The Detectability Gap: Hidden Heterogeneity in Hallucination Detection Across Language Models
Authors: Pranav Darshan, Pranav A, Sravan Karthick T, Minal Moharir, Ivan P. Yamshchikov
Organizations: Department of Computer Science and Engineering, R.V. College of Engineering, India · CAIRO, Technical University of Applied Sciences Würzburg-Schweinfurt, Germany
Sampling based consistency is widely used for hallucination detection, yet aggregate performance can conceal systematic differences in which errors are detectable. This work studies that heterogeneity across four language models and three factual question answering datasets. Partitioning hallucinations by answer agreement reveals high agreement (Ghost) and low agreement (Flickering) regimes with an apparent detectability gap of 0.35 to 0.46 AUC. Because the statistics used to define the regimes and measure this gap are strongly coupled (∣ρ∣≈0.94 to 1.00), the raw result is treated as a property of agreement based detection rather than independent evidence. After freezing regime assignments, lexical and semantic response dispersion preserve the asymmetry, with bootstrap 95% intervals excluding zero in all 12 model and dataset settings. A stricter test using individual diffusion trajectories and no cross seed information preserves the asymmetry across all three LLaDA datasets (p<0.005) and directionally across all three Dream datasets, with one reaching significance. The hard regime varies substantially in prevalence across models (16% to 77%), and matched prompts frequently change regimes between models. These findings show that aggregate detection metrics conceal persistent, model dependent heterogeneity in language model failures and motivate regime conditioned evaluation.
Figures & tables
Type
Question
Three sampled answers
Gold
Ghost
What sport does Masahito Noto play?
baseball / baseball / baseball
football
Flickering
Who composed “The Mission”?
various / James Horner / The Doors
Ennio Morricone
Table 1: Ghost hallucinations repeat incorrect answers; Flickering hallucinations produce different incorrect answers. No sampled answer contains the gold answer.
Figure 1: Decoupled gap Δ , defined as Flickering AUC minus Ghost AUC. Bootstrap 95% confidence intervals are shown for lexical and semantic dispersion. All twelve model and dataset settings have positive gaps.
Appendix figures & tables19 assets
Supplementary material from the paper’s appendix.
Appendix
Model
Corpus
Triv.
Hot.
Pop.
LLaDA
scaled
1000
800
1050
Dream
dream
200
200
200
Qwen2.5 7B
AR
400
400
400
Llama 3.1 8B
AR
800
800
800
Appendix
Table 2: Prompt counts per model and dataset. Each prompt uses K=3 seeds in the main analysis.
Conf.
Conf.
Conf.
% high
Dataset
correct
wrong
ECE
error AUC
wrong
TriviaQA
0.951
0.950
0.52
0.502
56.4
HotpotQA
0.955
0.959
0.72
0.502
76.7
PopQA
0.964
0.965
0.64
0.497
67.5
Appendix
Table 3: LLaDA confidence baseline. Mean confidence is similar for correct and wrong answers, while confidence to error AUC remains near chance.
Disag.
Disag.
First
Dataset
hall.
correct
AUC
sent. AUC
TriviaQA
0.41
0.24
0.61
0.71
HotpotQA
0.51
0.34
0.61
0.64
PopQA
0.59
0.34
0.66
0.73
Appendix
Table 4: Aggregate agreement across seeds on LLaDA. The first sentence variant uses content word disagreement in the first sentence.
Model
Dataset
N
hall.%
Ghost%
Ghost AUC
Flick. AUC
Gap [95% CI]
LLaDA
TriviaQA
1000
50.0
77.4
0.506
0.963
0.457[0.429,0.485]
LLaDA
HotpotQA
800
72.2
69.9
0.479
0.900
0.422[0.390,0.458]
LLaDA
PopQA
1050
61.9
65.1
0.521
0.917
0.396[0.365,0.425]
Dream
TriviaQA
200
49.5
30.3
0.511
0.881
0.370[0.302,0.441]
Dream
HotpotQA
200
75.5
28.5
0.340
0.796
0.455[0.388,0.519]
Dream
PopQA
200
61.0
16.4
0.443
0.795
0.352[0.279,0.425]
Appendix
Table 5: Raw agreement gap under disagreement score 1−π^ . Bootstrap confidence intervals use B=2000 prompt level resamples.
Model
Dataset
ρ(θ^,1−π^)
LLaDA
TriviaQA
−0.996
LLaDA
HotpotQA
−0.991
LLaDA
PopQA
−0.998
Dream
TriviaQA
−1.000
Dream
HotpotQA
−0.939
Dream
PopQA
−0.985
Appendix
Table 6: Mechanical coupling between plurality and disagreement. The raw agreement gap is therefore treated as descriptive rather than as independent evidence.
Raw agreement
Lexical dispersion
Semantic dispersion
Model
Dataset
G
F
Δ
G
F
Δ
G
F
Δ
LLaDA
TriviaQA
.506
.963
.457
.643
.770
.126
.690
.831
.142
LLaDA
HotpotQA
.479
.900
.422
.605
.824
.219
.642
.814
.172
LLaDA
PopQA
.521
.917
.396
.746
.880
.134
.809
.891
.083
Dream
TriviaQA
.511
.881
.370
.605
.835
.230
.618
.732
.115
Dream
HotpotQA
.340
.796
.455
.547
.789
.242
.534
.724
.190
Appendix
Table 7: Detectability gap for frozen Ghost and Flickering regimes. G and F denote Ghost and Flickering AUC. All twelve lexical and all twelve semantic confidence intervals exclude zero.
Reassign.
Ghost %
Lexical Δ
Semantic Δ
Model
Dataset
%
plur.
ent.
plur.
ent.
plur.
ent.
LLaDA
TriviaQA
38.4
77.4
43.8
.126
.164
.142
.223
LLaDA
HotpotQA
29.9
69.9
43.4
.219
.187
.172
.171
LLaDA
PopQA
47.2
65.1
19.7
.134
.163
.083
.170
Dream
TriviaQA
26.3
30.3
20.2
.230
.192
.115
.165
Dream
HotpotQA
22.5
28.5
11.3
.242
.321
.190
.390
Appendix
Table 8: Regime robustness under bidirectional entailment clustering. Ghost % is the share of hallucinations assigned to Ghost under the token level plurality criterion (plur.) and the entailment criterion (ent.). Lexical and semantic Δ are the decoupled Flickering minus Ghost AUC gaps under each partition. The entailment criterion reassigns a large fraction of prompts and lowers Ghost prevalence, yet both decoupled gaps remain positive in all twelve settings.
Lexical Δ
Semantic Δ
Dataset
mean
% >0
mean
% >0
TriviaQA
0.306
100
0.288
100
HotpotQA
0.135
100
0.078
100
PopQA
0.065
96
0.019
76
Appendix
Table 9: Disjoint generation control on the high depth LLaDA corpus ( 50 prompts, 18 seeds), averaged over 50 random nine by nine seed splits. Regime assignment uses one half of the seeds and the dispersion score uses the disjoint other half.
Analysis
Result
Interpretation
Three seed average vs. eighteen seeds
ρ≈.999
closely aligned
Three seed average vs. eighteen seeds
MAE ≈.009
low average error
Single three seed draw vs. eighteen seeds
MAE ≈.14
individual draws are noisy
Regime agreement
≈79%
most labels remain stable
HotpotQA gap, K=3 to 18
0.244 to 0.250
gap remains positive
Appendix
Table 10: Seed depth robustness on the high depth LLaDA corpus.
Dataset
τ=.34
τ=.50
τ=.67
τ=1.0
TriviaQA
.456
.457
.452
.452
HotpotQA
.422
.422
.428
.428
PopQA
.396
.396
.398
.398
Appendix
Table 11: Raw agreement gap under alternative token level Jaccard thresholds on LLaDA.
Model
Dataset
Ghost
Flick.
Δ [95% CI]
p
LLaDA
TriviaQA
.631
.737
.106[.033,.178]
.003
LLaDA
HotpotQA
.598
.721
.123[.076,.170]
<.001
LLaDA
PopQA
.794
.886
.092[.060,.123]
<.001
Dream
TriviaQA
.602
.637
.035[−.081,.153]
.60
Dream
HotpotQA
.626
.699
.072[−.039,.185]
.18
Dream
PopQA
.645
.808
.163[.035,.291]
.003
Appendix
Table 12: Trajectory only control. The detector uses dynamics within a single seed and no information across seeds.
Model
Architecture
Ghost share of hallucinations
LLaDA
diffusion
65 to 77
Dream
diffusion
16 to 30
Qwen2.5 7B
autoregressive
59 to 77
Llama 3.1 8B
autoregressive
62 to 67
Appendix
Table 13: Ghost prevalence across the three datasets.
Dream Ghost
Dream Flickering
LLaDA Ghost
67
181
LLaDA Flickering
17
82
Appendix
Table 14: Matched regime transitions among the 347 prompts hallucinated by both models.
Behavior
LLaDA
Dream
Repeat one answer
69.8%
19.1%
Diversify
29.4%
63.7%
Fragment
not separately reported
15.1%
Repeated abstention
at most 2.2%
at most 2.2%
Appendix
Table 15: Dominant behavior among matched hallucinated prompts.
Type
Data
Question
Gold
Seed answers
θ^
Ghost, LLaDA
PopQA
What sport does Masahito Noto play?
football
baseball, baseball, and baseball
1.00
Flickering, LLaDA
PopQA
Who composed “The Mission”?
Ennio Morricone
various, James Horner, and The Doors
0.33
Ghost, Dream
TriviaQA
In which city are the Oscar statuettes made?
Chicago
Hollywood, Los Angeles, and Los Angeles
0.67
Flickering, Dream
TriviaQA
Which composer wrote “The Dam Busters March”?
Eric Coates
an English composer, John Moore, and Edward Elgar
0.33
Ghost, Qwen
HotpotQA
Language of the people whose principal town was Anhaica?
Apalachee
Timucua, Timucua, and Timucua
1.00
Flickering, Qwen
PopQA
Who was the composer of “Hello”?
Masaharu Fukuyama
Bruno Mars, “a covered pop song”, and “various songs”
0.33
Appendix
Table 16: Representative hallucinations across models. Ghost examples show repeated incorrect answers, while Flickering examples show divergent incorrect answers. The final row shows a matched prompt whose regime changes between models.
TriviaQA
HotpotQA
PopQA
Ghosts initially incorrect
387
404
423
Verified correct
4
2
0
Relabeled percentage
1.0
0.5
0.0
Ghost percentage, original to relabeled
77.4 to 77.2
69.9 to 69.8
65.1 to 65.1
Agreement AUC, original to relabeled
.609 to .611
.606 to .604
.659 to .659
Raw Ghost AUC, original to relabeled
.506 to .507
.479 to .475
.521 to .521
Appendix
Table 17: Semantic reassessment of the Ghost population. Every quantity depending on Ghost moves by less than 0.005 .
AUC within group
Recall at FPR 30
Dataset
Ghost
Flick.
Ghost
Flick.
TriviaQA
0.71
0.97
58
92
HotpotQA
0.69
0.95
63
85
PopQA
0.88
0.97
84
94
Appendix
Table 18: Full online detector on the scaled LLaDA corpus.
Feature set
Triv.
Hot.
Pop.
Final answer agreement
0.61
0.61
0.66
Per step answer agreement
0.61
0.61
0.79
Plus text overlap
0.70
0.67
0.80
Full consistency block
0.70
0.70
0.81
Full detector
0.73
0.75
0.90
Appendix
Table 19: Per step agreement compared with final answer agreement on LLaDA.
Claim
Evidence
Establishes
Dependence status
Caveat
Raw agreement gap
Four models and three datasets
Descriptive agreement based asymmetry
Mechanically coupled
Not independent evidence
Lexical asymmetry persists
Positive gap in all twelve settings
Asymmetry survives a decoupled lexical measurement
No exact computational reuse
Still a dispersion measure
Semantic asymmetry persists
Positive gap in all twelve settings
Asymmetry survives a decoupled semantic measurement
No shared lexical computation
Still a dispersion measure
Trajectory asymmetry
LLaDA significant on all three datasets; Dream positive on all three
Within seed dynamics contain additional information
No information across seeds
Limited to diffusion models
Prevalence varies
Ghost share from 16% to 77%
Error population composition depends on model
Descriptive
Four models only
Regime membership varies
181 versus 17 matched transitions
Prompt identity alone does not determine regime
Descriptive matched result
One matched model pair
Appendix
Table 20: Summary of the central evidence. The trajectory analysis is the only analysis in which the evaluated signal uses no information across seeds.
Large language models (LLMs) hallucinate with confidence: their outputs can be fluent, authoritative, and simply wrong. In medical, legal, and scientific applications this failure causes direct harm, and detecting it from internal model states offers a path to safer deployment. A growing body of work reports that this problem is increasingly tractable, with recent methods achieving high detection performance on widely used benchmarks. We show, however, that much of this apparent progress does not survive scrutiny. Four of the six corpora embed the ground-truth answer directly in the input prompt. A naïve text-similarity baseline we call TxTemb exploits this to achieve near-perfect detection scores without any access to model internals. To measure what genuine detection capability remains once these artifacts are controlled, we conduct a large-scale evaluation spanning twenty-two detection methods, twelve open-source models spanning six architectural families, and six corpora. We further introduce DRIFT, a supervised probe over inter-layer hidden-state transitions, as a point of comparison for live-generation detection. Our findings suggest that the field's reported progress on hallucination detection is substantially explained by benchmark construction artifacts in widely used corpora, and that the majority of established baselines perform near chance under controlled conditions; the consistent exceptions are SAPLMA and DRIFT, both supervised probes on upper-layer hidden states.
Hallucinations in large language models (LLMs) arise from heterogeneous failure mechanisms, making reliable detection difficult for any single global uncertainty score. In this work, we formulate hallucination detection as a mechanism-aware evidence aggregation problem, where diverse representation- and token-level signals must be interpreted under multiple latent explanations. We propose FLaG, a lightweight hallucination detection framework that models correctness through a set of latent evidence groups. Each instance is softly associated with multiple groups via an energy-based routing mechanism, and group-conditional reliability signals are combined through a principled log-marginal aggregation. This design enables FLaG to capture heterogeneous hallucination patterns while remaining invariant to decision thresholds and evaluation metrics. The framework operates as a frozen-model head, requires no modification to the underlying language model, and incurs minimal computational overhead. We further provide a theoretical perspective that connects FLaG to optimal evidence aggregation under heterogeneous error mechanisms, showing that the Bayes-optimal test statistic necessarily admits a log-marginal form and that FLaG constitutes a tractable approximation with a controllable error bound. Extensive experiments across multiple benchmarks and LLM backbones demonstrate that FLaG consistently achieves SOTA performance, while exhibiting robust transfer across datasets and models, and remaining effective under limited supervision.
Wentao Ye, Liyao Li, Zhiqing Xiao +6
Zhejiang University · Hangzhou, Zhejiang, China · Nanyang Technological University +1
Hallucination detection is essential for the reliable deployment of large language models (LLMs). However, existing evaluations face two core challenges: inconsistent inference configuration and evaluation, and limited coverage of downstream domains and tasks. Consequently, reported detector performance is often difficult to compare, reproduce, and generalize beyond specific experimental settings. We introduce OpenHalDet, a unified benchmark for hallucination detection across diverse generation scenarios. OpenHalDet standardizes the evaluation pipeline, from prompt construction and response generation to truthfulness annotation, detector scoring, and metric computation. It supports heterogeneous detector families under different access settings, including black-box methods that use only generated outputs, gray-box methods that rely on probability-based signals, and white-box methods that exploit internal model signals. By bringing diverse tasks, models, and detectors into a shared framework, OpenHalDet enables controlled comparison and provides a systematic view of how different detection paradigms behave in LLM applications. We release OpenHalDet as an open and extensible codebase to facilitate reproducible evaluation and future development of hallucination detection methods. The code and datasets are available at https://github.com/Nellie179/Hallucination-Detection.
Xinyi Li, Zhen Fang, Yongxin Deng +12
University of Technology Sydney · University of Bristol · University of Wisconsin–Madison +2