as before, we compare the aleatoric and epistemic settings. As shown in Table taking into account epistemic uncertainty improves hallucination detection performance withour degrading model generation accuracy, as indicated by the ACC column. We further analyze the dual improvements in generation accuracy and hallucination detection using a Pareto analysis across varying noise magnitudes in Appendix G
Overall, our case study strongly supports our hypothesis regarding the relative importance of taking into account epistemic uncertainty in sampling.
EXPERIMENTS
In this section, we move beyond the case study and validate the effectiveness of our algorithm across diverse datasets and architectures. We also conduct comprehensive ablation study to understand the effects varying the number of samples, noise injection layers, noise magnitude, sampling temperature, and uncertainty metrics. As in Section [3.]] hallucination detection is evalu- ated using AUROC, complemented by a calibrated abstention analysis in Appendix Ablations are on Llama-2- 2B c unless otherwise specified.
4.1 MAIN RESULT
In Table 3
we validate the effectiveness of noise injection for enhancing hallucination detection.
Datasets: Beyond the mathematical reasoning task GSM8K, we perform evaluations on CSQA Talmor et al. 2019), which tests commonsense knowledge in multiple-choice format, and Triv- iQQA (Joshi et al. 2017). which measures factual QA in free-form setting. We use the CSQA validation set (1.221 questions) and the rc. nocontext subset of TriviaQA (18,669 questions). Following standard protocols for hallucination detection Kuhn et al. (002a)): Chen et al. (2024).
we generate plausible responses via in-context learning and treat incorrect answers as hallucinations
(details in Section A.I). These datasets cover diverse topics, formats, and prompting styles. We adopt answer entropy as unified uncertainty metric. For datasets with formatted answers (i.e.. GSM8K and CSQA), answer occurrences for entropy computation (Equation 4 are obtained via exact string matching. For the free-form dataset TriviaQA, semantically equivalent responses are clustered in the BERT embedding space prior to frequency estimation, as discussed in Section 3.1I
Model: We evaluate a diverse range of LLMs across various sizes, including Gemma 2B it Team al. (2024), Phi-3-ming -4-- 1e44-inntt ruct
L1 Llama-3, 33 2- ruct Grattafioni et al. (2024), (2.8B) Abdin et al. 2024)
Jiang al. 2023a), Llama-2- 1aamaa--7--haaae and Ll ama -ammaa2-1B-chhe
Setup:
we inject random uniform noise 40, a) into the MLP activation of upper layers. Since performance is not sensitive to specific layers (Section 4.5 we inject noise into
Following Section 3.1
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Table 3: Noise-Enhanced Sampling improves Hallucination Detection across Models and Datasets. The gain shows the benefits of epistemic uncertainty alongside aleatoric uncertainty. Hallucination detection is evaluated with answer entropy, which applies across answer formats, using K 10 samples. Detection AUROC is reported with mean and 95% confidence intervals. Higher mean values indicate better performance.
GSM8K
CSQA
TriviaQA
Gemma-2B-il
51.36 +/ 0.79
58.97 +/- 0.47
68.65 +/- 0.13
Gemma-2B-ir w/ Noise
57.11 +/- 0.67
61.71 +/- 0.37
69.38 +/- 0.11
-lama-3.2-3B-Instre
76.53 +/- 0.47
70.72 +/-0.49
77.40 +/- 0.07
Llama-3.2-3B-Imma Instruct w/ Noise
82.70 +/- 0.34
72.83 +/-0.46
78.49 +/- 0.10
Phi-3-minn-4KKiimtruutt (3.8B)
65.86 +/- 0.58
75.05 +/- 0.41
82.00 +/- 0.09
Phi---minii4KKiinttuuct w/ Noise
72.51 +/- 0.53
76.60 0,53
82.02 +/- 0.06
Mistral-BB-Instmutt-0..3
75.85 +/- 0.36
76.52 0.36
75.86 +/- 0.11
-istral-7B--nnstruut-0.333 w/ Noise
78.50 +/- 0.35
79.55 +/- 0.41
77.76 +/- 0.08
Llama-2-7B-chat
71.56 +/- 0.51
70.59 0.36
74.03 +/- 0.09
Llama-2-7B-chat w/ Noise
76.14 +/- 0.52
7/.56+/-00 0.36
75.05 +/- 0.08
Llama-2-13B-chat
77.20 +/- 0.33
67.55 +/- 1.02
73.39 +/- 0.09
Llamm-2-13B-chal Noise
79.25 +/- 0.32
69.10 +/- 0.94
75.10 +/- 0.07
Table 4: DoisneEn Sampling Improves Hallucination Detection Across Diverse Uncer-
tainty Metries. AUROC reported; higher is better. Evaluation on TriviaQA, whose free-form answers allow evaluation across all uncertainty metrics, using 10 samples.
noise
noise ((( 0.09)
Predictive Entropy (Malinin & Gales
2021)
79.28
79.92
Lexical Similarity (Lin et al. 2022)
77.40
78.90
Semantic Entropy (Kuhn al. 2023b)
75.70
77.21
EigenScore (Chen et al. 2024)
77.67
78.19
selfCheckGPT-NLI (Manakul al. 2023)
75.80
77.53
roughly the top third of the layers as the default configuration (see Appendix A.2 for exact layer ranges). For the noise magnitude a, we choose from 00.01, 0.03, 0.05, 0.07, 0.09, 0.11] based on validation, as detailed in Appendix [A.3] We fix the temperature at T = 0.5 and use answer entropy over K = 10 samples for hallucination detection. For each setup, bootstrap 25 times from total of 40 samples and report the mean AUROC with its 95% confidence interval.
Looking at Table B we observe that taking into account epistemic uncertainty consistently improves hallucination detection, indicated by higher AUROC scores. The improve- ment is more pronounced on GSM8K and CSQA than on TriviaQA. This may be because GSM8K and CSQA involve chain-of-thought reasoning, where the model is called across multiple steps, effectively accumulating uncertainty. This is unlike TriviaQA, which relies directly answers. Nonetheless, noise injection remains effective on TriviaQA. Notably, on TriviaQA with Phi-3 ---3--mnn---- -4 insiinstrus the baseline AUROC is already the highest across the board, suggesting performance saturation, which limits the impact of noise.
Performance:
short
4.2 ABLATION ON UNCERTAINTY METRICS
Here, show that noise-enhanced sampling is compatible with variety of uncertainty metrics H(()) from prior work, including Predictive Entropy (entropy normalized for sequence length)
MMalinin & Gales 202T). Lexical Similarity (based on Rouge-L scores) (Lin et al. 2022
2024
Semantic Entropy (clustering similar texts before computing entropy) (Kuhn et al. 2023b). Eigen-
Score (entropy in embedding space) (Chen al.! 2024). and selfCheckGPT.NIJ (which measures discrepencies using the contradiction score from natural language inference) (Manakul et al. 2023).
We evaluate on TriviaQA, which has free-from answers and is compatible with all the uncertainty metrics. Table reports AUROC for various metrics, at T'' = 0.5 and noise magnitudes {0, 0.09).
All metrics improve with noise injection, demonstrating the robustness of our approach.
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25.0
75
AUROC
ACC
22.5
70
20.0
Alpha 0.07 [A+E]
Alpha
0.07 [A+E]
10 Number Samples
Number of Samples
Figure 4: Noise-enhanced Sampling improves Hallucination Detection Across Different Number of Samples. Evaluation with T 0.5 for GSM8K across 20 samples. With noise magnitude a 0. only aleatoric uncertainty [A] is captured; with a 0.07, both aleatoric [A] and epistemic [E] uncertainty are captured. Hallucination detection AUROC (Left) and model genera- tion accuracy ACC (Right) reported; higher is better. Mean and 95% confidence intervals are shown.
Table 5: Noise-Enhanced Sampling Improves Hallucination Detection Across Noise Magni- tudes and Sampling Temperatures. AUROC values for different temperature-noise magnitude combinations are color-coded, with darker shades indicating better performance. Temperature adjustment only reaches plateau indicating the limit of aleatoric uncertainty while noise injec- tion further improves performance-shove the complementary effect of epistemic uncertainty. Evaluation GSM8K across K 10 samples.
No Naise
Noise U|0, 0.01)
Noise U|0, 0.03)
Noise UtO, 0.05)
Noise - UÑG, 0.07)
Noise-Uu (0,,,-UO,,,0000 0.09)
T-0,2
66.09
68.49
69.90
70.35
72.50
73.96
T=0.5
71.56
75.71
72.73
74.06
76.
75.24
T=0.8
72.43
77.56
77.22
77.67
78.78
79.03
T~1.0
72.34
77.12
77.68
78.34
78.14
78.22
4.3 ABLATION OF NUMBER OF SAMPLES
So far, we reported results using K 10 samples. We now study how performance changes with different sample sizes. Figure shows hallucination detection AUROC (left) and model accuracy (right) on GSM8K from report the mean and 95% interval across 25 bootstraps of K samples from total of 40 samples. Both AUROC and accuracy improve with more samples, and noise injection consistently enhances detection without degrading accuracy. In practice, K can be tuned to the computational budget, but the benefit of noise injection holds across sample sizes.
to K = 20, following the setup in Section 3.1 For each K, we
4.4 ABLATION TEMPERATURE AND NOISE MAGNITUDE
In Table we evaluate algorithm under varying temperatures and noise magnitudes, following the setup in Section 3.1 While the optimal noise level depends on temperature, moderate injection consistently improves hallucination detection. The results also show that epistemic and aleatoric uncertainty are complementary: as temperature increases from T = 0.8 to 1.0 without noise, AUROC plateaus, but injecting noise at T 0.8 boosts performance by capturing both sources of uncertainty.
4.5 ABLATION NOISE INJECTION LAYERS
We investigate the effect of noise injection across different layers, as examined on LLaMA-2-7B-chat (32 layers). Beyond the upper layers (20-32), we also inject noise into the middle (10-20), lower (0-10), and all layers (0-32) Table Ø reports hallucination detection AUROC for each setup. Noise magnitudes are set to 0.05, 0.01, 0.01 for upper, middle, and lower layers, respectively, each selected from 0.01, 0.03, 0.05, 0.07, 0.09 to achieve the best performance.

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Table 6: Noise injection across different layers consistently enhances hallucination detection. AUROC reported; higher is better. Evaluation CSQA across 10 samples.
Table 7: Complementary Gain from Input Perturbation. AUROC reported; higher is better Evaluation across 10 samples.
Llama-3. 2-----BBnttt--
Best results achieved by
combining both.
AUROC
GSM8K
CSQA
TriviaQA
No noise
67.55
input
model
Lower Layer Noise
70.03
X 76.53
70.72
77.40
Middle Layer Noise
69.68
X
76.10
72.07
78.33
Upper Layer Noise
69.10
x
v
82.70
72.83
78.49
All Layer Noise
70.68
82.84
72.98
79.20
As expected, lower layers require smaller magnitudes due to lower error tolerance for error propa- gation. For all-layer injection, we use noise magnitude 0.005 to account for cumulative effects.
Table 6 shows that injecting noise into different layers of the model consistently improves perfor- mance compared to the baseline with no noise. This indicates robustness to layer choice and under- scores the effectiveness of incorporating epistemic uncertainty into hallucination detection.
4.6 COMPLEMENTARITY GAIN FROM INPUT PERTURBATIONS
Jiang al. 2023b) Gao al. 2024 show that imput perturbations improve hallucination detec- tion. These methods emphasize aleatoric uncertainty in the data, making them conceptually orthog- onal and practically complementary our method. Table 7 evaluate input perturbation on top of noise injection using Ll Alama-2 3. 2- Instruct where the former is implemented by shuffling in-context learning examples following Jaang al. (2023b). The remaining experimental setup follows Section[4.] 4.1 We observe that combining both consistently yields the strongest results, confirming their complementarity.
RELATED WORK
Bayesian Neural Networks. Standard neural networks typically learn single point estimate, neglecting epistemic and aleatoric uncertainty. Bayesian methods (MacKay 1992
1992|Nec Neal 2012) learn
posterior distribution over models capture both uncertainty, but a high computational cost. Gal & Ghahramani] (2016b) addressed this using variational inference with a Bernoulli approximation of the weight distribution, subsequently extended CNNs (Gal & Ghahramani] 2016a). For LLMs, Hou et al. (2024) argue that Bayesian methods are computationally impractical and instead quantify epistemic and alcatoric uncertainty using clarification questions. Here, we tackle this challenge with a novel, training-free free Bayesian approach based on noise injection.
Hallucination Detection. As hallucinations cannot yet be fully eliminated, much research focuses on detecting them instead. A common strategy is to estimate model uncertainty across multiple samples (Lin et al. 2024 2022 Manakul et al. 2023 Xiao Wang 202T Kuhn et al. 2023a Chen et al. 2024). Orthogonal and complementary to them, we introduce sampling method that jointly captures epistemic and aleatoric uncertainty in a Bayesian framework. Another line of work avoids sampling by detecting hallucinations from single inference Azaria & Mitchell; Kossen et al.
(2024) Li al. (2023); Liu et al., Manakul et al. (203)) MMrks Tegmark] [Su et al. (202)): Wang al. (2025); Liu al. (2026). While efficient inference time, these methods typically require training auxiliary models on internal representations, adding computational overhead and falling outside the scope of sampling-based detection. Our work is also reminiscent of methods that perturb
inputs instead of model activations (Hou et al.) 2024] Diang et al., 2023b] Gao et al. 2024). which however addresses aleatoric uncertainty in the data rather than epistemic uncertainty the model,
making them complementary to our approach (see Section 4.6
CONCLUSION
This work tackles hallucination detection for the safe deployment of LLMs. While existing methods rely aleatoric uncertainty through next-token sampling, we propose very simple, training free sampling approach that incorporates both aleatoric and epistemic uncertainty in a Bayesian manner. Extensive experiments validate its effectiveness in improving hallucination detection in inference.
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A IMPLEMENTATION DETAILS
A.1 DATASETS
We use in-context examples to demonstrate correct answer formatting and simplify answer extrac- tion following free-form rationales, where applicable. For GSM8K and CSQA, we adopt the exem- plars presented by WWii et al. (2022) as our in-context learning examples. The prompts guide the model to output the final answer after the anchor string "The answer is", as illustrated Table 1, which we then extract accordingly for accuracy and answer entropy computation. For TriviaQA, we ensemble a 10-shot prompt from the first 10 training examples following Kuhn et al. (202aa)
On L. ama 22-7--chaa and I. ples to form prompt using format Q:...A...Q...AA...... An example prompt for TriviaQA is:
2B-3hhh we concatenate in-context learning exam-
Q: Which Rscar-nominater film had You Sexy Thing as its theme song? A: The Full Monty Q: Which Joan's s career revived in Whatever Happened to Baby Jane? A: Crawford O: Which much-loved actor won the Best Actor Oscar for The Philadelphia Story? A: James Stewart (...) Q: In which river is the Boulder Dam? A:
If the model continues the Q:..:... format after completing the answer, we trim generations using pattern matching with stopwords. For Gemma-2B-it Mistral-7B-Instruct-- 3, and Phi-3 mini- -inst ruct, we apply the chat template available on the respective model tokenizers available on Huggingface.
In evaluation, when the model fails to produce the answer with the correct format, we treat it as invalid.
A.2 MODELS
All models evaluated in this work off-the-shelf with additional fine-tuning. We inject noise into roughly the top third of layers. Specifically, Gemma 2B-it has 18 layers total, and we inject which has 28 layers, noise which has 30 layers, noise is
noise into layers 12-18. Similarly; 1..
injected into layers 20-28; for injected into layers 20-30; for Mistral- Intss-utt-ttt -v. and Llama 2-7B--- 2tt,, both with 32 layers, noise is injected into layers 20-32; and for Llama 2 1--11-Baa- B-chtt with 40 layers, noise is injected into layers 25-40.
Perturbations are implemented using the IntervenableMode interface of the open-source library pyvene (Wu et al.) 2024). where we specify the injected noise, target layers, and inter- vention modules. The resulting Intervenableeon supports generation with noise injection. We run all of our experiments on 80GB NVIDIA A100s. And there is no noticeable latency overhead with or without noise injection, confirming that our method introduces no practical delay.
wraps the original model and seamlessly
A.3 NOISE MAGNITUDE SELECTION
We select the noise magnitude a, based the results over the validation datasets. For GSM8K, CSQA, and TriviaQA, respectively, for Cemma-2B-it, we set as 0.05, 0.09, and 0.11, for Phi-3-mini-instane as 0.09, 0.09, and 0.07, for Mistral-7B-i www--------ttttttooooo-- for t.lama-2- -27hhcht,, as 0.07, 0.03, and 0.09, and for 12lama-2-138-0 0.05, 0.05, and 0.09.
as 0.05, 0.07, and 0.09, for 2ataaa...------ttteeee
as 0.03, 0.07, and 0.01,
as
Alternatively, noise magnitude can be selected per model by considering the signal to noise ratio (SNR). On L. A.lama-3 3. noise from Z4(0, 0.3s), with s being the activation magnitude. This improves detection AUROC for all datasets: GSM8K improves from 76.53 to 79.94, CSQA from 70.72 to 71.86, and TriviaQA from 77.4 to 78.35. Per-model selection offers a more efficient hyperparameter strategy than per-dataset tuning, remaining effective despite slight performance degradation.
we tune SNR combined validation set and inject
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B CONNECTION BETWEEN WEIGHTS AND BIAS PERTURBATION
We now show that injecting noise into the bias and the weight has a similar effect.
Consider an intermediate MLP layer with input h and activation ho Assume the model is well- regularized, such that the input nd has similar average magnitude Σj hej across samples. For computing the 1th output element h applying uniform noise into the corresponding weights fag equivalent to injecting uniform noise from a rescaled magnitude into the layer's bias "/- be noise sampled from uniform distribution (10), ,3). The output after injecting noise into the weights computed as follows:
out 0
Σ (Ois + +))h + +71)
(5)
Σ Oz ff Σ chjj + 7%))
Σ 0 bj + (E 1b
+ +r))).
where o-)) is the activation function. By our well-regularization assumption, this is equivalent to perturbing the bias y with noise sampled from U(0, 33 E, h
C PERTURBING WITH BOUNDED GAUSSIAN NOISE: AN ALTERNATIVE BAYESIAN APPROACH
As an alternative instantiation of the Bayesian approach, we conducted an auxiliary experiment by injecting Gaussian noise with the same mean and variance as the uniform distribution. In Table we experiment with Llama-3. 2- ruct on CSQA, where hidden unit activations layers 20-27 were perturbed with Gaussian noise bounded between [0, a:] to prevent unstable behaviors in the tails. sweep the noise magnitude a from 0.03, 0.05, 0.07, 0.09. Our results imply that, under bounded perturbation, the hallucination detection improvements are not tightly coupled to specific noise distribution, rather to the perturbation dynamics governed by statistical properties (i.e., mean and variance).
Table 8: AUROC Performance Across Different Perturbation Distributions. Perturbation with Gaussian noise (third row) performs comparably to perturbation with uniform noise (second row), as indicated by similar AUROC scores. Evaluation performed the CSQA dataset with the Llama-3. 3B Instruct model across 10 samples.
0.03
0.05
0.07
0.09
uniform
71.14
71.23
72.32
72.83
Gaussian
71.19
71.24
72.3
72.64
D PERTURBING THE ATTENTION BLOCK: AN ALTERNATIVE BAYESIAN APPROACH
In this section, we explore an alternative instantiation of the Bayesian perspective by injecting noise into the attention block, opposed to the MLP layer (see Fig Specifically, we inject noise into the attention block activation, akin to modifying the unperturbed (zero) bias of the attention mecha- nism. In Table 9 experiment with Llama-22 7B-B--B-- --cchat CSQA, perturbing the 20-32 layer activations with uniform noise. We sweep the noise magnitude a from 0.01, 0.03, 0.05, 0.07, 0.09, and report the best performance at 0.01. Our experiments show that this alternative perturba- tion achieves performance similar to aCP-activation perturbation, with both approaches enhancing hallucination detection. This further demonstrates the general effectiveness of Bayesian-inspired
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noise injection in capturing both aleatoric and epistemic uncertainty, ultimately enhancing halluci- nation detection.
Table 9: Analysis on Perturbation Position. Noise injection at the attention activation (third row) performs comparably to injection at the MLP activation (second row), both improving detec- tion effectiveness compared to no noise (first row), as indicated by higher AUROC scores. This further demonstrates the general effectiveness of Bayesian-inspired noise injection in capturing both aleatoric and epistemic uncertainty. Evaluation was performed on the CSQA dataset with the Llama-2- 2aima------char model across K 10 samples.
AUROC
No Noise
67.55
Noise Injection at MLP output
69.95
Noise Injection Attention output
69.10
E DROPOUT AND LARGE LANGUAGE MODELS
Many popular LLMs, such the LLaMA family (Touvron et al. 2023). do include dropout layers. Thus, the framework of Gal & Ghahramani (2016)). whith which casts dropout training as Bayesian approximation, does not extend naturally to LLMs. Nevertheless, we experiment with enabling dropout only at inference. Specifically, following the setup in Section [ we randomly drop outputs of higher MLP layers with a 1% rate and observe significant degradation genera- tion accuracy (Table TOp. In contrast, additive uniform perturbations preserve accuracy significantly better. Note that the model has not been trained under the additive noise condition. We hypothesize that additive noise is relatively benign, perturbing activations without entirely removing information. In contrast, dropout at inference can be more destructive, as dropping important units may disrupt critical information pathways and degrade performance sharply.
Table 10: Dropout noise Degrades Generation Accuracy. Model generation accuracy (ACC) is reported, with higher values indicating better performance. Evaluation performed on CSQA across K 10 samples.
ACC
No Noise
70.11
Additive Noise
70.83
Dropout Noise
67.50
F CALIBRATION VIA COVERAGE-ACCURACY ANALYSIS
To complement AUROC-based ranking evaluation, we assess calibrated abstention, which measures how well uncertainty scores guide selective prediction. Specifically, we compute coverage-accuracy curves for GSM8K on Llama-3 2-3B Instruct in Figure where coverage denotes the frac- tion of predictions retained after abstaining on the most uncertain cases, and accuracy measures correctness among the retained predictions. We sweep the coverage from 0.1 to I in steps of 0.1.
The results demonstrate that uncertainty scores derived from combined aleatoric and epistemic sources enable more effective selective prediction. In particular, the coise-injected setting achieves higher accuracy at low coverage and exhibits a steeper reduction in error as coverage decreases, indicating better calibration compared aleatoric-only baselines.
G PARETO ANALYSIS UNDER NOISE INJECTION
To further investigate the dual improvements of model generation accuracy and hallucination detec- tion effectiveness noted in Sections 3.4 and Section 3.3
we evaluate range of noise magnitudes
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74.5
0.1
Pareto
74.0
Other points
73.5
1%6
73.0
0.09
Accuracy
85
72.5
0.95
0.03
No nolse (a=0)
With noise (c-0.07)
0.00
70.5
0.2
0.4
0.6
0.8
1.0
72.1
72.2
72.3
12.4
72.5
72.6
72.7
Coverage
Accuracy (%)
Figure 5: Noise injection calibrated absten- tion. Experiments conducted GSMSK with Llama-3. 2---3.--3-Insttuuc ruct. Each point on the curve represents a coverage threshold, where the x-axis denotes the fraction of retained predictions after abstention and the y-axis reports the corresponding accuracy computed over those retained predictions. shows that noise injection achieves higher accuracy at low coverage compared to the no-noise baseline, indicating improved uncertainty calibration.
Figure 6: Pareto Analysis indicates Robust- ness to Noise Magnitude Selection. Exper- iments CSQA across 10 samples with Each point represents noise magnitude a, with x-axis showing generation accuracy (ACC) and y- axis showing hallucination detection (AUROC), Stars mark the Pareto front, highlighting noise magnitude that outperform the zero-noise base- line in both metrics, demonstrating robust gains across noise levels.
= (0, 0.03, 0.05, 0.07, 0.09, 0.15, 0.2) for CSQA on amaama-3 2- 1nB-Instrucee Figure visualizes the resulting Pareto front (starred points), representing noise magnitude that strictly outperform the zero-noise baseline a = in both metrics. The existence of this optimal region indicates that the benefits of noise injection robust to the specific choice of magnitude within moderate range.
H ZERO-MEAN NOISE INJECTION
In the main paper, we inject positive noise in MLP activations to preserve negative shift on activa- tions. To further examine the impact of alternative noise variations, we evaluate three settings: no noise, mositive-mean noise (0, a),, and zero-mean noise U(- 7: 2). Experiments are conducted on the CSQA dataset across k: 10 samples using
3.2 2-33- Instruct, with noise magni-
tudes a 0.09 as in Section 4.1
Table 11: Effect of Noise Mean on Performance. Experiment on CSQA across 10 samples using LLaMA-3.0 3.2-3B23-- Inst. AUROC and ACC reported, the higher the better.
AUROC
ACC
No Noise
70.72
72.11
Positive Noise
72.83
72.52
Zero-Mean Noise
72.27
72.22
As shown Table II both noise-injection strategies yield consistent improvements over the no- noise baseline. Specifically, positive-mean noise achieves the highest AUROC of 72.83, while zero- mean noise closely follows with 72.27, compared to only 70.72 without noise injection. similar trend is observed for generation accuracy ACC, where both positive and zero-mean noise outper- form the baseline. Notably, we observe that zero-mean noise remains stable at even larger noise magnitudes, exhibiting degradation in ACC.
Overall, these results suggest that the effectiveness of noise injection for hallucination detection does not critically rely noise injection strategies. Instead, both positive and zero-mean noise improve
17

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Published as a conference paper at ICLR 2026
Table 12: Under skip connections in LLMs, shared layer-wise noise outperforms independent
noise. Experiment GSM8K across 10 samples using LLaMA-3. 3. Instrruct.. AUROC reported, the higher the better.
AUROC
No Noise
76.53
Shared Noise
82.70
Independent Noise
80.20
model discriminability, indicating that the observed gains primarily stem from enhanced stochastic robustness.
I NOISE DESIGN UNDER SKIP CONNECTIONS
Modern transformer architectures employ skip connections, which can cause independently injected noise across layers to partially cancel out as representations are aggregated. To mitigate this effect, we reuse the same noise vector across all selected layers rather than sampling noise independently per layer. Table 12 compares reused noise and independent per-layer noise on GSM8K using LLaMA-3. 2-3B- Instruct, with noise sampled from (1, 0.09). Although independent noise improves over the noiseless baseline (80.20 vs. 76.53 AUROC), it underperforms relative to shared noise (82.70 70 AUROC). This result validates our design choice to inject shared noise across layers to mitigate cancellation effects.
18


Reviews:
[{"review_id": "SFLLGpr6h3", "reviewer": "Reviewer_VoHR", "summary": "The paper proposes introducing noise in LLMs during inference (by random perturbations of its parameters) as a way to capture epistemic uncertainty. Combined with temperature-based sampling, i.e., aleatoric uncertainty, the paper shows how the overall entropy is a better measure of uncertainty and thus does a better job in hallucination detection.", "questions": "1. Based on the trends in Figure 2, as well as the fact that improvements by adding epistemic uncertainty calculations are not extreme (although they are clearly substantial), it seems that epistemic uncertainty plays a smaller role in hallucination detection than aleatoric uncertainty. Can you comment on why you think that might be? Is the expectation that there would be less epistemic uncertainty? Or is the problem instead that the approximation is not good enough, and future work should focus on improving how we can measure epistemic uncertainty?\n2. Input perturbations should be a form of epistemic uncertainty, not aleatoric uncertainty as mentioned in the paper. I would like to hear the authors' reasoning if they disagree. Assuming it is a form of epistemic uncertainty (which I believe it is), why do input perturbations have a complementary effect to an existing measure of epistemic uncertainty? This probably connects to my first question, but a broader discussion on what is lost when trying to 'approximate' epistemic uncertainty, since we cannot perform a proper Bayesian treatment of LLMs, and how it can be supplemented with other additions, would help the paper.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper focuses on a targeted research question, and does a good job of providing an in-depth discussion.\n2. The improvement in hallucination detection is obvious. But for me, beyond these improvements, the paper provides a more accurate way to measure the overall uncertainty of an LLM, and thus, the technique here can be highly valuable.\n3. The paper is well written, and I enjoyed reading it. The depth of the experiments is good, and the paper provides answers to many different ablation questions.\n\nI should note that I'm not too familiar with the rapidly growing literature in hallucination detection, and separately, in LLM uncertainty measurement. So my assessment of the novelty of this work would be limited.", "weaknesses": "There are many other questions that could have been asked, but in my opinion, the paper did a good job focusing on one problem statement and providing appropriate depth.\n\nMy only complaint, and I hate to give such cliched feedback, but I really wanted to see experiments on a bigger variety of datasets. Different datasets seem to have different trends in the 3 datasets used in the paper, and an analysis over a larger set of datasets would have been very interesting. For instance, how well does this technique work for factual hallucinations vs faithfulness hallucinations? How well is it able to handle knowledge-intensive hallucination datasets vs commonsense reasoning datasets? Etc.", "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": "V4UVMP9gWW", "reviewer": "Reviewer_Wqmu", "summary": "There are many existing methods in literature for detecting hallucinations in an LLM that involve generating multiple samples from the LLM. This paper proposes adding noise to (some of) the parameters of the LLM during the sampling process. The authors argue that this noise injection is justified from a bayesian perspective and accounts for model uncertainty. The paper provides experimental results on the effect of adding noise to the intermediate layers of an LLM. The experiments section includes adequate comparisons to relevant baselines on established hallucination benchmarks, with noise injection showing favorable results.", "questions": "- Is there a need to limit the layers for which noise is added? Maybe it does not matter that you add noise to all the model parameters as long as the magnitude (in some $L_p$ sense, is under some threshold). In light of the fact that the AUROC numbers in table 6 are all close to each other, I am more inclined to believe that this is the case.\n- I understand you compare with Gaussian noise in Appendix C. But the AUROC performance is nearly identical with uniform noise. So does the noise distribution not matter? Why or why not?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- I like that the method is simple and justified from a theoretical perspective.\n- The discussion on the complementary effect of aleatoric and epistemic uncertainty was insightful. \n- The experiments section includes a variety of ablation studies which vary several relevant factors such as noise, temperature, layers in which noise is injected etc., Since, noise injection is easy to combine with other sample based approaches, I appreciate that the authors already included an ablation study that does this and it appears that injecting noise boosts the performance of those other methods.", "weaknesses": "Some choices and details were unclear to me and it would be nice to see more justification/discussion pertinent to these:\n- Why did you pick the uniform distribution for the noise? \n- How did you measure accuracy in Figure 4b? I am asking because there is no obvious way to judge the correctness of an LLM response compared to a ground truth. I believe it is important to be explicit about this detail (If you did include this in the manuscript already and I missed it, I apologize).\n\nI am happy to raise my score if the above points and the questions I list below are sufficiently addressed.\n\nMinor:\n- Table 1 formatting: answer strings are not in bold as stated in the caption.", "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": "6H0QVEiGUm", "reviewer": "Reviewer_XrUM", "summary": "The paper proposes a training-free, Bayesian-inspired sampling scheme for hallucination detection that perturbs a subset of model internals during generation to capture epistemic uncertainty, and combines it with standard temperature sampling that captures aleatoric uncertainty. Concretely, the method injects uniform noise into MLP activations (top layers by default), which is shown to be approximately equivalent to bias perturbation, and then samples answers K times; uncertainty is computed via Answer Entropy (and other metrics), yielding improved AUROC for hallucination detection across GSM8K, CSQA, and TriviaQA and multiple model families (Gemma, Phi-3, Llama-2/3, Mistral). Extensive ablations vary K, temperature, noise magnitude, and perturbed layers, and show complementarity with input perturbations.", "questions": "1. Why not adopt zero-mean perturbations by default? Do your AUROC and accuracy trends hold when eliminating mean shifts? \n2. How sensitive are results to reusing the same noise vector across layers vs. independent per-layer noise? Does structured, shared noise bias the uncertainty estimate? \n3. Can you report calibration (e.g., coverage vs. error curves) to complement AUROC and show that epistemic perturbations improve calibrated abstention? \n4. For long-form or multi-span answers (beyond a single numeric/string field), which aggregation metric worked best in your trials, and how robust is answer extraction? \n5. What is the worst-case degradation in task accuracy across α, K, and perturbed layers? A Pareto curve (AUROC vs. accuracy) would clarify trade-offs.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Simple, training-free mechanism with negligible latency overhead; easy to bolt onto many LLMs and sampling-based detectors. \n2. Principled motivation: separates aleatoric from epistemic uncertainty; implements the latter via internal perturbations approximating a posterior over models. \n3. Consistent gains across datasets/models/metrics. \n4. Thorough ablations. \n5. Complementarity with input perturbations and with standard sampling - jointly using both sources yields the strongest results.", "weaknesses": "1. Noise distribution centering: The paper repeatedly injects U(0, α) (positive-only) noise and even defines​ q(omega) such that it is not centered at zero around the checkpoint parameter; this can introduce a mean shift rather than a purely variance-based epistemic perturbation. A symmetric zero-mean alternative is only partially explored and merits direct head-to-head comparison. \n2. Metric dependence: A central result uses Answer Entropy (counting distinct final answers). This is natural for GSM8K/CSQA, but for long-form/free-form generation the mapping from perturbation to an “answer string” can be brittle; although the authors do show improvements for other metrics on TriviaQA, more analysis on long-form generation would strengthen claims. \n3. Hyperparameter tuning burden: α is selected per model/dataset (and even per layer range). While inexpensive, this introduces an extra validation loop and raises questions about sensitivity/transfer across domains.", "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": "K6xygNXnnI", "reviewer": "Reviewer_fG6Y", "summary": "The paper introduces an approach for uniform noise injection to LLMs which is motivated from a Bayesian point of view.\nThe authors use the approach for hallucination detection and show improvements over baselines on reasoning and QA tasks.", "questions": "- How exactly are the sequences y calculated in your algorithm? Is it correct that you are fixing the noise for a given input and then calculate the outputs by sampling from a model with the same noise applied for the entire sequence?\n\n- Can you please provide details on how you apply the baseline from Malinin & Gales 2021?\n\n- The citation Manakul et al. is broken.\n\n- How would you calculate answer entropy for more open-ended tasks? It seems to me like there might very often be cases where all counts are 1 leading to maximal entropy just because it is much less likely to sample the same output many times when the output sequences are long and open-ended.\n\n## References \n\nDepeweg, Stefan, et al. \"Decomposition of uncertainty in Bayesian deep learning for efficient and risk-sensitive learning.\" International conference on machine learning. PMLR, 2018.\n\nHüllermeier, Eyke, and Willem Waegeman. \"Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods.\" Machine learning 110.3 (2021): 457-506.\n\nMalinin, Andrey, and Mark Gales. \"Uncertainty estimation in autoregressive structured prediction.\" ICLR, 2021.\n\nShen, Yuesong, et al. \"Variational learning is effective for large deep networks.\" ICML, 2024.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The method improves over baseline hallucination detection methods on a range of benchmarks and clearly seems to separate hallucinated vs. non-hallucinated outputs better.", "weaknesses": "- I believe the paper is not precise enough about many of the theoretical concepts. First of all, the authors argue a lot for distinguishing between epistemic (connected to lack of knowledge) and aleatoric uncertainty (connected to inherent uncertainty in the problem).\nHowever, they claim that \"More formally, sampling from the model using next-token prediction can be considered as a way to capture uncertainty in the data distribution,\"(L80-82), i.e. aleatoric uncertainty. This is arguably (as discussed in e.g. Depeweg 2018, Hüllermeier & Waegemann 2021) only the case if there is no epistemic uncertainty, because then the model has sufficiently learned the true distribution and the randomness in the outputs is indeed the randomness of the problem. But this is generally not the case for e.g. LLMs.\nI am also surprised that the authors do not use any explicit decomposition of both uncertainties, which is discussed in these works and also in Malinin & Gales 2021, which is cited. Often Bayesian treatment is precisely motivated from this angle. The authors also motivated a Bayesian view but do not exploit it.\n\n- Connected to this, the formulation of Eq. 2 is imprecise. It shows a token-level model averaging but it is not clear why this should be a better choice than sequence-level averaging (these are in general not the same). This is heavily discussed in Malinin & Gales 2021 but not picked up here. Furthermore, Alg. 1 also seems to rather approximate a sequence-level average as all full sequences are sampled using the same noise sample for each token within them if I understand the pseudo code correctly. As a consequence, it is also not clear to me how the baseline from their paper is calculated here: do you use an ensemble on a token-level or sequence-level or no ensemble at all?\n\n- I believe claims that the claim \"since LLMs are very expensive to train, Bayesian treatment of LLMs for hallucination detection has remained elusive\" (L148-149) is not correct, as e.g. Shen et al. 2024 show Bayesian training of smaller LLMs using variational learning which could easily be used for hallucination detection.\n\n- Regarding the experiments, the work does not compare to any other Bayesian methods like Laplace or variational learning, which can feasibly be done for LLMs also using LoRA. Therefore, it remains unclear how the uniform noise added here compares to related works and especially to learned noise which might turn out to perform better.\n\n- For me it is unclear if the proposed answer entropy will work well outside of QA tasks, because it might be unlikely to sample the same (long and open-ended) answer twice. It would be good to add such an experiment if possible.", "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)