Detecting faithfulness hallucinations in large language models (LLMs) is crucial for their safe deployment in high-stakes domains. Recent approaches address this by contrasting contextual against parametric knowledge utilization, yet measuring context reliance typically demands noticeable overhead, such as materializing attention maps, running additional forward passes, or training auxiliary probes. In this work, we show that context reliance can be estimated by projecting hidden states onto the dark space - directions that compose weakly with the unembedding matrix. Beyond its recognized function as an initial-token attention sink, we show that this subspace actively mediates context processing, and that its share of hidden-state norm - termed the Dark Matter Ratio (DMR) - provides a direct score of context utilization. Pairing DMR with a parametric knowledge score yields DarkLens, a lightweight faithfulness detector operating strictly within a single forward pass. Evaluated across three QA and summarization benchmarks on six open-weight LLMs (4B-13B parameters), DarkLens matches or outperforms a wide range of baselines without requiring extra forward passes or probe training.
Figures & tables
Figure 1: Synthetic induction residual swaps on [x1…xT,x1…xT] . Each intervention covers a window of four consecutive layers. The first and third panels plot Δ NLL on the repeated half against the start layer of that window ( dark vs. mid-spectrum control); the dotted line is the average accuracy drop on the second half of the sequence. The second and fourth plot NLL (solid) and accuracy (dashed) against token position at the peak window; the vertical line marks the start of the repeat. Dark swaps impair copying far more than matched mid-spectrum swaps.
Figure 2: Language-modeling NLL under dark vs. mid-spectrum residual ablation. Each intervention covers a window of four consecutive layers; bars show NLL against the first layer of that window. Solid grey: unablated large model; dashed pink: smaller reference model (Qwen3-1.7B and Llama-3.2-1B-Instruct).
L20–23
Model
Dataset
No ablation
Middle
Dark
Qwen3-8B
NQ-Swap
0.88
0.81
0.22
ConflictQA
0.98
0.99
0.54
Cities
1.0
0.83
0.99
Sports
0.95
0.81
0.93
Celebrity
0.96
0.80
0.95
Table 1: Share of examples on which the target continuation has strictly lower mean NLL than the alternative. Datasets above the rule are contextual (NQ-Swap, ConflictQA); those below are parametric (Cities, Sports, Celebrity). Middle and dark permute layers 20–23. Dark subspace dimension 205 (last 5% of right singular vectors of WU ).
Figure 3: NQ-Swap answer NLL under dark vs. mid-spectrum residual permutation. Δ NLL is relative to the unablated model (positive: less likely). Solid: dark subspace; dashed: matched mid-spectrum control. Context, parametric, and distractor answers are scored separately.
Figure 4: Contextual hit rate under residual enhancement (top) and shrinking (bottom) on layers 20–23. The dark component (solid) or a matched mid-spectrum component (dashed) is scaled by strength α ; dotted lines are the unablated model. Amplifying the dark subspace raises context use on NQ-Swap and ConflictQA, while shrinking it reduces context use; the mid-spectrum control does not show the same effect.
MS MARCO
CNN/DM
Mistral-7B
Llama-2-7B
Llama-2-13B
Mistral-7B
Llama-2-7B
Llama-2-13B
Ours
0.77 ± 0.02
0.71 ± 0.04
0.72 ± 0.04
0.66 ± 0.07
0.58 ± 0.03
0.59 ± 0.05
LLM Check
0.49 ± 0.05
0.47 ± 0.07
0.51 ± 0.05
0.54 ± 0.04
0.50 ± 0.06
0.54 ± 0.03
Focus
0.67 ± 0.06
0.63 ± 0.03
0.61 ± 0.03
0.62 ± 0.04
0.51 ± 0.09
0.50 ± 0.06
LN-Entropy
0.65 ± 0.06
0.63 ± 0.03
0.62 ± 0.04
0.65 ± 0.04
0.63 ± 0.09
0.56 ± 0.04
LSC
0.68 ± 0.04
0.57 ± 0.03
0.57 ± 0.05
0.64 ± 0.04
0.62 ± 0.09
0.56 ± 0.05
Table 2: AUROC scores of hallucination detection methods. Bold and underline indicate the best and second-best results, respectively. All results are averaged over 5 runs.
MS MARCO
Ablation
Mistral-7B
Llama-2-7B
Llama-2-13B
PKS
0.74 ± 0.01
0.63 ± 0.04
0.70 ± 0.02
DMR
0.77 ± 0.02
0.72 ± 0.03
0.72 ± 0.04
Both
0.77 ± 0.02
0.71 ± 0.04
0.72 ± 0.04
XSum
Ablation
Qwen3-8B
gemma-3-4b
Llama-3.1-8B
Table 3: Ablation of DarkLens components (AUROC score, mean ± std over 5 runs) on MS MARCO and XSum. PKS: parametric knowledge score only; DMR: standalone negative dark matter ratio ( −DMR ); Both: combined DarkLens detector.
Figure 5: Response-level AUROC of DarkLens as a function of the dark subspace rank ( ddark ) on MS MARCO (left) and XSum (right).
Figure 6: Response-level AUROC of −DMR as a function of the residual readout layer on MS MARCO.
MS MARCO
XSum
Subspace
Mistral-7B
Llama-2-7B
Qwen3-8B
gemma-3-4b
Dark
0.74 ± 0.03
0.72 ± 0.03
0.71 ± 0.05
0.67 ± 0.05
Middle
0.57 ± 0.05
0.50 ± 0.05
0.56 ± 0.08
0.56 ± 0.05
Random
0.51 ± 0.04
0.52 ± 0.05
0.47 ± 0.09
0.57 ± 0.05
Table 4: Subspace ablation for −DMR (AUROC, mean ± std over 5 runs). Dark: bottom right singular vectors of WU ; middle: matched mid-spectrum subspace; random: random subspace of equal rank.
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
Llama-3.1-8B-It
Qwen3-8B
Layers
Rank
Sing. vectors
Rank
Sing. vectors
0–3
1636
1230–2865
1867
1114–2980
4–7
904
1596–2499
782
1657–2438
8–11
1174
1461–2634
205
1945–2149
12–15
954
1571–2524
2706
695–3400
16–19
760
1668–2427
3690
201–3890
Appendix
Table 5: Matched mid-spectrum ranks on WikiText-2. For each layer window, swapping within the indicated middle subspace reproduces the NLL increase of swapping the rank-205 dark subspace (bottom 5% of right singular vectors of WU ) within ±0.01 .
Figure 7: Language-modeling NLL under dark residual swaps on the first and last four-layer windows. Blue: first window (layers 0–3); orange: last window (layers 32–35 for Qwen3-8B, 28–31 for Llama-3.1-8B-Instruct); grey: unablated model; pink: smaller reference model (Qwen3-0.6B and Llama-3.2-1B-Instruct). Boundary interventions raise NLL above the unablated model and, on most corpora, to or above the smaller model.
Figure 8: Synthetic induction dark swaps on Qwen3-8B with reduced dark subspace ranks ( ddark=64 and 128 ). Bars show Δ NLL on the repeated half against the start layer of each four-layer window; the dotted line is the average accuracy drop.
Llama-3.1-8B-It
Qwen3-8B
Layers
Rank
Sing. vectors
Rank
Sing. vectors
0–3
1112
1492–2603
2161
967–3127
4–7
968
1564–2531
2107
994–3100
8–11
1200
1448–2647
3056
520–3575
12–15
1130
1483–2612
3270
413–3682
16–19
974
1561–2534
3085
505–3589
Appendix
Table 6: Matched mid-spectrum ranks on WikiText-2 (in-sample permutation). For each layer window, permuting within the indicated middle subspace reproduces the NLL increase of permuting the rank-205 dark subspace (bottom 5% of right singular vectors of WU ) within ±0.01 .
Model
Type
Dataset
No ablation
L16–19
L24–27
Middle
Dark
Middle
Dark
Qwen3-8B
Contextual
NQ-Swap
0.88
0.61
0.30
0.92
0.62
ConflictQA
0.98
0.98
0.69
0.99
0.78
Parametric
Cities
1.0
0.63
0.99
1.0
1.0
Sports
0.95
0.55
0.92
0.93
0.95
Celebrity
0.96
0.62
0.93
0.96
0.96
Appendix
Table 7: Same comparison as Table 1 for layers 16–19 and 24–27. Dark subspace dimension 205.
Dataset
no ablation
L16–19
L20–23
NQ-Swap
0.88
0.82
0.76
ConflictQA
0.98
0.98
0.98
Cities
1.00
0.99
1.00
Sports
0.95
0.94
0.96
Celebrity
0.96
0.96
0.96
Appendix
Table 8: Qwen3-8B contextual/factual hit rate under dark residual permutation (dark rank 32). Hit = target continuation has lower mean NLL than the alternative.
Dataset
no ablation
L16–19
L20–23
NQ-Swap
0.88
0.77
0.63
ConflictQA
0.98
0.98
0.97
Cities
1.00
1.00
1.00
Sports
0.95
0.94
0.94
Celebrity
0.96
0.94
0.96
Appendix
Table 9: Qwen3-8B contextual/factual hit rate under dark residual permutation (dark rank 64). Hit = target continuation has lower mean NLL than the alternative.
Dataset
no ablation
L16–19
L20–23
NQ-Swap
0.88
0.60
0.37
ConflictQA
0.98
0.96
0.85
Cities
1.00
1.00
1.00
Sports
0.95
0.92
0.94
Celebrity
0.96
0.94
0.95
Appendix
Table 10: Qwen3-8B contextual/factual hit rate under dark residual permutation (dark rank 128). Hit = target continuation has lower mean NLL than the alternative.
NQ-Swap
ConflictQA
Question
Who was the actor who played Crocodile Dundee?
Who is the author of How to Stop Worrying and Start Living ?
Context (incorrect answer injected)
Gyanendra of Nepal , AM (born 8 October 1939) is an Australian comedian, actor and television presenter. He was nominated for the Academy Award for Best Original Screenplay and won the Golden Globe Award for Best Actor — Motion Picture Musical or Comedy for his performance as outback adventurer Michael “Crocodile” Dundee in Crocodile Dundee (1986), the first in the Dundee film franchise.
Herbert Croly is indeed the author of How to Stop Worrying and Start Living . This can be confirmed by looking at the book’s cover page, which clearly states “By Herbert Croly” as the author. Additionally, a quick search on reputable book-selling websites such as Amazon or Barnes & Noble will also show that Herbert Croly is credited as the author of this book. Furthermore, Croly is a well-known author and political philosopher, having also written the influential book The Promise of American Life .
Injected incorrect answer
Gyanendra of Nepal
Herbert Croly
Parametric answer
Paul Hogan
Dale Carnegie
Appendix
Table 11: Illustrative knowledge conflicts from NQ-Swap and ConflictQA. In both datasets the provided context has been altered so that it supports an incorrect answer (bolded in the passage).
Dataset
Example question
Answer
Cities
Is the city of Tokyo in Japan?
Yes
Is the city of Tokyo in Pakistan?
No
Celebrities
Is Leonardo DiCaprio an Academy Award-winning actor?
Yes
Is Rihanna from Brazil?
No
Sports
Was Michael Jordan a famous basketball player?
Yes
Was Usain Bolt a famous swimmer?
No
Appendix
Table 12: Example yes/no questions from the Cities, Celebrities, and Sports factual probes. Each dataset mixes true and false statements; the model is asked to answer Yes or No .
Model
Total
Hal. Rate (%)
Mistral-7B
749
39.4
Llama-2-7B
746
34.9
Llama-2-13B
730
32.3
Llama-3.1-8B
650
28.9
Qwen3-8B
750
24.3
gemma-3-4b
650
31.3
Appendix
Table 13: Hallucination statistics for XSum (annotations from Kuleshova et al. (2026) ).
Large language models (LLMs) are expected to answer questions faithfully based on the provided context, abstaining when the context information is insufficient to answer the questions. Existing faithfulness evaluations typically assess each question-context instance in isolation; however, such instance-level evaluation fails to capture a fundamental requirement of faithful behavior: the ability to adapt model responses to changes in available contexts. In particular, a model should provide correct answers when sufficient evidence is present and abstain when it is not. In this work, we propose a Pairwise Faithfulness Benchmark (PFaithBench) that evaluates whether a model can switch between answering and abstaining for the same question under supporting versus non-supporting contexts. Our evaluations across thirty-nine models with seven model families demonstrate that faithfulness fundamentally involves a trade-off between answering and abstaining, and that most current models exhibit a strong bias toward answering, with most faithfulness errors arising from over-answering, i.e., models tend to fabricate a response even when the provided context is insufficient. We further conduct a series of studies on faithfulness training under different data constructions. Our results show that training outcomes are highly sensitive to the specific composition of answering and abstaining data. Constructing answering and abstaining data from mismatched sources can cause models to rely on dataset-specific shortcuts rather than actual context sufficiency. Moreover, increasing answer-supervised data improves answering performance but exacerbates over-answering, while increasing abstaining data reduces hallucination but leads to over-abstention. The code and data are released at https://github.com/tmlr-group/PFaithBench.
Zizhuo Zhang, Xiong Peng, Jingwei Sun +3
TMLR Group, Department of Computer Science, Hong Kong Baptist University · Huawei Noah’s Ark Lab.
Hallucination in Large Language Models (LLMs), characterized by the generation of content inconsistent with contextual facts or logical constraints -- remains a persistent challenge for reliable deployment. In this work, we address this issue through a geometric framework rooted in the linear representation hypothesis. We propose that hallucinations manifest as orthogonal noise relative to the semantic manifold of the residual stream. Specifically, we hypothesize that while attention heads ideally propagate information congruent with the context subspace, hallucinations arise when specific heads introduce components orthogonal to this subspace, disrupting the coherence of the latent representation. Based on this formulation, we introduce Dynamic Contextual Orthogonalization (DCO), an inference-time intervention method. DCO utilizes the input residual stream as a dynamic context anchor to perform orthogonal decomposition on attention head outputs. To distinguish between context-aligned semantic updates and divergent noise, DCO employs a layer-wise Z-score suppression mechanism that selectively attenuates outlier orthogonal components based on statistical distributions. Evaluations on Llama-3-8B and 70B across benchmarks such as XSum, NQ-Swap, and IFEval demonstrate that DCO achieves superior contextual faithfulness compared to state-of-the-art intervention baselines. Furthermore, DCO maintains high performance on knowledge-intensive tasks like TriviaQA and TruthfulQA, effectively mitigating the trade-off between hallucination suppression and parametric knowledge retention often observed in existing methods. Our findings validate the geometric interpretation of hallucinations and establish DCO as a computationally efficient approach for enforcing manifold alignment.Our code is available at https://github.com/Harry-Miral/DCO
Mingkuan Zhao, Wentao Hu, Tianchen Huang +6
Xi’an Jiaotong University · Xingchen AGI Lab, China Telecom AI Technology (Beijing) Co., Ltd. · University of Science and Technology of China +2
Large language models (LLMs) often produce content that contradicts or overlooks information provided in the input context, a phenomenon known as faithfulness hallucination. In this paper, we propose Context-Fidelity Boosting (CFB), a lightweight and general decoding-time framework that reduces such hallucinations by increasing the generation probability of source-supported tokens. Motivated by logit-shaping principles from watermarking techniques, CFB applies additive token-level logit adjustments based on a token's degree of support from the input context. Specifically, we develop three boosting strategies: static boosting, which applies a fixed bias to source-supported tokens; context-aware boosting, which scales this bias using the divergence between next-token distributions with and without context; and token-aware boosting, which further redistributes the adaptive bias according to local relevance estimated from source-position attention and source-scoped semantic similarity. CFB requires no retraining or architectural changes, making it compatible with a wide range of LLMs. Experiments on summarization and question answering tasks across multiple open-source LLMs show that CFB consistently improves faithfulness metrics with minimal generation overhead. Our implementation is fully open-sourced.
Weixu Zhang, Fanghua Ye, Qiang Gao +7
Hunyuan AI Digital Human, Tencent · McGill University · Mila - Quebec AI Institute +4